ok
Measures base = 3cm
height = 4cm
tall = x
volume = 144 cm^3
Volume = Area of the base * tall
Area of the base = (3 * 4) / 2 = 12/2 = 6 cm^2
144 = 6*x
x = 144/6
x = 24 cm
Result: The chocolate is 24 cm tall.
Darnell and emma are college students . darnell currently has 22 credits and he plans on taking 6 credits per semester . emma has 4 credits and plans to take 12 credits per semester . after how many semesters , s will darnell and emma have the same number of credits ?
After 3 semesters Darnell and Emma have same number of credits as 40.
Given,
Current credit score of Darnell = 22
Current credit score of Emma = 4
Darnell plans to score a credit per semester = 6
Emma plans to score a credit per semester = 12
Now, we have to find that after how many semesters will Darnell and Emma have the same number of credits .
Here,
Current credit score of Darnell = 22
Current credit score of Emma = 4
After 1 semester,Credit score of Darnell = 22 + 6 = 28
Credit score of Emma = 4 + 12 = 16
After 2 semester,Credit score of Darnell = 28 + 6 = 34
Credit score of Emma = 16 + 12 = 28
After 3 semester,Credit score of Darnell = 34 + 6 = 40
Credit score of Emma = 28 + 12 = 40
That is,
After 3 semesters Darnell and Emma have same number of credits as 40
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Please answer only if you know the answer thank you.
The equation of a line passing through the point (7, 8) with slope as -3 is option (A) 3x + y - 29 = 0 or y = -3x + 29
In the above question,
It is given that a line that passes through a point = (7 ,8)
The slope of the line = m = -3
The inclination of a line with respect to the horizontal is measured numerically is called as Slope
We know the slope intercept form of the line is
( y - y1) = m (x - x1)
where (x1 , y1 ) = ( 7 , 8)
and m = -3
Putting values in the slope intercept form of line, we get
( y - 8) = -3 ( x - 7)
y - 8 = -3x + 21
3x + y -8 - 21 = 0
3x + y - 29 = 0
y = -3x + 29
Hence, The equation of a line passing through the point (7, 8) with slope as -3 is y = -3x + 29
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One of the fastest species of beetle can actually run at a speed of about 9 kilometers per hour. Convert 9 kilometer per hour to centimeters per second.
Given:
The speed of the beetle is, s = 9 km/h.
The objective is to convert the speed into centimeters per second.
Explanation:
Since, it is known that,
[tex]\begin{gathered} 1\text{ km=1,00,000 cm} \\ 1\text{ hour=3600 s} \end{gathered}[/tex]Conversion;
Then, the speed can be converted as,
[tex]\begin{gathered} s=9(\frac{km}{hr})(\frac{1,00,000\text{ cm}}{1\text{ km}})(\frac{1\text{ hr}}{3600\text{ s}}) \\ =250\text{ cm/s} \end{gathered}[/tex]Hence, the the converted value is 250 cm/s.
At a conference 1 car was provided for every 4 people if there were 17 cars how many people were there
Answer:
just multiply 17×4=?
and it will give u an anserew..
Answer:68 people
Step-by-step explanation:
You take the 17 cars multiplied by four people and you get 68
HELp ASAP PLSSSPLSPLSPLSS
(view attatched image
Answer:
Ok...I've worked out the math and the correct answer should be the first one...
x | g(x)
1 | -2
2 | 4
3 | 10
Step-by-step explanation:
Hope this helps!!
can you take 73 devided by 17 and it be a whole number
all you need is in the photo please answer fastplease
Answer:
The cost of cupcakes and cookies are;
[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]Explanation:
Let x and y represent the cost of a cupcake and cookie respectively.
Given that;
Five cupcakes and two cookies cost $19.75.
[tex]5x+2y=19.75-------1[/tex]Two cupcakes and four cookies cost $17.50.
[tex]2x+4y=17.50-------2[/tex]Let's solve the simultaneous equation by elimination;
multiply equation 1 by 2;
[tex]10x+4y=39.50-------3[/tex]subtract equation 2 from equation 3;
[tex]\begin{gathered} 10x-2x+4y-4y=39.50-17.50 \\ 8x=22 \\ \text{divide both sides by 8;} \\ \frac{8x}{8}=\frac{22}{8} \\ x=2.75 \end{gathered}[/tex]since we have the value of x, let substitute into equation 1 to get y;
[tex]\begin{gathered} 5x+2y=19.75 \\ 5(2.75)+2y=19.75 \\ 13.75+2y=19.75 \\ 2y=19.75-13.75 \\ 2y=6 \\ y=\frac{6}{2} \\ y=3.00 \end{gathered}[/tex]Therefore, the cost of cupcakes and cookies are;
[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]
Suppose the commute times for employees of a large company follow anormal distribution. If the mean time is 24 minutes and the standarddeviation is 5 minutes, 95% of the employees will have a travel time within which range?
The empirical rule state that, for normally distributed data, almost all of the data fall within three standard deviations either side of the mean. Specifically,
-68% of data within 1 standard deviation.
-95% of data within 2 standard deviation
-99.7 of data within 3 standard deviation.
In our case the mean is
[tex]\mu=24[/tex]and the standard deviation is
[tex]\sigma=5[/tex]then, the empirical formula imply that
[tex]\begin{gathered} \mu-2\sigma=24-2\cdot5 \\ \mu-2\sigma=24-10 \\ \mu-2\sigma=14 \end{gathered}[/tex]and
[tex]\begin{gathered} \mu+2\sigma=24+2\cdot10 \\ \mu+2\sigma=24+10 \\ \mu+2\sigma=34 \end{gathered}[/tex]then, the answer is 14 minutes to 34 minutes
Answer:
D
Step-by-step explanation:
Use the number line shown below. What is the location of Z between X and Y such that the length of ZY is 3 times the length of XZ.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
X = -5
Y = 4
Answer:
z is -2
Step-by-step explanation:
x = -5 y = 4
<----------------------------------------->
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Z is between x and y but is 3 times the lenght of x&z
so jumb from -5 to -3 thats one, however jumb from -2 to 0 that is 1, and form 0 to 2 that is 2, and from 2 to 4 that is 3.
mad elf is a holiday beer that is 11.0% abv. a 12 oz bottle of mad elf has 300 calories. the rest of the calories, other than alcohol, come from carbohydrates. approximately how many grams of carbohydrates are in mad elf?
The bottle contains 9.36 g of carbohydrates.
We have,
12 oz bottle contains 300 calories
We know, 1 oz = 23.35 g
12 oz = 12 * 23.35 g =280.2 g of bottel
Alcohol content = 11 %
So, the total number of alcohol in the bottle is [tex]\frac{11}{100} *280.2 = 30.8 g[/tex]
So, the bottle contains 30.8 g of alcohol.
1 gram of alcohol 7 cal of energy,
So, 30.8 g of alcohol = 7 * 30.8 cal of energy
= 215.7 cal of energy
So, out of a total of 300 calories of mad elf, 215.7 calories come from alcohol.
So, (300-215.7 ) = 84.3 calories come from carbohydrates.
Each gram of carbohydrate produces 9 calories of energy.
9 calories of energy from 1 gram of carbohydrate,
1 calorie of energy from 1/9 of carbohydrate.
So, 84.3 calories from [tex]\frac{1}{9}*84.3 = 9.36 g[/tex]
Hence, the bottle contains 9.36 g of carbohydrates.
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Look at this table:
England
Wules
Birth rate per 1000 population
1961
1994
17.6
17.0
12.2
(a) In England, from 1961 to 1994, the birth rate fell by 26.1%
What was the birth rate in England in 1994? Show your working.
(b) In Wales, the birth rate also fell.
Calculate the percentage fall from 1961 to 1994. Show your working.
The birth rate in England in 1994 is 13 and the percentage fall in Wales is 28.23%
(a)In England, from 1961 to 1994, the birth rate fell by 26.1%
We need to find the birth rate in England in 1994
Birth rate in 1961 is 17.6
Birth rate in 1994 = 17.6 - 17.6 x26.1/100
= 17.6 - 17.6 x261/1000
= 17.6 - 4.6
= 13
(b) In Wales, the birth rate also fell.
The birth rate in 1961 is 17.0
The birth rate in 1994 is 12.2
Percentage fall is 100 x (17.0 - 12.2)/17.0
Percentage fall is 28.23 %
Therefore, the birth rate in England in 1994 is 13 and the percentage fall in Wales is 28.23%
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I REALLY NEED HELP WITH FACTORISING AFTER THIS CAN WE PLEASE DO SOME QUESTIONS BASED ON IT
Step 1:
Write the expression
[tex]14x^2\text{ }-\text{ x - 3}[/tex]Step 2:
To factorize the expression, multiply the leading coefficient with the constant term.
[tex]\begin{gathered} \text{Leading coefficent = 14} \\ \text{constant term = -3} \\ =\text{ 14 }\times\text{ -3 = -42} \end{gathered}[/tex]Step 4
Choose two numbers whose product is -42 and the sum is -1 (that is the coefficient of x)
[tex]\begin{gathered} \text{The two numbers are: 6 and -7} \\ \text{Then, split -x into -7x and 6x} \\ \text{Therefore} \\ 14x^2-x-3=14x^2\text{ - 7x + 6x }-3 \\ 14x^2\text{ - 7x + 6x - 3} \\ \text{Pair two terms and factor out the co}mmon\text{ factors} \\ 7x(2x\text{ - 1) + 3(2x - 1)} \\ (2x\text{ - 1)(7x + 3)} \end{gathered}[/tex]Final answer
(2x - 1)(7x + 3)
ILL Give one hundred points and Branly only if you do it right though
Answer:
1) -2
2) -2
3) -2
4) -3
5) -4
6) -15
7) -13
8) 3
1b) -9
2b) -2
3b) 7
4b) 17
5b) -4
6b) -9
7b) -16
8b) 0
1c) -5
2c) -3
3c) 0
4c) -2
5c) -8
6c) -11
7c) -3
8c) 15
Jeez, I hope this helps xD
Find the value of x that satisfies the given conditions. Then graph the line on a separate sheet of paper.
The line containing (4, -2) and (x,-6) is perpendicular to the line containing (-2, -9) and (3,-4).
The value of x will be 8.
And, Graph of the line y = -x + 2 is shown in figure.
What is Equation of line?
The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The condition is;
The line containing the points (4, -2) and (x,-6) is perpendicular to the line containing the points (-2, -9) and (3,-4).
Since, Multiplication of Slopes of perpendicular lines are -1.
That is;
m₁ m₂ = -1
Where, m₁ is slope of first perpendicular line and m₂ is slope of second perpendicular line.
Now, Find the slopes of lines as;
m₁ = (-6 - (-2)) / (x - 4)
m₁ = - 6 + 2 / x - 4
m₁ = - 4 / (x - 4)
And, Slope of second line,
m₂ = (-4 - (-9)) / (3 - (-2))
m₂ = (-4 + 9) / (3 + 2)
m₂ = 5 / 5
m₂ = 1
Hence,
m₁ m₂ = -1
Substitute all the values, we get;
- 4 / (x - 4) × 1 = -1
4 = x - 4
x = 4 + 4
x = 8
Thus, The points on the line is (4 , -2) and (8 , -6).
So, Slope (m₁) = (- 6 - (-2)) / (8 - 4)
= (-6 + 2) / 4
= - 4 / 4
= -1
Thus, The equation of line passing through the points (4 , -2) and
(8 , -6) with slope -1 is;
y - (-2) = - 1 (x - 4)
y + 2 = -x + 4
y = - x + 4 - 2
y = - x + 2
Therefore,
The value of x will be 8.
And, Graph of the line y = -x + 2 is shown in figure.
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consider a normal distribution with mean 20 and standard deviation 9. what is the probability a value selected at random from this distribution is greater than 20? (round your answer to two decimal places.)
The probability that a value selected at random from this distribution is greater than 20 is 0.5.
What is a probability with normal distribution?
The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean. The probabilities for values that are farther from the mean taper off equally in both directions.
Here,
Let us assume that X follows a normal distribution.
If X follows a normal distribution, then
z = (X−μ) /σ, follows a standard normal distribution.
The probability of a value selected at random from this distribution is greater than 20:
P (X > 20) = 1 − P (X ≤ 20)
P ((X − μ) / σ > 20) = 1−P((X − μ) / σ ≤ 20)
P (z > (20 − 20) /5) = 1 − P (z ≤ (20−20 / 5))
P (z > 0) = 1 − P (z ≤ 0)
The value of probability is obtained from the standard normal table as:
P (z > 0) = 1 − P (z ≤ 0)
= 1 - 0.5
= 0.5
Hence, the probability that a value selected at random from this distribution is greater than 20 is 0.5.
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The vertices of ∆DEF are D(2,5), E(6,3), and F(4,0). Graph ∆DEF and its image when you translate ∆DEF using the vector (-3,-7)
The resulting coordinate of △ D'E'F' is translated by the vector is
(-1, -2), (3,-4), and (1, -7)
Given the vertices of ∆DEF are D(2,5), E(6,3), and F(4,0).
we are asked to graph ∆DEF and its image when you translate ∆DEF using the vector (-3,-7).
If the coordinate of the vertices is translated by the vector (-3, -7), the resulting coordinates of △ D'E'F' will be expressed as:
D'= (2-3, 5 - 7) = (-1,-2)
E' = (6 - 3, 3 - 7) = (3, -4)
F' = (4 -3 , 0 - 7) = (1, -7)
Hence we get the required coordinates of the translated image.
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The time in seconds that it takes an object to fall d feet can be found
using the expression ((sqrt(d))/(4)) , Suppose aiden drops a tennis ball from a height of 50 feet at the same time masons drops a similar tennis ball from a height of 20 feet . How much longer will it take Aiden's tennis ball to reach the ground than Mason's tennis ball? Round to the nearest hundredth .
Aiden's tennis ball will reach the ground 0.65 seconds than Mason's tennis ball
How to determine the time difference in reaching the groundThe function of time with respect to distance is given as
(sqrt(d)/(4))
Rewrite the function properly
This is represented as follows
√d/4
It can also be written as
t = 1/4√d
From the question, we have
Aiden = 50 meters
Mason = 20 meters
The time difference is then calculated as
T = t₁ - t₂
So, we have
T = 1/4√d₁ - 1/4√d₂
The equation becomes
T = 1/4√50 - 1/4√20
This gives
T = 1/4(√50 - √20)
Evaluate
T = 0.65
Hence, the time difference is 0.65 seconds
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45 POINTS PLEASE HELP!!!
Decide whether inductive or deductive reasoning is used to reach the conclusion
the wolf population in a park has increased each year for the last 10 years. So, the wolf population will increase again next year
fine the value of x. please help
The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.
How do you find the value of x/ In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown. "x is a variable in x + 2 = 7, but we can figure out its value if we try! The order in which you perform operations in arithmetic and algebra is governed by a number of laws. The Commutative, Associative, and Distributive Laws are the three that receive the most attention.People have discovered over time that the sequence of the numbers has no bearing on the results of addition or multiplication.x+ 38+103= 180
x+141 =180
x =180- 141
x = 39
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two functions are given below: f(x) and h(x). state the axis of symmetry for each function and explain how to find it
HELP ME PLEASE
The axis of symmetry for function
f(x) is x = 8 and for h(x) is x = 3.
We know that the quadratic equation in vertex form is, y = a (x - m)² + n
where (m, n) is the vertex of the parabola.
And, the axis of symmetry is x = m.
Consider function f(x)
f(x) = -4(x - 8)² + 3
This function represents a quadratic equation in vertex form with vertex (8, 3)
So, the axis of symmetry for function f(x) would be x = 8
We know that the axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetrical.
Consider the function h(x)
We can observe that the vertex of parabola is (3, 2)
So, the axis of symmetry would be x = 3.
Therefore, the axis of symmetry for function
f(x) is x = 8 and for h(x) is x = 3.
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At a high school, the cafeteria staff provides optional comment cards to students eating in the cafeteria. Students who wish to make a comment can obtain and fill out a comment card and return it to a drop box in the front office. At the end of the semester, the staff analyzes the responses and finds that 72% of the students who filled out a comment card recommend major changes to the food selection. What conclusions can the cafeteria staff draw from these responses?.
Based on the described sampling approach, it should be concluded that the responses were from a voluntary response sample, so the cafeteria staff should not use the results to draw any conclusions. (Option D).
Voluntary response sample refers to a response sample in which the researcher puts out a request for population members to join the sample, and the decision of whether or not to be in the sample resides with the people. As it is a sample comprising of voluntarily participants, people who chose to participate usually do so as they have a strong opinion on the subject of the survey. Typically, voluntary response samples oversample members with strong opinions and under sample members with little to no opinion on the subject of the survey. Hence, inferences from a voluntary response sample are not as reliable as conclusions based on a random sample of the entire population under consideration.
Note: Question is incomplete. The options were missing which are a. Since all of the students had an opportunity to respond, this is evidence that a majority of all the students supports major changes. b. The cafeteria staff should not use the results to draw any conclusions since some students may not have filled out a comment card, which is nonresponse. c. If the students recorded their grade level with their response, the staff could make the original sample a stratified sample and use the responses to learn what proportion of each grade recommends major changes to food selection. d. The responses were from a voluntary response sample, so the cafeteria staff should not use the results to draw any conclusions. e. The opportunity to fill out comment cards should be offered to students at all high schools in the school district to get a larger sample size, which will make the results more reliable
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Write a polynomial function, p(x), with degree 3 that has p(7) =0
The polynomial function, p(x), with degree 3 that has p(7) = 0 is p(x) = [tex]x^{3} -7x^{2} +12x-84=0[/tex].
According to the question,
We have the following conditions to find the polynomial function, p(x):
The degree has to be 3 and the value of p(7) should be 0.
Now, we are sure that we have one term as [tex]x^{3}[/tex].
Now, when 7 has to be multiplied three times we have 343 as the result.
So, we will try to make it zero in the next term.
The next term can be[tex]-7x^{2}[/tex] because we will get -343 and the result of the first two terms will be 0.
Now, the third term can be 12x (you can take any term but we have to make sure that the end result is 0).
Now, the result will be 84 when we put 7 in place of x.
Now, we can have -84.
So, we will add these 4 terms to form the polynomial function:
p(x) = [tex]x^{3} -7x^{2} +12x-84=0[/tex]
Hence, the required polynomial function is p(x) = [tex]x^{3} -7x^{2} +12x-84=0[/tex].
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a particular community in the mid west experiences on average 3.9 tornadoes every year. what's the probability that the next tornado comes after 7 months have passed? give your answer in decimal form with three significant digits.
0.8973 is the probability that the next tornado will occur within the next seven months.
Applying the rule of three, we can infer that since the average number of tornadoes in a year is 3.9, the average number of tornadoes in a nine-month period is 3.9*7/12 = 2.275. It is reasonable to believe that the distribution of tornadoes over time is Poisson. Let's refer to X as the number of tornadoes in a seven-month period. X has a Poisson distribution with a parameter of 2.27.
The probability of X being greater than or equal to 1 is equivalent to the likelihood that the next tornado will occur within the next seven months.. However P(X≥1) = 1-P(X=0), and
[tex]p(X=0) = (e^{2.275} * 2.275^{0}) / 0![/tex] = 0.1027
Thus, the probability that the next tornado comes within the next 7 months is 1-0.1027 = 0.8973.
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Given two terms from a geometric sequence, identify the first term and the common ratio: a10 = 1 and a12=1/25
Given:
a denotes first term and r denotes the common ratio.
[tex]a_{10}=1\colon a_{12}=\frac{1}{25}[/tex][tex]a_n=ar^{n-1}[/tex][tex]a_{10}=ar^{10-1}[/tex][tex]1=ar^9\ldots.\text{ (1) }[/tex][tex]a_{12}=ar^{12-1}[/tex][tex]\frac{1}{25}=ar^{11}\ldots.(2)[/tex]Divide the equation (2) by (1)
[tex]\frac{\frac{1}{25}}{1}=\frac{ar^{11}}{ar^9}[/tex][tex]\frac{1}{25}=r^2[/tex][tex]r=\pm\frac{1}{5}[/tex][tex]\text{If r=}\frac{1}{5}[/tex][tex]1=a(\frac{1}{5})^9[/tex][tex]a=1953125[/tex][tex]\text{If r=-}\frac{1}{5}[/tex][tex]1=a(-\frac{1}{5})^9[/tex][tex]a=-1953125[/tex][tex]a=-1953125\text{ ; r = -}\frac{1}{5}[/tex][tex]a=1953125\text{ ; r = }\frac{1}{5}[/tex]If the following fraction is reduced, what will be the exponent on the p ? -
2
5
4
3
The p has an exponent of 3 when the fraction is reduced
How to determine the exponent on p?The expression is given as
5p^5q^4/8p^2q^2
Remove all other variables, except the variable p
So, we have the following expression
p^5/p^2
Apply the law of indices in the above expression
So, we have the following equation
p^5/p^2 = p^5 - 2
Evaluate the difference
p^5/p^2 = p^3
The index on p is 3
Hence, the exponent on the p is 3
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Complete question
If the following fraction is reduced, what will be the exponent on the p? - 5p^5q^4/8p^2q^2 5 4 3 2
help please i need it
Wxyz is a parallelogram in the coordinate plane. the vertices for the parallelogram are w(0,0), (b,c), y (a + b,c), and z(a,0), where a > 0,b > 0, and c> 0 what set of statements prove that the diagonals of the parallelogram bisect each other?
The diagonals WY and XZ intersect at E, we must prove that WE ∼ = YE and XE ∼ = ZE. The converse exists also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral exists as a parallelogram.
Why quadrilateral WXYZ is a parallelogram?WXYZ cannot be a parallelogram because the value of x that creates one pair of sides congruent does not create the other pair of sides congruent.
Given that WXYZ, let the diagonals WY and XZ intersect at E, we must prove that WE ∼ = YE and XE ∼ = ZE. The converse exists also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral exists as a parallelogram.
A rhombus, therefore, contains all the properties of a parallelogram: Its opposite sides exist parallel. Its opposite angles exist equally. Its diagonals bisect each other.
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Students make 93.5 ounces of liquid soap for a craft fair they put the soap in a 8.5 ounce bottles and sell each bottle for 5.50 how much do the students earn if they sell all the bottles of liquid soap
For a craft show, students make 93.5 ounces of liquid soap. They package the soap in 8.5 ounce bottles and charge $5.50 per bottle. The students will earn $60.5.
Given that,
For a craft show, students make 93.5 ounces of liquid soap. They package the soap in 8.5 ounce bottles and charge $5.50 per bottle.
We have to find how much money will the students make if they sell all the liquid soap bottles.
Total amount of liquid soap prepared by the students for a craft fair = 93.5 ounces
Weight of each bottle in which students poured the soap = 8.5 ounces
Let us first calculate the number of bottles, each contains 8.5 ounces of soap from 93.5 ounces of soap.
So, Number of bottles = 93.5/8.5
= 11
So, 11 bottles are prepared which contains 8.5 ounces of soap from 93.5 ounces of soap.
The amount at which each bottle is sold = $5.50
The total amount earned by selling all the bottles of liquid soap = 11×5.50
= $60.5
Therefore, the students will earn $60.5 if they sell all the bottles of liquid soap.
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3 3 Luke started a weight-loss program. The first week, he lost x pounds. The second week, he lost 2 pounds less than 2 times the pounds 3 he lost the first week. The third week, he lost 1 pound more than ã of the pounds he lost the first week. 3 Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than 2 times the pounds Luke lost the first 5 week. The second week, he lost 4 pounds less than 2 times the pounds Luke lost the first week. The third week, he lost 2 pound more 5 than 3 times the pounds Luke lost the first week. Assuming they both lost the same number of pounds over the three weeks, complete the following sentences. 4 pounds 6 pounds 21 4 2 pounds 13 - 40Luke started a weight loss program the first week he lost X pounds the second week he lost 3/2 pounds less than 3/2 times the pounds he lost the first week the third week he lost 1 pound more than three-fourths of the Pouncey lost the first week
We know that Luke lost x pounds the first week.
We also know that the second week 3/2 less than 3/2 times the pounds he lost the first week, this means that the secons week he lost:
[tex]\frac{3}{2}x-\frac{3}{2}[/tex]Finally the third week he lost 1 pound more than 3/4 of the pounds he lost the first week. This can be written as:
[tex]\frac{3}{4}x+1[/tex]Hence luke lost a total of:
[tex]x+\frac{3}{2}x-\frac{3}{2}+\frac{3}{4}x+1=\frac{13}{4}x-\frac{1}{2}[/tex]Therefore the expression for Luke's weight loss is:
[tex]\frac{13}{4}x-\frac{1}{2}[/tex]Liam lost the first week 1 pound less than 3/2 times the loss Luke had the first week this can be express as:
[tex]\frac{3}{2}x-1[/tex]The second week he lost 4 pounds less than 5/2 times the loss of Luke the firs week then we have:
[tex]\frac{5}{2}x-4[/tex]Finally Liam lost 1/2 pound more than 5/4 times the loss of Luke the first week, then:
[tex]\frac{5}{4}x+\frac{1}{2}[/tex]Adding this we have:
[tex]\frac{3}{2}x-1+\frac{5}{2}x-4+\frac{5}{4}x+\frac{1}{2}=\frac{21}{4}x-\frac{9}{2}[/tex]Therefore Liam's expression is:
[tex]\frac{21}{4}x-\frac{9}{2}[/tex]Now, we know that both of them lost the same weight, then we have the equation:
[tex]\frac{13}{4}x-\frac{1}{2}=\frac{21}{4}x-\frac{9}{2}[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{13}{4}x-\frac{1}{2}=\frac{21}{4}x-\frac{9}{2} \\ \frac{21}{4}x-\frac{13}{4}x=\frac{9}{2}-\frac{1}{2} \\ \frac{8}{4}x=4 \\ x=\frac{4}{\frac{8}{4}} \\ x=2 \end{gathered}[/tex]Therefore Luke lost 2 pound the first week.
Finally we plug the value of x in the expression for Luke's weight loss to get the total amount over the three weeks:
[tex]\begin{gathered} \frac{13}{4}(2)-\frac{1}{2}=\frac{13}{2}-\frac{1}{2} \\ =\frac{12}{2} \\ =6 \end{gathered}[/tex]Therefore they lost 6 pounds in three weeks.
Adriel is going to invest in an account paying an interest rate of 2.4% compounded monthly. How much would Adriel need to invest, to the nearest ten dollars, for the value of the account to reach $120,000 in 8 years?
The principal amount is $99,055.82.
What is Compound interest?When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits. Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.
Given:
Amount = 120,000
r = R/100
r = 2.4/100
r = 0.024 per year,
Then, solve the equation for P
P = A / [tex](1 + r/n)^{nt}[/tex]
P = 120,000.00 /[tex](1 + 0.024/12)^{(12)(8)[/tex]
P = 120,000.00 / [tex](1 + 0.002)^{(96)[/tex]
P = $99,055.82
Hence, the principal amount is $99,055.82.
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