g(x)=3(x+1)(x+3)(x-4)
Answer:
Step-by-step explanation:
Blake is going to invest in an account paying an interest rate of 5.7% compounded daily. How much would Blake need to invest, to the nearest hundred dollars, for the value of the account to reach $76,000 in 17 years
The amount that Blake should have invested is $28875.38
What is compound interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.
Given here: Interest rate=5.7% compounded daily
Let p be the principal that Blake needs to invest
76000=P(1+5.7%/365)³⁶⁵ ˣ ¹⁷
76000=P(1.000156)⁶²⁰⁵
P=$28875.38
Thus Blake should have invested $28875.38
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You start at point A and walk north for 12 meters. You turn right and walk for 8 additional meeters. Finally, you turn south and walk 3 meters. How far away are you from your original position. Leave your answer as a simplified radical.
Answer:
28m
Step-by-step explanation:
what is the value of the expression below 3/4 (-4/2) + (-3/4) +5/4
Answer:
-1
Step-by-step explanation:
I did it in my calculator soo i'm pretty sure its right
a sticky scale brings webster’s attention to whether caulking tubes are being properly capped. if a significant proportion of the tubes aren’t being sealed, webster is placing their customers in a messy situation. tubes are packaged in large boxes of 144. several boxes are inspected and the following number of leaking tubes are found. calculate the three-sigma control limits to assess whether the capping process is in statistical control.
0.064 the three-sigma control limits to assess whether the capping process is in statistical control.
Total number of leaked tubes = 72
Total number of tubes = 144*20 = 2880
Pbar = 72/2880 = 0.025
Number of tubes in each box (n) = 144
We need to calculate Lower and Upper control limits for P-chart which can be calculated as
LCLp = Pbar - 3*√Pbar * (1 - Pbar)/n = 0.025
UCLp = Pbar + 3* √Pbar * (1 - Pbar)/n = 0.025
- 3* √0.025 * (1 - 0.025)/144 = 0.025 - 0.039 = -0.014 or 0
+ 3* (1 - 0.025)/144 = 0.025 + 0.039 = 0.064.
Statistical Control is a quality control method that uses statistical techniques to monitor and control processes.
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Which point maximizes the objective function, z = 6x – y?
a. (1, 2)
b. (1, 5)
c. (6, 8)
d. (9, 1)
The point that maximizes the objective function is (9, 1) which gives the highest value of z = 53.
The answer is d. (9, 1).
To find the point that maximizes the objective function z = 6x - y, we need to evaluate the function at each given point and see which one gives the highest result.
a. z = 6(1) - 2 = 4
b. z = 6(1) - 5 = 1
c. z = 6(6) - 8 = 28
d. z = 6(9) - 1 = 53
To determine which point maximizes the objective function z = 6x - y, we will evaluate the function at each given point:
a. (1, 2): z = 6(1) - 2 = 4
b. (1, 5): z = 6(1) - 5 = 1
c. (6, 8): z = 6(6) - 8 = 28
d. (9, 1): z = 6(9) - 1 = 53
The point that maximizes the objective function is point d. (9, 1), with a value of z = 53.
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The graph of g(x) goes through the point (-4, 1) and is parallel to h(x) = 5x - 2 points
8. Determine the symbolic representation of g(x). Express your answer in
slope intercept form. *
Answer:
\(g(x)=5x+21\)
Step-by-step explanation:
The slope of g(x) is 5 because the slope of h(x) is 5 and g is parallel to h.
In point-slope form:
\(g(x)-1=5(x+4)\)
Rearranging for slope intercept form:
\(g(x)-1=5x+20\\g(x)=5x+21\)
The 4-It wall shown here slands 28 ft from the building. Find the length of the shortest straight bearn that will reach to the side of the building from the ground outside the wall. Bcom 2 Building 1'
The length of the shortest straight is approximately 28.01 ft.
What is the right triangle?
A right triangle is" a type of triangle that has one angle measuring 90 degrees (a right angle). The other two angles in a right triangle are acute angles, meaning they are less than 90 degrees".
To find the length of the shortest straight beam,we can use the Pythagorean theorem.
Let's denote the length of the beam as L and a right triangle formed by the beam, the wall, and the ground. The wall is 28 ft tall, and the distance from the wall to the building is 1 ft.
Using the Pythagorean theorem,
\(L^2 = (28 ft)^2 + (1 ft)^2\)
Simplifying the equation:
\(L^2 = 784 ft^2 + 1 ft^2\\ L^2 = 785 ft^2\)
\(L = \sqrt{785}ft\)
Calculating the value of L:
L ≈ 28.01 ft
Therefore, the length of the shortest straight beam is approximately 28.01 ft.
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There are 20 parrots at the animal sanctuary. Their population is increasing by 5 parrots each year. There are also 24 snakes at the sanctuary. Each year 4 more snakes are born. Part A: Write a function to represent the numbers of parrots at the sanctuary throughout the years. (6 points) Part B: Write a function to represent the numbers of snakes at the sanctuary throughout the years, (6 points) Part C: How many parrots are at the sanctuary after 10 years? How many snakes are at the sanctuary after the same number of years? Assume there are no deaths to the animals during this time. (6 points) Part D: After approximately how many years is the number of parrots and snakes the same? Justify your answer mathematically. (7 points)
Part A
Initial population of parrot in the animal sanctuary = 20 parrots
The population is increasing by 5 parrots per year.
let
number of years = x
y = population of parrot
The function can be represented as
\(y=5x+20\)Part B.
Initial population of snake in the sanctuary = 24
Each year 4 more snakes are born
let
number of year = x
y = population of the snake
The function can be represented below
\(y=24+4x\)Part C
Number of parrot in 10 years
\(\begin{gathered} y=5x+20 \\ y=5(10)+20 \\ y=50+20=70 \\ Number\text{ of parrot in 10 years = 70} \end{gathered}\)Number of snakes in 10 years
\(\begin{gathered} y=4x+24 \\ y=4(10)+24 \\ y=40+24=64 \\ Number\text{ of snakes in 10 years = }64 \end{gathered}\)Part D
The number of year where the number of parrot and snakes are the same can be calculated below
\(\begin{gathered} 5x+20=4x+24 \\ 5x-4x=24-20 \\ x=4 \end{gathered}\)The snakes and the parrot will be equal in population after 4 years time.
During a local high school football game, the height h feet of a football after t seconds can be represented by the function h(t) = −16t2+ 58t + 2. Find h(2.5) and explain its meaning.
h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.
In the question, we are given that during a local high school football game, the height of h feet of a football after t seconds can be represented by the quadratic function h(t) = -16t² + 58t + 2.
We are asked to find h(2.5) and explain its meaning.
To find h(2.5), we substitute t = 2.5, in the quadratic function h(t) = -16t² + 58t + 2.
Thus,
h(2.5) = - 16(2.5)² + 58(2.5) + 2,
or, h(2.5) = - 16(6.25) + 145 + 2,
or, h(2.5) = -100 + 147,
or, h(2.5) = 47.
Hence, h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.
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If the diagonal of a rhombus is ( x- 4d) and ( x+ 4d) then find the area of rhombus
If the diagonal of a rhombus id x-4d and x+ 4d then the area of rhombus is (x² - 16d²) / 4 unit²
In a rhombus, the diagonals are perpendicular bisectors of each other, and they divide the rhombus into four congruent right triangles. Let's call the length of one half of the diagonal "a" and the length of the other half of the diagonal "b". So we have:
a = (x - 4d) / 2
b = (x + 4d) / 2
The area of a rhombus can be calculated as half the product of its diagonals, or as half the product of its side lengths:
Area = (1/2) × a × b × 2
Area = a × b
Substituting the expressions for "a" and "b" from above, we get:
Area = [(x - 4d) / 2] × [(x + 4d) / 2]
Area = (x² - 16d²) / 4
Therefore, the area of the rhombus is (x² - 16d²) / 4 square units.
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Fill in the blank: so far as we know, the first person wo claimed that natural phenomena could be described by mathematics was ____
Thales of Miletus is believed to be the first person who claimed that natural phenomena could be described by mathematics.
Thales of Miletus was a Greek philosopher, mathematician, and astronomer who lived around 624 BCE to 546 BCE. He is widely regarded as one of the Seven Sages of Greece and is known for his contributions to various fields, including geometry, astronomy, and philosophy.
Thales believed that everything in the universe could be explained by natural causes rather than the actions of gods or other supernatural forces. He also believed that these natural phenomena could be described mathematically. For example, Thales was able to predict an eclipse of the sun using his knowledge of geometry and astronomy.
Therefore, Thales of Miletus is often regarded as the first scientist in history because of his emphasis on using reason and evidence to explain the natural world.
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The following data was obtained from the entire population in small town of Texas. Individuals were classified into whether they were of normal weight or overweight based on the Body Mass Index (BMI). Cholesterol levels were also measured from every individual and classified as high or low. High cholesterol Low cholesterol Overweight 324 450 Normal weight 368 890 Calculate the conditional probability of sampling an individual that is overweight given that the individual has high cholesterol.
If the number of people who are overweight and have high cholesterol is 324, the number of people who are overweight and have low cholesterol is 450, the number of people who are normal weight and have high cholesterol is 368, and the number of people who are normal weight and have low cholesterol is 890, then the conditional probability of sampling an individual that is overweight given that the individual has high cholesterol is 46.8%
To find the conditional probability of sampling an individual that is overweight given that the individual has high cholesterol, follow these steps:
Let A be the event of selecting an individual who is overweight and B be the event of selecting an individual who has high cholesterol. The formula for calculating conditional probability, P(A/B) = P(A ∩ B) / P(B), where P(A∩B) represents the probability of the intersection of A and B events and P(B) represents the probability of the occurrence of event B.P(A/B) = P(overweight ∩ high cholesterol) / P(high cholesterol) ⇒P(high cholesterol) = total number of individuals with high cholesterol / Total population= (324 + 368) / (324 + 450 + 368 + 890)= 692 / 2032P (overweight ∩ high cholesterol) = Number of overweight individuals with high cholesterol / Total population= 324 / 2032∴ P(A/B) = P(overweight ∩ high cholesterol) / P(high cholesterol)= 324 / 692= 0.468 = 46.8%Hence, the conditional probability of sampling an individual that is overweight given that the individual has high cholesterol is 46.8%.
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5+3 + 7 = 5 + 7 + 3 O A. True B. Fa
Answer:
its true
Step-by-step explanation:
Can a lesser number
represent a greater change in water
level than a greater number? Explain
Please I need it ASAP
help pleaseeeeee and quick too lol!
Step-by-step explanation:
2/root 9=2/3 = 0.6666666667
Answer:
0.66666
Step-by-step explanation:
hydrostatic weighing uses which statistic to predict the percentage of body fat?
Hydrostatic weighing uses the statistic known as density to predict the percentage of body fat.
Hydrostatic weighing, also known as underwater weighing or densitometry, is a method used to estimate body composition by measuring the density of an individual's body.
The principle behind hydrostatic weighing is that fat tissue is less dense than lean tissue, such as muscle and bone.
During a hydrostatic weighing test, the individual is submerged in water while their body volume is measured. By comparing the weight on land with the weight in water, the density of the body can be calculated.
The measured density is then used in equations or regression models to estimate the percentage of body fat.
The statistic of density is crucial in this process because it represents the ratio of an individual's mass to their volume.
By accounting for the density of fat and lean tissue, hydrostatic weighing provides an estimate of body fat percentage based on the differences in density between these components.
It is worth noting that while hydrostatic weighing has been widely used as a reference method for body composition assessment, more modern techniques such as dual-energy X-ray absorptiometry (DXA) and bioelectrical impedance analysis (BIA) have gained popularity due to their convenience and accessibility.
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At 8:00, the temperature was -6°. Three hours later, the temperature dropped 13°. What is the temperature at 11:00?
Answer:
-19 degrees
Step-by-step explanation:
13+6=19
you would need to add the negative since it said dropped in temperature and the temperature was already negative.
Heather performs an experiment to measure the acceleration of an object due to earths gravitational and discovers the acceleration of an object is 10.91 meters per second. The actual acceleration of the object is 9.80 meters per second.
The percentage error in the acceleration is 11.3%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The actual acceleration of the object is 9.80 meters per second.
The acceleration of an object is 10.91 meters per second.
Now,
Percentage error.
= (Experiment acceleration - Actual acceleration) / Actual acceleration x 100
= (10.91 - 9.80) / 9.80 x 100
= 1.11 / 9.80 x 100
= 11.33 %
Thus,
The percentage error is 11.3%.
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what is the smallest result that can be obtained by the following process? choose three different numbers from the set {3, 5, 7, 11, 13, 17}. add two of these numbers. multiply their sum by the third number.
3 x 5 x 7 = 105, which is the smallest result that can be obtained by the process. To reach this result, the three chosen numbers must be 3, 5, and 7. The first step is to add two of the three numbers, which in this case is 3 + 5 = 8. Then, the sum of the two numbers is multiplied by the third number, which in this case is 7.
The product of 8 x 7 is 56, which is the smallest result that can be obtained by this process. In general, the chosen numbers must be the smallest possible numbers in order to obtain the smallest result. The process involves adding two of the three chosen numbers and then multiplying the sum by the third number.
Thus, the three chosen numbers must be the numbers with the lowest sum when added together, and the third number must be the smallest number of the three. By following this process, the smallest result that can be obtained is the product of the three chosen numbers multiplied together.
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Directed line segment PT has endpoints whose
coordinates are P(-2, 1) and 1(4,7). Determine
the coordinates of pointſ that divides the segment
in the ratio 2 to 1.
Answer:
(2 , 5)
Step-by-step explanation:
point (x,y) that divides the segment PI in the ratio 2 to 1
PD=4 - (-2) = 6 PE/ED=2/1 PE=2ED PE+ED=6 3ED=6 ED=2 PE=4
coordinate of E (2,1) .... 2 is x coordinate of E
DI=7-1=6 DF/FI=2/1 DF=4
coordinate of F (4,5) .... .... 5 is y coordinate of E
CF // PD PC/CI=DF/FI=2/1
C (2,5)
Coordinates of the point intersecting segment PT in the ratio of 2 : 1 will be (2, 5).
Given in the question,
Segment PT with endpoints P(-2, 1) and T(4, 7).Point (h, k) divides the segment in the ratio of 2 : 1.If the endpoints of a segment PQ have been given as\(P(x_1,y_1)\) and \(Q(x_2,y_2)\) and a point \((h,k)\) divides this segment in the ratio of m : n,
\(h=\frac{mx_2+nx_1}{m+n}\)
\(k=\frac{my_2+ny_1}{m+n}\)
If the extreme ends of a segment PT are \(P(-2,1)\) and \(T(4,7)\) and a point (h, k) divides this segment in ratio of 2 : 1,
\(h=\frac{2(4)+1(-2)}{2+1}\)
\(h=2\)
\(k=\frac{2(7)+1(1)}{2+1}\)
\(k=5\)
Therefore, coordinates of the point intersecting segment PT in the ratio of 2 : 1 will be (2, 5).
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Mary’s mother invested in an internet stock the price went up and down over the next few months: +32, -10 +13 -25 at the end of the time period had the price of the stock finished higher or lower than it started show work
Answer:
higher
Step-by-step explanation:
add all of these numbers, if the sum is positive it is higher, if the sum is negative it is lower
32-10+13-25=10, this is positive so it is higher
helppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
Option D
Step-by-step explanation:
Area of triangle = \(\frac{1}{2}\) × (Base of triangle) × (Perpendicular height of triangle)
= \(\frac{1}{2}\) × [(20 - 10) inches] × [(15 - 5) inches]
= \(\frac{1}{2}\) × (10 inches) × (10 inches)
= 50 square inches
∴Area of each triangular piece = 50 square inches
∴Option D
Help asap: Sam is riding his bike home from
the library at a constant rate. The equation below describes the relationship between the number
of minutes (x) Sam has been riding and the distance (), in miles, Sam has left to travel
1 + 7 = 21
How many miles from Sam's home is the library?
O A. 3
OB
7
O C.
14
OD
21
Answer:
3 miles
Step-by-step explanation:
to find the amount of miles it is to the library you have to find how many miles it is when the minutes are zero
so when x = 0 what is y
0 + 7y = 21
7y = 21
y is 3
so that means the library is 3 miles away from his house
Which equation represents the line that is perpendicular to y=1/5 and passes through (-4,-3)?
10 pts please hurry.
Answer:
x=-4
Step-by-step explanation:
Just had it on a test and got it write
What number should be placed in the box to help complete the division calculation?
The number that should be placed in the box to help complete the division calculation is 390.
What is division?It should be noted that division is one of four basic operations of arithmetic, that illustrates the ways that numbers are combined to make new numbers. Here, the other operations are addition, subtraction, and multiplication
The division is simply a method of distributing a group of things into equal parts. The division is an operation inverse of multiplication.
The number that should be placed in the box to help complete the division calculation will be:
= 26 × 15
= 390
In conclusion, the number is 390.
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use a graph to estimate all the solutions of tan x=2.7 between 0 and 2π. enter your answers in increasing order, rounded to three decimal places.
The solutions of the equation tan(x) = 2.7 between 0 and 2π can be estimated by analyzing the graph of the tangent function. There are three solutions within this interval, which occur at approximately x = 0.858, x = 2.287, and x = 3.429.
1. To estimate the solutions of tan(x) = 2.7, we can examine the graph of the tangent function. The graph of y = tan(x) has a repeating pattern with vertical asymptotes occurring at x = π/2, 3π/2, etc., and horizontal asymptotes at y = -1 and 1. It also passes through the origin (0, 0).
2. We are interested in finding the x-values where the graph intersects the line y = 2.7. By observing the graph, we can see that it intersects the line y = 2.7 in three different places within the interval from 0 to 2π. To determine the approximate values of these intersections, we can visually estimate the x-coordinates of the points of intersection on the graph.
3. Using this approach, we can estimate the solutions as x = 0.858, x = 2.287, and x = 3.429 (rounded to three decimal places). These values represent the x-coordinates where the tangent function crosses the line y = 2.7.
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Which expression is a factor of both (x - 2)^2 and -3x + 6
A. 2
B. 3
C. x+2
D. x-2
E. (x-2)^2
Answer:
-x+2or-1x+2
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If you calculate sle to be $25,000 and that there will be one occurrence every four years (aro), then what is the ale?
If you calculate SLE to be $25,000 and that there will be one occurrence every four years (ARO), then the ALE is $40,000.
What is Single-loss expectancy (SLE)?A expected monetary decline each moment an asset is at risk is referred to as single-loss expectancy (SLE). It is a term that is most frequently used during risk analysis and attempts to assign a monetary value to each individual threat.
Quantitative risk analysis predicts the likelihood of certain risk outcomes as well as their approximate monetary cost using relevant, verifiable data.
IT professionals must consider a wide range of risks, including the following:
Errors caused by humansCyber attacks, unauthorised data disclosure, or data misuse are examples of hostile action.Errors in applicationSystem or network failuresPhysical harm caused by fire, natural disasters, or vandalism.To know more about the Single-loss expectancy (SLE), here
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Determine whether the series converges or diverges. 00 n + 1 ח + n = 1 converges diverges
The given series, 00 n + 1 ח + n = 1, diverges.
The series 00 n + 1 ח + n = 1 can be rewritten as ∑(n=1 to ∞) (n + 1) / (n^2). To determine its convergence or divergence, we can examine the behavior of its terms as n approaches infinity. Taking the limit of the nth term, we have lim(n→∞) [(n + 1) / (n^2)] = lim(n→∞) (1/n + 1/n^2) = 0. This limit indicates that the terms of the series approach zero as n becomes large.
However, even though the terms tend to zero, it does not guarantee convergence of the series. To further investigate, we can use the integral test. Considering the function f(x) = (x + 1) / (x^2), we can integrate this function from 1 to infinity. The integral ∫(1 to ∞) (x + 1) / (x^2) dx can be evaluated as [ln(x) - 1/x] evaluated from 1 to ∞, which diverges to infinity.
Since the integral diverges, the original series also diverges. Therefore, the series 00 n + 1 ח + n = 1 does not converge.
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