The working equation when dealing with problems regarding compounded interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A is the future value, P is the principal value, r is the annual rate, and n is the number of compounding periods.
The problem compounds quarterly, hence, we have n = 4.
We derive the working equation to solve for t, as follows:
[tex]\begin{gathered} \frac{A}{P}=(1+\frac{r}{n})^{nt} \\ \ln (\frac{A}{P})=\ln ((1+\frac{r}{n})^{nt}) \\ nt\ln ((1+\frac{r}{n}))=\ln (\frac{A}{P}) \\ t=\frac{\ln (\frac{A}{P})}{n\ln ((1+\frac{r}{n}))} \end{gathered}[/tex]Substitute the values of A, P, n, and r on the derived equation above and solve for t, we get
[tex]\begin{gathered} t=\frac{\ln (\frac{5780}{4000})}{4(\ln (1+\frac{0.04}{4}))} \\ t=\frac{\ln (1.445)}{4(\ln (1.01))} \\ t=\frac{0.368}{4(0.00995)} \\ t\approx9.25 \end{gathered}[/tex]Therefore, the $4000 investment grows to $5780 in 9.25 years.
I need helping finding out the answers … I’m confused.
To solve this problem, we will use the following formula for the area of a trapezoid:
[tex]A=\frac{a+b}{2}h,[/tex]where a, and b are the lengths of the bases and h is the height.
Now, we are given that ( we will omit the units to simplify the calculations):
[tex]\begin{gathered} h=\frac{1}{4}(a+b), \\ h=2\frac{1}{2}. \end{gathered}[/tex]Therefore:
[tex]\frac{(a+b)}{2}=2(\frac{a+b}{4})=2h=2(2+\frac{1}{2})=4+1=5.[/tex]Substituting in the above formula, we get:
[tex]A=\frac{5}{2}\times(2\frac{1}{2}).[/tex]Simplifying the above result, we get:
[tex]A=\frac{25}{4}ft^2.[/tex]Answer:
[tex]\begin{gathered} A=\frac{1}{2}(2\frac{1}{2})(2\frac{1}{2}\cdot2) \\ =\frac{1}{2}(\frac{5}{2})(\frac{5}{2}\cdot2) \\ =\frac{50}{8}=\frac{25}{4}=6.25ft^2. \end{gathered}[/tex]Solve each equation. Show solutions on number line |x-4|=1
The solutions to the equation are x = 5 and x = 3
How to solve the equation?The equation is given as
|x - 4|= 1
The above equation is an absolute value equation
When the absolute value sign is removed from the equation, we have
x - 4 = 1 or x - 4 = -1
Add 4 to all sides of the equation
So, we have the following equations
x = 1 + 4 or x = 4 - 1
Evaluate
x = 5 or x = 3
This means that the value of the equation is x = 5 or x = 3
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11. A researcher in a personal submarine begins at the surface of the ocean.
The submarine descends 20.6 meters and then ascends 57 meters. What
is the depth of the personal submarine?
A-26.3 meters
14.9 meters
B-14.9 meters
26.3 meters
The depth of the personal submarine is -14.9 meter.
What is an integer?An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.
Given that,
The submarine descends 20.6 meters and then ascends 5.7 meters. it means 20.6 is a negative number and 5.7 is a positive number.
Now,
To find the depth adding the -20.6+5.7
-20.6+5.7
-14.9
Hence, The depth of the personal submarine is -14.9 meter
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what’s the inequality
17 < 9 + x
Answer:
x > 9
Step-by-step explanation:
Which relations are functions? Select all that apply.
Options A and B are functions as either if of the inputs is relating to a different output or different inputs relating to a single output.
What is a function?A function can be thought of as a set of inputs that produces some output.
We know a relation is a function if every input relates to a different output sometimes many input relates to one output but one input relates to different outputs is not a function.
Option A is a function as every input relates to a different output.
Option B is not a function as the input - 4 relates to two different outputs 12 and 15.
Option C is also a function as every preimage has a different image.
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your ethics professor decides to conduct a survey in your class about whether voluntary euthanasia should be legal in the united states. for her survey, she takes all 30 students' names and assigns them each a number. then she has a computer program indiscriminately choose 15 students. we could say that her survey will be:
Hence, the survey of professor will be representative survey.
What is survey?A survey is a technique for acquiring data from a sample of people by asking pertinent questions with the goal of comprehending populations as a whole.
Everyone involved in the information economy, from corporations to the media to the government and academia, relies on surveys as a vital source of information and insights.
The survey of professor will be representative survey.
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What is the ratio in the question reduced to the lowest terms?
The total of animals is a prime number and hence the ratio can only be expressed as fraction.
Ratios of NumbersTo find the ratio in the given question, we must first of all add the total sum of the animals given and then find the ratio to each one.
Total number of items given
[tex]12 + 5 + 6 = 23[/tex]
The ratio of spiders to mosquitoes to rats are
[tex]\frac{12}{23}:\frac{5}{23}:\frac{6}{23}[/tex]
The total sum of animals is a prime number and can't be divided, however, the ratio is expressed as simple as possible.
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Rebecca wants to prove that if the diagonals in a parallelogram are perpendicular, then it is a rhombus.
It is shown that if a parallelogram's diagonals are perpendicular, the parallelogram is a rhombus.
In mathematics, what is a parallelogram?A parallelogram is a quadrilateral with two parallel sides (and therefore opposite angles equal).
What exactly is a rhombus?A rhombus is a quadrilateral with all of its sides equal. Because opposite sides of a parallelogram are equal, a rhombus is a type of parallelogram in which all sides are equal.
We must demonstrate that if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
Let ABCD be a parallelogram .
Consider Δ AOD and Δ COD
Since, a parallelogram's diagonals bisect each other we can say that,
AO = CO
∠AOD = ∠COD = 90°
DO = OD
Δ AOD ≅ Δ COD [SAS rule]
∴ AD = CD
Because the parallelogram's adjacent sides are equal, we can conclude that all four sides are equal.
As a result, it is demonstrated that if the diagonals of a parallelogram are perpendicular, the parallelogram is a rhombus.
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What is the value of x?
Answer:
x = 15
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
3x - 5 is an exterior angle of the triangle, then
3x - 5 = x + 25 ( subtract x from both sides )
2x - 5 = 25 ( add 5 to both sides )
2x = 30 ( divide both sides by 2 )
x = 15
Answer:
40° and 115°
Step-by-step explanation:
x+3x-5+25°=180°(angle on a straight line)
4x+20=180°
4x=180°-20
4x=160°
x=160/4
x=40°
The other angle
3x-5=3(40)-5
120-5=115°
total
40°+25°+115°=180°
pls help im faling geometry
Find the slope:
(-3, 3) and (7, 6)
Answer:
slope = (3/10)
Step-by-step explanation:
(-3, 3) and (7, 6)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 6 - 3 3 3
m = ------------ = ------------ = ------------ = ----------
x₂ - x₁ 7 - (-3) 7 + 3 10
I hope this helps!
Solve each equation by factoring. Then solve the quadratic formula. (Show all work)
[tex] - {k}^{2} + 3k = 28 - 2 {k}^{2} \\ - {k}^{2} + 2 {k}^{2} + 3k - 28 = 0 \\ {k}^{2} + 3k - 28 = 0 \\ (k + 7)(k - 4) = 0 \\ \\ k + 7 = 0 \\ \\ ork - 4 = 0 \\ \\ k = - 7 \\ \\ or \\ \\ k = 4[/tex]
ATTACHED IS THE SOLUTION
I GROUPED THE LIKE TERMS TOGETHER FIRST AFTER THAT THEN FACTORISED.
\theta=310^\circθ=310
∘
The degrees to radians conversion is given as 1° = π/180 radian thus the conversion of 310° is (31/18)π.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
It is known that π radian = 180°.
1° = (π/180) radian.
Multiply both sides by 310
310° = (π/180)310
310° = (31/18)π
Hence "The degrees to radians conversion is given as 1° = π/180 radian thus the conversion of 310° is (31/18)π".
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The given question is incomplete complete question is ;
Convert the angle \theta=310^\circθ=310∘
theta, equals 310, degrees to radians.
Find the quotient of.(4.617 × 10 ^3 ) ÷ (5,700 ÷ 10^ 2 )
The quotient of the expression (4.617 × 10³ ) ÷ (5,700 ÷ 10² ) is 81.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
The expression is;
(4.617 × 10³ ) ÷ (5,700 ÷ 10² )
Now, Solve the expression by using BODMAS rule;
= (4.617 × 10³ ) ÷ (5,700 ÷ 10² )
= 4,617 ÷ 57
= 81
Thus, The quotient of the expression (4.617 × 10³ ) ÷ (5,700 ÷ 10² ) is 81.
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I'm doing linear equations and one if the things says y = -x so do i plug in the x that i have already and just switch it to the opposite integer????
To solve for y we will have to simply replace the value of x and the solution we write it in the equivalent palce for y, that is:
For x = -5:
[tex]y=-(-5)\Rightarrow y=5[/tex]For x = -2:
[tex]y=-(-2)\Rightarrow y=2[/tex]For x = 0:
[tex]y=0[/tex]For x = 3:
[tex]y=-3[/tex]find the values of a,b,c, and d so that h(x)=a|bx+c|+d is a translation 7 units up and 1 unit right, followed by a reflection in the y-axis of the graph of g(x)=1/3|x+3|-4
The translation shift the coordinates of the expression in the right side. And there is no change in the reflection based equation because of the absolute symbol.
What is translation and reflection?
In mathematics, the translation shift the coordinates either on the horizontal axis or on the vertical axis. It compress the expression also. Similarly, in reflection, the expression get reflected on the coordinate axis either on the upper side or downward side.
According to the question, the given expression for the translation as well as for the reflection are as follows:
h(x)=a |b(x) + c| + d
g(x)=1/3 | x + 3| - 4
And the given condition state that the translation is for 7 units and reflection is on the y-axis. Translation shift the expression and reflection reflects the expression.
Translation expression: h(x+7)=a |b(x+7) + c| + d
Reflection expression: g(-x)=1/3 | -x + 3| - 4 = 1/3 | x + 3| - 4
Therefore, the translation shift the coordinates of the expression in the right side. And there is no change in the reflection based equation because of the absolute symbol.
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Evaluate the arithmetic series described:
a (subscript 1) = 12
a (subscript n) = 64
Find S (subscript 14)
Answers:
541
532
1082
1064
...the subscript thing isn't working for some reason
Answer:
532
Step-by-step explanation:
Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac{n}{2}(a_1+a_n)}[/tex]
Where:
aₙ is the nth term.a₁ is the first term.n is the position of the term.Given terms:
[tex]a_1=12[/tex][tex]a_n=64[/tex]Substitute the given terms into the formula to create an equation for the nth term:
[tex]\implies S_n=\dfrac{n}{2}(12+64)[/tex]
[tex]\implies S_n=\dfrac{n}{2}(76)[/tex]
[tex]\implies S_n=38n[/tex]
To find S₁₄, substitute n = 14 into the found equation:
[tex]\begin{aligned}n=14 \implies S_{14}&=38(14)\\ & = 532\end{aligned}[/tex]
A restaurant chain is measuring the levels of arsenic in chicken from its suppliers. The question is whether there is evidence that the mean level of arsenic is greater than 80 ppb, so we are testing vs , where represents the average level of arsenic in all chicken from a certain supplier. It takes money and time to test for arsenic so samples are often small. A sample of chickens from one supplier is tested, and the resulting sample mean is . Subtracting 11 from the sample data to move the mean down to the null mean of results in the following data: . 62, 78, 89, 95, 95, 137
The p-value of the test is 0.1515 which concludes that the average amount of arsenic in chicken from suppliers is 80 ppb.
The test hypothesis is as follows:
H₀: The mean amount of arsenic is 80 ppb, i.e. μ= 80.
Hₐ: The mean amount of arsenic is more significant than 80 ppb, i.e.μ > 80.
We will apply a t-test for a single mean because the population standard deviation is unknown,
It is assumed that the sample means [tex]\bar{x}[/tex] = 91.
The adjusted sample presented is:
S = { 62, 78, 89, 95, 95, 137}
Calculate the sample standard deviation as follows:
[tex]\bar{x}[/tex] = 62 + 78 + 89 + 95 + 95 + 137 =80
[tex]s =\sqrt{\frac{1}{6-1} \times [(62-80)^2 + (78-80)^2 + (89-80)^2 + (95-80)^2 + (95-80)^2 + (137-80)^2]}[/tex]
s =28.66
[tex]t =\dfrac{\bar{x}-\mu}{s/ \sqrt{n} } = \dfrac{{91}-80}{28.6/ \sqrt{6} }=0.94[/tex]
Thus, the test statistic value is 0.94.
Compute the p-value of the test as follows:
p-value = p(tₙ₋₁ < t)
p-value = p(t₆₋₁ < t)
p-value = p(t₅ < t)
*Make use of a t-table.
As a result, the test has a p-value of 0.1515.
Rule of decision:
The null hypothesis will be rejected if the p-value of the test is less than the significance threshold, and vice versa.
p-value = 0.1515 > α = 0.05
At 5% significance, the null hypothesis will not be rejected.
As a result, we may conclude that the average amount of arsenic in chicken from suppliers is 80 ppb.
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Last year, Lena biked 565 miles. This year, she biked k miles. Using k, write an expression for the total number of miles she biked
Please help me please I’m begging I WILL GIVE YOU BRAINLEST
The value of x is 54.
What is the Same Side Interior Angles Theorem?If a transversal meets two parallel lines, each pair of same-side interior angles is supplementary (their sum is 180°), according to the theorem for the "same-side interior angle theorem."
The given angles in the figure are 2x + 42° and x - 24°, which are interior angles formed on the same side of the transversal.
By Same Side Interior Angles Theorem,
2x + 42° + x - 24° = 180°
3x + 18° = 180°
3x = 180° - 18°
3x = 162°
x = 54
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I need help with finding the coordinates of B, I found A but I can't seem to get the right answer for B.
The graph represents the cosine graph, the coordinates of B is (-180, -1 )
what is cosine graph?This is a type of graph used to depict cosine values of angles. The maximum and minimum points in these type of graph is 1 and -1.
The zero points gives the maximum point on the graph, hence the graph starts at ( 0, 1 )
Point B is found by analyzing the graph.
The point is located at the minimum which is -1. this is for the output value.
The input value which is the x direction we look at the cycles covered. one full cycle is 360 degrees or -360 degrees.
Point B is in the negative and coves half cycle which is -180
Hence B ( -180, -1)
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What is the answer: 4(3x+2)-2
Answer:
12x + 6Step-by-step explanation:
What is the answer:
4(3x+2)-2=
12x + 8 - 2 =
12x + 6
The figures below are congruent. Name the corresponding sides.
Answer:
KM
KL
LM
Step-by-step explanation:
help meeeeeeeeeeee pleaseeeeeeeeeeeeee!!
Answer:
324 square inches
Step-by-step explanation:
A = S squared
A = 18 x 18
A = 324square inches
11. The price of a sweater changed from $20 to $12. By what percentage was the price of the sweater
changed?
The price of the sweater decreased by __ %
well, the change was 8 bucks.
if we take 20 to be the 100%, what is 8 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 20 & 100\\ 8& x \end{array} \implies \cfrac{20}{8}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2}=\cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40[/tex]
the half-life of palladium-100 is 4 days. after 12 days a sample of palladium-100 has been reduced to a mass of 4 mg. what was the initial mass (in mg) of the sample? what is the mass (in mg) 7 weeks after the start? you may enter the exact value or round to 4 decimal places.
Using the half life of palladium, mass seven weeks after start was 0.7931 gm.
The half-life is the amount of time it takes for a quantity (of material) to fall to the cost. In nuclear physics, the phrase usually refers to how rapidly neutrons become radioactive atoms or how long stable atoms survive.
The term can also refer to any sort of hyperbolic (or, in rare situations, non-exponential) decay.
The half life of palladium 100 = 4 days
after 24 days sample has reduced to a mass of 5mg
standard exponential function is
[tex]P = P_o e^{kt}[/tex]
plugging P = P₀ /2
[tex]P_o/2 = P_o e^{4k }[/tex]
[tex]1/2 = e^{4k }[/tex]
ln (1/2) = 4k
k = -0.1733
function becomes
[tex]P = P_o e^{- 0.1733 t }[/tex]
plugging P = 5 and t = 24
[tex]5 = P_o e^{( - .1733\times 24 ) }[/tex]
P₀ = 320.10
In the medical sciences, for example, the biological half of drugs and other chemicals in the human body is referred to. The flipside of half-life is doubling time in exponential growth.
For the second part of the problem:
7 weeks = 5 × 7 =49 days
plugging t = 49
[tex]P = 320.10 e^{(-.1733 * 35 ) }[/tex]
mass 7 weeks after = 0.7431 mg
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WILL GIVE BRAINLIST IF ANSWERED CORRECTLY!!
Any transformation that leaves the sides and angles of flat figures unaltered is referred to as rigid transformation or isometry. Congruent pictures are produced by reflection in the plane, translations, rotations, or a combination of them.
What is meant by rigid transformations?A transformation that maintains the size and shape of a geometric figure is known as a rigid transformation (or isometry). is a unique kind of transformation that doesn't alter a figure's size or shape.
Any transformation that leaves the sides and angles of flat figures unaltered is referred to as rigid transformation or isometry.Congruent pictures are produced by reflection in the plane, translations, rotations, or a combination of them.This suggests that two figures can only be said to be congruent if and only if a rigid transformation, or a combination of one or more rigid transformations, can map one planar figure onto another.The complete question is:
Make a conjecture. How are rigid transformations and congruent figures related? Check all that apply
a) rigid transformations preserve segment lengths and angle measures.
b) Rigid transformations produce congruent figures.
c) If two figures are congruent, then there is a rigid transformation or a combination of rigid transformations that will map one onto the other.
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Which of the following is the best estimate of the slope of the best -fit line for the graph at the right?
The best estimate of the slope of the best-fit line for the graph at the right will be 7/4.
What is the slope?The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope. A line that is moving up will have a positive slope, and a line that is moving down will have a negative slope if you view the line from left to right. A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x₁,y₁) and (x₂,y₂), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
Given Data
x coordinate = 4
y coordinate = 7
Slope = y-coordinate/ x-coordinate
Slope = 7/4
The best estimate of the slope of the best-fit line for the graph at the right will be 7/4.
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Find the value of p in the inequality.
three fourths times p plus 8 is greater than or equal to 3
The value of p that we get by solving the inequality given in the question is [tex]p\geq \frac{-20}{3}[/tex]
The given inequality is
[tex]\frac{3}{4}p+8\geq 3[/tex]
⇒[tex]\frac{3}{4}p\geq 3-8[/tex] (subtracting 8 on both sides)
⇒[tex]3p\geq -5*4[/tex] (multiplying both sides by 4)
⇒[tex]p\geq \frac{-20}{3}[/tex] (dividing both sides by 3)
⇒[tex]p\geq -6.667[/tex]
Therefore the value of p must be greater than or equal to -20/3 or -6.667
That is, [tex]p\geq -6.667[/tex]
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Which of these is best used for displaying frequency distributions when one or two categories make up a large proportion of the total?
A. Pie chart
B. Bar graph
C. Comparative pie chart
D. Comparative bar graph
Option A, Pie chart best used for displaying frequency distributions when one or two categories make up a large proportion of the total.
A piechart is best which is used for displaying frequency distribution when one or two categories make up a large proportion.
Hence, the Pie chart is best.
Pie chart - A pie chart is a statistical visualization in the shape of a split region that displays numerical information. The arc length of each slice in a pie chart is proportionate to the quantity represented.
Explanation of incorrect options,
Bar graph - A bar chart is a form of chart or graph that depicts categorical data using rectangular bars whose height or length is proportionate to the value they represent. face. Bars can be drawn vertically or horizontally. A histogram is another name for a vertical bar chart.
Comparative pie chart - Pie graphs have pie graphic areas comparing ratios by frequency. The greater the radius of the pie chart, the greater the number of individuals it depicts. This allows you to compare the two data sets visually.
Comparative bar graph - Chart displaying continuous comparisons of columns indicating different portions of the same category. This facilitates the comparison of visual data.
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