The order to determine whether the sample size of 81 people is adequate to compute a confidence interval for the percentage of U.S. adults who spend more than 20 hours a week on a home computer.
we must take into account the conditions for using normal approximation methods.For the normal approximation to be trustworthy, often both the sample size and the projected number of successes and failures need to be significant. A basic guideline is that both np and n(1-p) should be more than or equal to 5, when n is the sample size and p is the predicted proportion.We have 36 achievements in this case out of 81 people (those that use a computer for more than a.
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how many pieces of wood can be cut from a board that is 107/8 feet long is each piece is 227/140 feet long?
The number of pieces of wood that can be cut from the board is 8.
A fraction is a mathematical expression that represents a part of a whole. It is written as two numbers separated by a slash ( / ). The top number, called the numerator, represents the number of parts being considered, and the bottom number, called the denominator, represents the total number of parts in the whole. For example, 1/2 is a fraction that represents one part of a whole that has been divided into two equal parts.
To determine the number of pieces of wood that can be cut from a board that is 107/8 feet long, if each piece is 227/140 feet long, you need to divide the length of the board by the length of each piece.
You can calculate the number of pieces by dividing the length of the board which is 107/ 8 feet by the length of each piece which is 227/ 140 feet:
= 107/ ( 8 * 227/ 140)
= (107/8) * (140/ 227)
= 8.25
= 8
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What can you say about a sample mean or a sample proportion being about 2 ses away from the population mean or the true proportion? what can you not say?
When we have a normal model for the sampling distribution, we cannot say that a sample mean or sample proportion is approximately 2 standard errors (ses) away from the population mean or the true proportion.
Instead, we can say that 95% of the sample proportions fall within two standard errors of the population proportion. Similar to this, the percentage of sample proportions decreases as the standard error distance decreases and increases as the standard error distance increases.
Therefore, the standard error distance will be greater than 2 standard errors (ses) if 99% of the sample proportions are within a given standard error distance of the population proportion.
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Which of these expressions is equivalent to:
3x^3 y^5 + 3x^5 y^ 3 − (4x^5 y^3 − 3x^3 y^5)
The equivalent expression is: \(-x^5 y^3 + 6x^3 y^5\).
Let's simplify the given expression step by step using the given terms:
Expression:
\(3x^3 y^5 + 3x^5 y^3 - (4x^5 y^3 − 3x^3 y^5)\)
Distribute the negative sign outside the parentheses to the terms inside:
\(3x^3 y^5 + 3x^5 y^3 - 4x^5 y^3 + 3x^3 y^5\)
Combine like terms, which are terms that have the same variables raised to the same power:
\((3x^3 y^5 + 3x^3 y^5) + (3x^5 y^3 - 4x^5 y^3)\)
Add or subtract the coefficients of the like terms:
\(6x^3 y^5 - x^5 y^3\)
So, the simplified expression is:
\(6x^3 y^5 - x^5 y^3\)
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4-2×=×+8 what is the result
Answer:
x = -4/3
Step-by-step explanation:
4 - 2x = x + 8
4 - 3x = 8
-3x = 4
x = -4/3
10. A hobby pack of baseball cards contain 9 cards and a jumbo pack
contains 35 cards. Ethan bought 7 packs for a total of 141 cards. How
many packs of hobby and jumbo did Ethan buy?
Answer:
He bought 3 jumbo packs and 4 hobby packs.
Step-by-step explanation:
Ethan bought 4 number of hobby packs and 3 number of jumbo packs.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Let x be the number of hobby pack that Ethan buy and y be the number of jumbo packs that Ethan buy.
Ethan bought 7 packs for a total of 141 cards.
We got two linear equations here :
x + y = 7
9x + 35y = 141
Multiplying the first equation throughout by 9,
9x + 9y = 63
Subtracting the resulting equation we get from the second equation,
(9x + 35y) - (9x + 9y) = 141 - 63
35y - 9y = 78
26y = 78
y = 3
x = 7 - y = 4
Hence Ethan bought 4 hobby packs and 3 jumbo packs.
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What is the composition of the translations
(T〈−3, 4〉 ∘ T〈8, −7〉)(x, y) as one translation?
Answer:
P=5 and Q=-3
Step-by-step explanation:
-3+8=p=5
4-7=q=-3
<p, q>= <5,-3>
The composition of the translations; T < − 3 , 4 > ⋅ T < 8 , − 7 > (x, y) as one translation gives;
T < 5 , − 3 > (x, y)
We want to compose the translations; T < − 3 , 4 > ⋅ T < 8 , − 7 > (x, y) as one translation;
Now, translation is usually a map defined as;
T < a , b> < x , y> = (x + a, y + b)
Thus, the image of the first translation is given as;
T < 8 , − 7 > (x, y) = (x + 8, y - 7)
Finally;
T < − 3 , 4 > ⋅ T < 8 , − 7 > (x, y) = T < − 3 , 4 > ⋅ (x + 8, y - 7)
⇒ (x + 8 - 3, y - 7 + 4)
⇒ (x + 5, y - 3)
Since T < a , b> < x , y> = (x + a, y + b)
Then; (a, b) = (5, -3)
As one translation gives;
T < 5 , − 3 > (x, y)
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The following are the major balance sheet classifications:
Current assets (CA) Current liabilities (CL)
Long-term investments (LTI) Long-term liabilities (LTL)
Property, plant, and equipment (PPE) Stockholders’ equity (SE)
Intangible assets (IA)
Match each of the items to its proper balance sheet classification, shown below. If the item
would not appear on a balance sheet, use "NA."
______ Salaries and wages payable ______ Equipment
______ Service revenue ______ Accumulated depreciation—
______ Interest payable equipment
______ Goodwill ______ Depreciation expense
______ Debt investments (short-term) ______ Retained earnings
______ Mortgage payable (due in 3 years) ______ Unearned service revenue
______ Investment in real estate
Here are the major balance sheet classifications and their proper balance sheet classification.Current assets (CA)Long-term investments (LTI)Property, plant, and equipment (PPE) Intangible assets (IA) Stockholders’ equity (SE) Current liabilities (CL) Long-term liabilities (LTL).
Matching of balance sheet items to its proper balance sheet classification: Salaries and wages payable - Current Liabilities (CL) Equipment - Property, plant, and equipment (PPE) Service revenue - Current assets (CA)Depreciation expense - NA Interest payable - Current liabilities (CL) .
Goodwill - Intangible assets (IA)Debt investments (short-term) - Current assets (CA)Retained earnings - Stockholders’ equity (SE)Mortgage payable (due in 3 years) - Long-term liabilities (LTL)Unearned service revenue - Current liabilities (CL)Investment in real estate - Long-term investments (LTI)Accumulated depreciation—equipment - Property, plant, and equipment (PPE)
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what feature(s) about a relationship can be observed from examining a scatterplot of two quantitative variables x and y?
By examining a scatterplot, you can gain valuable insights into the relationship between the two quantitative variables x and y, such as direction, strength, form, and outliers.
From examining a scatterplot of two quantitative variables x and y, you can observe the following features about the relationship between the variables:
1. Direction: You can determine whether the relationship between the variables is positive (both variables tend to increase or decrease together) or negative (one variable tends to increase while the other tends to decrease).
2. Strength: You can assess the strength of the relationship by observing how closely the data points are clustered around an imaginary line (e.g., a straight or curved line). A strong relationship has points closely clustered, while a weak relationship has points more scattered.
3. Form: You can identify the form of the relationship, such as linear (points form a straight line) or nonlinear (points form a curve).
4. Outliers: You can detect any outliers, which are data points that do not follow the general pattern of the relationship between the variables.
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A CD usually sells for $15.00. If the CD is 30% off, and sales tax is 8%, what is the total price of the CD, including tax? A. $11.45 B. $12.15 C. $10.53 D. $11.34
whats the answer for 0.2x-6=11
Answer:
\(\huge\boxed{\sf x = 85}\)
Step-by-step explanation:
Given equation:0.2x - 6 = 11
Add 6 to both sides0.2x = 11 + 6
0.2x = 17
Divide both sides by 0.2x = 17/0.2
x = 85\(\rule[225]{225}{2}\)
Given:-
\( \rm \: 0.2x - 6 = 11\)\( \: \)
Solution:-
\( \rm{0.2x - 6 = 11}\)\( \: \)
\( \rm \: 0.2x = 11 + 6\)\( \: \)
\( \rm \: 0.2x = 17\)\( \: \)
\( \rm \: x = \cancel \frac{17}{0.2} \)\( \: \)
\( \underline { \boxed{ \rm \color{skyblue} \: x = 85 \: }}\)\( \: \)
\( \purple {━━━━━━━━━━━━━━━━━━━━━━━━━━━━}\)
hope it helps!
Watch help video Find the length of the third side. If necessary, write in simplest radical form. 7 4√2
In simplest radicle form, the length of the third side = 9 units.
Given,
Side A = 7 units.
Side B = 4√2 units.
To find Side C, we use the Pythagorean formula,
a² = b² + c²
7² = \(4\sqrt{2}^{2}\) + c²
c² = 49 + 32
c² = 81
√c² = √81
c = -9,9.
c ≠ -9 as negative values are not considered for dimensions.
Hence, the length of the third side is 9 units.
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Your question is incomplete. The complete question is:
With reference to the figure below, find the length of the third side. If necessary, write in the simplest radical form.
Given the polynomial P(x) = 2x3+ 9x2 + 7x – 6, if (x+ 3) is one of its factors, then what are the other two factors of P(x)?
The other two factors of given polynomial are (x+2) and (2x-1).
What is polynomial?A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.
Sums of terms with the pattern kxn—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5. Polynomials: An introduction Using the sum of powers in one or more variables multiplied by coefficients, a polynomial is a type of mathematical expression.
Given that x+3 is a factor of polynomial 2x³ + 9x² + 7x - 6. So that
2x³ + 9x² + 7x - 6
⇒ 2x³ + 6x² + + 3x² + 7x - 6
⇒ 2x²(x+3) + 3x² + 7x - 6
⇒ 2x²(x+3) + 3x² + 9x - 2x - 6
⇒ 2x²(x+3) + 3x(x+3) - 2(x+3)
⇒ (x+3)(2x² + 3x - 2)
⇒ (x+3)(2x² + 4x - x - 2)
⇒ (x+3)[2x(x+2) -1(x+2)]
⇒ (x+3)(x+2)(2x-1)
Hence, Factors of given expression are (x+3)(x+2)(2x-1)
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based on derivative how many times can function cross the x-asix
Based on the derivative, a function can cross the x-axis a certain number of times depending on the number of times the derivative changes sign.
A derivative is a mathematical tool that measures the rate of change of a function at a specific point. Specifically, it is the slope of the tangent line to the function at that point. The derivative can be used to determine where a function is increasing, decreasing, or reaching a maximum or minimum value.
When a function crosses the x-axis, it means that the y-value of the function is equal to zero. In order for a function to cross the x-axis, it must change sign from positive to negative or vice versa. This happens when the function passes through a maximum or minimum point.
If the derivative of the function is positive at a point, it means that the function is increasing at that point. If the derivative is negative, the function is decreasing. If the derivative is zero, it means that the function is neither increasing nor decreasing, and it could be at a maximum or minimum point.
Therefore, the number of times a function can cross the x-axis depends on the number of times the derivative changes sign. If the derivative changes sign twice, the function can cross the x-axis twice. However, if the derivative changes sign an odd number of times, the function can only cross the x-axis once.
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A video posted on the internet has gone viral, and the total number of views is increasing by 25% every hour. If the video currently has 155, 000views how many views will it have in 6 hours?
\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &155000\\ r=rate\to 25\%\to \frac{25}{100}\dotfill &0.25\\ t=hours\dotfill &6\\ \end{cases} \\\\\\ A=155000(1 + 0.25)^{6}\implies A=155000(1.25)^6\implies A\approx 591278\)
Given y = 3x + 1 State the quadrants in which this graph is in. (Use the numbers 1-4)
Answer:
1, 2 and 3 (I, II and III)
Step-by-step explanation:
Since the slope is positive (3) in the equation y = 3x + 1, it means that the graph has a positive slope, meaning the line slopes up from left to right.
The y intercept is 1
the x intercept is:
0 = 3x + 1
x = 1/3
Therefore, the graph of y = 3x + 1 lies in quadrants I, II and III. Graph the equation to prove this.
D
select the correct teamwork characteristic from the drop-down menu.
a characteristic that denotes integrity and truthfulness, along with the absence of lying, cheating,
or theft
an act of working together for a common purpose or benefit
a characteristic of being able to complete a required task at a previously designated time
you can demonstrate cooperation by
listening respectfullyv.
retry
Honesty is a quality that indicates morality and sincerity as well as the absence of deception, fraud, or theft.
What is honesty?Honor, integrity, probity, and a sense of uprightness in reference to character or deed are all known to be connoted by the phrase "honesty."
It should be noted that the quality is one that demonstrates or indicates positive, virtuous qualities, such as integrity, truthfulness, and straightforwardness, and that it is comprised of the lack of lying, cheating, or any other sort of thievery.
Hence, Honesty is a quality that indicates morality and sincerity as well as the absence of deception, fraud, or theft.
Being honest and upholding high moral standards are qualities of integrity. Even in the presence of others, a person of integrity acts morally and honorably.
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if the value stated by a null hypothesis is ______ the confidence interval, then the decision would have likely been to retain the null hypothesis.
If the value stated by a null hypothesis is within the confidence interval, then the decision would have likely been to retain the null hypothesis.
In hypothesis testing, the null hypothesis represents the default assumption or the claim that there is no significant difference or relationship between variables. The confidence interval, on the other hand, provides a range of plausible values for the population parameter based on sample data. If the value stated by the null hypothesis falls within the confidence interval, it means that the null hypothesis value is considered plausible or consistent with the observed data.
In this case, there is insufficient evidence to reject the null hypothesis, and the decision would be to retain it. On the other hand, if the null hypothesis value is outside the confidence interval, it suggests that the null hypothesis is unlikely, and the decision would be to reject it in favor of an alternative hypothesis.
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The dimension of the row space of a 3 x 3 matrix A is 2. (a) What is the dimension of the column space of A? (b) What is the rank of A? (c) What is the nullity of A? (d) What is the dimension of the solution space of the homogeneous system Ax = 0?
a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.
(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.
(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.
(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:
nullity = number of columns - rank
nullity = 3 - 2 = 1
Therefore, the nullity of matrix A is 1.
(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.
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help me with this please
Answer:
Here is the sample space:
(1, 1), (1, 2) (1, 3), (2, 1), (2, 2), (2, 3), (3, 1),
(3, 2), (3, 3)
Solve by substitution. Eq #1 y = -2x - 9 Eq #2 y = 3x + 1
y = -2x - 9 ----------- 1
y = 3x + 1 -------------- 2
Step 1
Substitute y from equation 1 to equation 2.
y = -2x - 9
3x + 1 = -2x - 9
Step 2
Collect like terms
3x + 2x = - 9 - 1
5x = -10
Step 3
Divide through by 5
x = -10/5
x = -2
Step 4
Substitute x in equation 2 to find y.
y = 3x + 1
y = 3(-2) + 1
y = -6 + 1
y = -5
So the solution is (-2, -5)
2 1/5 x 3/4
help please? :)
Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of \$65$65dollar sign, 65 along with an hourly rate of \$28$28dollar sign, 28. The plumber only charges for a whole number of hours. Anand would like to spend no more than \$250$250dollar sign, 250, and he wonders how many hours of work he can afford. Let HHH represent the whole number of hours that the plumber works. 1) Which inequality describes this scenario? Choose 1 answer: Choose 1 answer: (Choice A) A 28+65H \leq 25028+65H≤25028, plus, 65, H, is less than or equal to, 250 (Choice B) B 28+65H \geq 25028+65H≥25028, plus, 65, H, is greater than or equal to, 250 (Choice C) C 65+28H \leq 25065+28H≤25065, plus, 28, H, is less than or equal to, 250 (Choice D, Checked) D 65+28H \geq 25065+28H≥25065, plus, 28, H, is greater than or equal to, 250 2) What is the largest whole number of hours that Anand can afford? hours
Answer: (1) C. 65 + 28H < 250
(2) 6
Step-by-step explanation:
Here is the correct question:
Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $65 along with an
hourly rate of $28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $250, and he wonders how many hours of work he can afford.
Let H represent the whole number of hours that the plumber works.
1) Which inequality describes this scenario?
Choose 1 answer:
A. 28 + 65H < 250
B. 28 + 65H > 250
C. 65 + 28H < 250
D. 65 +28H > 250
2) What is the largest whole number of hours that Anand can afford?
Since the initial fee charged by the plumber is $65 and an hourly rate of $28, and Anand would like to spend no more than $250. This means that the addition of the initial fee plus the hourly fee based on number of hours worked will have to be less than $250. This can be mathematically expressed as:
= 65 + 28H < 250
That means option C is the correct answer.
Option B and D are incorrect because the greater sign was used but Anand doesn't want to spend more than $250 but the options denoted that he spent more than $250 which isn't correct.
2)'The largest whole number of hours that Anand can afford goes thus:
65 + 28H < 250
28H < 250 - 65
28H < 185
H < 185/28
H < 6.6
Therefore, the largest whole number of hours that Anand can afford is 6.
Answer: The Answer is 65+28H < 250 and the largest amount of hours is 6
Step-by-step explanation:
The function g(x) is a transformation of the cube root parent function, f(x) = 3¬x. what function is g(x)?
The function g(x) is changed from the function f(x) by deciphering function f(x) by 4 units in the correct direction and afterward by interpreting that graph 3 units in a downward direction.
Given :
Function - - \(f(x)= \sqrt[3]{x}\)
The accompanying advances can be utilized to decide the obscure function g(x):
Stage 1 - As per the given graph, decipher function f(x) 4 units in the positive x-pivot that is in the correct direction.
Stage 2 - Presently, again as per the given graph, decipher function f(x) 3 units in the downward direction that is in the negative y-pivot.
Stage 3 - The resulting graph is the graph of the function g(x). Whose equation is composed as:
g(x) = \(\sqrt[3]{x-4-3}\)
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Sphere A has a diameter of 2 and is dilated by a scale factor of 3 to create sphere B. What is the ratio of the volume of sphere A to sphere B?
A 2:6
B 4:36
C 1:3
D 1:27
Answer:
1:27
Step-by-step explanation:
I will use solve in terms of pi
Know that Original volume * scale factor cubed = new volume.
The scale factor is 3 and 3^3 is 27,
Therefore the ratio is 1:27
Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. The correct option is D.
What are Scaled figures?Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. They have scaled versions of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.
So, if a side of a figure is of length L units, and that of its similar figure is of M units, then:
\(L = k \times M\)
where 'k' will be called a scale factor.
The linear things grow linearly like length, height etc.
The quantities which are squares or multiple linear things twice grow by the square of the scale factor. Thus, we need to multiply or divide by k²
to get each other corresponding quantities from their similar figures' quantities.
So the area of the first figure = k² × the area of the second figure
Similarly, increasing product-derived quantities will need increased power of 'k' to get the corresponding quantity. Thus, for volume, it is k cubed. or
The volume of the first figure = k³ × volume of the second figure.
It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.
Given that the diameter of sphere A is 2 units, it is dilated by a scale factor of 3 to create sphere B. Therefore, the diameter of sphere B is,
Diameter of sphere B = 3 × Diameter of sphere A
= 3 × 2 units
= 6 units
Now, the ratio of diameters of the sphere and the volume of the sphere can be written as,
\((\dfrac{\text{Diameter of sphere A}}{\text{Diameter of sphere B}})^3 = \dfrac{\text{Volume of sphere A}}{\text{Volume of sphere B}} \\\\\\(\dfrac{2}{6})^3 = \dfrac{\text{Volume of sphere A}}{\text{Volume of sphere B}}\\\\\\\dfrac{\text{Volume of sphere A}}{\text{Volume of sphere B}} = \dfrac{1}{27}\)
Hence, the correct option is D.
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Please help me and answer
4 > |x+1| + 2
======================================================
Explanation:
Choice A can be ruled out because the result of any absolute value is never negative.
This means |x+1| cannot be smaller than -3.
In other words: -3 > |x+1| has no solutions
Similarly, choice B also leads to "no solutions" because we subtract 2 from both sides to get -1 > |x+2|. Therefore, we rule out choice B as well.
------------------
Choice C can be solved through these steps
2 < |x+3| - 2
2+2 < |x+3|
4 < |x+3|
|x+3| > 4
x+3 > 4 or x+3 < -4
x > 4-3 or x < -4-3
x > 1 or x < -7
x < -1 or x > 1
The graph of this will have open holes at -7 and 1. Then you shade to the left of -7 and to the right of 1. This does not match the graph given to us.
We'll rule out choice C.
-------------------
Choice D can be solved through these steps
4 > |x+1| + 2
4-2 > |x+1|
2 > |x+1|
|x+1| < 2
-2 < x+1 < 2
-2-1 < x < 2-1
-3 < x < 1
The graph will have open holes at -3 and 1, with shading in between. This matches perfectly with the given graph.
This is why choice D is the answer.
are 12/32 and 24/60 equivalent
Answer:Yes, 12/32 and 24/60 are equivalent.
Step-by-step explanation:
PLEASE HEEEELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
You invest an amount in an account that has a annual interest rate of 5%. If the interest is compounded quarterly for four years, find the equivalent interest rate. How many times will the money be compounded? (To find the quarterly, divide by 4)
8% and 4 times
1.25% and 1 time
8% and 16 times
1.25% and 16 times
Answer:
Below
Step-by-step explanation:
Equivalent interest rate in decimal form will be ( 1+i)^n - 1
where i = periodic interest in decimal = .05/4 n = periods = 4 per year
(1+ .05/4)^4 -1 = 5.09 % equivalent interest per year
.05 / 4 = .0125 or 1.25% 16 times ( 4 times per year x 4 years)
What is a formula for Simple Interest
Answer:
Simple Interest =PRT/100
Step-by-step explanation:
P*R*T/100
at the fidelity credit union, a mean of 4.9 customers arrive hourly at the drive-through window. what is the probability that, in any hour, less than 1 customer will arrive? round your answer to four decimal places.
At the fidelity credit union, the mean number of customers who arrive hourly at the drive-through window is 4.9. It is required to determine the probability of fewer than 1 customer arriving in any hour.
Answer: 0.00796.
The solution to this problem is discussed below:
The given information implies that the mean value of the Poisson distribution, λ = 4.9.
In a Poisson distribution, the probability of x occurrences during a particular interval is given by:
P(x; λ) = e–λ λx / x!
Where e is approximately equal to 2.71828.
Let x = 0 since we need the probability of less than 1 customer in an hour.
P(x < 1) = P(x = 0) + P(x = 1) + P(x = 2) + …P(x < 1) = e-4.9 4.90 / 0!P(x < 1) = e-4.9 1P(x < 1) = 0.00796
The probability of fewer than 1 customer arriving in any hour is 0.00796 (rounded to four decimal places)
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Find an explicit formula for the arithmetic sequence -5, 13, 31,
49,....
Note: the first term should be b(1).
B(n)=(blank)
Answer:
b(n) = -23 + 18n
Step-by-step explanation:
NOTE - This is an arithmetic sequence, so each number is increasing by addition. If you were in a geometric sequence, however, you'd be multiplying. This means that the explicit formula for the geometric sequence you'll be learning later on will be different.
The formula for explicit formula is b(n)=b(1)+d(n-1). The variable d represents the common difference and the a is whatever number of the term you are using.
Since you have b(1), you look at what your first term is. Plug -5 into a(1).
To find your common difference, find 13-(-5). This is 18, and adding it to the others you can see that it continues.
So, plugging in what you have so far it looks like b(n) = -5 + 18(n - 1)
All we need to do now is simplify.
1. Distribute: -5 + 18n - 18
2. Add like terms: -23 + 18n
Hope this helped and made sense lol.