The present p value which have to be invest in future is $7619.05 at simple interest rate r.
Simple Interest:
Simple interest (S.I) is a method of calculating the amount of interest on a specific amount of money.
The simple interest formula helps determine the amount of interest given a principal, interest rate, and term.
The formula for simple interest is:
SI = PTR/100
where SI = simple interest
P = principal
R = interest rate (percentage)
T = term (years)
For calculating total amount
Amount (A) = principal Book (P) + Interest (I)
where
Amount (A) is the total amount repaid at the end of the borrowed period.
The simple interest total amount formula can also be written as:
A = P(1 + RT)
where
A = Total amount after specified period
P = Principal or original loan amount
R = Interest rate (annual)
T = Time (annual )
According to the Question:
Simple interest: I = PTR ---------------------------- (1)
Future amount : A = p + I = p + PTR ------------------ (2)
Given that:
r = 10% = 0.1
t = 6 months = 0.5 year
A = future amount = 8000
Now,
8000 = p + p (. 1)(0.5)
⇒ 8000 = 1.05 p
⇒ p = 8000/1.05
⇒ p = $ 7,619.05
Now,
Putting the value of p in equation (2)
I = 7619.05 (0.1) (0.5 ) = 380.95
7619.05 + 380.90 = $8,000
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The manager of a food company wants to conduct a survey to find out whether consumers like or dislike a new brand of soup that was recently launched. Which of the following data collection methods is mostly likely to get unbiased results? a. Ask distributors who supply the products to local retailers about the popularity of different soup brands. b. Ask the employees in the company which soup is the best. c. Ask customers who visit retailers within a 15 mile radius of the company headquarters. d. Ask customers who visit the grocery store nearest to the manager's house which soup they like the best.
Option c is most likely to get unbiased results.
The best option for collecting unbiased data in this case would be option c: asking customers who visit retailers within a 15 mile radius of the company headquarters. This method would involve sampling a diverse group of customers who are not affiliated with the company in any way, and therefore are likely to provide more objective feedback about the new brand of soup.
Option a, asking distributors who supply the products to local retailers about the popularity of different soup brands, could be biased because the distributors may have their own interests in promoting certain brands over others.
Option b, asking the employees in the company which soup is the best, could also be biased because the employees may have a vested interest in the success of the company and its products, and therefore may not provide completely objective feedback.
Option d, asking customers who visit the grocery store nearest to the manager's house which soup they like the best, could also be biased because it may not be representative of the overall customer base for the soup. It is important to sample a diverse group of customers in order to get a more accurate sense of how the new brand of soup is being received.
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The National Weather Service says that the mean daily high temperature for October in a large Midwestern city is 56 degree F. A local weather service suspects that this value is not accurate and wants to perform a hypothesis test to determine whether the mean. is actually lower than 56 degree F. A simple of mean daily high temperatures for October over past 37 years yields x = 54 degree F. Assume that the population standard deviation is 5.6 degree F. Perform the hypothesis test at the 1% significance level.
The result of the hypothesis test is that we cannot say if the mean is lower than 56.
Hypothesis are ,
H0 : ц = ц 1
H1 : ц ≠ ц 1
It is to be tested whether the mean daily high temperature for October in a large Midwestern city is actually lower than
56 F or not.
Then the test statistic is equal to minus 2.64610 degrees of tritomas degree of to equal to 1 equal to 29 point,
The appropriate conditions to be sufficed before performing the one-sample z-test are:
(i) The measurement of the sample drawn for the observation must be extensive. The desired threshold is 30.
(ii) Each observation should have an equal opportunity of getting selected in the sample.
(iii) The data need to be normal.
On performing the analysis we conclude that it can not be said with 99 % confidence that the true mean temp is less than 56 F.
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Find all values of x for which f(x)=3x^4+4x^3-120x^2+120 has local maxima and minima, as well as the inflection points. Please show all of your work.
The Local maxima and minima will be at X = 0 , 4 , -5 and point of inflation will be at [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex].
What is Maxima and Minima ?The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.
Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.
The peaks and minima of the function that appear in a certain interval are known as local maxima and minima. The value of a function at a place in a certain interval for which the values of the function near that point are always smaller than the value of the function at that point would be considered a local maximum. Local minima, on the other hand, would be the value of the function at a location where the values of the function nearby are higher than the value of the function at that location.
When the concavity of a function's graph (or picture) changes, a point of inflection is identified. We need to determine where the second derivative of the function switches from negative to positive, or vice versa, in order to determine this in algebra. So, we calculate the provided function's second derivative.
The fuction is :
[tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex]
So for local Maxima and minima first derivatives should be zero
Therefore,
[tex]\frac{d}{dx}\\[/tex] ([tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex] ) = 0
⇒ [tex]12x^{3} + 12x^{2} - 240x = 0[/tex]
⇒ [tex]x^{3} + x^{2} - 20x = 0[/tex]
⇒[tex]x(x^{2} + x - 20) = 0 \\[/tex]
⇒x(x-4)(x+5) = 0
For x = 0, 4 , -5 there is a local maxima or minima.
Now for Point of Inflation second derivative is zero
Therefore,
[tex]\frac{d^{2} }{dx^{2} }[/tex] ( [tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex]) = 0
⇒ [tex]\frac{d}{dx}[/tex][tex]12x^{3} + 12x^{2} - 240x = 0[/tex]
⇒ [tex]36x^{2} + 24x - 240 = 0[/tex]
⇒[tex]3x^{2} + 2x - 20 = 0[/tex]
⇒ x = [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex]
So the point of inflations are [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex].
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During one flu epidemic the proportion of adults nationwide who have come down with the flu is 8%. The manufacturer of a flu vaccine claims that those who have been vaccinated are less likely to catch the flu.
The hypotheses are as follows:
Null hypothesis: proportion of those vaccinated catching the flu = 8%
Alternative hypothesis: proportion of those vaccinated catching the flu < 8%
Select one:
A.
Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than 8%
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is less than 8%.
B.
Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is not equal to 8%
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%.
C.
Rejecting the null hypothesis means there is insufficient evidence that the proportion of those vaccinated catching the flu is equal to 8%
Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%.
D.
Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than 8%
Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%.
The test hypothesis is
H₀: p=0.08 (null hypothesis) and
Hₐ: p<0.08 (alternative hypothesis )
Given that,
8% of adults in the country contract the flu at any given time during a flu epidemic. The following are the hypotheses:
0% of people who received the vaccine contracted the flu.
8% or less of people who received the vaccine ended up getting the flu.
In order to reject the null hypothesis, there must be proof that 8% of individuals who received the vaccine did not also get the flu.
If the null hypothesis is not rejected, then there is insufficient data to draw the inference that the proportion of people who receive the flu shot is 8%.
The test hypothesis is H₀: p=0.08 (null hypothesis) and Hₐ: p<0.08 (alternative hypothesis )
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the quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is .
The quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant b^2 - 4ac is either positive or zero .
Given :
the quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is .
Quadratic equation :
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.
Formula :
= -b ± [tex]\sqrt{b^2 - 4ac / 2a}[/tex]
Discriminant = b^2 - 4ac
if b^2 - 4ac = 0 or positive value then only the formula give us the coordinates of the points of intersection of a line .
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PLEASE HELP IM GOING TO FAIL
4. What is the graph of the system? (1 point)
y≤x +4
2x+y≤-4
Answer:
A
Step-by-step explanation:
The answer is option A
Hope this helps :)
Figure 1 and 2 are shown in the coordinate below.
Saorise claims the there is a sequence of transformations that Carries figure 1 onto figure 2. Select all actions that she could take to justify this claim
A. show that a rotation of 180° counterclockwise about the origin carries Figure 1 onto Figure 2
B. show that a reflection over the x-axis followed by a reflection over the y-axis carries Figure 1 onto Figure 2
C. show that a translation of 4 units right followed by a translation of 5 units down carries Figure 1 onto Figure 2
D. show that a rotation of 90° clockwise about the origin followed by a reflection over the x-axis carries Figure 1 onto Figure 2
Answer:
A and B
Step-by-step explanation:
actually the 180° rotation does the same as the reflection over the x-axis and then the reflection over the y-axis.
show that if \lamdba is in the point spectrum, the the conjugate is in the union of the point and residual spectra of the adjoint
We are given that [tex]\overline\lambda[/tex] is in the point spectrum and we are to prove that the conjugate is the union of the point and residual spectra of the adjoint.
If [tex]\overline\lambda[/tex] ∈ σp(T∗), then T∗v = [tex]\overline\lambda[/tex]v for some v ∈ D(T∗).
Hence, for all u ∈ D(T) we have -
⟨Tu,v⟩ = ⟨u,T∗v⟩ = ⟨u,[tex]\overline\lambda[/tex]⟩ = λ⟨u,v⟩,
⟨(T−λ)u,v⟩ = 0, for all u ∈ D(T)
If λ ∈ σp(T∗), then T∗v = [tex]\overline\lambda[/tex]v for some v∈D(T∗).
Hence, for all u∈D(T), we have ⟨Tu,v⟩=⟨u,T∗v⟩=⟨u,[tex]\overline\lambda[/tex]v⟩=λ⟨u,v⟩,
and therefore,
⟨(T−λ)u,v⟩=0, for all u∈D(T)
i.e. the range of T−λ is not dense and we will have λ ∈ σr(T) ∪ σp(T).
Hence, proved.
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Help me with this math please. Help me quick please.
Answer:
f(x) = 5/2x
Step-by-step explanation:
The parent function for the given equation is f(x) = 1/2x. When this function is vertically stretched by a factor of 5, the resulting function will be f(x) = 5/2x. This means that for any value of x, the output of the transformed function will be 5 times greater than the output of the parent function.
For example, if x = 2, then f(x) = 1/2 * 2 = 1 for the parent function, and f(x) = 5/2 * 2 = 5 for the transformed function. Similarly, if x = 3, then f(x) = 1/2 * 3 = 1.5 for the parent function, and f(x) = 5/2 * 3 = 7.5 for the transformed function.
tell me if this helped :)
Translate this phrase into an algebraic expression.
19 increased by twice a number
Use the variable n to represent the unknown number.
The algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.
What is an algebraic expression?
An algebraic expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated. It is a fundamental concept in algebra, which is the branch of mathematics that deals with the study of symbols and the rules for manipulating them.
To translate the phrase "19 increased by twice a number" into an algebraic expression, we can use the following steps:
Identify the operation being performed: In this case, the phrase "increased by" indicates that we need to use the addition operator (+).
Identify the constants and variables: The constant in this expression is 19, and the variable is "a number", which we will represent with the variable n.
Write the expression: Using the information from steps 1 and 2, we can write the expression as follows:
19 + 2n
Hence, the expression represents the result of adding 19 to twice a number is 19 + 2n.
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The algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.
What is an algebraic expression?
An algebraic expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated. It is a fundamental concept in algebra, which is the branch of mathematics that deals with the study of symbols and the rules for manipulating them.
To translate the phrase "19 increased by twice a number" into an algebraic expression, we can use the following steps:
Identify the operation being performed: In this case, the phrase "increased by" indicates that we need to use the addition operator (+).
Identify the constants and variables: The constant in this expression is 19, and the variable is "a number", which we will represent with the variable n.
Write the expression: Using the information from steps 1 and 2, we can write the expression as follows:
19 + 2n
Hence, the algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.
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Calculate the average rate of change between x=-1 and x=1.
Between x=-1 and x=1, the average rate of change is 1.
What is meant by average rate of change?It represents the average change in the function's per-unit value during that time period. Calculating the average rate of change is very helpful for tracking changes in measurable parameters like average speed or average velocity. As the slope of the straight line that links the two spots, the average rate of change between the two points is determined. Use the formula:
(f(b)-f(a))/(b-a) to get the average rate of change of f(x) between x=a and x=b.
Given line in the figure passes through the points A(4, 0), B(-1, -5)
Let the equation of the line be:
y=mx+ c
Slope m=(-5-0)/(-1-4)
m=1
Therefore, y=x+ c
It passes through (4, 0)
y+ c=0
c=-4
y=x-4=f(x)
f(-1)= -1-4=-5
f(1)= 1-4=-3
The average rate of change=(f(b)-f(a))/(b-a)
=(f(1)-f(-1))/1-(-1)
= -3-(-5)/(1+1)
=2/2
=1
Therefore, Between x=-1 and x=1, the average rate of change is 1.
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Amy is going to spend What she saves from her rent budget on entertainment. How much will she’s have for entertainment each month?
Since Amy's rent is 60 percent of the budget for Rent, Utilities, and Food, she will have $853 to spend on entertainment each month.
How is the rent budget determined?The total budget for rent, utilities, and food for nine months is given as $12,798.
Using the mathematical operation of multiplication, the proportion that belongs to rent alone is $7,678.80, representing 60%.
This rental proportion is divided by 9 to determine the monthly budget for rent, which will then be spent on entertainment.
The total budget for rent, utilities, and food for nine months = $12,798
The percentage of the budget for rent = 60%
The amount for rent for nine months = $7,678.80 ($12,798 x 60%)
The monthly rent amount is $853.20 ($7,678.80/9)
Thus, we can conclude that Amy will spend $853 monthly on entertainment if she saves the rent budget.
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Question Completion:The percentage of the rent to the total rent, utilities, and food budget is 60%.
Enter the missing values below.
83
18xy +48x y
25
(3x+8y²)
According to the given algebraic expression the missing value is [tex]$18 x^8 y^3+48 x^2 y^5= 6x^2y^3 \left(3 x^6+8 y^2\right)$$[/tex].
What is the formula for algebraic expressions?An equation that includes constants, variables, and a few algebraic procedures is said to be algebraic. A good example of an algebraic equation is 3x2 2xy + d. So, three different sorts of fundamental building blocks make up an algebraic expression: Correlation (i.e. integers) (i.e. numbers)
Which five algebraic expressions are there?The subsequent five categories provide further categorization of various algebraic expression forms. These include the monomial, polynomial, binomial, trinomial, and multinomial.
Briefing:[tex]$6.3 x^2x^6 y^3+8.6 x^2 y^3y^2[/tex]
[tex]$18 x^8 y^3+48 x^2 y^5= 6x^2y^3 \left(3 x^6+8 y^2\right)$$[/tex]
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The complete question is-
[tex]\\$factor the algebraic expression.\\$$18 x^8 y^3+48 x^2 y^5=x-y-\left(3 x^6+8 y^2\right)\\\\$Enter the missing values below\\\\$18 x^8 y^3+48 x^2 y^5=\square x\square y\square (3 x^6+8 y^2)$$[/tex]
Using traditional methods, it takes 100 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 260 students and observed that they had a mean of 99 hours. Assume the standard deviation is known to be 6. A level of significance of 0.01 will be used to determine if the technique performs differently than the traditional method. Find the value of the test statistic. Round your answer to 2 decimal places.
The value of the Test statistic =z=-1.67
We have the value of sigma = 6, n = 260
In a hypothesis test, a test statistic—a random variable—is computed from sample data. To decide whether to reject the null hypothesis, you can utilize test statistics. Your results are compared to what would be anticipated under the null hypothesis by the test statistic. The p-value is computed using the test statistic.
Now using the formula of Test static
Test statistic will be: [tex]\mathrm{z}=\frac{\overline{\mathrm{x}}-\mu}{\frac{\sigma}{\sqrt{\mathrm{n}}}}\\[/tex]
Where, n = total number of sample = 100
[tex]\bar x[/tex] = mean of the given data
[tex]\mu[/tex] = total number of hours taken to receive a basic driving licence.
So, putting the value given in the question,
We will get the value of test static as:
[tex]=\frac{99-100}{\frac{6}{\sqrt{260}}}=-1.67[/tex]
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please help its holding back my grade 50 points
Answer:
X=54
Step-by-step explanation:
equate both the equations since angles of opposite sides are equal
2x+2=3x-52
3x-2x= 52+2
x=54
answer:
x=54
Step-by-step explanation:
2x+2=3x-52
move the 2x to 3x because x can't be negative
and add 52 to 2 so x=54
What integer is tripled when 9 is added to three-fourths of it?
Answer:
4
Step-by-step explanation:
let n be the integer , then n tripled is 3n, so
[tex]\frac{3}{4}[/tex] n + 9 = 3n ( multiply through by 4 to clear the fraction )
3n + 36 = 12n ( subtract 3n from both sides )
36 = 9n ( divide both sides by 9 )
4 = n
the required integer is 4
if a crew of six workers completes a job in 15 hours how long will it take 10 workers to complete the same job
As no. of crews and time are inversely proportional 10 workers will finish the job in 10 hours.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, A crew of six workers completes a job in 15 hours.
We know more crew will finish the job in less no. of hours so they are inversely proportional.
So, C = k/t.
6 = k/15.
k = 90.
Now, C = 10 hence,
10 = 90/t.
t = 90/10.
t = 10 hours.
So, They can finish in 10 hours.
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write x^2+10x+12 in the form (x+a)^2-b
Answer:
(x+5)^2 - 13
Step-by-step explanation:
If you work out the target expression, you get:
(x+a)^2-b = (x+a)(x+a)-b = x^2 + 2ax + a^2 - b
so 2ax must be 10x, hence a = 5
also a^2 - b must be 12, and with a being 5, this means b = 25-12 = 13
Answer:
[tex](x+5)^2 - 13[/tex]
Step-by-step explanation:
In order to convert the given quadratic [tex]x^2 + 10x + 12[/tex] into the form [tex](x+a)^2 - b[/tex], you need to put the given quadratic into vertex form.
⭐What is vertex form?
a way you can rewrite a quadratic equation[tex](x-h)^2 + k[/tex]-(-h) = x-value of the vertex+k = y-value of the vertex⭐How do you rewrite a quadratic in vertex form?
you partially complete the squareI will demonstrate how to "partially complete the square" with the given quadratic.
Given: [tex]x^2 + 10x + 12 = 0[/tex]
Subtract the constant from the LHS and RHS.
[tex]x^2 + 10x = -12[/tex]
Divide the coefficient of the middle term by 2, square that result, and add it to the LHS and RHS.
[tex](\frac{10}{2})^2\\(5)^2\\= 25[/tex]
[tex]x^2 + 10x + 25 = -12 + 25[/tex]
[tex]x^2 + 10x + 25 = 13[/tex]
Write the LHS into the polynomial identity: [tex](a+b)^2[/tex] by factorising
[tex]x^2 + 5x + 5x + 25 = 13[/tex]
[tex]x(x + 5) + 5(x + 5) = 13[/tex]
[tex](x+5)(x+5) = 13[/tex]
[tex](x+5)^2 = 13[/tex]
Subtract 13 from the LHS and RHS.
[tex](x+5)^2 - 13[/tex]
That's it!
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Subtract.
−135−(−278)
Enter your answer as a simplified fraction by filling in the boxes.
Answer:143
Step-by-step explanation: When subtracting a negative number from a negative number(a minus sign followed by a negative turns the two signs into a positive sign) you are then adding a positive
Sketch the curve with the given vector equation by finding the following points. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) r(t) = (t, 9 – t, 2t) r(-9) (x, y, z) r(0) (x, y, z) r(9) (x, y, z)
For sketching the graph we need to know the coordinate of the vector which are r(1) = ⟨−1, 2⟩, r′(1) = ⟨1, 2⟩
Given:-
x = t − 2,
y = t² + 1 ⇒ t = x + 2
⇒ y = (x + 2)2 + 1
⇒ y = x² + 4x + 5
For find r′(t) we have to ,
r′(t) = ⟨1, 2t⟩
To sketch the position vector r(t) and the tangent vector r′(t) for t = 1.
r(1) = ⟨−1, 2⟩, r′(1) = ⟨1, 2⟩
See the above figure. The red vector is r(1) and the blue one is r′(1)
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8. The number 86.345 correct to one decimal place is
Answer:
86.3
Step-by-step explanation:
86.345
step 1
identify their place values
8 — Tens
6 — Units
.3 — tenth( 1 decimal place)
.34 — Hundredth (2 decimal place)
.345 — Thousandth ( 3 decimal place)
to one decimal place is
= 86.3
remember 4 is a round down number so .345 can't actually affect the 3
i hope this answered helped.
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the value of y varies directly with x.when y=75 x=1/2 what is the value of y when x equals 2 1/4
The value of y from the equation y = 150x when x = 2(1/4) is 337.5.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 9 is an equation.
We have,
y varies directly with x.
y ∝ x
y = kx
Now,
y = 75 when x = 1/2
75 = k(1/2)
k = 75 x 2
k = 150
Now,
y = kx
y = 150x
When x = 2(1/4) = 9/4
y = 150 x 9/4
y = 337.5
Thus,
The value of y is 337.5.
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Solve for X : x + (7 x5) = 25
Use spherical coordinates to Find the average distance from a point in a ball of radius a to its center.
The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A
Given the radius in the question = a
The integration of the total distance before dividing the volume will be =
⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a\cdot a^2\sin\theta\,da\,d\theta\,d\phi[/tex]
⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a^3\sin\theta\,da\,d\theta\,d\phi[/tex]
⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}\int_0^\pi \sin\theta\,d\theta\,d\phi[/tex]
⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}1\,d\phi[/tex]
⇒ [tex]\pi A^{4}[/tex]
Let us divide the average distance by the ball's volume,
⇒ [tex]\frac{\pi a^4}{(4/3)\pi a^3}[/tex]
⇒ [tex]{\frac{3a}4}[/tex]
By the use of the Parcly Taxel's way,
Let the radius of the ball be = A
f(x) = probability density function
Distance = D from the given point to the center.
P( D < a )
[tex]\begin{align}P(D\leq r)&= \frac{ \frac 43 \pi r^3 }{\frac 43 \pi R^3}=\frac {r^3}{R^3}, \ \ \ 0\leq r\leq R. \end{align}[/tex][tex]\frac{\frac{4}{3} \pi a^{3} }{\frac{4}{3} \pi A^{3} } = \frac{a^{3} }{R^{3} }[/tex]. 0 [tex]\leq[/tex] a [tex]\leq[/tex] A
Therefore, The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A
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Need help fast thank you
TRUE/ FALSE. A researcher compares the BMI of two populations of individuals from different socioeconomic backgrounds and finds that the proportion of individuals considered obese and from a poor background is .37 (n = 112), and the proportion of individuals considered obese and from an affluent background is .27 (n = 87); a 95% confidence interval for the risk difference for obesity among members of the poor population compared to the affluent population is (-0.03, 0.23).
True , a 95% confidence interval for the risk difference for obesity among members of the poor population compared to the affluent population is (-0.03, 0.23).
The critical value for alpha is 0.05 and z is 1.96 .
The corresponding confidence interval is ( 6.235 , 7.165).
Therefore the above statement is true.
Confidence Interval, to put it simply, is a range within which we are confident that the genuine value exists. The probability that a confidence interval will contain the real parameter value depends on the confidence level that is chosen for the interval.
The phrase "Confidence Interval" refers to the range of values that is typically used to handle population-based data, extracting precise, important information with a given level of confidence.
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Given f(x)=3x+4 find f(4)
Answer:
Step-by-step explanation:
To find f(4), you can substitute 4 for x in the equation f(x) = 3x + 4. This gives you:
f(4) = 3(4) + 4
= 12 + 4
= 16
Therefore, f(4) = 16.
19 points all i have really..Gavin is hoping to buy his first car in 3 years. He is considering two options to help him save and grow his money. If he currently has $800, should he deposit his money into a savings account that is compounded annually at an interest rate of 9% or in a savings account that is compounded quarterly at an interest rate of 3%?
Gavin should deposit his money into a savings account that is compounded annually at an interest rate of 9%.
What is compound interest?
The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.
Given that the current balance is $800.
There were two types of schemes.
First scheme offer compounded annually at an interest rate of 9%
Second scheme offer compounded quarterly at an interest rate of 9%.
The formula of compound interest annually is
A = P(1+r)^t
P = principal = 800
r = rate of interest = 9% = 0.09
t = time = 3 year
A = 800(1+0.09)³
A = 1036.02.
The formula of compound interest annually is
A = P(1+(r/n))^tn
P = principal = 800
r = rate of interest = 3% = 0.03
t = time = 3 year
n = 4
nt = 4×3 =12
A = 800(1+0.03/4)¹²
A = 875.04
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I need help with my math homework
The multiplications, applying the associative property, are given as follows:
1. (5 x 2) x 3 = 10 x 3 = 30.
2. 4 x (3 x 3) = 4 x 9 = 36.
3. (6 x 1) x 4 = 6 x 4 = 24.
4. 5 x (2 x 4) = 5 x 8 = 40.
5. (2 x 2) x 8 = 4 x 8 = 32.
6. 3 x (2 x 2) = 3 x 4 = 12.
7. (4 x 2) x 4 = 8 x 4 = 32.
8. 6 x (3 x 3) = 6 x 9 = 54.
What is the associative property of multiplication?The associative property of multiplication defines that the order in which the factors are multuiplied does not change the product.
In this problem, we have to consider that the parenthesis gives the precedence of the factors, meaning that the terms inside the parenthesis are multiplied first, and their result should be placed on the blanks below the parenthesis.
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Modeling multiplication and division fraction pls help
The area of each section is 3/4 square feet. To solve the give question use division operation.
What is mixed fraction?
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.
Given that the area of the garden is [tex]5\frac{1}{4}[/tex] square feet.
Now convert the mixed fraction with improper fraction:
[tex]5\frac{1}{4}[/tex] = [(5×4) + 1]/4
[tex]5\frac{1}{4}[/tex] = 21/4
We have to divide the area 7 equal area.
Thus divide 21/4 by 7.
21/4 ÷ 7
To convert the division sign into multiplication sign, take the reciprocal of 7:
21/4 × 1/7
= (21 × 1)/(4 × 7)
Divide the denominator and numerator by 7:
= 3/4
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