In multiple regression analysis, there can be several independent variables, but only one dependent variable
The link between several independent or predictor variables and one dependent or criterion variable is typically explained using multiple regression. The constant term, along with a number of independent variables and their corresponding coefficients, are used to model a dependent variable. Thus, it refers to a regression model that uses two or more predictor variables.
It is a statistical method that can be used to examine the relationship among a single dependent variable and a number of independent variables. The variables are quantified because an equation is used to represent the model. Although the independent variables are almost always positive, their coefficients occasionally aren't.
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A new phone cost £679
The value of the phone decreases at a rate of 4% per year.
Work out the value of the phone at the end of 3 years.
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &\pounds 679\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &3\\ \end{cases} \\\\\\ A=679(1 - 0.04)^{3} \implies A=679(0.96)^3\implies A \approx 600.74[/tex]
The value of the phone after 3 years is equal to £600.73
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here, the present value of the phone is £679 and we are required to find the future value of the phone after 3 years when it depreciates every year by 4%
thus, FV= £679 × (1-4%)³
= £679 × 0.96³
= £600.73
Hence The value of the phone after 3 years is equal to £600.73
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a set v is given, together with definitions of addition and scalar multiplication. determine which properties of a vector space are satisfied. (select all that apply.) v is the set of polynomials with real coefficients and degree 2 or less. addition is defined by (a2x2 a1x a0) (b2x2 b1x b0)
The properties of a vector space are satisfied Properties 1,2, 5(a) and 5(c) are satisfied, the relaxation of the homes aren't legitimate are if[tex]v = x ^ 2 1× v=1^ ×x ^ 2 = 1 #V[/tex]
Property three does now no longer follow: Suppose that Property three is legitimate, shall we name[tex]v = a * x ^ 2 +bx +c[/tex]the neuter of V. Since v is the neuter, then O have to be constant with the aid of using the neuted, consequently [tex]0 = O + v = (O x ^ 2 + Ox + O) + (a × x ^ 2 + bx + c) = c × x ^ 2 + b ^ 2 + a[/tex]
= 0 If O is the neuter, then it ought to restore x², but [tex]0+ x² = (0x²+0x+zero) + (x²+0x+zero) = 1.[/tex]This is a contradiction due to the fact x² isn't 1. We finish that V doesnt have a neuter vector. This additionally method that belongings four would not observe either. A set with out 0 cant
have additive inverse
[tex]Let r= v ×2x ^ 2 + v × 1x +v0 , w= w ×2x ^ 2 + w × 1x +w0 . We have that\\v+w= (vO + wO) ^ x^ 2 +(vl^ × wl)^ x+ ( v 2^ × w2)• w+v= (wO + vO) ^x^ 2 +(wl^ × vl)x+ ( w 2^ ×v2)[/tex]
Since the sum of actual numbers is commutative, we finish that v + w = w + v Therefore, belongings 5(a) is valid.
Property 5(b) isn't valid: we are able to introduce
a counter example. we could use z = 1 then[tex]v = x ^ 2 w = x ^ 2 + 1\\(v + w) + z = (x ^ 2 + 2) + 1 = 3x ^ 2 + 1[/tex]
v + (w + z) = x ^ 2 + (2x ^ 2 + 1) = x ^ 2 + 3
Since 3x ^ 2 +1 ne x^ 2 +3. then the associativity rule doesnt hold.
[tex](1+2)^ * (x^ 2 +x)=3^ * (x ^ 2 + x) = 3x + 3\\1^ × (x^ 2 +x)+2^ × (x ^ 2 + x) = (x + 1) + (2x + 2) = 3x ^ 2 + x ( ne 3x + 3 )\\(1^ ×2)^ ×(x^ 2 +x)=2^ × (x ^ 2 + x) = 2x + 2\\1^ × (2^ × (x ^ 2 + x) )=1^ × (2x+2)=2x^ 2 +2x( ne2x+2)[/tex]
Property f doesnt observe because of the switch of variables. for instance, if v = x ^ 2 1 × v=1^ × x ^ 2 = 1 #V
Properties 1,2, 5(a) and 5(c) are satisfied, the relaxation of the homes arent legitimate.
Step-with the aid of using-step explanation:
Note that each sum and scalar multiplication entails in replacing the order from that most important coefficient with the impartial time period earlier than doing the same old sum/scalar multiplication.
Property three does now no longer follow: Suppose that Property three is legitimate, shall we name v = a × x ^ 2 +bx +c the neuter of V. Since v is the neuter, then O have to be constant with the aid of using the neuted, consequently[tex]0 = O + v = (O × x ^ 2 + Ox + O) + (a × x ^ 2 + bx + c) = c × x ^ 2 + b ^ 2 + a[/tex]
= zero If O is the neuter, then it ought to restore x², but zero [tex]+ x² = (0x²+0x+zero) + (x²+0x+zero) = 1.[/tex]This is a contradiction due to the fact x² isn't 1. We finish that V doesnt have a neuter vector. This additionally method that belongings four would not observe either. A set with out 0 cant have additive inverse
Let [tex]r= v × 2x ^ 2 + v × 1x +v0 , w= w2x ^ 2 + w × 1x +w0 . \\We have thatv+w= (vO + wO) ^ x^ 2 +(vl^ wl)^x+ ( v 2^ w2)w+v= (wO + vO) ^ x^ 2 +(wl^ vl)x+ ( w 2^v2)[/tex]
Since the sum of actual numbers is commutative, we finish that v + w = w + v Therefore, belongings 5(a) is valid.
Property 5(b) isn't valid: we are able to introduce
a counter example. we could use[tex]z = 1 then v = x ^ 2 w = x ^ 2 + 1(v + w) + z = (x ^ 2 + 2) + 1 = 3x ^ 2 + 1v + (w + z) = x ^ 2 + (2x ^ 2 + 1) = x ^ 2 + 3\\Since 3x ^ 2 +1 ne x^ 2 +3.[/tex]then the associativity rule doesnt hold.
Note that each expressions are same because of the distributive rule of actual numbers. Also, you could be aware that his assets holds due to the fact in each instances we 'switch variables twice.
[tex]· (1+2)^ * (x^ 2 +x)=3^ * (x ^ 2 + x) = 3x + 31^ * (x^ 2 +x)+2^ * (x ^ 2 + x) = (x + 1) + (2x + 2) = 3x ^ 2 + x ( ne 3x + 3 )(1^ * 2)^ * (x^ 2 +x)=2^ * (x ^ 2 + x) = 2x + 21^ * (2^ * (x ^ 2 + x) )=1^ ×* (2x+2)=2x^ 2 +2x( ne2x+2)[/tex]
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determine whether rolle's theorem can be applied to f on the closed interval [a, b]. (select all that apply.) f(x)
Rolle's Theorem can be applied on [tex]-x^2 + 9x[/tex] on [0, 9]
What is Rolle's Theorem?
Rolle's Theorem states that
1) If f is continuous on [a, b]
2) f is differentiable on (a, b)
3) f(a) = f(b)
Then there exist a point c in (a, b) such that [tex]f^{'}(c) = 0[/tex]
Here, f(x) = [tex]-x^2 + 9x[/tex]
f is continuous on [0, 9] as it is a polynomial function.
f is differentiable on (0, 9)
f(0) = [tex]-0^2+9\times 0 = 0[/tex]
f(9) = [tex]-9^2+9 \times 9 = 0[/tex]
f(0) = f(9)
So Rolle's Theorem has been applied here
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Niamh carrie out an experiment dropping piece of toat to ee if they land jam up or jam down. Here are her reult. Complete the miing relative frequency value in the table. (1 mark)
Using Relative frequency formula ,
We can easily compute the relative frequency missing terms in given table.
the missing terms in relative frequency are 0.14,0.2,0.26
Relative frequency:
Relative frequency can be defined as the number of occurrences of an event divided by the total number of events occurring in a given scenario.
To calculate the relative frequency,
Relative frequency = f / n
Creating a relative frequency table is a two-step process:
Create a table with category names and counts.Add a second column called "relative frequency". I shortened it to rel. freq. here for space.Determine your first relative frequency by dividing the count by the total count.Complete the rest of the table by determining the remaining relative frequencies.we have given a table of values of experiment results carried by Nimah .
we have to find out the relative frequency for given data .
total frequency= 10+11+15+17+20 = 75
dropping
toat piece frequency relative frequency
3 10 10/75 = 0.13
4 13 11/75= 0.14
5 15 15/75= 0.2
6 17 17/75 = 0.22
7 20 20/75 = 0.26
Hence, we computed the relative frequency table for given data.
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Complete question:
Niamh carrie out an experiment dropping piece of toat to ee if they land jam up or jam down. Here are her reult. Complete the miing relative frequency value in the table. (1 mark)
total frequency terms are 75 .
given data :
dropping
toat piece frequency relative frequency
3 10 0.13
4 13
5 15
6 17 0.22
7 20
What are the three steps for finding the mean absolute deviation?.
The three steps for finding the mean absolute deviation are - i)Find the mean of the given observations, ii)Find difference between each observation and calculated mean, iii)Evaluate the mean of the differences obtained in the second step.
Absolute deviation is somewhat same with mean deviation in some extent. The measurement of spread represents the amount of dispersion in a data-set, that is how spread-out are the values of data-set around the central value(example- mean/mode/median).It tells how far away the data points to fall from the central value.
The lower is the value of the measure of spread reflects that the data points are close to the central value. In this case, the values in a data-set are considered as more consistent.Further, the distance of the data points from the central-value, although spread of data points are greater in amount, the values are still not much consistent.To know more about absolute deviation, visit here:
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Dole Pineapple, Inc., is concerned with the 16-ounce can of sliced pineapple is being overfilled. Assume the standard deviation of the process is .03 ounces. The quality control department took a random sample of 50 cans and found that the arithmetic mean weight was 16.05 ounces. At the 5% level of significance, can we conclude that the mean is greater than the 16 ounces? Determine the p-value.
The required value Z = 11.792 >1.96 at a 0.05 level of significance.,he null hypothesis is rejected,the alternative hypothesis is accepted at a 0.05 level of significance.
As the mean weight is less than 16 ounces.
How to solve the P-value ?Given that the mean of the Population = 16
Given that the standard deviation of the process
σ = 0.03 ounce
Given that the mean of the sample = 16.05 ounces
Null hypothesis: H₀:μ > 16 ounces
Alternative HypothesisH₁: μ <16 ounces
According to given data:Z = x-mean/SD/√n
Z = 16.05-16/0.03/√50
Z = 11.792
Level of significance = 0.05
Z₀.₀₅ = 1.96
The required Z = 11.792 >1.96 at 0.05 significant level,null hypothesis is rejected and alternate hypothesis is accepted.
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Can you pls do this fast
3x² - 7x + 9 is x² - 11x + 17 less than 2x² + 4x - 8.
The value of the expression, x² - 11x + 17, when x = 2 is: -1.
How to Find the Value of an Expression?To find the value of an expression, simply replace the given value of the variable and solve to simplify.
To find how much less the expression, 3x² - 7x + 9 is less than 2x² + 4x - 8, subtract 2x² + 4x - 8 from 3x² - 7x + 9:
(3x² - 7x + 9) - (2x² + 4x - 8)
3x² - 7x + 9 - 2x² - 4x + 8
Combine like terms
x² - 11x + 17
Substitute x = 2 into the expression:
2² - 11(2) + 17
= -1.
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What are some examples of parallel lines in real life?.
Parallel lines Examples from Real Life
The railway tracks run parallel to each other.The edges of a ruler are parallel to each other.Cricket bats have parallel stumps.On ruled paper, the lines are parallel.White lines run parallel at the zebra crossing.Parallel lines are straight lines that never meet each other no matter how long we extend them. Observe the following figure that shows parallel lines.
Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are complementary, others are congruent (equal).
Hence we get the required answer.
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a game involves a two-sided coin, as well a six-sided die. to play the game, each player flips the coin once and rolls the die once. what is the number of individual outcomes from flipping and rolling one time?
Answer:
12
Step-by-step explanation:
Number of outcomes for a coin = 2
Number of outcomes of a die = 6
2*6 = 12
What doubles fact can help you find 7 8?.
The doubles fact for 7 8 is 7+7+1=15.
In simple words, Double Plus One Fact is a strategy for adding two consecutive numbers . To get final result then simply add a smaller number to itself or double it then and add 1.
The numbers that are added together are known as doubles. For example, 5+5=10, 3+3=6, so the doubles plus one fact are simply adding 1 to the resultant of the double fact.
For given, the doubles fact is 7+7=14, then add 1 to get 15.
As a result, 7+7+1=15 is the doubles fact for 7 8.
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What is the answer? Please help!!!!
Answer:
a) 14
b) 13
Step-by-step explanation:
P= Purse W= Watch
1P + 1W = 27 (So think about different combinations that make 27)
2P + 1W = 41 (Multiply this by negative 1)
So now you have
1P + 1W = 27
-2P - 1W = -41
You can subtract them
-1P = -14 or 1P = 14
So 1 purse = 14
Now plug it in
14 + 1W = 27 (Subtract 14 from both sides)
1W = 13
So 1 watch = 13
Furthermore, 1 watch = 13 and 1 purse = 14
if the area of the vegetable garden is 170 square feet, which equation could be use to find the length of the tomato patch? select the correct answer.
work out the value of m in the equation below.
give your answer as a decimal.
3(2m+5)=4(9-m)
(pls help with this!!!)
Answer:
Step-by-step explanation:
6m+15=36-m
Plus m to both sides
7m+15=36
Minus 15 from both sides
7m=14
Divide by 2
m=2
What is SSS AAS SAS ASA?.
Answer:
SSS: Side-Side-Side
AAS: Angle-Angle-Side
SAS: Side-Angle-Side
ASA: Angle-Side-Angle
Step-by-step explanation:
These are all used for triangles and proofs :)
what is the inductive hypothesis in the proof by strong induction that every integer greater than 1 can be written as the product of primes?
Using the Induction hypothesis,
strong induction that every integer greater than 1 can be written as the product of primes
Induction Hypothesis:
This is the assumption that given a general element a[n], if something is true about the elements of an ordered set, we can show that it is also true for a[n+1]. is. This means it must be true for all elements. A classic example is the proof that the sum of the natural numbers is triangular.
Induction Has Strong and Weak Versions
This is a case where strong induction is needed because factoring n gives no information about the factorization of n+1.
For brevity, we say that even prime numbers are products of prime numbers. So the statement is: "Every number n≥2 is a product of primes". So the steps are:
base case, where we prove n=2.
If n>2 and every number m with 2≤m prove that n is also a product of primes. The
base case is because 2 is prime.
Let n>2. If n is prime, we are done. Otherwise, n=ab and 1 products of prime numbers.
Strong Induction: Base Case: n=2 and n has a factor of 1.2 n is prime:
Assume k is prime or can be expressed as the product of sets of prime factors for all k≤n To do.
We need to show that n+1 is prime or that n+1 can be expressed as the product of a set of prime factors.
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which of the following would be the scatterplot for the given data? x 1 4 7 12 14 18 y 24 29 30 40 31 44
Answer:
Below is a picture
Step-by-step explanation:
Demos is a free calculator that can do things like this for you.
f + 8 = b5q could you guys help me i don't understand at all
Answer:
Step-by-step explanation:
are there values for f or b or q? What are we trying to solve?
help, I've been stuck on this for forever... rise/run
The slope of the line in the simplest form is 1 / 2.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
The slope is rise over run.
The slope of the line can be found as follows:
m = slope = y₂ - y₁ / x₂ - x₁
Therefore, using (7, 0) and (3, -2)
Hence,
x₁ = 7
x₂ = 3
y₁ = 0
y₂ = -2
Therefore,
slope = - 2 - 0 / 3 - 7
slope = - 2 / -4
slope = 1 / 2
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The total cheese production in 2006 was about 7.7 billion pounds and the total cheese production in 2014 was about 9.7 billion pounds
The total cheese production in 2006The equation of the function is given as
y = 7(1.03)ˣ
From the question, we understand that:
x represents the number of years after 2003
So, we calculate x when the year is 2006 using
x = 2006 - 2003 = 3
Substitute x = 3 in the equation y = 7(1.03)ˣ
y = 7(1.03)³
Evaluate the equation
y = 7.7 (approximately)
The total cheese production in 2014We calculate x when the year is 2014 using
x = 2014 - 2003 = 11
Substitute x = 11 in the equation y = 7(1.03)ˣ
y = 7(1.03)¹¹
Evaluate
y = 9.7 (approximately)
Hence, the amount of cheese is 9.7 billion pounds
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a triangle has altitudes of length 21, 28, and 60 and perimeter 420. find the length of the shortest side of the triangle. (a) 70 (b) 75 (c) 84 (d) 90 (e) 105
A triangle field has sides that are 6:7:8 and a perimeter of 420 meters.
What is the Perimeter of a Triangle?The total of a triangle's three sides is the perimeter. The Greek words "peri" (which means around) and "metron," which means measure, are combined to get the English word perimeter. The perimeter of any 2D shape is the total distance encircling it. Since a shape's perimeter indicates how long its boundary is, it is stated in linear units.Triangle's perimeter in Real Life: Consider that we need to fence the below-shown triangle park. We now add the lengths of the park's three sides to determine the fence's size. The perimeter of a triangle refers to the length or distance of the triangle's edge.Hence, A triangle field has sides that are 6:7:8 and a perimeter of 420 meters.
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Is quadratic function non-linear?.
Quadratic functions are one type of non linear function.
Given,
We have to find whether quadratic function non-linear;
The graph is not a straight line if it is non-linear. A non-linear function has a curved line as its graph. A line that continuously changes in direction is said to be curved.
These are the so-called nonlinear functions, and they can take many various shapes. A quadratic function is one of these nonlinear functions, and its typical form is y = ax2 + bx + c. A parabola represents the graph of a quadratic function.
Therefore,
Quadratic functions are one type of non linear function.
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Tell whether the lines through the given points are parallel, perpendicular, or neither. Line 1: $\left(10,\ 5\right),\ \left(-8,\ 9\right)$ line 2: $\left(2,-4\right),\ \left(11,-6\right)$.
The slope of line 2 is -2/9, The lines have the same slope & the two lines are parallel.
To find out whether the lines through the given points are parallel, perpendicular, or neither:
The slope of a line is calculated as:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
The slope of line 1 is:
[tex]m_1 = \frac{9-5}{-8-10} \\\\m_1 = \frac{4}{-18} \\\\m_1 = -\frac{2}{9}[/tex]
Hence, the slope of line 1 is -2/9.
The slope of line 2 is:
[tex]m_1 = \frac{-6--4}{11-2} \\\\m_1 = \frac{-2}{9} \\\\m_1 = -\frac{2}{9}[/tex]
Hence, the slope of line 2 is -2/9.
Hence the answer is, the slope of line 2 is -2/9, The lines have the same slope & the two lines are parallel.
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dave and martin have sweets in the ratio of 2:3 martin gives dave 15 sweets how many sweets does dave have now
The number of sweets that Dave have equals to 18 sweets.
What is the meaning of ratio?In mathematics, a ratio is a metric that shows how many times one number contains another. For instance, if we have 8 oranges and 6 lemons in a bowl of fruit, then, the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.
Given data
Dave and martin ratio = 2:3
Dave is given 15 sweets.
The number of sweets that dave have now is computed as follows:
2/5 = 0.4= 40%
3/5 = 0.6 = 60%
Dave sweets will equals to:
= 15 sweets + (15 sweets * 1/5)
= 15 sweets + 3 sweets
= 18 sweets.
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T/F strategic fit between two or more businesses exists whenever one or more activities comprising the value chains of different businesses are sufficiently similar to present opportunities:
When one or more of the activities that make up each business's value chain offer chances for cross-business cooperation to develop important new resource strengths and competitive capabilities, there is a strategic fit between the firms.
Given,
Strategic fit between two or more businesses exists when one or more activities comprising their respective value chains present opportunities:
We have to find the correct definition from the options given;
Strategic Fit;-
The degree to which a business is aligning its resources and talents with the opportunities in the external environment is expressed by its strategic fit. The organization must therefore have the actual resources and competencies to implement and support the plan because the matching is done through strategy.
Here,
The correct answer is Option D;- For cross-business collaboration to build valuable new resource strengths and competitive capabilities
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Question is incomplete. Completed question is given below;
Strategic fit between two or more businesses exists when one or more activities comprising their respective value chains present opportunities:
A. to prevent the transfer of expertise or technology or capabilities from one business to another.
B. to independently preserve common brand names from cross-business usage.
C. to increase costs by combining the performance of the related value chain activities of different businesses.
D. for cross-business collaboration to build valuable new resource strengths and competitive capabilities.
E. to maintain business value chain activities separate and apart from one business to another to protect company independence.
What are the 5 steps to solve a linear equation?.
Answer:
1. Distribute
2. Combine like terms
3. Get all variable on one side and everything else on the other (Inverse operations: Add / subtract)
4. Solve for one of your variables (inverse operation: Multiple / Division
5. Simplify
each of two teams has seven players numbered 1 to 7. in the first game, the two players numbered 1 play each other. the loser of each game is eliminated and replaced by the next player of the same team, until all players from one team have been eliminated. let be the number of possible sequences of games. find the remainder when is divided by 1000.
Remainder formula helps us to find the remainder when total number of possible sequence of games (i.e 3452) is divided by 1000.
The Remainder is 432.
We have given that
Number of players in team A = 7
Number of players in team B = 7
This problem is the same as the number of combinations problem. Let's assume team A is the winner (and we must remember to multiply our final result by 2 to account for the possibility that B is the winner).
A can win exactly 6 of the first k+6 games, and then Game k+7 (ending the series in exactly k+7 games), in (k+66) = (k+6k) ways, so we want
2∑k=06(k+6k).
This is 2⋅(1+7+28+84+210+462+924)= 3432.
Conversely, given a permissible series, allow the losing team to win all of the remaining (unplayed because superfluous) games, and you end up with a 7-7 tie.
Now, we calculate the remainder when 3432 is divided by 1000.
Using Remainder Formula ;
Dividend = Divisor × Quotient + Remainder
3432 = 1000× 2 + 432
so, remainder is 432 .
Hence , toatal number of possible sequence of games is 3432.
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What is central angle theorem?.
The central angle theorem states the ratio of arc length and its radius.
What is a Central Angle?
The central angle is the angle that a circle's arc occupies in its centre. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the centre of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's centre subtends is known as the central angle.
According to the central angle theorem, we state that:
Theorem: An arc's angle at the circle's centre is twice as large as its angle at any other point along the circle's circumference.
OR
According to the central angle theorem, the angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the centre of the circle.
Hence,
The central angle theorem states the ratio of arc length and its radius.
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DeShawn needs grass seed to cover Field A. One bag of grass seed covers `5\ 000` square feet.
Field A is a circular field with a `100`-foot radius.
What is the fewest number of bags DeShawn must buy to cover Field A?
The fewest number of bags DeShawn must buy to cover Field A is 6.5 bags.
Define area of circle.A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r², (Pi r-squared), where r is the circle's radius. The square unit, such as m2, cm2, etc., is the unit of area. Area of a circle is equal to r² or d²/4, where = 22/7 or 3.14. A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.
Given,
DeShawn needs grass seed to cover Field A. One bag of grass seed covers `5000` square feet.
Field A is a circular field with a `100`-foot radius.
Area of circular field:
Area = πr²
Where r = 100
Area = 3.14 × 100²
Area = 31400 square feet
Each bag seeds cover 5000 square feet,
So, dividing area by 5000
5000÷ 31400
6.28
The fewest number of bags DeShawn must buy to cover Field A is 6.5 bags.
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Complete the steps of a one-mean hypothesis test with Population SD unknown ritical Value Approach Complete the steps of a one-mean hypothesis test with Population SD unknown - Critical Value approach Question An investment blog states the average small business loan is 20 thousand dollars. A business loan broker would like to test the claim that the average small business loan is different than the amount stated in the investment blog. To test this claim at the 5% significance level, the business loan broker collects the following data on a sample of 25 small business loans and records the amount of the loan. The following is the data from this study: Sample size=25 small business loans Sample mean= 18.5 thousand dollars Sample standard deviation = 5 thousand dollars Identify the null and alternative hypothesis for this study by filling in the blanks with the correct symbol (=..<, or > to represent the correct hypothesis.) Provide your answer below: null hypothesis: 20 alternative hypothesis: 20
There is the not sufficient evidence that the average small business loan is different that the amount stated in the investment blog.
What is standard deviation?
The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.
Here we have given that,
Claim: To check whether the average small business loan is different that the amount stated in the investment blog.
The hypothesis is,
H0: μ= 20 thousand dollars Versus H0: μ ≠ 20 thousand dollars
We have given that,
n= Number of observation = 25
x bar = sample mean =18.5
S= sample standard deviation =5
Here, population standard deviation is unknown, we use the one sample t test.
t - statistics = (x bar - μ) / (s / √n)
= (18.5 - 20) / (5 / √25)
= -1.342
we get,
the Test statistic is -1.342
Now we find the P-value
α = level of significance = 0.05
Degrees of freedom = n - 1 = 25 - 1 = 24
This is two tailed test as our interest is to show the population mean is equal or not equal to zero.
Now, we can find the P-value
P-value = 0.1922 Using EXCEL = TDIST( | t-statistics | = 1.342 , D.F=24, tail=2)
Hence, There is the not sufficient evidence that the average small business loan is different that the amount stated in the investment blog.
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a conical cup is 64/125 full of liquid.. what is the ratio of the depth of the liquid to the depth of the cup?
The ratio of the depth of the liquid to the depth of the cup is 4/5.
Geometry and Ratio
The formula for the volume of a cone is:
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
where r is the radius of the base of the cone and h is the height of the cone.
When the conical cup is filled with water, there will be a difference in the radius of the water and the cup and a difference in the height of the water and the height of the cup (can be seen in the picture).
From the difference in radius and height of the water with the conical cup, a ratio can be made of similarity rule of triangle (see picture).
If the radius of water is [tex]r_{1}[/tex] and the height of water is [tex]h_{1}[/tex], radius of cup is [tex]r_{2}[/tex] and the height of cup is [tex]h_{2}[/tex], so:
[tex]\frac{r_{1} }{r_{2} } =\frac{h_{1} }{h_{2} }[/tex]
[tex]r_{1}[/tex] with [tex]r_{2}[/tex] and [tex]h_{1}[/tex] with [tex]h_{2}[/tex] have the same certain ratio. Let's assume the ratio is x, then it can be written:
[tex]r_{2}=x.r_{1} \\h_{2}=x.h_{1}[/tex]
The ratio of the volume of water to the volume of the conical cup is 64/125, meaning that 64 of the water in the conical cup with a volume of 125.
From here we can substitute it in the volume ratio:
[tex]\frac{V_{1} }{V_{2}}=\frac{\frac{1}{3}\pi r_{1}^{2}h_{1} }{\frac{1}{3} \pi r_{2}^{2}h_{2}} =\frac{64}{125} \\\frac{V_{1} }{V_{2}}=\frac{\frac{1}{3}\pi r_{1}^{2}h_{1} }{\frac{1}{3} \pi (xr_{1})^{2}(x.h_{1})} =\frac{64}{125} \\\frac{V_{1} }{V_{2}}=\frac{\frac{1}{3}\pi r_{1}^{2}h_{1} }{\frac{1}{3}\pi r_{1}^{2}h_{1}x^{3} } =\frac{64}{125} \\\frac{V_{1} }{V_{2}}=\frac{1}{x^{3}}=\frac{64}{125}\\ \frac{1}{x^{3}}=\frac{64}{125}\\\\x^{3}=\frac{125}{64} \\x=\frac{5}{4}[/tex]
The ratio between the radius and height of the cup and the water is 5/4. This means that the ratio between the radius and height of the water and the cup is 4/5.
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