Answer:
Step-by-step explanation:
The identities you need here are:
[tex]r=\sqrt{x^2+y^2}[/tex] and [tex]r^2=x^2+y^2[/tex]
You also need to know that
x = rcosθ and
y = rsinθ
to get this done.
We have
r = 6 sin θ
Let's first multiply both sides by r (you'll always begin these this way; you'll see why in a second):
r² = 6r sin θ
Now let's replace r² with what it's equal to:
x² + y² = 6r sin θ
Now let's replace r sin θ with what it's equal to:
x² + y² = 6y
That looks like the beginnings of a circle. Let's get everything on one side because I have a feeling we will be completing the square on this:
[tex]x^2+y^2-6y=0[/tex]
Complete the square on the y-terms by taking half its linear term, squaring it and adding it to both sides.
The y linear term is 6. Half of 6 is 3, and 3 squared is 9, so we add 9 in on both sides:
[tex]x^2+(y^2-6y+9)=9[/tex]
In the process of completing the square, we created within that set of parenthesis a perfect square binomial:
[tex]x^2+(y-3)^2=9[/tex]
And there's your circle! Third choice down is the one you want.
Fun, huh?
The polar equation r = 6 sinθ is converted to rectangular form using the sine and cosine functions, eventually leading to a quadratic equation in terms of x and y as (x^2 + y^2)y^2 = 36x^2 + 36y^2..
To convert the polar equation r = 6 sinθ into rectangular form, we use the relationships
x = rcosθ and y = r *sinθ.
Substituting for r from the given equation, we have
y = (6sinθ) * sinθ = 6 sin^2θ. Now, since sin^2θ = 1/2 - 1/2cos(2θ), and
cos(2θ) = 1 - 2sin^2θ,
we can express this in terms of x and y as
cos(2θ) = 1 - 2(y/6)^2.
Therefore, y =1/2 - 1/2(1 - 2(y/6)^2) simplifies to y^2 = 36(1 - cos^2 θ).
Since cos^2 θ =x^2/r^2 = x^2/x^2+y^2, we plug this back into the equation to get
y^2 = 36 -36x^2/x^2+y^2.
Multiplying through by (x^2+y^2) we end up with (x^2 + y^2)y^2 = 36x^2 + 36y^2.
A road sign between Cincinnati and Dayton shows both mile and kilometer measurements. According to the sign at that point, a driver is 54 kilometers or 34 miles from Dayton. If the sign is accurate, 1 mile=__________Kilometers?
Answer:
The answer to your question is 1.59 km
Step-by-step explanation:
Data
Sign 54 km or 34 mi
1 mi = ? km
Process
1.- Use proportions and cross multiplication to find the answer
54 km ----------------- 34 mi
x km ---------------- 1 mi
x = (1 mi x 54 km) / 34 mi
-Simplification
x = 54 km / 34
-Result
x = 1.59 km
2.- Conclusion
1 mile is equivalent to 1.59 km
To determine the squirrel population in a city park, researchers tagged 90 squirrels. Later, they counted 630 squirrels, 42 of which had tags. Based on this data, what is the total number of squirrels in the park?
Answer:
1350
Step-by-step explanation:
Initially 90 squirrels were tagged out of a total population of x squirrels.
Similarly, 42 squirrels out of a sample of 630 squirrels had tag
We can use ratio equality to find the total population x.
42:90=620:x
[tex]\frac{42}{90} =\frac{630}{x}[/tex]
Cross multiplying
42 X x = 630 X 90
Dividing both sides by 42
[tex]x=\frac{630 X 90}{42} \\=1350[/tex]
The total number of squirrels in the city park is 1350.
The total number of squirrels in the park is approximately 1350.
To estimate the total squirrel population in the park, we can use the Lincoln-Petersen method, which is a mark-recapture technique. The formula for this method is:
[tex]\[ N = \frac{(M \times n)}{m} \][/tex]
Given the data:
- ( M = 90 ) (the number of tagged squirrels),
- ( n = 630 ) (the total number of squirrels counted in the second sample),
- ( m = 42 ) (the number of tagged squirrels found in the second sample).
Plugging these values into the formula, we get:
[tex]\[ N = \frac{(90 \times 630)}{42} \] \[ N = \frac{56700}{42} \] \[ N = 1350 \][/tex]
Therefore, the total number of squirrels in the park is estimated to be 1350.
Cathy fills a 10-cup bucket with pond water. She uses a 2-cup jar to scoop out water from the pond and pours it into her bucket. How many times does cathy need to scoop water from the pond to fill the bucket?
Answer:
5
Step-by-step explanation:
Very early in your study of multiplication tables, you learned that ...
5 × 2 = 10
Cathy must fill the 2-cup jar 5 times to transfer a total of 10 cups.
Final answer:
To fill a 10-cup bucket using a 2-cup jar, Cathy must scoop water from the pond 5 times, as 10 divided by 2 equals 5.
Explanation:
The question is how many times Cathy needs to scoop water from the pond with a 2-cup jar to fill her 10-cup bucket.
To find the answer, we simply divide the total capacity of the bucket by the capacity of the jar. So, the calculation would be:
Calculate the total number of cups needed: 10 cups (capacity of the bucket).
Calculate the number of cups per scoop: 2 cups (capacity of the jar).
Divide the total number of cups by the number of cups per scoop: 10 cups/ 2 cups per scoop
= 5 scoops.
Cathy needs to scoop water from the pond 5 times to fill her 10-cup bucket.
If sample variance is computed by dividing SS by n, then the average value of the sample variances from all the possible random samples will be _______ the population variance.
Answer:
Less than
Step-by-step explanation:
Sample variance is computed by dividing the Sum of Squares (SS) by the number of samples (n).
Population variance is computed by dividing the Sum of Squares (SS) by the difference between the number of samples and 1 (n-1).
After computing, it would be found that the sample variance is less than the population variance.
The average of sample variances, computed by dividing the Sum of Squares by sample size (n) from all possible samples, will be less than the population variance.
Explanation:If sample variance is computed by dividing Sum of Square (SS) by sample size (n), then the average value of the sample variances from all possible random samples would be biased. In fact, it will be less than the actual population variance. This is commonly known as Bessel's correction in statistics. For an unbiased estimate of the population variance, we should rather divide the SS by degrees of freedom (n-1), not by the sample size n. So, when you average the sample variances, obtained by dividing by n from all possible samples, the result will be less than the population variance.
Learn more about Sample Variance here:https://brainly.com/question/32939966
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You bought 15 1 gallon bottles of orange juice and apple juice for school breakfast. The apple juice was on sale for $1.50 per gallon bottle. The orange juice was two dollars per gallon bottle. You spent $26. How many bottles of each type of juice did you buy
Answer: you bought 7 bottles of orange juice and 8 bottles of apple juice.
Step-by-step explanation:
Let x represent the number of 1-gallon bottles of orange juice that you bought.
Let y represent the number of 1-gallon bottles of apple juice that you bought.
You bought 15 1 gallon bottles of orange juice and apple juice for school breakfast. This means that
x + y = 15
The apple juice was on sale for $1.50 per gallon bottle. The orange juice was two dollars per gallon bottle. You spent $26. This means that
2x + 1.5y = 26 - - - - - - - - - - - - -1
Substituting x = 15 - y into equation 1, it becomes
2(15 - y) + 1.5y = 26
30 - 2y + 1.5y = 26
- 2y + 1.5y = 26 - 30
- 0.5y = - 4
y = - 4/ - 0.5
y = 8
x = 15 - y = 15 - 8
x = 7
Using the distributive property to find the product (y - 4x)(y ^ 2 + 4y + 16) results in a polynomial of the form y ^ 3 + 4y ^ 2 + ay - 4x * y ^ 2 - axy - 64x . What is the value of a in the polynomial?
Answer:
a=16
Step-by-step explanation:
The distributive property states that
[tex]a(b+c)=ab+ac[/tex]
Therefore using the distributive property
[tex](y - 4x)(y ^ 2 + 4y + 16)[/tex]
=[tex]y(y ^ 2 + 4y + 16) - 4x(y ^ 2 + 4y + 16)[/tex]
Expanding the brackets
[tex]y ^ 3 + 4y^2 + 16y - 4xy ^ 2 - 16xy - 64x[/tex].....(i)
Comparing with the form
[tex]y ^ 3 + 4y ^ 2 + ay - 4x y ^ 2 - axy - 64x[/tex]-----(ii)
The coefficient of y in (i) is 16 which corresponds to a and the likewise the coefficient of xy
Therefore, a=16
Answer:
C.) 16
Step-by-step explanation:
The mean salary for a new teacher in your town is $48,000. You believe it is higher for new teachers in a neighboring town. State the null and alternative hypotheses.
Answer:
Step-by-step explanation:
Given that the mean salary for a new teacher in your town is $48,000
You believe it is higher for new teachers in a neighboring town.
So to prove or disprove your claim you have to show statistical evidence.
For that hypothesis testing is necessary.
You must conduct a hypothesis test for comparing the mean of salary of new teacher with neighbouring places
The hypotheses wouldbe
[tex]H_0: \mu = 48000\\H_1: \mu >48000[/tex]
where mu is the average for neighbouring states.
Horace is a professional hair stylist. Let CCC represent the number of child haircuts and AAA represent the number of adult haircuts that Horace can give within 777 hours. 0.75C+1.25A \leq 70.75C+1.25A≤70, point, 75, C, plus, 1, point, 25, A, is less than or equal to, 7 Horace gave 555 child haircuts. How many adult haircuts at most can he give with the remaining time? Choose 1 answer:
Answer:
At most 2 adult haircuts
Step-by-step explanation:
The equation given is:
[tex]0.75C+1.25A \leq 70[/tex]
This equation dictates the number of haircuts Horace gives in 7 hours.
Horace gave 5 child haircuts (C=5). So, that would make the equation:
[tex]0.75C+1.25A \leq 7\\0.75(5)+1.25A \leq 7\\3.75+1.25A \leq 7\\1.25A \leq 7 - 3.75\\1.25A \leq 3.25\\A \leq \frac{3.25}{1.25}\\A \leq 2.6[/tex]
This means Horace can give LESS THAN or EQUAL to 2.6 haircuts.
2.6 haircuts doesn't make sense, so the maximum would be "2" haircuts.
Atmost 2 adult haircuts
You are ordering a hamburger and can get up to 7 toppings, but each topping can only be used once. You tell the cashier to surprise you with the toppings you get. What is the probability that you get 2 toppings
Answer:
Probability, P(getting 2 toppings)= 0.1984
Step-by-step explanation:
Probability, P(1 toppings)= 1/7
Probability P of getting a particular topping is q = 1 - P = 1 - 1/7 = 6/7
Probability of( getting 2 toppings)= 7!/(2!5!)(1/7)^2 × (6/7)^5
P(getting 2 toopings)= (5040/240) × (0.020)× (0.4627)
P(getting 2 toppings)= 21 × 0.00948 = 0.1984
HELP!! I NEED THIS QUICKLY
Jakita examines the ordered pairs ( 3/4, 2/3), (1/4, 2), (1, 1/2) and (1/2, 1), and determines the points form a direct variation with a k value of 1/2.
Which statements about Jakita's conclusion are true? Select two options.
A.) The points actually represent an inverse variation.
B.) The k value of the direct variation is actually 2.
C.) The ordered pairs can be represented by the function y = x/2
D.) The ordered pairs can be represented by the function y = 1/2x
E.) As one quantity increases, the other also increases.
Answer:
A and D
Step-by-step explanation:
We are given that
(3/4,2/3),(1/4,1),(1,1/2) and (1/2,1)
[tex]x_1=\frac{3}{4}[/tex]
[tex]y_1=\frac{2}{3}[/tex]
[tex]x_2=\frac{1}{4},y_2=1[/tex]
[tex]x_3=1,y_3=\frac{1}{2}[/tex]
[tex]x_4=\frac{1}{2},y_4=1[/tex]
k=[tex]\frac{1}{2}[/tex]
Direct proportion:
[tex]\frac{x}{y}=k[/tex]
Inverse proportion:[tex]xy=k[/tex]
[tex]\frac{x_1}{y_1}=\frac{3}{4}\times \frac{3}{2}=\frac{9}{8}\neq \frac{1}{2}[/tex]
Therefore, it is not in direct proportion.
[tex]\frac{1}{4\times 2}=\frac{1}{8}\neq\frac{1}{2}[/tex]
[tex]\frac{1}{\frac{1}{2}}=2\neq \frac{1}{2}[/tex]
[tex]x_1y_1=\frac{3}{4}\times \frac{2}{3}=\frac{1}{2}[/tex]
[tex]x_2y_2=\frac{1}{4}\times 2=\frac{1}{2}[/tex]
[tex]x_3y_3=1\times \frac{1}{2}=\frac{1}{2}[/tex]
[tex]x_4y_4=\frac{1}{2}\times 1=\frac{1}{2}[/tex]
Therefore, [tex]xy=k=\frac{1}{2}[/tex]
Hence, the given points form an inverse variation .
[tex]xy=\frac{1}{2}[/tex]
[tex]y=\frac{1}{2x}[/tex]
Option A and D is true.
Answer: A and D
Step-by-step explanation:
Cause edg2020
A particle is moving horizontally along the x-axis. Its position (in ft) is: s(t)=t^3-18t^2+33t+14 where t is in sec.
Find the time at which the particle switches from moving left to moving right.
t= ___ sec.
Answer:
t=11 sec
Step-by-step explanation:
The position of the particle moving along the x-axis is given by:
[tex]s(t) = {t}^{3} - 18 {t}^{2} + 33t + 14[/tex]
The velocity is given by:
[tex]s'(t) = 3 {t}^{2} - 36{t} + 33[/tex]
If s'(t)>0 then the particle is moving right.
[tex]3 {t}^{2} - 36{t} + 33 \: > \: 0 \\ {t}^{2} - 12{t} + 11\: > \: 0[/tex]
[tex] \implies \: t \: < \: 1 \: or \: t \: > \: 11[/tex]
This means that the particle is moving left when
[tex]1 \: < \: t \: < \: 11[/tex]
The particle changes direction at time t=1 or t=11
What steps should be used to find the range of a set of data? Put the values in order, then locate the value that is far away from every other value. Subtract the maximum and minimum values. Add all of the values together, then divide the sum by the number of values. Add the two middle values together, then divide the sum by two.
Answer:
Subtract the maximum and minimum values.
Step-by-step explanation:
The range of a data set is the interval that contains all values in the set and is determined as the difference between the maximum and the minimum values within the data set. Therefore, in order to find the range of a set of data, simply subtract the maximum and minimum values.
Answer:
Subtract the maximum and minimum values.
Step-by-step explanation:
PLLLZ HELP Find the coefficient of the indicated term in each expansion. (2x – y)4, x2y2 term
4
24
48
12
Coefficient of [tex]x^2y^2[/tex] = 24
Solution:
Given that:
[tex](2x - y)^4[/tex]
We have to find the coefficient of [tex]x^2y^2[/tex] term
Use the following algebraic formula
[tex](a-b)^4 = a^4 - 4a^3b+6a^2b^2-4ab^3+b^4[/tex]
From given,
[tex](2x - y)^4[/tex]
Where,
a = 2x
b = y
Therefore, by using formula, we get,
[tex](2x - y)^4 = (2x)^4 - 4(2x)^3(y) + 6(2x)^2(y)^2 - 4(2x)(y)^3 + y^4\\\\Simplify\\\\(2x - y)^4 = 16x^4 - 32x^3y + 24x^2y^2-8xy^3 + y^4[/tex]
Find the coefficient of [tex]x^2y^2[/tex]
From above simplified expression,
coefficient of [tex]x^2y^2[/tex] = 24
Answer:
24
Step-by-step explanation:
#2 math help needed
Answer:
Step-by-step explanation:
False. Asymptotes are the walls that the function can't get over. This wall has no gaps or holes, nor does it have a gate. The function has to stay on one side of the asymptote in order for it to be a legit asymptote. Since our function is both above and below the dotted line, the dotted line is not an asymptote.
What is the leading coefficient of the polynomial?
30x2 + 12x + 18x3 + 10
A) 10
B) 12
C) 18
D) 30
Answer: It is C because if you organize the equation numerically the equation is 18x^3+30x^2+12x+10. So it is 18.
M is a degree 3 polynomial with m ( 0 ) = 53.12 and zeros − 4 and 4 i . Find an equation for m with only real coefficients (i.E. No i in your equation.
Answer:
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
Step-by-step explanation:
Given that M is a polynomial of degree 3.
So, it has three zeros.
Let the polynomial be
M(x) =a(x-p)(x-q)(x-r)
The two zeros of the polynomial are -4 and 4i.
Since 4i is a complex number. Then the conjugate of 4i is also a zero of the polynomial i.e -4i.
Then,
M(x)= a{x-(-4)}(x-4i){x-(-4i)}
=a(x+4)(x-4i)(x+4i)
=a(x+4){x²-(4i)²} [ applying the formula (a+b)(a-b)=a²-b²]
=a(x+4)(x²-16i²)
=a(x+4)(x²+16) [∵i² = -1]
=a(x³+4x²+16x+64)
Again given that M(0)= 53.12 . Putting x=0 in the polynomial
53.12 =a(0+4.0+16.0+64)
[tex]\Rightarrow a = \frac{53.12}{64}[/tex]
=0.83
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
PLEASE HELP...
Write a simplified polynomial expression in standard form to represent the area of the rectangle below:
A picture of a rectangle is shown with one side labeled as 2 x minus 2 and another side labeled as x plus 4.
2x2 + 3x − 20
2x2 + 13x − 1
2x2 + 13x − 20
2x2 + 3x − 1
The area of the given rectangle is of the standard form option 1.[tex]2x^{2} + 3x - 20[/tex].
Step-by-step explanation:
Step 1:
The parameters needed to determine the area of a rectangle are the base length and the width.
The base length of this rectangle is [tex]2x-5[/tex] units while its width is [tex]x+4[/tex] units.
The area of a rectangle is determined by multiplying the base length with the width.
Step 2:
The area of the rectangle [tex]= (length)(width).[/tex]
Here length is [tex]2x-5[/tex] units and the width is [tex]x+4[/tex] units.
The area of the rectangle[tex]= (2x-5)(x+4) = 2x^{2} + 8x -5x-20 = 2x^{2} + 3x - 20.[/tex]
So the area of the given rectangle is of the standard form [tex]2x^{2} + 3x - 20[/tex] which is the first option.
To find the area of the rectangle, we need to multiply the expressions for the lengths of its sides. The sides are given as [tex]\(2x - 2\) and \(x + 4\).[/tex]
First, write the expressions for the sides of the rectangle:
- One side is[tex]\(2x - 2\)[/tex]
- The other side is[tex]\(x + 4\)[/tex]
To find the area, multiply these two expressions:
[tex]\[(2x - 2)(x + 4)\][/tex]
Use the distributive property (also known as the FOIL method for binomials) to expand this product:
[tex]\[(2x - 2)(x + 4) = 2x(x) + 2x(4) - 2(x) - 2(4)\][/tex]
Simplify each term:
[tex]\[= 2x^2 + 8x - 2x - 8\][/tex]
Combine like terms:
[tex]\[= 2x^2 + 6x - 8\][/tex]
So, the polynomial expression in standard form representing the area of the rectangle is:
[tex]\[2x^2 + 6x - 8\][/tex]
Given the options:
- 2x^2 + 3x − 20
- 2x^2 + 13x − 1
- 2x^2 + 13x − 20
- 2x^2 + 3x − 1
None of these options exactly match our result of [tex]\(2x^2 + 6x - 8\),[/tex] indicating a potential error in the problem statement or options provided. The correct simplified polynomial expression for the area, based on the given side lengths, is[tex]\(2x^2 + 6x - 8\).[/tex]
Which equation could you use to solve for x in the proportion StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction? 4 x = 14 4 x = 45 5 x = 13 5 x = 36
Answer:
(b) 4 x = 4 5 is the needed expression to solve for the value of x.
Step-by-step explanation:
Here, the given proportion is simplified as:
[tex]\frac{4}{5} = \frac{9}{x}[/tex]
Now, to simplify any proportion of the form [tex]\frac{a}{b} = \frac{c}{d}[/tex] the simplest way is CROSS MULTIPLICATION.
So, cross multiplying [tex]\frac{a}{b} = \frac{c}{d} \implies ad = bc[/tex]
Similarly cross multiplying [tex]\frac{4}{5} = \frac{9}{x}[/tex], we get:
4 (x) = (9) (5)
or, 4 x = 45
Hence, 4 x = 45 is the needed expression to solve for the value of x.
Answer:
4x=45
Step-by-step explanation:
4/5=9/x, so first you would multiply 5×9 (because cross products are always equal) and you would get 45. Since 4x has to also equal 45, the answer is 4x=45.
Hope this helps (P.S. I got it right on the test)!
At the moment a hot iron rod is plunged into freezing water, the difference between the rod's and the water's temperatures is 100\degree100°100, degree Celsius. This causes the iron to cool and the temperature difference drops by 60\%60%60, percent every second. Write a function that gives the temperature difference in degrees Celsius, D(t)D(t)D, left parenthesis, t, right parenthesis, ttt seconds after the rod was plunged into the water.
Answer:
[tex]D(t)=100(0.4)^t[/tex]
Step-by-step explanation:
The temp is 100 at time t = 0
After 1 sec, the temp difference would be:
[tex]100-(\frac{100-60}{100})[/tex]
After 2 sec, the temp difference would be:
[tex]100-(\frac{100-60}{100})^2[/tex]
Similarly for 3 seconds, 4 seconds etc.
We notice that the parenthesis part is 40% of it, so we can also write:
100(40%)^t,
where
t is the time
40% can be written as 40/100 = 0.4
SO, the function is:
[tex]d(t)=100(0.4)^t[/tex]
Answer:
[tex]D(t)=100*0.4^t[/tex]
Step-by-step explanation:
Initially, the difference between the rod's and the water's temperatures is 100°
i.e D(t)=100 When t=0
After 1 seconds, the temp drops by 60%.
Therefore, the new value of D will be the old value multiplied by (100-60)%.
D(1)=100 X (100%-60%) = 100*0.4
After 2 seconds, the temp difference would be:
D(2)=100*0.4*0.4= [tex]100*0.4^2[/tex]
We notice that for any t, the percentage at which the difference is reduced is raised to the power of t.
Therefore, temperature difference in degrees Celsius, D(t), t seconds after the rod was plunged into the water is given as:
[tex]D(t)=100*0.4^t[/tex]
There are about 320 million residents on the United States if 38% of them live in the south,estimate how many live in other areas of the United States?
Answer:
198,400,000
Step-by-step explanation:
Total Approximate Number of Residents in the United States = 320 million
38 per cent of the total number of residents live in the South
That means, as a percentage, 100%-38%=62% live in other areas of the Unjted States.
[tex]62 \% of 320 million[/tex] = [tex]\frac{62}{100}X320000000[/tex]=198,400,000.
Therefore a total of about 198,400,000 live in other areas of the United States.
A building contractor buys 7070% of his cement from supplier A and 3030% from supplier B. A total of 9595% of the bags from A arrive undamaged, while 7070% of the bags from B arrive undamaged. Find the probability that anan undamagedundamaged bag is from supplier Upper AA.
Title:
The answer is [tex]\frac{133}{174}[/tex].Step-by-step explanation:
Let the building contractor bought 1000 cement in total.
70% of 1000 = 700 cements were from A and (1000 - 700) = 300 cements were from B.
The number of undamaged bag from A was 95% of 700 = [tex]\frac{95}{100} \times700 = 7\times95 = 665[/tex] and the number of undamaged bags from B was 70% of 300 = [tex]\frac{70}{100} \times300 = 210[/tex].
Total undamaged bags were (665 + 210) = 870.
The probability that an undamaged bag is from A is [tex]\frac{665}{870} = \frac{133}{174}[/tex].
To discourage students from driving to campus, a university claims students spend an average of 20 minutes looking for a parking spot. One student does not believe it takes so long to find a spot. After taking a random sample of 45 students, a sample mean of 17.4 minutes to find a parking spot was calculated.
To assess the evidence provided by the sample data, what is the appropriate question to ask?
1. The true mean amount of time needed to find a parking spot 17.4 minutes?
2. How likely is it that the true mean amount of time needed to find a parking spot is 20 minutes?
3. How likely is it that, in a sample of 45, the true mean amount of time needed to find a parking spot is 17.4 minutes or less if the true mean is 20?
4. How likely is it that, in a sample of 45, the true mean amount of time needed to find a parking spot is less than 20 minutes?
Answer:
The correct answer to the question is
4. How likely is it that, in a sample of 45, the true mean amount of time needed to find a parking spot is less than 20 minutes?
Step-by-step explanation:
Confidence interval provides a range of likely values for an unknown parameter. The interval is weighted based on probabilities of occurrence, such as 95% or 99% based on the result of a sample of test data.
It gives the probability that a given parameter such as the mean will be of a certain value range based on a given number of times.
As such the confidence level of the given mean amount of time needed to find a parking spot should be known.
Margie needs to know the square footage for the first floor of the condo her client wants to make an offer on. The kitchen is 10 feet by 15 feet, the living/dining combo is 20 feet by 25 feet, and the office and sunroom are each 10 feet by 10 feet. What’s the total square footage?
Answer: the total square footage is
850 ft³
Step-by-step explanation:
The kitchen is 10 feet by 15 feet. This means that the volume of the kitchen would be
10 × 15 = 150 ft³
The living/dining combo is 20 feet by 25 feet. This means that the volume of the living/dining combo would be
20 × 25 = 500 ft³
The office and sunroom are each 10 feet by 10 feet. This means that the volume of the office would be
10 × 10 = 100 ft³
Also, the volume of the sunroom would be
10 × 10 = 100 ft³
Therefore, the total square footage is
150 + 500 + 100 + 100 = 850 ft³
A local car dealership is holding a year-end event because new car models have just been released. Declan has $35,000 to spend on a car. The car Declan decides to buy for his family costs $35,000. However, it is part of the year-end event, which means he receives a 15% discount on the new car. Declan plans to put the money he saves on the car into a new bank account. The bank account has a yearly simple interest rate of 4%, paid at the end of each year. If Declan does not add any other money to this bank account, it will take 6 years for Declan's bank account to reach $6,720.
Answer:
The amount Declan saves from the discount is 15% of $35,000
which is $5250
This Amount $5250 is the amount Declan invests in the bank
This is the Amount the bank pays at the end of the time T of saving
Step-by-step explanation:
The simple Interest is calculated by
I = (P x R x T) / 100
where I is the Interest
R is the rate in percentage
T is the time the money will be saved
Another Important quantity is the Amount A
A = I + P
Moshe is playing cards and is grouping the cards that have already been played by suit (hearts, clubs, diamonds, and spades). Moshe is using what type of encoding?
Answer:
organizational
Step-by-step explanation:
organizational encoding iis process of categorizing information according to. the relationships among a series of items. Here the categorizing information are hearts, clubs, diamonds, and spades.
Hope it will find you well.
Moshe is using categorical encoding to group the cards that have already been played by suit
Explanation:Moshe is using categorical encoding to group the cards that have already been played by suit. Categorical encoding is a type of semantic encoding, where information is organized and stored based on categories or groups. In this case, Moshe is categorizing the cards into the four suits: hearts, clubs, diamonds, and spades.
Learn more about Categorical Encoding here:https://brainly.com/question/31144201
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What is the volume of the rectangular prism below?
24 in 3
48 in 3
72 in 3
108 in 3
Answer:
72
Step-by-step explanation:
3 x 4 = 12
12 x 6 = 72
hope i helped
Which equation is the inverse of y = 9x2 – 4? y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 9 EndFraction y = plus-or-minus StartRoot StartFraction x Over 9 EndFraction + 4 EndRoot y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 3 EndFraction y = StartFraction plus-or-minus StartRoot x EndRoot Over 3 EndFraction + two-thirds
The inverse of the equation y = 9x² − 4 is found by switching x and y and solving the equation for the new y. The correct inverse function after simplification is y = ±√(x / 9 + 4).
Explanation:To find the inverse of the equation y = 9x2 − 4, you need to switch the roles of x and y and then solve for y once again. Here is a step-by-step explanation:
Replace y with x and x with y to get x = 9y2 − 4.Add 4 to both sides to isolate the perfect square term: x + 4 = 9y2.Divide both sides by 9 to get (x + 4) / 9 = y2.Take the square root of both sides note that there are always two solutions when taking a square root, a positive and a negative: y = ±√((x + 4) / 9).Finally, simplify to express y: y = ±√(x / 9 + 4/9).Comparing the result with the choices given, we find that y = ±√(x / 9 + 4) is the correct inverse function.
Quiz 2 Problem The double number line shows that 444 bottles of water cost 101010 dollars at a music festival. Based on the ratio shown in the double number line, how much does 333 bottles of water cost? dollars Report a problem
Answer:
Cost of 3 bottles will be $7.5.
Step-by-step explanation:
Given:
According to double number line.
Cost of 4 bottles = $10
Based on this we need to find the cost of 3 bottles of water.
Solution:
Now we know that;
4 bottles = $10
1 bottle = Cost of 1 bottle
By using Unitary method we get;
Cost of 1 bottle = [tex]\frac{10}{4}=\$2.5[/tex]
So we can say that;
Cost of n bottles = [tex]\$2.5n[/tex]
Cost of 3 bottles = [tex]\$2.5\times 3 = \$7.5[/tex]
Hence Cost of 3 bottles will be $7.5.
Now we have drawn the double number line.
Bottom line(Line 1) will be number of bottles:
1 2 3 4 5 6
Top line (Line 2) will be the cost of corresponding bottles:
2.5 5 7.5 10 12.5 15
Answer:
$7.5 Dollars
Step-by-step explanation:
The cost of 4 bottles is $10. So, 1 bottle is going to be $2.50.
Now, to find the cost of 3 water-bottles, we have to multiply.
$2.50 * 3 = $7.50.
So, the answer to this question is 3 bottles = $7.50
(Hope this helps!)
The polynomial y=−0.73x4+3.1x3+26.5 describes the billions of flu virus particles in a person's body x days after being infected. Find the number of virus particles, in billions, after 3 days. There are billion virus particles in a person's body 3 days after being infected.
To find the number of virus particles after 3 days, substitute x=3 into the given polynomial. The number of virus particles, in billions, after 3 days is approximately 48.37 billion.
Explanation:To find the number of virus particles after 3 days, substitute x=3 into the polynomial:
y = -0.73(3)^4 + 3.1(3)^3 + 26.5
Calculating this expression:
y = -0.73(81) + 3.1(27) + 26.5 = -59.13 + 81 + 26.5 = 48.37
Therefore, the number of virus particles, in billions, after 3 days is approximately 48.37 billion.
Leah asked her dance students to each hand out at least 10 flyers advertising their upcoming dance recital. She constructed a histogram to display the number of recital flyers handed out by the students.
Leah asked her dance students to hand out at least 10 flyers for their upcoming dance recital and construct a histogram to display the data.
Explanation:In this question, Leah asked her dance students to each hand out at least 10 flyers for their upcoming dance recital. Then, she constructed a histogram to display the number of recital flyers handed out by the students.
To solve this, Leah can tally the number of students who handed out a specific number of flyers and create intervals on the x-axis of the histogram to represent the number of flyers. The height of each bar in the histogram will represent the number of students who handed out the corresponding number of flyers. By constructing the histogram, Leah can visualize the distribution of the number of flyers handed out by her dance students.
Final answer:
The question is related to Mathematics, specifically the creation and analysis of histograms, frequency tables, and probability distributions, often used in statistics to visualize and interpret various sets of data.
Explanation:
The student's question falls under the subject of Mathematics, specifically related to statistics and data analysis. In this instance, various exercises are mentioned where the creation and interpretation of histograms are central. These exercises are multifaceted, requiring students to compile data, calculate statistical measures such as means and probabilities, and graphically represent data using histograms and other charts.
For example, when Leah asks her dance students to hand out flyers, she is gathering data that can be represented in a histogram to visualize the distribution of flyers handed out. Similarly, the ballet instructor's data on retention rates can form a probability distribution. When Jill delivers flyers for her yard sale, her travel distances and times could be used to create a time series graph.
Histograms, frequency tables, and probability distributions are tools used in these exercises to better understand the data collected, whether it's related to dance flyer distribution, car sales, or family size among classmates.