Answer:
$3577.20
Step-by-step explanation:
You can save 11% of your income each month, so in 12 months, you can save ...
12×0.11×$2710 = $3577.20
HELP PLZ!!!!!!
[tex] \times + 1 = 7[/tex]
Determine the location and value of the absolute extreme values of f on the given interval, if they exist. f (x )equals2 sine squared x on [0 comma pi ]Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Type an exact answer, using pi as needed. Use a comma to separate answers as needed.) A. The absolute maximum is nothing at xequals nothing, but there is no absolute minimum. B. The absolute minimum is nothing at xequals nothing and the absolute maximum is nothing at xequals nothing. C. The absolute minimum is nothing at xequals nothing, but there is no absolute maximum. D. There are no absolute extreme values for f (x )on [0 comma pi ].
Answer:
A. The absolute maximum is nothing at x equals nothing, but there is no absolute minimum.
Step-by-step explanation:
The equation is :
f(x) = 2x2 + x2
The function has not absolute maximum value and it has absolute minimum value 0. The both function has maximum value as nothing.
A group of 4 friends went to lunch and spent a total of $40, which included the $34 food bill and the tip. They decided to split the bill and tip evenly among themselves.
One of the friends used the equation One-fourth (t + 34) = StartFraction 40 over 4 EndFraction to represent the situation, where t represents the total amount of the tip. Which describes the amount each friend paid for the food and for the tip?
Answer:
The individually paid $1.5 for the tip and $8.5 for the food
Step-by-step explanation:
Total money spent = $40
Food bill = $34
if the situation is represented by the equation [tex]\frac{1}{4}(t+34) = \frac{40}{4}[/tex] where t is the amount of the tip, the amount for the tip can be calculated as shown;
[tex]\frac{1}{4}(t+34) = \frac{40}{4}\\ t+34 = 40\\t = 40-34\\t = 6[/tex]
Amount of the tip = $6
If they decided to split the bill and tip evenly among themselves, amount paid by each friend for the food and the tip can be gotten using the equation representing the situation where t = $6 as shown;
[tex]= \frac{1}{4}(t+34) \\= \frac{1}{4}(6+34)\\= \frac{1}{4}(6)+\frac{1}{4}(34)\\= 1.5+8.5\\[/tex]
From the result above, it can be seen that each friend paid $1.5 for their tip and $8.5 for their food
Answer:
A) Each friend paid $8.50 for the food and $1.50 for the tip.
Ujalakhan01! Please help me! ASAP ONLY UJALAKHAN01. What's (x-1)(x-1)?
Answer:
[tex]x^2-2x+1[/tex]
Step-by-step explanation:
=> (x-1)(x-1)
Using FOIL
=> [tex]x^2-x-x+1[/tex]
=> [tex]x^2-2x+1[/tex]
Answer:
Step-by-step explanation:
simply :
(x-1)(x-1)= (x-1)²= x²-2x=1
What is the value of d in the equation?
1 3/4d=14
4
8
18 2/3
24 1/2
Answer:
its 13/56.
Step-by-step explanation:
13/4d= 14
or , 13 = 14×4d
or, 13=56 d
or, d = 13/56.
Answer:
The answer is D
Step-by-step explanation:
1 3/4d= 14
7/4d = 14
d = 8
Hope I helped pls tell me if i'm wrong :D
Which represents a unit rate? The cost of cat food is $36 per 3 bags
Step-by-step explanation:
To find unit rate
1 bag = 36÷ 3 = 12
So unit rate = $12
The red figure is similar to the blue figure. Which choice describes a sequence of transformations in which the blue figure is the image of the red figure. ***MUST ANSWER BEFORE 10:00 AM TODAY****
Answer:
Diluation, then Translation, or Slide, in sorts.Step-by-step explanation:
1. Divide the sides of the red triangle by 2. That will get your size
2. Translate 5 units down across the x-axis
3. Translate 6 unit to the right across the y-axis.
So your answer would be (5,6)/2= A prime
Hope this helped!
Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. The correct option is A.
What is dilation?Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. This transformation yields a picture that is identical to the original shape. However, there is a size discrepancy in the form.
The red figure is similar to the blue figure. The dilation factor is,
Dilation factor = Image/Pre-image = 2/4 = 1/2
Now, the position of the right-most vertice will be (0.5,1), if we see the transformation of this vertice, then after transformation, it will be at (4,-4).
Hence, the correct option is A.
Learn more about Dilation:
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A professor gives a statistics exam. The exam has 100 possible points. The scores for the students in the second classroom are as follows:
88 88 92 88 88 72 96 88 84
Calculate the sample size, n, and the sample mean, M n = M =
While grading the exam, the professor realizes that one of the questions covered material that was not yet covered in the lectures. This question was worth 20 points, so he decides to add 20 points to everyone's score.
Calculate the new n and M.
Answer:
N = 9
M = 87.11
Step-by-step explanation:
According to the situation, the data provided and the solution are as follows
The scores for the student in the classroom is
= 88 88 92 88 88 72 96 88 84
The different student's number of scores is 9
The solution of new n and M is shown below:-
Sample size (n) = 9
Sample mean (m) is
[tex]= \frac{Sum\ of\ all\ data\ values}{Sample\ size}[/tex]
= [tex]\frac{88 + 88 + 92 + 88 + 88 + 72 + 96 + 88 + 84}{9}[/tex]
[tex]= \frac{784}{9}[/tex]
= 87.11
John has two jobs. For daytime work at a jewelry store he is paid
$15,000 per month, plus a commission. His monthly commission is
normally distributed with mean $10,000 and standard deviation
$2000. At night he works occasionally as a waiter, for which his
monthly income is normally distributed with mean $1,000 and
standard deviation $300. John's income levels from these two
sources are independent of each other. For a given month, what is
the probability that John's commission from the jewelry store is
between $9,000 and $11,000?
Given Information:
John's mean monthly commission = μ = $10,000
Standard deviation of monthly commission = σ = $2,000
Answer:
[tex]P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%[/tex]
The probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%
Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
We want to find out the probability that John's commission from the jewelry store is between $9,000 and $11,000?
[tex]P(9,000 < X < 11,000) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(9,000 < X < 11,000) = P( \frac{9,000 - 10,000}{2,000} < Z < \frac{11,000 - 10,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( \frac{-1,000}{2,000} < Z < \frac{1,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( -0.5 < Z < 0.5 )\\\\P(9,000 < X < 11,000) = P( Z < 0.5 ) - P( Z < -0.5 ) \\\\[/tex]
The z-score corresponding to 0.50 is 0.6915
The z-score corresponding to -0.50 is 0.3085
[tex]P(9,000 < X < 11,000) = 0.6915 - 0.3085 \\\\P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%[/tex]
Therefore, the probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.4, 2.2, 0.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.50 then go for 0.00 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
Two similar biscuit tins hold the same type of biscuits. The net mass of biscuits in the smaller tin is 1 kg. Find the net mass of biscuits in the larger tin. Net mass of biscuits in larger tin = __?_ kg
Answer:
1.5 kg
Step-by-step explanation:
Assuming it scales linearly: the higher tin holds 9/6 as many biscuits, so:
9/6 · 1 kg = 1.5 kg
What do you go by for the pattern 360,60,10 would it be add 60, divided by 6 ,multiply by 6 or subtract 300?
Answer:
divided by 6
Step-by-step explanation:
Given pattern
360,60,10
would it be add 60
lets
add 60 to each term
360 +60 = 420
but next term is 60, hence it incorrect choice
divided by 6
lets divide each term by 6
360/6 = 60 which is the next term in the series as well
60/6 = 10 which is also the next term in the series as well
hence divided by 6 is the correct option.
multiply by 6
multiply by 6 to each term
360 *60 = 21600
but next term is 60, hence it incorrect choice
subtract 60 from each term
360 -300 = 60 which is the next term in the series
60 -300 = -240 which is not same the next term in the series that is 10
hence this is incorrect choice
The hourly rate for a staff nurse is £13.75.
A staff nurse works 30 hours a week and 6 hours overtime at time-and-a-half.
What is her total pay for the week?
Answer:
P = £536.25
Her total pay for the week is £536.25
Step-by-step explanation:
The total pay can be written as;
P = t1(r1) + t2(r2)
Where;
t1 = normal time
r1 = normal time pay rate
t2 = overtime
r2 = overtime pay rate
Given;
t1 = 30 hours
t2 = 6 hours
r1 = £13.75
r2 = 1.5(r1) = 1.5(£13.75)
Substituting the given values into the equation 1;
P = 30(£13.75) + 6(1.5(£13.75))
P = £536.25
Her total pay for the week is £536.25
In a 2-card hand, what is the probability of holding only face cards?
Answer:
12
Step-by-step explanation:
( J , Q, K 4 each)
so prob that for 2 cards, both cards are face
= C(12,2)/C(52,2) = 66/1326 = 11/221
Extend the rate table to find the unknown value in the proportion
A. a = 132
B. a = 216
C. a = 324
D. a = 972
Answer:
a = 324
Step-by-step explanation:
The last entry in the table can be multiplied by 3:
3(27/2, 108) = (81/2, 324)
Apparently, ...
a = 324
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
y=x^2, x=y^2 about y = - 6.
Answer:
13.5
Step-by-step explanation:
We are given that two curves and a line
[tex]y=x^2,x=y^2[/tex] about y=-6
[tex]x=\sqrt{y}[/tex]
Height=[tex]\sqrt{y}-y^2[/tex]
Radius=y-(-6)=y+6
Now, we find intersecting points of two curves
[tex]y=(y^2)^2[/tex]
[tex]y=y^4[/tex]
[tex]y^4-y=0[/tex]
[tex]y(y^3-1)=0[/tex]
[tex]y=0[/tex]
[tex]y^3-1=0[/tex]
[tex]y^3=1\implies y=1[/tex]
Now, volume generated by rotating the region by using cylindrical shell method is given by
[tex]V=\int_{a}^{b}2\pi(height)(radius)dy[/tex]
Using the formula
[tex]V=\int_{0}^{1}2\pi(\sqrt{y}-y^2)(y+6)dy[/tex]
[tex]V=\int_{0}^{1}2\pi(y^{\frac{3}{2}}+6\sqrt{y}-y^3-6y^2)dy[/tex]
[tex]V=2\pi[\frac{2}{5}y^{\frac{5}{2}}+4y^{\frac{3}{2}}-\frac{1}{4}y^4-2y^3]^{1}_{0}[/tex]
[tex]V=2\pi(\frac{2}{5}+4-\frac{1}{4}-2)[/tex]
[tex]V=13.5 [/tex]
Which of the binomials below is a factor of this trinomial?
x² + 3x - 4
Answer:
(x+4) or (x-1)
Step-by-step explanation:
Do this by factoring out your equation. To do this, think about which two numbers multiply to be -4 but also add up to be 3 (the -4 came from multiplying the first value (the 1 that is attached to the [tex]x^{2}[/tex]) and the last value, which is -4. The 3 came from the middle term).
The two numbers you should have gotten are 4 and -1. Therefore, (x+4) and (x-1) are both of the binomials that could be your answer
Find the solution of the differential equation that satisfies the given initial condition.
Answer:
[tex]y = \sqrt{x^2+4}[/tex]
Step-by-step explanation:
The question is incomplete. Here is the complete question.
Find the solution of the differential equation that satisfies the given initial condition. dy/dx = x/y, y(0) = -2
Using the variable separable method.
Step 1: Separate the variables
dy/dx = x/y
x dx = y dy
Step 2: Integrate both sides of the resulting equation
[tex]\int\limits {x} \, dx = \int\limits{y} \, dy\\\frac{x^2}{2} = \frac{y^2}{2} \\ \frac{y^2}{2} = \frac{x^2}{2} + C\\y^2 = x^2 + 2C\\y^2 = x^2 + K; K = 2C[/tex]
Note that the constant of integration added to the side containing x
Step 3: Apply the initial condition y(0) = -2
This means when x = 0, y = -2. From step 2:
[tex]y^2+x^2 = K\\(-2)^2+0^2 = K\\4 = K[/tex]
Step 4: Substitute K = 4 into the resulting differential equation above
[tex]y^2=x^2+4\\y = \sqrt{x^2+4}[/tex]
This gives the solution to the differential equation.
Alex is on a boat going to an island twelve miles away for a picnic. The way there, with the current, it takes her 3 hours while the way back, against the current, it takes her 4 hours. What is the speed of her boat and what is the speed of the current?
Answer:
the boat is going at 3.5 mph and the current is going at .5 mph
Step-by-step explanation:
Pediatricians prescribe 5ml of cough syrup for every 25lb of a child’s weight. How many milliliters of cough syrup will the doctor prescribe for Jocelyn, who weighs 45lb?
Answer:
x=9
Step-by-step explanation:
for this sort of a problem, I would set up a proportion
5/25=x/45
multiply both sides by 25 and 45
45*5=x*25
225=25x
x=9
I NEED HELP PLEASE THANKS! :) Find the seventh partial sum of 13, 22, 31, 40, ...
9
67
106
280
Answer:
Step-by-step explanation:
Arithmetic sequence
First term a = 13
Common difference = 2nd term - first term
= 22 - 13
d = 9
[tex]a_{n}= a + (n-1)d\\\\a_{7}= 13 + 6*9[/tex]
= 13 + 54
= 67
Sum of 7 terms = [tex]\frac{n}{2}(2a + (n-1)d)\\\\[/tex]
= [tex]\frac{7}{2}(2*13+6*9)\\[/tex]
=[tex]\frac{7}{2}(26+54)\\[/tex]
= [tex]\frac{7}{2}*80\\[/tex]
= 7 *40
= 280
Answer:
280
Step-by-step explanation:
the 7th number is
Conscientiousness is a tendency to show self-discipline, act dutifully, and aim for achievement. The trait shows a preference for planned rather than spontaneous behavior. A random sample of 650 students is asked to fill out the Hogan Personality Inventory (HPI) to measure their level of conscientiousness. The 350 graduate students had a mean score of 153 with a standard deviation of 21. The 300 undergraduate students scored an average of 148 with a standard deviation of 16. We are interested in determining whether graduate students score higher, on average, on the HPI than undergraduate students. What is the value of the test statistic for testing these hypotheses using a pooled two sample t-test?
Answer:
a
The Null hypothesis represented as
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
The Alternative hypothesis represented as
[tex]H_a: \mu_1 - \mu_2 < 0[/tex]
b
p-value = P(Z < -3.37 ) = 0.000376
c
There is insufficient evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students
Step-by-step explanation:
From the question we are told that
The population size is [tex]n= 650[/tex]
The sample size for graduates is [tex]n_1 = 300[/tex]
The sample mean for graduates is [tex]\= x _1 = 148[/tex]
The sample standard deviation for graduates is [tex]\sigma_1 = 16[/tex]
The sample size for under-graduates is [tex]n _2 = 350[/tex]
The sample mean for under-graduates is [tex]\= x _2 = 153[/tex]
The sample standard deviation for graduates is [tex]\sigma_2 = 21[/tex]
The Null hypothesis represented as
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
The Alternative hypothesis represented as
[tex]H_a: \mu_1 - \mu_2 < 0[/tex]
Where [tex]\mu_1 \ and \ \mu_2[/tex] are the population mean
Now the test statistic is mathematically represented as
[tex]t = \frac{(\= x_1 - \= x_2 ) }{ \sqrt{ \frac{ (n_1 - 1 )\sigma_1 ^2 + (n_2 - 1)\sigma_2^2}{n_1 +n_2 -2} } * \sqrt{ \frac{1}{n_1} + \frac{1}{n_2} } }[/tex]
substituting values
[tex]t = \frac{(148 - 153 ) }{ \sqrt{ \frac{ (300- 1 )16 ^2 + (350 - 1) 21^2}{300 +350 -2} } * \sqrt{ \frac{1}{300} + \frac{1}{350} } }[/tex]
[tex]t = -3.37[/tex]
The p-values is mathematically evaluated as
p-value = P(Z < -3.37 ) = 0.000376
The above answer is gotten using a p-value calculator at (0.05) level of significance
Looking the p-value we see that it is less than the level of significance (0.05) so Null hypothesis is rejected
Hence there is insufficient evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students
Following are the two-Sample of the T-Test and CI:
[tex]\boxed{\boxed{\begin{matrix}Sample& N &Mean& StDev& SEMean\\ 1 &350 &153.0& 21.0 &1.1 \\ 2& 300& 148.0& 16.0& 0.92\end{matrix}}}[/tex]
Calculating the difference:
[tex]= \mu (1) - \mu (2)\\\\[/tex]
The estimated difference: [tex]5.00[/tex]
When the [tex]95\%[/tex] of CI so, the difference:[tex](2.09, 7.91)[/tex]
Therefore the T-Test difference value = 0
[tex]\to (vs \neq): T-Value = 3.37 \\\\\to P-Value = 0.001 \\\\\to DF = 648[/tex]
When the both use Pooled so, the StDev = 18.8583
Therefore, the final value of t is "3.37".
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After scoring a touchdown, a football team may elect to attempt a two-point conversion, by running or passing the ball into the end zone. If successful, the team scores two points. For a certain football team, the probability that this play is successful is 0.40.
a.â Let X =1 if successful, X= 0 if not. Find the mean and variance of X.
b.â If the conversion is successful, the team scores 2 points; if not the team scores 0 points. Let Y be the number of points scored. Does Y have a Bernoulli distribution? If so, find the success probability. If not, explain why not.
c.â Find the mean and variance of Y.
Answer:
a) Mean of X = 0.40
Variance of X = 0.24
b) Y is a Bernoulli's distribution. Check Explanation for reasons.
c) Mean of Y = 0.80 points
Variance of Y = 0.96
Step-by-step explanation:
a) The probability that play is successful is 0.40. Hence, the probability that play isn't successful is then 1 - 0.40 = 0.60.
Random variable X represents when play is successful or not, X = 1 when play is successful and X = 0 when play isn't successful.
The probability mass function of X is then
X | Probability of X
0 | 0.60
1 | 0.40
The mean is given in terms of the expected value, which is expressed as
E(X) = Σ xᵢpᵢ
xᵢ = each variable
pᵢ = probability of each variable
Mean = E(X) = (0 × 0.60) + (1 × 0.40) = 0.40
Variance = Var(X) = Σx²p − μ²
μ = mean = E(X) = 0.40
Σx²p = (0² × 0.60) + (1² × 0.40) = 0.40
Variance = Var(X) = 0.40 - 0.40² = 0.24
b) If the conversion is successful, the team scores 2 points; if not the team scores 0 points. If Y ia the number of points that team scores.Y can take on values of 2 and 0 only.
A Bernoulli distribution is a discrete distribution with only two possible outcomes in which success occurs with probability of p and failure occurs with probability of (1 - p).
Since the probability of a successful conversion and subsequent 2 points is 0.40 and the probability of failure and subsequent 0 point is 0.60, it is evident that Y is a Bernoulli's distribution.
The probability mass function for Y is then
Y | Probability of Y
0 | 0.60
2 | 0.40
c) Mean and Variance of Y
Mean = E(Y)
E(Y) = Σ yᵢpᵢ
yᵢ = each variable
pᵢ = probability of each variable
E(Y) = (0 × 0.60) + (2 × 0.40) = 0.80 points
Variance = Var(Y) = Σy²p − μ²
μ = mean = E(Y) = 0.80
Σy²p = (0² × 0.60) + (2² × 0.40) = 1.60
Variance = Var(Y) = 1.60 - 0.80² = 0.96
Hope this Helps!!!
To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75° from the horizontal. An observer D = 585 m away measures the angle of elevation to the spot of light to be 45°. Find the height h of the cloud cover. (Round your answer to the nearest meter.)
Answer:
585m
Step-by-step explanation:
using SOHCAHTOA to solve the question
the angle of elevation is 45° so therefore the answer is 585 m
A soccer team sold raffle tickets to raise money for the upcoming season. They sold three different types of tickets: premium for $6, deluxe for $4, and regular for $2. The total number of tickets sold was 273, and the total amount of money from raffle tickets was $836. If 118 more regular tickets were sold than deluxe tickets, how many premium tickets were sold?
Answer:
45 premium tickets were sold
Step-by-step explanation:
p = premium
d = deluxe
r = regular
p+d+r = 273
6p+4d + 2r = 836
118+d = r
Replace r with 118+d
p+d+118+d = 273
p +2d = 273-118
p+2d = 155
6p+4d + 2(118+d) = 836
6p+4d + 236+2d = 836
6p +6d = 836-236
6p + 6d = 600
Divide by 6
p+d = 100
d = 100-p
Replace d in p +2d= 155
p +2(100-p) = 155
p+200-2p = 155
-p = 155-200
-p =-45
p =45
45 premium tickets were sold
Answer:
Step-by-step explanation
We get three linear equations from the information given, where
p= number of premium tickets
d = number of deluxe tickets
r = number of regular tickets:
[tex]\left \{ {{p+d+r=273} \atop \\{6p+4d+2r=836} \right.[/tex]
and the applying third r=118+d, we get
[tex]\left \{ {p+d+118+d=273} \atop {6p+4d+2d+236=836}} \right.[/tex]
[tex]\left \{ {{p+2d=115} \atop {6p+6d=600}} \right.[/tex]
Now we get from the upper one
p=115-2d
solving the another equation gives us
6*115-12d+6d=600,
hence d=15
and by replacing
p=115-2*15=85.
85 premium tickets were sold
Type the correct answer in each box. If necessary, use/for the fraction bar(s).
In this triangle, the product of Sin B and tan C is_____, and the product of sin C and tan B is_____.
please view picture at the top
Answer:
1). sinB × tanC = [tex]\frac{c}{a}[/tex]
2). sinC × tanB = [tex]\frac{b}{a}[/tex]
Step-by-step explanation:
From the figure attached,
A right triangle has been given with m∠A = 90°, m(AC) = b, m(AB) = c and m(BC) = a
SinB = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{\text{AC}}{\text{BC}}[/tex]
= [tex]\frac{b}{a}[/tex]
tanB = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{\text{AC}}{\text{AB}}[/tex]
= [tex]\frac{b}{c}[/tex]
SinC = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{\text{AB}}{\text{BC}}[/tex]
= [tex]\frac{c}{a}[/tex]
tanC = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{c}{b}[/tex]
Now sinB × tanC = [tex]\frac{b}{a}\times \frac{c}{b}[/tex]
= [tex]\frac{c}{a}[/tex]
And sinC × tanB = [tex]\frac{c}{a}\times \frac{b}{c}[/tex]
= [tex]\frac{b}{a}[/tex]
How much must be deposited today into the following account in order to have $ 50,000 in 6 years for a down payment on a house? Assume no additional deposits are made. An account with monthly compounding and an APR of 5%
Answer:
The Amount initially deposited is $37046.64
Step-by-step explanation:
A = p (1+r/n)^(nt)
A= final amount= $5000
P = principal amount=
r = rate = 0.05
n = number of times compounded
= 6*12
= 48
t = years= 6
A = p (1+r/n)^(nt)
50000 = p (1+0.05/48)^(48*6)
50000= p(1.001041667)^288
50000= p (1.34965)
50000/1.34965= p
37046.64 = p
The Amount initially deposited is $37046.64
Find the x-intercepts of the parabola with vertex (4,-1) and y-intercept (0,15). Write your answer in this form: (x1,y1),(x2,y2). If necessary, round to the nearest hundredth.
Answer:
(3,0) and (5,0)
Step-by-step explanation:
First let's write the generic model of a parabola:
[tex]y = ax^2 + bx + c[/tex]
Now, using the points (0, 15) and (4, -1), we have:
(0, 15):
[tex]15 = 0a + 0b + c[/tex]
[tex]c=15[/tex]
(4, -1):
[tex]-1 =16a+4b+15[/tex]
[tex]16a + 4b = -16[/tex]
[tex]4a + b = -4[/tex]
The x-coordinate of the vertex is given by the equation:
[tex]x_v = -b/2a[/tex]
[tex]-b/2a = 4[/tex]
[tex]b = -8a[/tex]
Now, using this value of b in the equation [tex]4a + b = -4[/tex], we have:
[tex]4a - 8a = -4[/tex]
[tex]a = 1[/tex]
[tex]b = -8[/tex]
The x-intercepts are where we have y = 0, so:
[tex]0 = x^2 -8x + 15[/tex]
Using Bhaskara's formula, we have:
[tex]\Delta = b^2 - 4ac = 64 -60 = 4[/tex]
[tex]x = -b \±\sqrt{\Delta}/2a[/tex]
[tex]x_1 = (8 + 2)/2 = 5[/tex]
[tex]x_2 = (8 - 2)/2 = 3[/tex]
So the x-intercepts are (3,0) and (5,0).
In interval estimation, the t distribution is applicable only when
a. the population has a mean of less than 30.
b. the sample standard deviation is used to estimate the population standard deviation.
c. the variance of the population is known.
d. the mean of the population is unknown.
Answer:
b. the sample standard deviation is used to estimate the population standard deviation.
Correct since that's the best approximation in order to use the t distribution to estimate the mean
Step-by-step explanation:
For this problem let's analyze the possible options:
a. the population has a mean of less than 30.
False since the mean can be any value and not makes sense
b. the sample standard deviation is used to estimate the population standard deviation.
Correct since that's the best approximation in order to use the t distribution to estimate the mean
c. the variance of the population is known.
False if the variance is know we can use the z distribution for the confidence interval and is not neccessary the t distribution
d. the mean of the population is unknown.
False we create the confidence interval since we don't know the true mean beacuse if we know the mean we don't need to create an interval
5% of adults participate in at least 30 minutes of exercise each day. How likely is it that a randomly chosen adult will exercise 30 minutes each day?
Answer:
5 out of 100 adults so not very likely
0.05 or 5% likely that a randomly chosen adult will exercise 30 minutes each day.
What is Probability?Probability is the possibility of occurrence of a particular event.
In other word, Probability is the ratio of number of favorable incident under an event to the Total number of incident under that event.
[tex]\text{Probability}=\frac{\text{Number of Favorable Cases}}{\text{Number of Total cases}}[/tex]
In this problem it is given that 5% of adults participate in at least 30 minutes of exercise each day.
Then it implies 5 adults out of total 100 adults participate in at least 30 minutes of exercise each day.
Here the event is that one adult exercises 30 minutes each day.
Number of adults in favor is 5
Number of total adults is 100
Probability that one randomly chosen adult will exercise 30 minutes each day is [tex]=\frac{5}{100}=0.05[/tex]
Hence 0.05 or 5% likely that a randomly chosen adult will exercise 30 minutes each day.
Learn more about Probability here -
https://brainly.com/question/25870256
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Which equation is a function of x?
Answer:
x" means that the value of y depends upon the value of x, so: y can be written in terms of x (e.g. y = 3x ). If f(x) = 3x, and y is a function of x (i.e. y = f(x) ), then the value of y when x is 4 is f(4), which is found by replacing x"s by 4"s . this should help I asked my brother for the answer and he told me to put this happy to help :0
