Answer:
(a)∴A=$6753.71.
(b)∴A=$1480.24
(c) ∴P=$7424.70
(d)∴P=$49759.62
(e)∴P=$5040.99
(f) ∴P=$2496.11
Step-by-step explanation:
We use the following formula
[tex]A=P(1+\frac rn)^{nt}[/tex]
A=amount in dollar
P=principal
r=rate of interest
(a)
P=$2,500, r=5%=0.05,t =20 years , n= 4
[tex]A=\$2500(1+\frac{0.05}{4})^{(20\times 4)[/tex]
=$6753.71
∴A=$6753.71.
(b)
P=$1,000, r=8% =0.08,t =5 years , n= 2
[tex]A=\$1000(1+\frac{0.08}{2})^{(5\times 2)[/tex]
=$1480.24
∴A=$1480.24
(c)
A=$10,000, r=6% =0.06,t =5 years , n= 4
[tex]10000=P(1+\frac{0.06}{4})^{(5\times 4)}[/tex]
[tex]\Rightarrow P=\frac{10000}{(1+0.015)^{20}}[/tex]
[tex]\Rightarrow P=7424.70[/tex]
∴P=$7424.70
(d)
A=$100,000, r=6% =0.06,t =10 years , n= 12
[tex]100000=P(1+\frac{0.07}{12})^{(10\times 12)}[/tex]
[tex]\Rightarrow P=\frac{100000}{(1+\frac{0.07}{12})^{120}}[/tex]
[tex]\Rightarrow P=49759.62[/tex]
∴P=$49759.62
(e)
A=$100,000, r=10% =0.10,t =30 years , n= 12
[tex]100000=P(1+\frac{0.10}{12})^{(30\times 12)}[/tex]
[tex]\Rightarrow P=\frac{100000}{(1+\frac{0.10}{12})^{360}}[/tex]
[tex]\Rightarrow P=5040.99[/tex]
∴P=$5040.99
(f)
A=$100,000, r=7% =0.07,t =20 years , n= 4
[tex]100000=P(1+\frac{0.07}{4})^{(20\times 4)}[/tex]
[tex]\Rightarrow P=\frac{100000}{(1+\frac{0.07}{4})^{80}}[/tex]
[tex]\Rightarrow P=2496.11[/tex]
∴P=$2496.11
To find the balance A, we use the formula A = P(1 + r/n)^(nt). To find the principal P, we rearrange the formula to P = A / ((1 + r/n)^(nt)).
Explanation:(a) To find the balance A, we can use the formula A = P(1 + r/n)^(nt). Plugging in the given values, we have:
A = $2,500(1 + 0.05/4)^(4*20) = $2,500(1.0125)^80 ≈ $9,005.29
(b) Using the same formula, we can calculate:
A = $1,000(1 + 0.08/2)^(2*5) = $1,000(1.04)^10 ≈ $1,483.11
(c) To find the principal P, we rearrange the formula: P = A / ((1 + r/n)^(nt)). Plugging in the given values, we get:
P = $10,000 / ((1 + 0.06/4)^(4*5)) ≈ $7,772.22
(d) Using the rearranged formula, we can calculate:
P = $50,000 / ((1 + 0.07/12)^(12*10)) ≈ $23,022.34
(e) Since the compounding is monthly, we need to calculate the value of r/n first: r/n = 0.10/12 ≈ 0.0083. Plugging in the values, we have:
P = $100,000 / ((1 + 0.0083)^(12*30)) ≈ $3,791.61
(f) Similarly, we calculate:
P = $100,000 / ((1 + 0.07/4)^(4*20)) ≈ $24,084.48
Polygon ABCDE is an irregular pentagon. Find the perimeter of the polygon. Round to the nearest tenth. Round to give final answer only.
Answer:
12.9
Step-by-step explanation:
AB = [tex]\sqrt{2^{2}+3^{2} }[/tex] = [tex]\sqrt{13}[/tex]
BC = [tex]\sqrt{2^{2}+2^{2} }[/tex] = [tex]2\sqrt{2}[/tex]
CD = [tex]\sqrt{1^{2}+2^{2} }[/tex] = [tex]\sqrt{5}[/tex]
DE = 3
EA = [tex]\sqrt{1^{2} + 2^{2} }[/tex] = [tex]\sqrt{5}[/tex]
The sum of all of these (in decimal form) is (approx.) 12.9
Answer:
13.9 units
Step-by-step explanation:
AB = sqrt(2² + 3²) = sqrt(13)
BC = sqrt(2² + 2² = sqrt(8)
CD = sqrt(1² + 2²) = sqrt(5)
DE = 3
EA = sqrt(1² + 2²) = sqrt(5)
Add all these:
13.9 units
Walt made an extra $7000 last year from a part-time job. He invested part of the money at 3% and the rest at 3.25%. He made a total of $220.00 in interest. How much was invested at 3.25%?
A $4000
B $3000
C $5000
D $3500
Answer: A $4000
Step-by-step explanation:
Let x represent the amount which he invested at 3% interest.
Let y represent the amount which he invested at 3.25% interest.
Walt made an extra $7000 last year from a part-time job. He invested part of the money at 3% and the rest at 3.25%. This means that
x + y = 7000
The formula for determining simple interest is expressed as
I = PRT/100
Considering the account paying 3% interest,
P = $x
T = 1 year
R = 3℅
I = (x × 3 × 1)/100 = 0.03x
Considering the account paying 3.25% interest,
P = $y
T = 1 year
R = 3.25℅
I = (y × 3.25 × 1)/100 = 0.0325y
He made a total of $220.00 in interest., it means that
0.03x + 0.0325y = 220 - - - - - - - -- -1
Substituting x = 7000 - y into equation 1, it becomes
0.03(7000- y) + 0.0325y = 220
210 - 0.03y + 0.0325y = 220
- 0.03y + 0.0325y = 220 - 210
0.0025y = 10
y = 10/0.0025
y = 4000
A home security system is designed to have a 99% reliability rate. Suppose that nine homes equipped with this system experience an attempted burglary. Find the probability that eight or fewer alarms are triggered.
Answer:
0.0865
Step-by-step explanation:
Binomial Problem with n = 9 and p(triggered) = 0.99
And the photo below is the full answer,
I could not insert the fomula and hope it will find you well.
The vector r = xˆi + y ˆj + zkˆ, called the position vector points from the origin (0, 0, 0) to an arbitrary point in space with coordinates (x, y, z). Use what you know about vectors to prove the following: All points (x, y, z) that satisfy the equation Ax + By + Cz = 0, where A, B, and C are constants, lie in a plane that passes through the origin and that is perpendicular to the vector Aˆi + Bˆj + Ckˆ. Sketch this vector and the plane.
Answer:
The vectors r and p = Aˆi + Bˆj + Ckˆ are perpendicular between them. Thus, the plane equation come from the fact that the dot product is equal to zero.
Step-by-step explanation:
The dot product of r and p
r*p = (xˆi + y ˆj + zk)*(Aˆi + Bˆj + Ckˆ) = Ax + By + Cz = 0
HELP !
10 POINTS & BRANLIEST
Answer:
Name the congruent triangles:
triangle RWS, triangle SWT, and triangle TSR
45 percent of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions.
The solution is in the attachment
For married couples living in a certain suburb, the probability that the husband willvote on a bond referendum is 0.21, the probability that his wife will vote in thereferendum is 0.28, and the probability that both the husband and wife will vote is0.15. What is the probability that:
Answer:
niglgapopfart
Step-by-step explanation:
12(5)6$78$???98
Combined with the equation −9x + 3y = 12 creates a system of linear equations with no solution? Select one: A. 18x - 6y = 20 B. 3x - y = -4 C. -16x + 9y = 30 D. 5x + 8y = -1
Answer:
The correct option is A. 18x - 6y = 20
Step-by-step explanation:
A system of two equations has no solution if the lines having these equations are parallel to each other.
Also, two lines [tex]a_1x+b_1y=c_1[/tex] and [tex]a_2x+b_2y=c_2[/tex] are parallel,
If [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]
While,
They coincide ( infinitely many solution ) if [tex]\frac{a_1}{a_2}=\frac{ b_1}{b_2}=\frac{c_1}{c_2}[/tex],
They are non parallel ( a unique solution ) if [tex]\frac{a_1}{a_2}\neq \frac{ b_1}{b_2}\neq \frac{c_1}{c_2}[/tex],
Here, the given equation,
-9x + 3y = 12
Since in lines -9x + 3y = 12 and 18x - 6y = 20,
[tex]\frac{-9}{18}=\frac{3}{-6}\neq \frac{12}{20}[/tex]
Hence, system −9x + 3y = 12, 18x - 6y = 20 has no solution.
In lines -9x + 3y = 12 and 3x - y = -4,
[tex]\frac{-9}{3}=\frac{3}{-1}= \frac{12}{-4}[/tex]
Hence, system −9x + 3y = 12, 3x - y = -4 has infinitely many solutions.
In lines -9x + 3y = 12 and -16x + 9y = 30 ,
[tex]\frac{-9}{-16}\neq \frac{3}{9}\neq \frac{12}{30}[/tex]
Hence, system −9x + 3y = 12, -16x + 9y = 30 has a solution.
In lines -9x + 3y = 12 and 5x + 8y = -1,
[tex]\frac{-9}{5}\neq \frac{3}{8}\neq \frac{12}{-1}[/tex]
Hence, system −9x + 3y = 12, 5x + 8y = -1 has a solution.
A family has a rectangular back yard that measures 5x+4 by 3x-2 they are building a square patio with side lengths that measure x+3. write an expression for the area of grass that will be left in the back yard after the patio is built. show your work.
Answer: 14x² - 4x - 17
Step-by-step explanation:
The formula for determining the area of a rectangle is expressed as
Area = length × width
The rectangular back yard measures 5x + 4 by 3x - 2. This means that the area of the rectangular back yard would be
Area = (5x + 4)(3x - 2)
Area = 15x² - 10x + 12x - 8
= 15x² + 2x - 8
The formula for determining the area of a square is expressed as
Area = length²
Length of square patio = x + 3
Area of square patio = (x + 3)(x + 3)
= x² + 3x + 3x + 9
= x² + 6x + 9
The expression for the area of grass that will be left in the back yard after the patio is built is
15x² + 2x - 8 - (x² + 6x + 9)
= 15x² + 2x - 8 - x² - 6x - 9
= 15x² - x² + 2x - 6x - 8 - 9
= 14x² - 4x - 17
Nick likes to use 12 of a chocolate bar to make a s'more Tasha will only eat a s'more that is made with exactly 25 of a chocolate bar what fraction of a chocolate bar will nick and Tasha use in total if they each eat one s'more
Question:
Nick and Tasha are buying supplies for a camping trip. They need to buy chocolate bars to make s’mores, their favorite campfire dessert. Each of them has a different recipe for their perfect s’more. Nick likes to use 1/2 of a chocolate bar to make a s’more. Tasha will only eat a s’more that is made with exactly 2/5 of a chocolate bar.
Answer:
The fraction of a chocolate bar will Nick and Tasha will use in total if they each eat one s'more is [tex]\frac{9}{10}[/tex] bar.
Step-by-step explanation:
Here, we are meant to learn how to add fractions and to know about the essence of a common denominator
The portion of the chocolate that Nick makes an s'more with is 1/2
The portion of the chocolate that Tasha makes an s'more with is 2/5
Therefore the fraction of the chocolate bar Nick and Tasha use in total if they each eat one s'more is 1/2 + 2/5
Where [tex]\frac{1}{2}[/tex] + [tex]\frac{2}{5}[/tex] multiplying the fraction [tex]\frac{1}{2}[/tex] by [tex]\frac{5}{5}[/tex] and [tex]\frac{2}{5}[/tex] by [tex]\frac{2}{2}[/tex] wee have
[tex]\frac{5}{5}[/tex]× [tex]\frac{1}{2}[/tex] + [tex]\frac{2}{2}[/tex]× [tex]\frac{2}{5}[/tex] = [tex]\frac{5}{10}[/tex] + [tex]\frac{4}{10}[/tex] = [tex]\frac{9}{10}[/tex] bar
Therefore the fraction of the chocolate bar that would be left is
1 bar - [tex]\frac{9}{10}[/tex] bar = [tex]\frac{1}{10}[/tex] bar.
Here is the complete question
Nick and Tasha are buying supplies for a camping trip. They need to buy chocolate bars to make s’mores, their favorite campfire dessert. Each of them has a different recipe for their perfect s’more. Nick likes to use 1/2 of a chocolate bar to make a s’more. Tasha will only eat a s’more that is made with exactly 2/5 of a chocolate bar.
Answer:
Both Nick and Tacha will use 9/10 of the chocolate bar
Step-by-step explanation:
Nicks share of the chocolate bar is 1/2(fraction of the chocolate bar need to make the s'more
And Tasha requires 2/5 to make her own s'more.
Then if both of them share a single chocolate bar,then it will be:
2/5(Tasha's share) + 1/2(Nick's share)
= 9/10 of a single chocolate bar will be used.
In case they were interested to know the amount remaining, it will be:
1 - 9/10 = 1 1/10
Tom is in dire need of a new washing machine. He knows what model he would like to get, but doesn't have the cash to pay for it. He plans to get a line of credit (credit card) at the store when he purchases his new washer. He found four different stores that carry the same washing machine for different prices. The lines of credit they offer also come with different APRs. Tom's primary goal is to minimize his monthly payment as he pays the washing machine off over the next 18 months. From which of the four stores should Tom purchase his washing machine? a. Bob's Nuts and Bolts b. Steve's Scratch and Dent c. Wally's Washing Machines d. Al's Appliances Please select the best answer from the choices provided A B C D
Answer:
b. Steve's Scratch and Dent.
Step-by-step explanation:
Tom should purchase his washing machine from Steve's Scratch and Dent.
A pair of children shoes comes in a box that measures 10.2 cm x 15 cm x 8 cm what is the volume of a shoebox A pair of children shoes comes in a box that measures 10.2 cm x 15 cm x 8 cm what is the volume of a shoebox
Answer:
1224 cm^3
Step-by-step explanation:
The shape of the box is a rectangular prism.
The volume of a rectangular prism is given by the formula below.
volume = length * width * height
volume = 10.2 cm * 15 cm * 8 cm
volume = 1224 cm^3
Final answer:
The volume of a shoebox with dimensions 10.2 cm x 15 cm x 8 cm is calculated by multiplying these three dimensions together, resulting in a volume of 1224 cm³.
Explanation:
To calculate the volume of a shoebox, you multiply its length by its width by its height. For a shoebox with dimensions of 10.2 cm, 15 cm, and 8 cm, the calculation would look like this:
Volume = Length × Width × Height
Volume = 10.2 cm × 15 cm × 8 cm
Volume = 1224 cm³
Therefore, the volume of the shoebox is 1224 cubic centimeters.
Kristen bought a Home Theater for $750 and rented movies every month. The cost of each rental is $4.49 and the membership charges are $12/month. Which equation gives the total amount, A, she spent during the first six months on the number of rented movies, r, including the cost of the Home Theater?
Answer:
A = $822 + $4.49r
Step-by-step explanation:
The question asks to know the equation that describes how much spent in the first six months and also the cost of the home theater.
Firstly, the equation asks to represent the total amount spent by A. She spent $4.49 per rental and made a total of r rentals in the first six months, thus, the total amount of money she spent on rentals is thus 4.49 * r = $4.49r. Now, she also spends $12/month as membership charges. The total membership charges in the first 6 months is thus 6 * 12 = $72
Lastly, she bought the home theater itself $750. Thus, the total amount of money spent A is $750 + $72 + $4.49r
This translates to $822 + $4.49r
In equation form, A = $822 + $4.49r
Faith and Shawna are shopping for shirts. The available styles are short sleeve (s), tank top (t), and long sleeve (L). they make a list to show all possible outcomes if each girl buys a new shirt. is the list complete? Explain. (s,t), (s,s), (s,L), (T,T), (T,S), (T,L), (L,L), (L,T), (L,S)
Answer:
The number of ways of selection of 3 items taking 2 at a time in addition to the possible ways in which each girl selects the same style is 9 different ways. Since the list contains 9 different ways in which each of them can select a style, the list is complete.
Step-by-step explanation:
Here we have the number of ways the available styles can be arranged between each girl is given by the number of permutation of 3 items, taking two at a time plus the number of possible selections where both of them select the same style as follows
We note that the formula for permutation is
[tex]_n[/tex]P[tex]_r[/tex] = [tex]\frac{n!}{(n-r)!}[/tex]
Therefore ₃P₂ = [tex]\frac{3!}{(3-2)!}[/tex] = 6 different ways
The number of possible selections where both of them select the same style is given by
(T, T), (s, s), (L, L) = 3 different ways
Total number of ways = 6 + 3 = 9 ways
Number of different ways available in the list = 9 ways
Therefore the list is complete
Am I correct for the following questions? because I'm not sure if I am.
If not what are the correct choices?
Which of the lines are parallel?
(1) a and b
(2) a and c
(3) a and D
(4) b and c
(5) b and D
(6) c and D
Which of the lines are perpendicular?
(1) a and b
(2) a and c
(3) a and D
(4) b and c
(5) b and D
(6) c and D
Please show all the work on how you got your answers
Answer:
The answer to your question is C and D are parallel
B and C and B and D are perpendiculars.
Step-by-step explanation:
Data
Line A (-2, 3) (2, 2)
Line B (-3, 0) (3, -2)
Line C (2, 4) (0, -2)
Line D (0, 6) (-2, 0)
Process
1.- Calculate the slope of each line
m = (y2 - y1)/(x2 - x1)
Line A m = (2 - 3) / (2 + 2)
m = -1/4
Line B = (-2 - 0) / (3 + 3)
= -2/6
= -1/3
Line C = (-2 -4)/(0 - 2)
= -6/-2
= 3
Line D = (0 - 6) / (-2 - 0)
= -6/-2
= 3
2.- Conclusion
If the slopes are the same, the lines are parallel if are reciprocal, the lines are perpendicular
Line C ║ Line D
Line B ⊥ Line C and Line B ⊥ Line D
The difference of the product of 10 and x and the product of 6 and y is -8. The sum of the product of -5 and x and the product of 3 and y is -1. What are the values of x and y
The system of equations is inconsistent, meaning there is no solution for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfies both equations simultaneously.
The given information can be translated into equations:
1. "The difference of the product of 10 and (x) and the product of 6 and y is -8":
[tex]\[10x - 6y = -8\][/tex]
2. "The sum of the product of -5 and x and the product of 3 and y is -1":
[tex]\[-5x + 3y = -1\][/tex]
Now, we have a system of two equations with two variables:
[tex]\[ \begin{cases} 10x - 6y = -8 \\ -5x + 3y = -1 \end{cases} \][/tex]
Let's solve this system step by step:
Step 1: Eliminate one variable from one of the equations.
Multiply the second equation by 2 to make the coefficients of [tex]\(y\)[/tex] in both equations opposites:
[tex]\[ \begin{cases} 10x - 6y = -8 \\ -10x + 6y = -2 \end{cases} \][/tex]
Now, add the two equations to eliminate [tex]\(y\)[/tex]:
[tex]\[ 0 = -10 \][/tex]
The result is a contradiction, indicating that the system is inconsistent. This means there is no solution that satisfies both equations simultaneously.
Conclusion:
The system of equations is inconsistent, meaning there is no solution for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfies both equations simultaneously. The given information might contain an error or contradiction. Please double-check the equations and conditions provided.
At a banquet, the ratio of the number of boys to the number of girls is 5 : 3. 20 boys leave and the ratio becomes 5 : 4. How many girls are at the banquet?
Answer:
There are 48 girls at the banquet
Step-by-step explanation:
Let the number of boys =x
Let the number of girls=y
Ratio Of boys to girls=5:3
Therefore, x:y=5:3......(1)
If 20 boys leave, the ratio becomes 5:4
Sine number of boys=x
If 20 boys leave, new number = x-20
Therefore, x-20:y=5:4......(2)
From (1),
3x=5y
From Equation (2),
4(x-20)=5y
Therefore: 3x=4x-80
x=80
From (1),
3x=5y
5y=3X80
y=240/5=48
Therefore, there are 48 girls at the banquet
A company has 8 cars and 11 trucks.The state inspector will select 3 cars and 4 trucks to be tested for safety inspections in how many ways can this be done
Answer:
Number of ways to select 3 cars and 4 trucks = 18,480
Step-by-step explanation:
Let x be the number of ways to select 3 cars and 4 truck.
Given:
Total number of cars = 8
Total number of Trucks = 11
We need to find out how many ways can the inspector select 3 cars and 4 truck.
Solution:
Using combination formula.
[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]
Where, n = Total number of object.
m = Number of selected object.
We need to find out how many ways can the inspector select 3 cars and 4 truck from 8 cars and 11 trucks.
So, we write the the combination as given below.
[tex]8C_{3}\times 11C_{4} = Number\ of\ ways\ to\ selection[/tex]
[tex]\frac{8!}{3!(8-3)!} \times \frac{11!}{4!(11-4)!}= x[/tex]
[tex]x = \frac{8\times 7\times 6\times 5!}{3!\times 5!} \times \frac{11\times 10\times 9\times 8\times 7!}{4!\times 7!}[/tex]
Factorial 5 and 7 is cancelled.
[tex]x = \frac{8\times 7\times 6}{6} \times \frac{11\times 10\times 9\times 8}{24}[/tex] ([tex]3! = 6\ and\ 4! = 24[/tex])
[tex]x = (8\times 7) \times (11\times 10\times 3)[/tex] ([tex]\frac{9\times 8}{24}=\frac{72}{24}=3[/tex])
[tex]x=56\times 330[/tex]
x = 18480
Therefore, the Inspector can select 3 cars and 4 trucks in 18,480 ways,
To determine how many ways the state inspector can select 3 cars from 8 and 4 trucks from 11, we need to calculate the combinations separately for each type of vehicle and then multiply them together to find the total number of ways to make both selections simultaneously.
### Selection of Cars:
The number of ways to choose 3 cars from 8 is a combination problem, because the order in which we select the cars does not matter. The formula for combinations, denoted as C(n, k), where n is the total number of items to choose from, and k is the number of items to be chosen, is given by:
C(n, k) = n! / (k! * (n - k)!)
Let's apply this formula to select 3 cars from 8:
C(8, 3) = 8! / (3! * (8 - 3)!) = 8! / (3! * 5!) = (8 × 7 × 6) / (3 × 2 × 1)
Simplify the factorials by canceling out common terms:
C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1) = (8/2) × (7/1) × (6/3) = 4 × 7 × 2 = 56
So, there are 56 ways to choose 3 cars out of 8.
### Selection of Trucks:
Similarly, to choose 4 trucks out of 11 we use the combination formula again:
C(11, 4) = 11! / (4! * (11 - 4)!) = 11! / (4! * 7!) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1)
Simplify the factorials:
C(11, 4) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1) = (11/1) × (10/2) × (9/3) × (8/4) = 11 × 5 × 3 × 2 = 330
So, there are 330 ways to choose 4 trucks out of 11.
### Total Ways:
To find the total number of ways to select both the cars and trucks for inspection, we multiply the number of ways to choose the cars by the number of ways to choose the trucks:
Total number of ways = number of ways to choose cars × number of ways to choose trucks
Total number of ways = 56 (from choosing cars) × 330 (from choosing trucks)
Total number of ways = 56 × 330 = 18480
Therefore, the state inspector can select 3 cars out of 8 and 4 trucks out of 11 in 18,480 different ways.
The sample consisted of 50 night students, with a sample mean GPA of 3.02 and a standard deviation of 0.08, and 25 day students, with a sample mean GPA of 3.04 and a standard deviation of 0.06. The test statistic is:
Answer: The test statistic is t= -0.90.
Step-by-step explanation:
Since we have given that
n₁ = 50
n₂ = 25
[tex]\bar{x_1}=3.02\\\\\bar{x_2}=3.04\\\\\sigma_1=0.08\\\\\sigma_2=0.06[/tex]
So, s would be
[tex]s=\sqrt{\dfrac{n_1\sigma_1^2+n_2\sigma_2^2}{n_1+n_2-2}}\\\\s=\sqrt{\dfrac{50\times 0.08^2+25\times 0.06^2}{50+25-2}}\\\\s=0.075[/tex]
So, the value of test statistic would be
[tex]t=\dfrac{\bar{x_1}-\bar{x_2}}{s(\dfrac{1}{n_1}+\dfrac{1}{n_2})}\\t=\dfrac{3.02-3.04}{0.074(\dfrac{1}{50}+\dfrac{1}{25})}\\\\t=\dfrac{-0.04}{0.074(0.02+0.04)}\\\\t=\dfrac{-0.04}{0.044}\\\\t=-0.90[/tex]
Hence, the test statistic is t= -0.90.
Multiply.
−3y(5y3+11y2−y+8)
Express the answer in standard form.
Final answer:
The result of multiplying −3y by the polynomial (5y³+11y²−y+8) is −15y⁴ − 33y³ + 3y² − 24y when expressed in standard form.
Explanation:
To multiply the expression −3y(5y³+11y²−y+8), we will distribute the −3y across each term inside the parentheses. The process involves the use of the distributive property, often also known as the multiplication of polynomials. Here are the steps:
Multiply −3y by 5y³ to get −15y⁴.
Multiply −3y by 11y² to get −33y³.
Multiply −3y by −y to get 3y².
Multiply −3y by 8 to get −24y.
Combining all these products gives us the expression in standard form:
−15y⁴ − 33y³ + 3y² − 24y
Abraham throws a ball from a point 40 m above the ground. The height of the ball from the ground level after ‘t' seconds is defined by the function h(t) = 40t – 5t2. How long will the ball take to hit the ground?
Answer:
8.899s
Solve: -5t^+40t+40
4-2√2 is the time taken by the ball to hit the ground.
What is Distance?Distance is the total movement of an object without any regard to direction
Given that Abraham throws a ball from a point 40 m above the ground. The height of the ball from the ground level after ‘t' seconds is defined by the function h(t) = 40t – 5t². then we need to find the time for ball to hit the ground.
The given function is
h(t)=40t-5t²
Let h(t)=40
We get,
40t-5t²=40
5t²-40t+40=0
t²-8t+8=0
(t-4)²=8
t-4=±√8
t=±√8+4
t=√8+4; t=4-√8
By considering the reality we know t>0
t=4-2√2
Hence t=4-2√2 is the time taken by the ball to hit the ground.
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Which statement is true? Use the diagram to answer.
Select one:
a. are alternate interior angles.
b. are same-side interior angles.
c. are alternate interior angles.
d. are same-side interior angles.
The statement that is: a. ∠1 and ∠5 are alternate interior angles.
What is the alternate interior angles ?
A pair of angles that are inside the two parallel lines and on opposing sides of the transversal line are known as alternate internal angles. 1 and 5 are situated on opposite sides of the transversal line and inside the parallel lines in the diagram. They are thus different internal angles.
The fact that alternate inner angles have the same measure and are congruent is significant.
Therefore the correct option is A.
A circle in the xyxyx, y-plane has its center at the point (-6,1)(−6,1)(, minus, 6, comma, 1, ). If the point (7,12)(7,12)(, 7, comma, 12, )lies on the circle, what is the radius of the circle? Round the answer to the nearest tenth.
Answer:
r=17.0
Step-by-step explanation:
In a circle with center (h,k) and any point (x,y) on the circle, the radius of the circle is given as:
[tex](x -h)^2 + (y - k)^2 =r^2[/tex]
Center (h,k)=(-6,1)
(x,y)=(7,12)
[tex]r^2=(x -h)^2 + (y - k)^2 \\r^2=(7 -(-6))^2 + (12 - 1)^2\\r^2=(7 +6)^2 + 11^2\\r^2=13^2 + 11^2=169+121=290\\r=\sqrt{290}=17.03[/tex]
radius, r=17.0 (to the nearest tenth)
The radius of the circle with center (-6,1) and passing through the point (7,12) can be found using the distance formula. The radius, or distance between these two points, calculates to approximately 17.0 units when rounded to the nearest tenth.
Explanation:In Mathematics, you can determine the radius of a circle if you have the coordinates of the center and a point on the circle. Here, we have the center of the circle at (-6,1) and a point (7,12) lying on the circle. We will use the distance formula to find the radius, r, which is essentially the distance between these two points.
Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
By substituting the given points into the distance formula, we get
Radius (r) = sqrt((7 - (-6))^2 + (12 - 1)^2)
Sample calculation: r = sqrt((7 - (-6))^2 + (12 - 1)^2) = sqrt(169 + 121) = sqrt(290). Therefore, the radius of the circle, rounded to the nearest tenth, is approximately 17.0 units.
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Death Valley CA is 282 feet below sea level. Black Mountain, KY is 750 feet above sea level . How many more feet above sea level is Black Mountain than Death Valley?
From the Death Valley to Black Mountain, it rises 1032 feet because Death Valley is 1032 ft lower than Black Mountain in elevation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
Death Valley CA is 282 feet below sea level.
Black Mountain, KY is 750 feet above sea level.
Death Valley (282ft) + 282ft = sea level (0).
0 + 750ft = Black Mountain (750ft).
282ft + 750ft = 1032ft.
From Death Valley to Black Mountain, it rises 1032 feet. Death Valley is 1032 ft lower than Black Mountain in elevation.
Thus, from the Death Valley to Black Mountain, it rises 1032 feet because Death Valley is 1032 ft lower than Black Mountain in elevation.
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Diedre drew a quadrilateral with 4 right Angles and opposite sides of the same length. Name all the kinds of polygons that could be Diedre's quadrilateral.
Answer:
The answer to the question is
The kinds of polygons that could be Diedre's quadrilateral are rectangle and square
Step-by-step explanation:
We note the conditions of the polygon as thus
Number of sides = 4, Which include trapezoid, square, rectangle
Size of angles = 90 ° which eliminates trapezoid
Sizes of opposite sides = Equal opposite sides, includes square and rectangle
With the above we conclude that the possible polygons in Diedre's quadrilateral are rectangle and square
The solution set for -18 < 5x - 3 is _____.
-3 < x
3 < x
-3 > x
3 > x
Solution set for given inequality [tex]-18 < 5x - 3[/tex] is [tex]-3 < x[/tex].
What is solution set?" Solution set is defined as the such set of values which satisfies the given equation or any inequality."
According to the question,
Given inequality,
[tex]-18 < 5x - 3[/tex]
Add 3 both the side of inequality we get,
[tex]-18 +3 < 5x - 3 +3[/tex]
[tex]= -15 < 5x[/tex]
Divide both the side by 5 to get the solution set ,
[tex]-3 < x[/tex]
Hence, solution set for given inequality [tex]-18 < 5x - 3[/tex] is [tex]-3 < x[/tex].
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Final answer:
The solution set for the inequality -18 < 5x - 3 is -3 < x, after adding 3 to both sides and then dividing by 5.
Explanation:
The student has asked to find the solution set for the inequality -18 < 5x - 3. To solve this, we first isolate the variable x by adding 3 to both sides of the inequality:
-18 + 3 < 5x - 3 + 3
-15 < 5x
Then, we divide both sides by 5 to solve for x:
-15 / 5 < 5x / 5
-3 < x
This simplifies to the inequality x > -3, which means that the correct answer is: -3 < x.
Which of the following equations represents the line with a slope of 5/2 and a y-intercept of 1?
y = 5/2x + 1
y = 2/5x - 1
y = 2/5x + 1
y = 5/2x - 1
Answer:
[tex]y = \frac{5}{2} x + 1[/tex]HOPE U UNDERSTOOD
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Joan is building a sandbox in the shape of a regular pentagon. The perimeter of the pentagon is 35y4 – 65x3 inches. What is the length of one side of the sandbox? 5y – 9 inches 5y4 – 9x3 inches 7y – 13 inches 7y4 – 13x3 inches
Answer:
Step-by-step explanation:
given that Joan is building a sandbox in the shape of a regular pentagon.
The perimeter of the pentagon is
[tex]35y^4 - 65x^3[/tex]inches.
Since regular pentagon we know that all sides are equal and there are totally five sides.
Perimeter of regular pentagon = 5*side
= 5a where a = length of side
Equate 5a to given perimeter to get
[tex]5a=35y^4 - 65x^3\\[/tex]
divide by 5
[tex]a=\frac{35y^4 - 65x^3}{5} \\=7y^4-13x^3[/tex]
Answer:
D. 7y^4 - 13x^3 inches
Jane invested $2500 into an RRSP that earned interest at 6% compounded semi annually for ten years a) find the balance of account at end of peroid b)how much interest is earned c) what is effective rate of interest
Answer:
Step-by-step explanation:
PV = $2500
r = 6%
Compounded semi annually for ten years => number of periods: 10*2 = 20
a. the balance of account at end of peroid (FV)
FV = PV [tex](1+r)^{n}[/tex] = 2500[tex](1+0.06)^{20}[/tex] = 8017.8386
b. How much interest is earned; FV - PV = 8017.8386 - 2500 = 5517.8686
c. what is effective rate of interest :
Answer:
The answers to the question are
a) The balance of account at end of period $4515.278
b) The interest earned $2515.278
c) The effective rate of interest is 0.0609 or 6.09 %
Step-by-step explanation:
To solve the question
a) Here we have the compound interest formula given by
[tex]A = P(1+\frac{r}{n})^{nt}[/tex] Where,
P = Initial investment = $2500
r = Annual interest rate = 6% =0.06
n = Number of compounding periods per year = 2
t = Number of years 10
From which we have
[tex]A = 2500*(1+\frac{0.06}{2})^{2*10}= 2500(1.03)^{20}[/tex] = $4515.278
The balance of account at end of period $4515.278
b) Interest earned = Balance - initial investment = $4515.278 - $2500 = $2515.278
c)
The effective interest rate is the interest rate that accrues to an investment or loan as a result of the compounding the interest for a given time period of time. It is also known as the effective annual interest rate
The effective rate of interest is given by
Effective rate = [tex](1+\frac{r}{n} )^n -1[/tex]Where
r = Annual interest rate
n = Number of annual compounding periods
this gives [tex](1+\frac{0.06}{2} )^{2} -1[/tex] = 0.0609 = 6.09 %
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Answer:
c=f(x)−ax^2−bx
Step-by-step explanation:
Answer:
C=1
Step-by-step explanation:
Put the first point in the equation y=ax^2+bx+c where x=0 and y=1 you get
1=a*0+b*0+c
1=c