Answer:
$275.6
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.
In this question:
[tex]P = 4000, r = 0.08, t = 12[/tex]
Anually:
[tex]n = 1[/tex]
Then
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(12) = 4000(1 + \frac{0.08}{1})^{12}[/tex]
[tex]A(12) = 10072.68[/tex]
Quarterly:
[tex]n = 4[/tex]
Then
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(12) = 4000(1 + \frac{0.08}{2})^{12*4}[/tex]
[tex]A(12) = 10348.28[/tex]
How much would the future value of the investment increase?
10348.28 - 10072.68 = 275.6
The future value of the investment would increase by $275.6.
K.Brew sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet. Random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale. A random sample of 18 sales receipts for mail-order sales results in a mean sale amount of $74.90 with a standard deviation of $21.75. A random sample of 9 sales receipts for internet sales results in a mean sale amount of $87.30 with a standard deviation of $19.75. Using this data, find the 95% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed.
Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.
Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Step 3 of 3: Construct the 95% confidence interval. Round your answers to two decimal places.
Answer:
Step-by-step explanation:
Step 1. The point estimate is the difference between the the mean amount of mail-order purchases and the mean amount of internet purchases. It becomes
74.9 - 87.3 = - 12.4
Step 2. The formula for determining margin of error is expressed aa
Margin of error = z√(s1²/n1 + s2²/n2)
Where
z = z score
s1 = sample standard deviation for data 1
s2 = sample standard deviation for data 2
n1 = number of samples in group 1
n2 = number of samples in group 2
For a 95% confidence interval, the z score is 1.96
From the information given,
s1 = 21.75
n1 = 18
s2 = 19.75
n2 = 9
z√(s1²/n1 + s2²/n2) = 1.96√(21.75²/18 + 19.75²/9) = 1.96 × 8.343
= 16.35
Step 3. Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
95% Confidence interval = - 12.4 ± 16.35
Victor wants to have at least 10 dozen cookies for the bake sale. Which of the following inequalities correctly represents the number of cookies Victor wants for the bake sale?
c > 10 dozen
c ≥ 10 dozen
c ≤ 10 dozen
c < 10 dozen
Answer:
c ≥ 10 dozen
Step-by-step explanation:
Victor wants to have at least 10 dozen cookies for the bake sale.
In layman terms it can be understood as that Victor wants either 10 dozen cookies or more than that such as 11, 12, 13, 50 , 100 whatever number is greater than 10.
Let the no. of dozen of cookies wanted by him is c
according to condition
if victor wants either 10 dozen cookies
it can be represented mathematically as
c = 10 dozen (1)
_____________________________________
If victor wants no. of dozens of cookies greater than 10 .
it can be written as
c >10 dozen (2) (">" is symbol for greater than . expression simply means value of x should be greater than 10)
______________________________________________
now combining equation one and two, we have
c ≥ 10 dozen . It can means that x can take value starting from 10 to any no greater than..
00:00
Hei has the element shown for his science experiment. How many kilograms of the material does he have?
(1.000 grams = 1 kilogram)
Copper
3,508 g
350.8 kilograms
35.08 kilograms
3.508 kilograms
0.3508 kilograms
Answer:
3.508 kilograms
Step-by-step explanation:
This question can be solved using a rule of three.
We have that each kilogram is 1000 grams. How many kilograms are there for 3508 grams?
1kg - 1000g
xkg - 3508g
[tex]1000x = 3508[/tex]
[tex]x = \frac{3508}{1000}[/tex]
[tex]x = 3.508[/tex]
So the correct answer is:
3.508 kilograms
For the past 50 days, daily sales of laundry detergent in a large grocery store have been recorded (to the nearest 10). Units sold Number of Times. 30 8 40 12 50 15 60 10 70 5 a). Determine the relative frequency for each number of units sold. Please show your work on EXCEL. b). Suppose that the following random numbers were obtained using Excel .12 .96 .54 .55 .66 .77 .88 .99 .33. 304894 Use these random numbers to simulate 10days of sales. Please show your work on EXCEL.
Answer:
The answer to this question can be described as follows:
Step-by-step explanation:
Please find the attachment
Please solve this in a paper and send the answers with steps.
*marking as brainlist.
Answer: 2. 121 could be the dividend and 11 will be the quotient. 3) 35 could be the dividend and -5 could be the divisor.
4) 256 could be the dividend and -16 would be the quotient. 5) 12 could be the divisor and 144 could be the dividend. 6) 17 could be the divisor and and 9 could be the quotient.
Step-by-step explanation:
2. 121/11= 11
3. 35/-5= -7
4.256/-16 =-16
5.144/12= 12
6.153/17=9
a.
In a family with eight children, what is the probability there are at least six boys?
(Hint: Add the three probabilities for either six, seven, or eight boys.)
0.00390625
b. 0.109375
C. 0.03125
d. 0.1445
Answer:
There are many ways to solve this problem, here let's follow the hints
Probability of having exact 6 boys in 8 children:
8C6 x P(boys)^6 x P(girls)^2 = 8C6 x (1/2)^6 x (1/2)^2 =8C6 x (1/2)^8
Probability of having exact 7 boys in 8 children:
8C7 x P(boys)^7 x P(girls)^1 = 8C7 x (1/2)^7 x (1/2)^1 =8C6 x (1/2)^8
Probability of having exact 8 boys in 8 children:
8C8 x P(boys)^8 = 8C8 x (1/2)^8
Add these three, we have the solution
P = (8C6 + 8C7 + 8C8) x (1/2)^8 = (28 + 8 + 1) x (1/2)^8 = 0.1445
=> Option D is correct.
Note: 8C6, 8C7, 8C8 are combination notation.
Hope this helps!
:)
Answer:
the answer is d
Step-by-step explanation:
sam can mow his yard in 5 hours. Lucy can mow the same yard in 3.5 hours. How long will it take them to mow the lawn together?
Answer:
Sam workrate 1/5
Lucy workrate 1/3.5 = reciprocal of 7/2 = 2/7
combined workrate: 1/5 + 2/7 = 17/35
they will mow the lawn in 35/17 = 2 and 1/17 hours
2 hours 3 1/2 mins
Step-by-step explanation:
The article Effect of Environmental Factors on Steel Plate Corrosion Under Marine Immersion Conditions (C. Soares. Y. Garbatov, and A. Zayed, Corrosion Engineering, Science and Technology, 2011 :524? 541 ) describes an experiment in which nine steel specimens were submerged in seawater at various temperatures, and the corrosion rates were measured. The result are presented in the following table (obtained by digitizing a graph).
Temperature (C) Corrosion (mm/y)
26.6 1.58
26.0 1.45
27.4 1.13
21.7 0.96
14.9 0.99
11.3 1.05
15.0 0.82
a. Construct a scatterplot of corrosion (y) versus temperature (x). Verify that a linear model is appropriate.
b. Compute the least-squares line for predicting corrosion from temperature.
c. Two steel specimens whose temperatures differ by 10◦ C are submerged in seawater. By how much would you predict their corrosion rates to differ?
d. Predict the corrosion rate for steel submerged in seawater at a temperature of 20◦ C.
Answer:
Check the explanation
Step-by-step explanation:
a) from the scatter plot in the attached image below, it appears that relationship is approximately linear
b) least square line: that =0.3940+0.0355x
c) for 10 C difference expected difference in corrosion rate =0.0355*10=0.355
d) for x=20 ; predicted temperature =0.3940+0.0355*20=1.1041
e) fitted values are:
X ŷ
26.600 1.3385
26.000 1.3172
27.400 1.3669
21.700 1.1645
14.900 0.9230
11.300 0.7952
15.000 0.9266
8.700 0.7029
8.200 0.6851
Apply distributive property to factor out the greatest common factor.
Explanation:44h-33 I need an answer?
Answer:11(4h-3)
Step-by-step explanation:
44h-33
11(4h-3)
Brainliest for whoever if they get this CORRECT.
c
All the information you need is in the quadratic trinomial ... Read from right to left:
Find factors of 49 which ADD (+) to give 14.
These will be 7 and 7 because: 7 × 7 = 49 and 7 + 7 = 14
The + sign shows that the signs in the brackets will be the SAME, the minus (-) shows that they will be negative:
( x − 7 ) ( x − 7 ) = ( x − 7 ) 2
If 5 potatoes together have a mass of 1 kilogram and 8 pears together have a mass of 1200 grams, which has the greater mass, a potato or a pear?
Patricia, Luca and Dauda shared an amount of money such that, Patricia had twice as much
s Dauda and Luca had GH<600.00 more than Dauda. Il Patricia had GH2,000.00. W
was the average share, to the nearest GH!
Answer:
Answer:
GH 1533
Step-by-step explanation:
Let Dauda's share of the money=x
Patricia had twice as much as Dauda, therefore:
Patricia's share=2x
Luca had GH 600.00 more than Dauda, therefore:
Luca's Share =x+600
If Patricia had GH 2,000.00
Then: 2x=2000
x=1000
Therefore:
Dauda's Share=GH 1000Patricia's share=GH 2000Luca's Share =1000+600=GH 1,600Next, we determine the average share.
[tex]\text{Average Share=}\dfrac{1000+2000+1600}{3}\\=\dfrac{4600}{3}\\\\=$GH 1533.33\\\text{Average Share} \approx $GH 1533 (to the nearest GH)[/tex]
A small company manufactures both large and small grandfather clocks. The company can make no more than 8 clocks a day. They want to build no more than 5 large clocks and no more than 6 small clocks per day. The company makes a profit of $100 on each large clock and $75 on each small clock. The company wishes to maximize its profit.
What is the objective function for this situation?
8 ≥ x + y
8 ≥ 100x + 75y
P ≥ 100x + 75y
P = 100x + 75y
Answer:
P = 100x + 75y
Step-by-step explanation:
The objective is profit, so the objective function is the function that defines profit:
P = 100x + 75y
where x is the number of large clocks made and y is the number of small clocks made per day.
__
Comment on other choices
Inequalities are generally associated with constraints on the manufacturing. Here, those would be ...
0 ≤ x ≤ 5 no more than 5 large clocks0 ≤ y ≤ 6 no more than 6 small clocksx + y ≤ 8 no more than 8 clocks totalThe variables are constrained to be non-negative, because we cannot build a negative number of clocks.
__
To maximize profit in this situation, the maximum possible number of large clocks should be produced, since they are the most profitable. Then the remaining capacity should be used to produce as many small clocks as possible: 5 large clocks and 3 small clocks for a profit of $725 per day.
A manufacturer of bolts has a quality-control policy that requires it to destroy any bolts that are more than 4 4 standard deviations from the mean. The quality-control engineer knows that the bolts coming off the assembly line have mean length of 13 13 cm with a standard deviation of 0.10 0.10 cm. For what lengths will a bolt be destroyed?
Answer:
13.4 centimeters
Step-by-step explanation:
In this case to calculate the distance we must take into account the data that they give us in the exercise.
The final length would be equal to the initial length added to the product of standard deviations from the mean and standard deviation given by the engineer, like this:
L = 13 + 4 * 0.10
L = 13 + 0.4
L 13.4
That means that lengths will a bolt be destroyed when the value is 13.4 centimeters
During Ashland High School basketball games, the snack bar sells both cheese and pepperoni pizza slices. Last night, the snack bar sold 143 slices of pizza. They sold 10 times as many pepperoni slices as cheese slices.
How many slices of cheese pizza did the snack bar sell last night?
slices of cheese pizza
Answer:
13 slices of cheese pizza
Step-by-step explanation:
Consider grouping the slices so there are 10 pepperoni and 1 cheese in each group of 11. Then 143 slices represents 143/11 = 13 groups. Since there is 1 cheese slice in each group, ...
13 slices of cheese pizza were sold
How many grams are in a kilogram
Answer:
1000 grams
Step-by-step explanation:
Rewrite the expression 5(2x+1) using the Distributive Property
Answer:
10x+5
Step-by-step explanation:
5(2x+1)
Using distributive property, which is
A(B+C)=(A×B)+(A×C)
=(5×2x)+(5×1)
=10x+5
Hope it helps :)
A tree grows 20 percent taller every year after it is planted. The tree was 12 feet tall when planted. How tall will it be after 10 years? 74.3 feet 120 feet 144 feet 146.3 feet
Answer:
74.3 feet
Step-by-step explanation:
Each year, the height is multiplied by 1 +20% = 1.20. After 10 years, the original height is multiplied by 1.20^10, so is ...
(12 ft)1.20^10 ≈ (12 ft)(6.19174) ≈ 74.3 ft
Create an equation for the graph Above,Answer should be in y=kx or
y=x+b*
Your answer
Answer:
y=2x
Step-by-step explanation:
Every one x is two y.
Lena is 10 years old. She asks her dad how old he is. He tells her that the lcm of their ages is 14 times the hcf of their ages. She knows that her dad is at least 30 years old but younger than 45. Work out how old her dad is.
Answer:
35
Step-by-step explanation:
Let x represent the HCF of the ages. Then we can have ax = 10 represent Lena's age, and bx can represent her dad's age.
The LCM will be abx = 14x, so we have ab = 14.
Factors of 14 are 1·14 and 2·7. Since the ratio of ages is between 30/10 = 3 and 45/10 = 4.5, we must have b/a in that range. This will be the case for ...
a=2, b=7
For a=2 and ax=10, we have x=5.
The dad's age is bx = 7·5 = 35.
Uta invests an amount into a compound interest investment account that pays 6% a year. After six years, she withdraws her
total balance of $500. Using the formula A - P(1 + r), how much money did Uta initially invest?
$180.00
$320.00
$352.48
$471.70
Answer:
$352.48
Step-by-step explanation:
500 = P(1+6/100)^6
500 = P(1.141851912)
P = 500 / 1.1418519112 = 352.48
The owner of a bicycle store had a sale on bicycles (two-wheelers) and tricycles (three-wheelers). Each cycle had two pedals. When he counted the total number of pedals of the cycles, he got 50. When he counted the total number of wheels of the cycles, he got 64. Explain how you figured out how many tricycles were offered in the sale.
Let x represent number of bicycles and y represent number of tricycles.
We know that a bicycle has 2 pedals and a tricycle has 32 pedals as well.
We have been given that when the owner counted the total number of pedals of the cycles, he got 50. We can represent this information in an equation as:
[tex]2x+2y=50...(1)[/tex]
[tex]2x=50-2y...(1)[/tex]
We know that a bicycle has 2 wheels and a tricycle has 3 wheels.
We have been given that when the owner counted the total number of wheels of the cycles, he got 64. We can represent this information in an equation as:
[tex]2x+3y=64...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]50-2y+3y=64[/tex]
[tex]50+y=64[/tex]
[tex]50-50+y=64-50[/tex]
[tex]y=14[/tex]
Therefore, 14 tricycles were offered in the sale.
ASAP HELP PLEASE GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing!!
Answer:
B
Step-by-step explanation:
Hmm... I would think it is B...
b^2-4ac is discrimant. It is 0?
The table shows the travelling time to work of 50 people.
-Travelling time (t)
in minutes-
0 <t<10
10 < t < 20
20 < t < 30
30 < t < 40
40 < t < 50
-Frequency-
5
15
13
10
7
Calculate an estimate of the mean travelling time.
Answer:
24.8 mins
Step-by-step explanation:
Time > timemark > frequency
0 – 10 > 10/2 = 5 > 5
10 – 20 > (10+20)/2 = 15 > 15
20 – 30 > (20+30)/2 = 25 > 13
30 – 40 > (30+40)/2 = 35 > 10
40 – 50 > (40+50)/2 = 45 > 7
The mean time for the 50 people is given by:
Mean = summation (mid time x frequency) / total frequency
Mean = [5x5 + 15x15 + 25x13 + 35x10 + 45x7] / 50
Mean = [25 + 225 + 325 + 350 + 315] / 50
Mean = 1240 / 50
Mean = 24.8 mins
The mean traveling time of the given data will be 24.8 minutes.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean.
Time > timemark > frequency
0 – 10 > 10/2 = 5 > 5
10 – 20 > (10+20)/2 = 15 > 15
20 – 30 > (20+30)/2 = 25 > 13
30 – 40 > (30+40)/2 = 35 > 10
40 – 50 > (40+50)/2 = 45 > 7
The mean time for the 50 people is given by:
Mean = summation (mid time x frequency) / total frequency
Mean = [5x5 + 15x15 + 25x13 + 35x10 + 45x7] / 50
Mean = [25 + 225 + 325 + 350 + 315] / 50
Mean = 1240 / 50
Mean = 24.8 mins
The mean traveling time of the given data will be 24.8 minutes.
More about the mean link is given below.
https://brainly.com/question/521501
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Which mixes number is equivalent to the improper fraction 17/10
1 7/10 is equivalent to the improper fraction 17/10
Which best explains whether a triangle with side lengths 2 inches 5 inches in 4 inches is an acute triangle
Answer:
The Pythagorean Theorem is a helpful tool that best explains whether a triangle with side lengths 2 inches, 5 inches, and 4 inches is an acute triangle or an obtuse type of triangle. Under the Pythagorean Theorem, a certain triangle is an acute triangle if a^2 + b^2 is greater than c^2.
Step-by-step explanation:
im not sure if this helps but....
Triangle with side 2 in , 4 in and 5 in is an Obtuse angled triangle; it is not an Acute angles triangle.
How are triangles discriminated based on angles?If all of three angles of a triangle are < 90° then triangle is acute.
If one of the angle is of 90° then the triangle is right angled triangle.
If one of the angle is > 90° then triangle is called obtuse triangle.
How to identify if a triangle is acute, right angled or obtuse?
Let we have:
H = biggest side of the triangle
And let we get A and B as rest of the two sides.
Then we get:
If A^2+B^2 > H^2 , then triangle is obtuse
Given:
Length of the sides of the triangle; 2 , 5 and 4inches
If a , b and c is sides of the triangle such that c is the longest side then;
1). if c² > a² + b² implies that triangle is Acute angled.
2). if c² = a² + b² implies that triangle is Right angled.
3). if c² < a² + b² implies that triangle is Obtuse angled.
We have, a = 2 in , b = 4 in and c = 5 in
So, c² = 5² = 25
a² + b² = 2² + 4² = 4 + 16 = 20
therefore; c² > a² + b²
Therefore, Triangle with side 2 in , 4 in and 5 in is an Obtuse angled triangle. It is not an Acute angles triangle.
Learn more about the triangles;
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In triangle DOC, cos(D) = 20/29. What is the value of tan(D)?
Answer:
[tex]tan(D) = \frac{21}{20}[/tex]
Step-by-step explanation:
Step(i):-
Given in triangle DOC
Cos(D) = 20/29
now
[tex]Sec(D) = \frac{1}{Cos(D)} = \frac{1}{\frac{20}{29} } = \frac{29}{20}[/tex]
We Know that trigonometry formulas
[tex]sec^{2}(D) -tan^{2} (D) =1[/tex]
[tex]tan^{2} (D) = sec^{2} (D) -1[/tex]
= [tex](\frac{29}{20} )^{2} -1[/tex]
= [tex]\frac{841 -400}{400} = \frac{441}{400}[/tex]
[tex]tan^2(D) = \frac{441}{400}[/tex]
[tex]tan(D) = \sqrt{\frac{441}{400} } = \frac{21}{20}[/tex]
[tex]tan(D) = \frac{21}{20}[/tex]
2 people are evenly sharing 15 milliliters of perfume.
How much perfume should each person get?
Answer:Each person should get 7.5 milliliters or seven and a half perfume.
Step-by-step explanation:
15/2=7.5
Each person should get 7.5 milliliters or seven and a half perfume.
How to calculate unit price of something?Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in maths and science.
Thus, unit price of something is price of 1 thing.
Suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.
WE know that 2 people are evenly sharing 15 milliliters of perfume.
So, one person will share;
15/2
=7.5
Therefore, Each person should get 7.5 milliliters or seven and a half perfume.
Learn more about unit price here:
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what does linear regression represent
Step-by-step explanation:
In statistics, linear regression is a linear approach to modeling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables). The case of one explanatory variable is called simple linear regression. ... Linear regression has many practical uses.
If a room is 18ft long and 12 ft wide how many 1 ft by 1 ft tiles would be needed to completely cover the floor?
Answer:
216
Step-by-step explanation: If they are 1 by 1 tiles that means that all you need to do is multiply 18 by 12 to get 216. Hope this helps :)
Answer:
216 Tiles
Step-by-step explanation:
18 by 12
8*12=216
Use a Tile Calculator plus this is easy
Wastage: 5%
Tiles with Wastage = 227 Tiles
