Answer:
The person must leave the money for 11.8 years until the investment reaches 1600 dollars.
Step-by-step explanation:
Given that a person invests 1000 dollars in a bank, and the bank pays 4% interest compounded quarterly, to determine to the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 1600 dollars the following calculation must be done:
1000 x (1 + 0.04 / 4) ^ Xx4 = 1600
1000 x 1.01 ^ 4X = 1600
1010 ^ 4X = 1600
X = 11.8
Therefore, the person must leave the money for 11.8 years until the investment reaches 1600 dollars.
A group of 4 frieds decide to attend a night of dinner and dancing on a cruise ship. The dinner and dance cruise will last 4 hours. The ship travels 18 km upstream and then travels back to the starting point. The river has a current of 2 km an hour. What is the cruise ship's speed and how long was the upstream journey
Answer:
The speed of the cruise ship relative to the current is approximately 9.424 kilometers per hour.
The cruise ship's will need 2.425 hours for its upstream journey.
Step-by-step explanation:
The total time of the cruise ([tex]t[/tex]), in hours, is the sum of the times for the upstream ([tex]t_{u}[/tex]) and downstream journeys ([tex]t_{d}[/tex]), in hours. Let suppose that both river and cruise ship travel at constant velocity, the cruise ship travels against the current in its upstream journey, whereas it is in favor of the current in the downstream journey, meaning that:
[tex]t = t_{u} + t_{d}[/tex]
[tex]t = \frac{x}{v_{S/C} - v_{C}} + \frac{x}{v_{S/C} + v_{C}}[/tex] (1)
Where:
[tex]v_{C}[/tex] - Speed of the current, in kilometers per hour.
[tex]v_{S/C}[/tex] - Speed of the cruise ship relative to the current, in kilometers per hour.
If we know that [tex]t = 4\,h[/tex], [tex]x = 18\,km[/tex] and [tex]v_{C} = 2\,\frac{km}{h}[/tex], then we have the following expression:
[tex]4\,h = (18\,km)\cdot \left(\frac{1}{v_{S/C} - 2\,\frac{km}{h} } + \frac{1}{v_{S/C}+2\,\frac{km}{h} }\right)[/tex]
[tex]\frac{2}{9} = \frac{1}{v_{S/C}-2} + \frac{1}{v_{S/C}+2}[/tex]
[tex]\frac{2}{9} = \frac{2\cdot v_{S/C}}{v_{S/C}^{2}-4}[/tex]
[tex]2\cdot v_{S/C}^{2} - 8 = 18\cdot v_{S/C}[/tex]
[tex]2\cdot v_{S/C}^{2}-18\cdot v_{S/C}-8 = 0[/tex]
The roots of the second order polynomial are, respectively:
[tex]v_{S/C,1} \approx 9.424\,\frac{km}{h}[/tex], [tex]v_{S/C,2} \approx -0.424\,\frac{km}{h}[/tex]. Since the speed is the magnitude of the velocity, a realistic solution must be a positive quantity and the solution is:
[tex]v_{S/C} \approx 9.424\,\frac{km}{h}[/tex]
The speed of the cruise ship relative to the current is approximately 9.424 kilometers per hour.
And the time needed for the upstream journey is:
[tex]t_{u} = \frac{x}{v_{S/C}- v_{C}}[/tex] (2)
If we know that [tex]x = 18\,km[/tex], [tex]v_{S/C} \approx 9.424\,\frac{km}{h}[/tex] and [tex]v_{C} = 2\,\frac{km}{h}[/tex], then time for the upstream journey is:
[tex]t_{u} = \frac{18\,km}{9.424\,\frac{km}{h}-2\,\frac{km}{h} }[/tex]
[tex]t_{u} = 2.425\,h[/tex]
The cruise ship's will need 2.425 hours for its upstream journey.
A scale factor of 5 was applied to this figure. What would be the new length of the height and width of the triangle?
Answer:
8 units
Step-by-step explanation: Hope it helps.
zoom in if beaded and pls help pronto
Answer:
F. six times a number less 9
Step-by-step explanation:
The statement doesn't make sense.
it would make sense if it was:
six times a number less than 9
9 - 6x
Others would make sense:
8(6/3)
x - 12
5x = 30
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
What is the greatest common factor between 18 36 27
Answer:
GCF = 9
Step-by-step explanation:
18/9 = 2
36/9 = 4
27/9 = 3
Find all the missing elements.
Round to the nearest tenth.
C
a
b
a = 5
b = 2
C = 6
B
A
С
A = [?]° B = [ 1° C = [ 1°
Answer: A= 51.3 B= 18.2 C=110.5
Step-by-step explanation:
Simplify the expression by combining like terms.
Write the terms from the highest to the lowest
power of the variable.
-9x^2 + 19x - 9x + 6 - 17x^2 + 25 + 10x^2 + 3x
Answer:
The answer: is 118
I hope this help you enjoy :D
Step-by-step explanation:
Need help urgently right now
Answer:
m<CAD= 23 degrees
m<CAB= 67 degrees
Step-by-step explanation:
From the diagram shown;
arc ADC + arc CAB = 360
226 + arcCAB = 360
arc CAB = 360 - 226
arc CAB = 134
Also arcCD = 226 - 180
arcCD = 46degrees
Since <A = 1/2arcCD
m<CAD = 1/2* 46
m<CAD= 23 degrees
m<CAB = 90 - <A
m<CAB = 90 - 23
m<CAB = 67degrees
The accounting department analyzes the variance of the weekly unit costs reported by two production departments. A sample of 16 cost reports for each of the two departments shows cost variances of 2.8 and 5.7, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance
Answer:
We can conclude that the result is significant and production differ in cost variance.
Step-by-step explanation:
Given :
n1 = 16
n2 = 16
s1² = 5.7
s2² = 2.8
α = 0.10
H0 : σ1² = σ2²
H1 : σ1² ≠ σ2²
The test statistic :
Ftest = s1² / s2² =
Ftest = 5.7 / 2.8
Ftest = 2.036
Using the Pvalue from Fratio calculator :
df numerator = 16 - 1 = 15
df denominator = 16 - 1 = 15
Pvalue(2.036, 15, 15) = 0.0898
Pvalue = 0.0898
Since the Pvalue is < α ; We can conclude that the result is significant and production differ in cost variance.
A dot plot titled Number of Hours Spent on Homework goes from 1 to 6. There is 1 dot above 1, 5 dots above 2, 6 dots above 3, 4 dots above 4, 1 dot above 5, and 1 dot above 6. What is a dot plot and how do you read it? Check all that apply. A dot plot is a simple plot that displays data values as dots above a number line. Dot plots show the frequency with which a specific item appears in a data set. 3 students spent 4 hours on homework. 5 students spent 2 hours on homework. Dot plots show the distribution of the data. Students spent 1 to 6 hours on homework.
1.) Apply the distributive property and simplify the expression : 4(2x + y)
Your answer
Answer:
8x + 28
Step-by-step explanation:
increased in price by 1/4. After the increase it was priced at £85 what was the original price of the tshirt?
PLEASE HELP!!! WILL MARK BRAINLIEST!!!
What is the explicit rule for the sequence?
- 114, -109, -104, -99,
An= -5n - 109
An= -5n - 119
An= 5n - 119
An= 5n - 109
Answer:
5n - 119
Step-by-step explanation:
First, we notice that the sequence is going up by 5, so we could rule out 2 answers: -5n - 109, and -5n -119 (They go by -5). Then all we have to find is the constant, -119 or -109. Well we could rule out -109 because -114 is included in the sequence, and if we start by -109 and start counting up, we will never get to -114. So, the solution is 5n - 119
We have been given that - 114, -109, -104, -99. the explicit rule for the sequence is 5n - 119.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
[tex]T_n = a + (n-1)d[/tex]
(for all positive integer values of n)
And thus, the common difference is
[tex]T_{n+1} - T_n[/tex]
for all positive integer values of n
We have been given that
- 114, -109, -104, -99,
a = -114
[tex]T_n = a + (n-1)d[/tex]
T = -114 + (n - 1)5
T = 5n - 119
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For what values of X are the statements below true
A. 1x>x+1
B. |1-x| > 3
C.|x-15| < 0
Answer:
See solutions below
Step-by-step explanation:
For what values of X are the statements below true
A. 1x>x+1
x >x+1
x-x>1
0x > 1
x > 1/0
X >∞
B) |1-x|>3
The fucntion can both be positive and negative
For the negative function
-(1-x) > 3
-1+x > 3
x > 3+1
x > 4
For the positive function
1-x > 3
-x > 3 - 1
-x > 2
x < -2
Hence the required solutions are x > 4 and x < -2
c) For the equation
|x-15| < 0
-(x - 15) < 0
-x + 15 < 0
-x < -15
x > 15
Also x-15 < 0
x < 0+15
x < 15
Hence the required solution is x > 15 and x < 15
Can someone please help me I will mark u brilliant for both
Answer:
1. 1/2
2. 4
Step-by-step explanation:
2. 14x = 56
56 / 14
x = 4
mz3 = 10x and mz5= 12x - 25.
Answer:
[tex]x = 12.5[/tex] degrees
Step-by-step explanation:
Since lines a and b are parallel, we have that angles 3 and 5 are congruent, that is, they have the same measure.
We have that:
[tex]m<3 = 10x[/tex]
[tex]m<5 = 12x - 25[/tex]
Value of x:
Since they are congruent:
[tex]m<3 = m<5[/tex]
[tex]10x = 12x - 25[/tex]
[tex]-2x = -25[/tex]
[tex]2x = 25[/tex]
[tex]x = \frac{25}{2}[/tex]
[tex]x = 12.5[/tex] degrees
The two triangles below are congruent by which case of congruence?
O SSA
O SAS
O ASA
SSS
Answer:
SSS
Step-by-step explanation:
SSS
Find the measure of ⦨ R . Round to nearest whole degree. Choose which method to use: Law of Sines or Use Law of Cosines.
Answer:
Law of sine
Angle R = 34°
Step-by-step explanation:
From the question given above, the following data were obtained:
Side opposite angle Q (q) = 54 ft
Angle Q = 96 °
Side opposite angle R (r) = 30 ft
Angle R =?
The value of angle R can be obtained by using the law of sine as illustrated below:
r / Sine R = q / Sine Q
30 / Sine R = 54 / Sine 96
Cross multiply
54 × Sine R = 30 × Sine 96
54 × Sine R = 30 × 0.9945
54 × Sine R = 29.835
Divide both side by 54
Sine R = 29.835 / 54
Sine R = 0.5525
Take the inverse of Sine
R = Sine¯¹ 0.5525
R = 34°
Thus, the value of angle R is 34°
What is the spread of the data in the dot plot?
Number of Apples in Each Bag
10
11
12
13
14
15
from 0 to 5
Ofrom 10 to 15
ОООО
O from 12 to 15
O from 0 to 6
Answer:
from 10 to 15
Step-by-step explanation:
because when your finding the spread you take the highest and lowest number.
Marlon's Cat will be having four kittens. Marlon Performs a simulation by tossing a coin to model whether these kittens will be male or female. Let heads (H)= female kittens and Let tails (T) = male kitten
Answer:
20
Step-by-step explanation:
Answer:
2/10 = 20%
Step-by-step explanation:
Can someone please help me with question 5 and 6 Please
Answer:
x=36
y=54
Step-by-step explanation:
tan(x) = 15/21
x=tan^-1(15/21)
x=35.537677792
x~36
To solve for y, either repeat the same process:
tan(y)=21/15
y=tan^-1(21/15)
y=54.462322208
y~=54
OR
180-90-x=y
180-90-36=54
y=54
For each of the following research scenarios, decide whether the design uses a related sample. If the design uses a related sample, identify whether it uses matched subjects or repeated measures. (Note: Researchers can match subjects by matching particular characteristics, or, in some cases, matched subjects are naturally paired, such as siblings or married couples).
A researcher is interested in whether people eat more or less when they are in a hurry. The researcher collects a random sample of 80 adults and invites them to eat two (identical) free meals one month apart. For one of the meals, no time restriction is placed on the meal. For the other meal, participants are told when their meal is served that they have only 10 minutes until another group is due to sit down. Half of the participants eat their hurried meal first; the other half eat it second. The researcher compares the amount eaten at each sitting. The design described_____.
John Cacioppo was interested in possible mechanisms by which loneliness may have deleterious effects on health. He compared the sleep quality of a random sample of lonely people to the sleep quality of a random sample of nonlonely people. The design described____.
a. uses a related sample (repeated measures).
b. uses a related sample (matched subjects).
c. does not use a related sample.
Answer:
A.) uses a related sample (repeated measures).
B.) does not use a related sample.
Step-by-step explanation:
The first scenario uses a related sample whereby same subjects were used to over the course of each related experiment (comparing if people eat more or less when in a hurry). After the completion of both experiment, we'll have two different reading for each subject which a b further be used to compare the difference in consumption when in a hurry and when not.
The second scenario here fails to employ a related sample design as the the subjects used have contrasting characteristics, a group consisting of lonely people and another consisting of those who aren't lonely.
PLEASE HELP
Select the correct answer from each drop-down menu.
8 cm
4 cm
9 cm
3 cm
3 cm
6 cm
The given composite shape has an area of
cm² and a perimeter of
cm.
Answers:
Area = 78 cm^2
Perimeter = 42 cm
============================================================
Explanation:
Refer to the diagram below.
I've added points and labels, along with the dashed lines to break up the figure into three rectangles. The points in blue are the corner points of the original figure. The red points help set up the dashed lines.
Along the very top, we have BC = 8 cm, which breaks down into BK = 6 and KC = 2. Opposite of side KC is GJ = 2. For any rectangle, the opposite sides are always the same length.
Side AB = 9 cm. The three vertical sides of CD, EF, and GH all must add to get 9 cm in total, since the right side is the same height as the left side. We are given that EF = 3 and GH = 3, which must mean CD = 3 as well.
Through similar logic, the sides BC = 8 and DE = 4 add to 8+4 = 12 cm total. This total distance across the top must match the total distance along the bottom; i.e. the bottom horizontal sides of AH and GF must add to 12 as well. We are given AH = 6, so GF = 6 also.
Recall earlier we found GJ = 2. If GF = 6, then that leads to JF = 4.
In other words, GJ+JF = 2+4 = 6 = GF.
All of this is visually shown in the diagram shown below.
Once you have the diagram set up as shown, it's fairly straight forward from here. Compute the area of each of the three smaller rectangles and then add up those smaller areas to get the overall area.
I'll work from left to right to find the areas:
Rectangle ABKH has area of 9*6 = 54 cm^2Rectangle GKCJ has area 6*2 = 12 cm^2Rectangle JDEF has area 3*4 = 12 cm^2The total area of the composite figure is therefore: 54+12+12 = 78 cm^2
---------------------------
The perimeter is the sum of all the external sides. We'll ignore the dashed lines as they are not exterior segments.
perimeter = sum of exterior sides
perimeter = AB+BC+CD+DE+EF+FG+GH+HA
perimeter = 9+8+3+4+3+6+3+6
perimeter = 42 cm
Notes:
To keep things organized, I'm working clockwise when going from AB to BC to CD etcThere are a total of 8 exterior sides being added up to get the perimeter.The table below represent a linear relationship between x and Y. Which statement correctly compares the rate of change of the values in the table with the rate of change of the equation Y=2X+107?
Answer:
c. the rate of change in the table is greater than the rate of change of y=2x+10
Step-by-step explanation:
rate of change in table is 3x and the given one is 2x
Answer:
c. the rate of change in the table is greater than the rate of change of y=2x+10
Step-by-step explanation:
rate of change in table is 3x and the given one is 2x
A motorcycle can go 40 miles using one gallon of gas. About how many gallons of gas will be used to go 325 kilometers?
Answer:
5.025 gallons
Step-by-step explanation:
Step 1: Convert 325 kilometers to miles
[tex]325 = 201[/tex]
Step 2: Set up a fraction
[tex]\frac{40}{1}=\frac{201}{x}[/tex]
Step 3: Cross multiply
[tex]40 \times x = 40\\\\201 \times 1 = 201[/tex]
Step 4: Divide the values left
[tex]201 \div 40\\\\= \frac{201}{40}\\\\= 5.025[/tex]
Therefore, about 5.025 gallons of gas will be used to go 325 kilometers.
HELP ASAP I WILL GIVE BRAINIEST AND 100 POINTS PLEASEE
Answer:
What are the options tho?
Step-by-step explanation:
Answer:
1/10?
Step-by-step explanation:
total:250
red:25
25/250 simplified=1/10
the spinner below is spun twice. What is the probability of the arrow landing on a 3 and then an odd number?
Please help
Answer:
4/3
Step-by-step explanation:
What is the explicit formula for this sequence?
-9, -3, 3, 9, 15, ...
Answer:
What is the explicit formula for this sequence? -9, -3, 3, 9, 15, ... - did not match any news results.
Suggestions:
Make sure that all words are spelled correctly.
Try different keywords.
Try more general keywords.
Try fewer keywords
Evaluate each series.
50 points and brainless!
Answer:
Sum of n terms of a GP:
Sₙ = a₁(rⁿ - 1)/(r - 1)#1
a₁ = 5r = 2n = 9S₉ = 5(2⁹ - 1)/(2 - 1) = 5(511) = 2555Correct choice is C
-----------------------------
#2
a₁ = 12r = 1/2n = 5S₅ = 12(1 - (1/2)⁵)/(1 - 1/2) = 12(31/32)/(1/2) = 23.25Correct choice is A
write the equation for a parabola with a focus at (-3,-5) and a directrix at x=-7
x=
Answer:
hope this helps
Step-by-step explanation:
equation for a parabola is:
What is parabola?The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus.
Given: focus= (3,-5), directrix at x =-7.
To find equation of parabola we will use distance formula,
√(x+7)²=√(x+3)² + (y+5)²
(x+7)²=(x+3)² + (y+5)²
x²+14x+49= x²+9+6x + (y+5)²
8x + 40 = (y+5)²
x= (y+5)²/8 -5
Hence, the equation of parabola is x= (y+5)²/8 -5
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(x-4)2 + 3x at the value x = 7
Answer:
30
Step-by-step explanation:
x = 7
( x - 4 )^2 + 3x
= ( 7 - 4 )^2 + 3 ( 7 )
= 3^2 + 21
= 9 + 21
= 30
Answer:
The answer is 27
Step-by-step explanation:
(X-4)2 + 3x
x is equal to 7
first substitute the values.
(7-4)2 + 3 x 7
solve-
(3)2 + 21
=27