[tex]6000 = 3000(1+0.0424)^{t}[/tex]
t = 16.73 years
Step-by-step explanation:This can be solved using the "exponential growth" formula.
Steps:
A = Final Amount
S = Starting Value
r = rate
c = times in a year ( c = 1 in this equation which is why it's not shown in the actual equation )
1. [tex]A=S(1+\frac{r}{c})^{ct}[/tex] → cancel out S → [tex]\frac{A}{S} = \frac{S(1+\frac{r}{c})^{ct} }{S}[/tex]
2. [tex]\frac{A}{S} = {(1+\frac{r}{c})^{ct} }[/tex] → sperate ct from equation by logging both sides (logging a value with an exponent brings the exponent in front of log) → [tex]log(\frac{A}{S}) = ctlog(1+\frac{r}{c})[/tex]
3. [tex]log(\frac{A}{S}) = ctlog(1+\frac{r}{c})[/tex] → transfer right side log to left side along with the c value to only have t remaining → [tex]\frac{log(\frac{A}{S})}{clog(1+\frac{r}{c})} = \frac{ctlog(1+\frac{r}{c})}{clog(1+\frac{r}{c})}[/tex]
4. Solve for answer: [tex]\frac{log(\frac{A}{S})}{clog(1+\frac{r}{c})} = t[/tex]
Answer: its option D) 17 years
Step-by-step explanation: the answer is 16.7 but you round it up because thats not an option
a rectangle measures 1 1/4 by 2 3/4 inches what is the area
let's firstly convert the mixed fractions to improper fractions, and then get their product.
[tex]\stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}} ~\hfill \stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}\cdot \cfrac{11}{4}\implies \cfrac{(5)(11)}{(4)(4)}\implies \cfrac{55}{16}\implies 3\frac{7}{16}[/tex]
(4, 2) reflected over y axis
You want to know the opinions of homo-schooled students across America on whether they prefer to loarn at home versus at a public school with other students. You obtain a list of all home-schooled students and mail a survey to a random sample of 7,500 students. Of those, 4,195 responded and 39% say they prefer to learn at home. Which of the
following statements is true?
The results of this survey may be affected by nonresponse blas.
The results of this survey cannot be trusted because of convenience response bias.
O Bocauso random sampling is used, wo can fool confident that the porcont of all homo-schooled students who say they favor learning at home is close to 39%.
O Because more than half of those who were mailed the survey actually responded, va can feel fairly confident that the actual percentage of all home-schooled
students who prefer to learn at homo is close to 39%.
In this survey, the results can be trusted because more than half of the people responded which makes this sample to be representative.
What is nonresponse bias?This occurs when most of the people who were intended to be surveyed do not respond, which causes the results to be biased as the sample does not represent the population.
Can the results of this survey be trusted?Considering more than 50% answer it is likely the results can be trusted as the sample is still representative.
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In circle O below, segment RA is a diameter, arc RP = 104 degrees, and arc RQ = 70 degrees. Find the
measure of the indicated angle
m<=5
Answer:
76°
Step-by-step explanation:
Arc RP = 104
Major arc RPA = 180 (half a circle)
180-104 = 76
Arc AP = 76, so Angle 5 = 76
Central Angles and their arcs are equal
Answer:
76°
Step-by-step explanation:
Finding m∠4 :
The angle is equal to arc RP∠4 = ° 104Finding m∠5 :
∠4 + ∠5 = 180° (property of linear angles)∠5 = 180° - 104°∠5 = 76°The coordinates of the vertices of a quadrilateral are (8, 11) (11, 7) (8, 3) (2, 3). What is the area, in square units, of the quadrilateral?
Check the picture below.
so the quadrilateral is really just a parallelogram below a triangle, so let's simply get the area of each and sum them up.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{parallelogram}{(6)(4)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(6)(4)}}\implies 24~~ + ~~12\implies 36[/tex]
A jewelry designer is making identical bracelets. She has
21 blue beads and 14 red beads. What is the greatest number of bracelets she can make using all of the beads?
Answer
great common factor of 14 and 21 is 15. so your answer is 15
(y−2)=3(x−1) whats the slope
Answer:
the slope is 3
(2 + 3i) + (3 – 4i)
(3 – 5i) – (–2 – i)
(2 − 4i)(1+ 3i)
2i(−1+ 3i)
Answer:
See below ~
Step-by-step explanation:
Question 1
(2 + 3i) + (3 - 4i)5 - iQuestion 2
(3 – 5i) – (–2 – i)3 - 5i + 2 + i5 - 4iQuestion 3
(2 − 4i)(1+ 3i)2 - 4i + 6i - 12i²14 + 2iQuestion 4
2i(-1 + 3i)-2i + 6i²-6 - 2i-7a - a=
Explain please
Step-by-step explanation:
-7a - a
Take common -a from that equation
-a(7+1)
= -8a
Easy peasy
Answer:
- 8a
Step-by-step explanation:
- 7a - a
= - 7a + (- a)
= - 8a
____
Hope it helps ⚜
Please i need your help for number 6
Conversion:
1 feet = 12 inch
Explanation:
a) 19 inch = 12 inch and 7 inch = 1 feet and 7 inch
b) 38 inch = 36 inch and 2 inch = 3 feet and 2 inch
What is the perimeter of the triangle?
A. 18.3 units
B 9 units
C 15.5 units
D 18.2 units
Answer:
answer is B, 9 units
Step-by-step explanation:
Answer:
C) 15.5 units
Step-by-step explanation:
25
Find the value of
20
Answer:
[tex]\sqrt{20}[/tex] or 4.472
Step-by-step explanation:
Value of 20
find the mean and median of 1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5
Answer:
Mean - 3.3793103448276
Median - 3
Step-by-step explanation:
Define:
Mean ⇒ Average
Median ⇒ Middle Number
Solve:
Mean ( Adding all number then divide by total number in data set)
1 + 1 + 2+2+2+2+3+3+3+3+3+3+3+3+3+4+4+4+4+4+4+4+4+5+5+5+5+5=94
94/29 = 3.3793103448276
Mean - 3.3793103448276
Median ( Find Middle Number)
1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5
Kavinsky
A 6-sided number cube is rolled. Find the Probability of NOT getting a 2 or 5
Answer:
4/6
Step-by-step explanation:
each number on the cube has a 1/6 Probability of getting chosen, so since we want the Probability of not choosing these 2 numbers there's 4 numbers out of six that we could get, making it 4/6
Answer: The probability would be 2/4 because there is a chance that a 2 or 5 can be rolled and there is only one two and five and 4 other numbers.
Step-by-step explanation:
What's solid figure could be formed from the net shown 15 cm 9 cm
Answer:
triangular pyramid
..................
Amanda works at a store that pays her 7% commission on the total amount of clothes she sells. Last week, she sold $1600.00 worth of clothes. What is the amount of commission Amanda earned last week?
$112
$22.86
$11.2
$228.57
A certain rectangular prism has a height of 4 m, a length of 6 m, and a width of 8 m. Give the dimensions of a second rectangular prism that will have the same surface area of the first one.
Step-by-step explanation:
in its basic structure such a prism is like a cube (just rectangular and not squared) : 6 sides (rectangles).
2 rectangles top and bottom 6×8 = 48 m²
48 × 2 = 96 m²
2 rectangles front and back 6×4 = 24 m²
24 × 2 = 48 m²
2 rectangles left and right 8×4 = 32 m²
32 × 2 = 64 m²
the total surface area is
96 + 48 + 64 = 208 m²
it is hard to find other integer dimensions for the same surface area.
but as long as we are not restricted to integer numbers :
let's cut e.g. the height in half.
and we get
2 rectangles left and right 8×2 = 16 m²
16 × 2 = 32 m²
that "nails" already 2 dimensions (width and height).
we need to set now the third dimension (length) to create the same surface area :
length×8×2 + length×2×2 = 208 - 32 = 176
20×length = 176
length = 8.8 m
so, with
length = 8.8 m
width = 8 m
height = 2 m
we still get
2 rectangles top and bottom 8.8×8 = 70.4 m²
70.4 × 2 = 140.8 m²
2 rectangles front and back 8.8×2 = 17.6 m²
17.6 × 2 = 35.2 m²
2 rectangles left and right 8×2 = 16 m²
16 × 2 = 32 m²
as total surface area
140.8 + 35.2 + 32 = 208 m²
please please help will give brainlist
What is the volume of the prism?
it has to be simplest mixed number form
Step-by-step explanation:
[tex]13 \frac{1}{8} [/tex]
is the required answer
DIGANME YA LES PREGUNTE ALGO
Answer:
yee yee I'm a rodeo cowboy and I don't know what you mean brother
what will 7dozen of pencil cost at 1k per dozen
Answer: $7000
Step-by-step explanation:
7 * 1000 = $7000
Ben's family went to NYC for their vacation. At the gift shop on Liberty Island, Steven bought three t-shirts
and two keychains for $120, and Jennifer bought five t-shirts and four key chains for $212. Find the price of
each item
Each t-shirt is $28 and each keychain is $18
Each t-shirt is $17 and each keychain is $31
Each t-shirt is $31 and each keychain is $17
Each t-shirt is $18 and each keychain is $28
Answer:
Step-by-step explanation:
Elizabeth's family went to NYC for their vacation. At the gift shop on Liberty Island, Scott bought four t-shirts and five keychains for $291, and Michelle bought seven t-shirts and six key chains for $424. Find the price of each item. Each t-shirt is $31 and each keychain is $34 Each t-shirt is $37 and each keychain is $30 Each t-shirt is $30 and each keychain is $37 Each t-shirt is $34 and each keychain is $31 > Next Question
Previous question
Complete number pattern 88,79, _,_, 52,43,34
Look at the number line below what value does point X show
Answer:
let xtake the part to be 1.2
Find the distance between the points (4,-2), (4,-5)
[tex]\text{Given that,}\\\\(x_1,y_1) = (4,-2)~~ \text{and}~~ (x_2 ,y_2) = (4,-5)\\\\\text{Distance} = \sqrt{(x_2-x_1)^2 + (y_2 -y_1)^2}\\\\~~~~~~~~~~~~=\sqrt{(4-4)^2 + (-5+2)^2}\\\\~~~~~~~~~~~~=\sqrt{0^2+(-3)^2}\\\\~~~~~~~~~~~~=\sqrt{0+9}\\\\~~~~~~~~~~~~=\sqrt 9\\\\~~~~~~~~~~~~=3[/tex]
HELP ME PLEASE FAST I REALLY NEED THIS DONE NOW
Answer:
Step-by-step explanation:
What is the coefficient in the mathematical expression?
- 7
point 2 1/3 is on the right of 2 plus 2 small marks
point -5/6 is on the right of -1 plus 1 small mark
point -3 1/2 is on the left of -3 plus 1 small mark
sorry I don't know how to draw a number line on brainly
Answer:
- for the number line check out the attached photo
- 7
Step-by-step explanation:
- on the number line, each small mark represents 1/6 so to make it easier I made the fraction into 1/6 form
- a coefficent is a numerical value placed before and multiplying the variable in an algebraic expression (ex. 4x)
In this case 7 is before the m making 7 the coefficent
Hope this helps, Let me know if you have any other questions !
The product of two whole numbers is 832 and their sum is 58. What are the two numbers?
Answer:
33 and 25
33 + 25 = 58
33 x 25 = 825
Are you able to help me: Simplify (4x + 2)3
Answer:
64x^3 + 996x^2 + 48x + 8
Step-by-step explanation:
Answer:
12x+6
Step-by-step explanation:
[tex](4x+2)3[/tex]
Use the distributive property to multiply (4x+2) by 3:-
[tex]12x+6[/tex]
A bag of plugs contains 500 pieces. Each piece is $0.03. There is a 10% discount if the customer orders 10 bags or more. How much is a customer paying for 7,000 pieces?
Answer:
They would be paying $189
The amount of money that the customer paying for 7,000 pieces is $189.
What is an equation?An equation is an expression that shows the relationship between two or more variables or numbers.
Number of bags for 7000 pieces = 7000/500 = 14
Cost for 7000 pieces = $0.03 * 7000 = $210
Discount = 210 - (0.1 * 210) = $189
The amount of money that the customer paying for 7,000 pieces is $189.
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Solve for x in 2•8 X 867•5x
Step-by-step explanation:
867.5x ×2.8
is is equal to 2429x
You wish to test the following claim (
H
a
) at a significance level of
α
=
0.01
.
H
o
:
μ
=
61.5
H
a
:
μ
<
61.5
You believe the population is normally distributed and you know the standard deviation is
σ
=
17.6
. You obtain a sample mean of
M
=
59.1
for a sample of size
n
=
34
.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
Using the z-distribution, it is found that the desired measures are given as follows:
The test statistic is z = -0.795.The p-value is of 0.2133.What are the hypotheses tested?At the null hypotheses, it is tested if the mean is of 61.5, that is:
[tex]H_0: \mu = 61.5[/tex]
At the alternative hypotheses, it is tested if the mean is less than 61.5, that is:
[tex]H_1: \mu < 61.5[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The values of the parameters are given as follows:
[tex]\overline{x} = 59.1, \mu = 61.5, \sigma = 17.6, n = 34[/tex]
Hence, the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{59.1 - 61.5}{\frac{17.6}{\sqrt{34}}}[/tex]
z = -0.795.
What is the p-value?We have a left-tailed test, as we are testing if the mean is less than a value, with z = -0.795. Hence, using a z-distribution calculator, the p-value is of 0.2133.
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