well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8[/tex]
[tex]\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r[/tex]
now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02[/tex]
The zeros for this function are -7, 2, and -3. Verify the zeros. Show all working
(-3)^(3) + 8(-3)^(2) + (-3) - 42
The polynomial p(x) = x³ + 8 · x² + x - 42 contains the zeros - 7, 2 and - 3.
How to derive a polynomial that contains a given set of real roots
Polynomials are algebraic expressions, whose standard form is shown below:
p(x) = Σ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., m}
Where:
cₙ - n-th Coefficientm - Grade of the polynomialAnd whose factor form is:
p(x) = a · Π (x - rₙ), for n = {1, 2, 3, ..., m}
Where:
a - Lead coefficientrₙ - n-th ZeroIn this problem we need to find a polynomial whose zeros are only real and represented by r₁ = - 7, r₂ = 2 and r₃ = - 3, respectively. If we know that a = 1, r₁ = - 7, r₂ = 2 and r₃ = - 3, then the factor form of the polynomial is:
p(x) = 1 · (x + 7) · (x - 2) · (x + 3)
p(x) = (x + 7) · (x - 2) · (x + 3)
p(x) = (x + 7) · (x² + x - 6)
p(x) = x³ + x² - 6 · x + 7 · x² + 7 · x - 42
p(x) = x³ + 8 · x² + x - 42
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19) Which two integer values is 17 between?
C) 3 and 4
A) 13 and 14
B) 5 and 6
D) 2 and 3
Answer: D
Step-by-step explanation:
The exact answer is 2.571281591, which is between:
D) 2 and 3
What are the domain and range of the function shown on this graph?
Domain is z>0, and range is y ≥ 0.
O Domain is 0 ≤z ≤0, and range is 0 ≤ y ≤ 200.
O Domain is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
O Domain is all real numbers, and range is all real numbers.
and range is y ≥ 0.
Distance
300
275
250
200
175
150
125
100
75
50
2
The domain and range of the function shown on the graph are (a) Domain is x ≥ 0, and range is y ≥ 0
How to determine the domain and the rangeFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see that the line is a straight line
This means that the graph is a linear function
However, the function only covers the positive axes
This means that
Domain is x ≥ 0, and range is y ≥ 0
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are required to complete the work in ays! 12 workers can complete a piece of work in 20 days. How many workers are needed to complete the work in 16
days?
Answer:
The answer is 15 workers are needed to complete the work in 16 days.
Step-by-step explanation:
To this incomplete sentence. ill try to answer it
a coin has two sides: heads and tails. a die has six sides, numbered through . if you flip the coin and roll the die, what is the probability that you flip ''heads'' and roll a number less than
The probability that you flip 'heads' and roll a number less than 5 is 1/3.
The probability of flipping heads is 1/2, and the probability of rolling a number less than 5 is 4/6.
The probability of both occurring is the product of the two probabilities, or 1/2 multiplied by 4/6, which is equal to 1/3.
This means that the probability of flipping heads and rolling a number less than 5 is 1/3.
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You downloaded a video game to your computer. You have a 60 minute free trial of the game. It takes 5 1/6 minutes to set up the game and 7 1/3 minutes to play each level. You want to find out how many levels you can play for free.
5 1/6+7 1/3l<60
what is l?
The value of I in the obtained inequality is the number of levels that can be played for free.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
Set up time + time taken in complete levels ≤ 60
For I number of levels,
5(¹/₆) + 7(¹/₃)I ≤ 60
By comparing the given inequality,
I = number of levels that are played for free.
Hence "The number of levels that can be played for free is the value of I in the resulting inequality".
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what is the sum of the expressions
(2/7x-6) and (3/7x+8)?
Answer:
[tex]\frac{5}{7}[/tex] x + 2
Step-by-step explanation:
([tex]\frac{2}{7}[/tex] x - 6) + ([tex]\frac{3}{7}[/tex] x + 8) ← remove parenthesis
= [tex]\frac{2}{7}[/tex] x - 6 + [tex]\frac{3}{7}[/tex] x + 8 ← collect like terms
= ( [tex]\frac{2}{7}[/tex] x + [tex]\frac{3}{7}[/tex] x ) + ( - 6 + 8 )
= [tex]\frac{2+3}{7}[/tex] x + 2
= [tex]\frac{5}{7}[/tex] x + 2
if a chicken and a half can lay an egg and a half in a day and a half, how long would it take a pair of chickens to lay three dozen eggs? show your work.
It would take about 18 days for a pair of chickens to lay three dozen of eggs.
The unitary method is a method for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. Finding the value of just one unit is the key to answering such questions.
Given that 1.5 chickens can lay 1.5 eggs in a day.
The number of eggs 1 chicken can lay in a day = (1.5/1.5) eggs = 1 egg.
Then, two chickens can lay about 2 eggs in a day.
The number of days it takes for two chickens to lay 3 dozen (3×12=36) eggs is given by
[tex]\frac{\text{total number of eggs}}{\text{number of chicken}}=\frac{36}{2}=18\;\text{days}[/tex]
The answer is 18 days.
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Multiply. –4x(7 – 3x)
–28x – 3x^2
7 + 12x^2
–3x – 7x^2
–28x + 12x^2
What is the solution to the system? For the first tour on Monday, a museum sells 6 child tickets and 8 adult tickets for $140. For the second tour, the museum sells 12 child tickets and 9 adult tickets for $189. Find the price of one child ticket and the price of one adult ticket.
Answer:
children = $6 ; adults = $13
Step-by-step explanation:
6c + 8a = 140
12c + 9a = 189
3c + 4a = 70
4c + 3a = 63
3c = 70 - 4a
c = 70/3 - 4/3 a
4(70/3 - 4/3 a) + 3a = 63
280/3 - 16/3 a + 3a = 63
(-16a + 9a)/3 = 63 - 280/3
-7/3 a = (189 -280)/3
-7/3 a = -91/3
a = - 91/3 · -3/7
a = 91/7
a = $13
c = 70/3 - 4/3 · 13
c = 70/3 - 52/3
c = (70-52)/3
c = 18/3
c = $6
The vertices of ABC are A(2,-1), B(0, 4), and C-3,5). Find the coordinates of the vertices of the image after the translation (x, y)-(x-1, y + 3).
Answer:
A(1,2), B(-1,7) C(-4,8)
Step-by-step explanation:
I think that is the answer.
Please Help!!
\What additional information is needed to prove ΔTUX ≅ ΔDEO by HL?
The information required for ΔTUX to be congruent with ΔDEO by Hl is the corresponding legs of the right triangle. i.e. option a. TX ≅ DO
How to find congruent triangle?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal.
Congruent triangles are triangles that have the same size and shape.
Therefore, ΔTUX is congruent to ΔDEO.
Triangle can be congruent base of HL(hypotenuse and leg).
Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.
Therefore, the additional information needed to prove ΔTUX ≅ ΔDEO by HL is TX ≅ DO.
TX and DO are the corresponding legs which are suppose to be equal.
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What percentage of seeds from the packet sprouted?
A gardener plants 50 seeds from the same packet into three pots.
This table shows the number of seeds planted and the percentage of seeds that sprouted.
Answer: 56%
Step-by-step explanation:
Pot A
75% = 0.75
12 times 0.75 = 9 seeds sprouted
Pot B
50% = 0.5
20 times 0.5 = 10 seeds sprouted
Pot C
50% = 0.5
18 times 0.5 = 9 seeds sprouted
Add total; we get 28 seed sprouted
Then we take 28 divided by 50, times 100% = 56%
So, 56% of the seeds from the packet sprouted!
Please help me respond this question. I am struggling!
Viktor is in the 60th percentile, which is 85, while the percentile for 71 is 26.666.
What is percentile?Percentile is defined as the value below which a given percentage falls under. Ben, for instance, is the fourth tallest child in a group of 20, and eighty percent of the kids are shorter than you. As a result, Ben is in the 80th percentile.
We have the data
Sort the data as follows: 58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96
employing the percentile formula,
Percentile is calculated as follows: 71 Percentile
(4 / 15)*100 Percentile
26.666 Percentile = (Number of Values Below "x" / Total Number of Values) 100
Consequently, 71's percentile is equal to 26.666.
Identifying the rank
Thus, the ranking is 0.6.
To find the rank for viktor
Find the percentile using the formula,
Percentile = Rank × Total number of the data set
Percentile = 0.6 × 15
Percentile = 9
Now, counting 9 values from left to right we reach 85, and we can say that all the values below 85 will come under the 60th percentile. In other words, 60% of the values are below 85.
The 60th percentile is 85
Thus viktor is in 60th percentile is 85
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When an investor considers putting their money into a potentially high rate of return investment, they should understand there will be
risk involved with the investment. Higher potential returns often come with a higher level of risk, as the investor is taking on the possibility of losing some or all of their investment in exchange for the chance to earn a higher return. It's important for investors to carefully consider the level of risk they are comfortable with and to do their due diligence before making any investment decisions. This may include researching the company or investment, reviewing financial statements, and consulting with financial professionals. Investors should also consider the potential tax implications of any investment, as well as how it fits into their overall financial plan.
When designing a study to determine a population proportion, what minimum number would you need to survey, e. G. , n, to be 90% confident that the population proportion is estimated to be within 0. 03?.
The minimum number would you need to survey sample Size N = 752.
A population proportion is the percentage of a population that falls into a specific category. Population proportions are estimated using confidence intervals.
Given,
A margin of error of 0.03
Z = 1.645 at a 90% confidence level
We use P=0.5 because there is no prior information about the population proportion.
To find the minimum number of subjects n= (Z*/M.E.)2 x P (1-P)
Solving by entering the given values into a formula: -
n = (1.645/0.03)2 × 0.5(1-0.5)
n = 3006.70 X 0.25
n= 751.67
Sample Size N = 752
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what does the number .05 represent in the following: t(58) = 2.001, p < .05?
The number 58 represents the Degree of freedom in the equation: t(58)=2.001, p<.05.
Option (c) is the correct choice.
The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. When calculating degrees of freedom, one is subtracted from the total number of items in the data sample.
A straightforward statistical method may be used to calculate degrees of freedom. It reads as follows: df = N-1 and indicates that degrees of freedom are equal to the number of values in a data collection minus 1. N is the number of values in the data collection, in this case (sample size).
The degrees of freedom, or the number of free data points available in a t-test to compare two groups, are shown in the above t-test by the number 58.
(A T-test is employed in statistics to compare the means of two groups. The t-value, p-value, and degrees of freedom are the values needed for a t test.)
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The complete question may be:
What does the number 58 represent in the following: t(58)=2.001, p<.05?
(a) Test statistic
(b) T-value
(c) Degrees of freedom
(d) Significance level
Kerry bought a bag of dog food for $37. 99. If ale tax i 7. 6%, how much did he pay in tax?
The tax paid by Kerry is $2.89
As per the given data in question:
Kerry bought a bag of dog food for $37. 99.
Total cost = $37. 99
Rate of sales tax is 7.6 %
A sales tax is a consumption tax paid to a government on the sale of certain goods and services.
Sales tax: = Sales tax percent / 100.
[tex]=\frac{7.6}{100}[/tex]
= $0.076
Tax paid by Kerry = Total cost × Sales tax
= 37. 99 × 0.076
= $2.89
Therefore the tax paid by Kerry is $2.89
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in writing a report, the researcher produced a single histogram of the combined data for region i and region ii. describe the shape of the histogram for the combined data.
Between $80,000 and $85,000, there is an outlier. Means are not immune to outliers, but medians are.
How do you define medians?
The middle number in a sorted series of numbers is referred to as the median in mathematics. Ordering the numerals reveals the center one. In descending sequence, the numbers are listed. The middle number, when the numbers are arranged, is referred to as the data set's median.
Why is median significant?
A useful way to determine where a dataset is in the middle is to use the median. You may gain a sense of a dataset's distribution by comparing both median and mean. The dataset is almost uniformly scattered from the mean if both mean and median are equal.
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Evaluate 1/4xy if x=−2/3 and y=3/5 . Write your answer as a fraction in simplest form.
Answer:
(-1/10)
Step-by-step explanation:
I'll assume 1/4xy is (1/4)xy and not 1/(4xy).
(1/4)xy
(1/4)(-2/3)(3/5)
Multiple the numerators and denominators separately:
Numerator + 1*(-2)*3 = -6
Deniominator 4*3*5 = 60
Put them back together: (-6/60) This reduces to (-1/10)
Find values of p, q, r and s such that (2x + 3) (px^3 + qx^2+rx+ s) = 2x^4+ 13x^3 + 7x^2 + 18
Answer:
p = 1q = 5r = -4s = 6Step-by-step explanation:
You want values of p, q, r and s such that (2x + 3) (px^3 +qx^2 +rx +s) ≡ 2x^4 +13x^3 +7x^2 +18.
Find coefficientsMultiplying out the left side of the equation, we have ...
2px^4 +(3p+2q)x^3 +(2r +3q)x^2 +(2s +3r)x +3s
Match coefficientsWhen we match coefficients between the two polynomials, this gives rise to 5 equations in the four unknown values:
2p = 23p +2q = 132r +3q = 72s +3r = 03s = 18The first and last equations tell us ...
p = 2/2 = 1
s = 18/3 = 6
Using these values in the 2nd and 4th equations makes them be ...
3 +2q = 13 ⇒ q = 10/2 = 5
12 +3r = 0 ⇒ r = -12/3 = -4
The values of p, q, r, s are ...
p = 1q = 5r = -4s = 6__
Check
We can use the 3rd equation to check these results:
2r +3q = 7
2(-4) +3(5) = 7
-8 +15 = 7 . . . . . . . true
8. You have an investment of $20,000 with
4.2% simple interest and weekly payments.
How much money (to the nearest dollar)
will you have after three years?
[A] $23,030
[B] $19,730
IC] $21,200
[D] $24,250
[E] $20,048
Answer:
[D] $ 24,250
Step-by-step explanation:
$24,250 dollar will I have after three years.
x (2x - 4) = (2x + 1) (x - 2) solve
Answer:
2
Step-by-step explanation:
First distribute the first x into the first parenthesis: x (2x - 4) = (2x + 1) (x - 2)
x times 2x is [tex]2x^{2}[/tex] and x times -4 is -4x
This changes the equation to: [tex]2x^{2}[/tex]-4x = (2x + 1) (x - 2)
Now multiply the other parentheses: [tex]2x^{2}[/tex]-4x = (2x + 1) (x - 2)
Do this by using the Foil method (I attached a picture of the method if you don't know it)
First: (2x + 1) (x - 2)
Do 2x times x which = [tex]2x^{2}[/tex]
Then 2x times -2 which = -4x
Then 1 times x which = x
Lastly, 1 times -2 which = -2
The order you do this is the order that the foil method says.
Now the equation is:
[tex]2x^{2}[/tex]-4x =[tex]2x^{2}[/tex]-4x+x-2 (I just added all the numbers we just got)
Next cancel out the equal terms. To combine like terms you'd usually move the right [tex]2x^{2}[/tex] over to the left one and subtract it. But since they are the same number, subtracting it would leave you with 0. So you can just get rid of both.
You can also do this with both -4x
This leaves you with:
0=x-2
Now you move the variable to the left
you also make it negative since it is going to the other side of the =
this leaves: -x=-2
You can't have a negative x so now you have to change the signs for both. Make them both positive.
Now you have x=2
so your answer is 2
Find the measure of each angle indicated.
A. 47 degrees
B. 133 degrees
Help!!!
answer is a. this is the long method but there is a short method — angles on a "z" since there are 2 parallel lines and a straight line across
Answer:
A. 47
Step-by-step explanation:
they are two parallel lines where by a transversal has passed throw them ; but first of all you have to look at the corresponding angles followed by alternative angles and so on;as angles on a str
. Which list shows the numbers in descending order?
a
-19/2, -3 1/4, -1.2, 38/6, 7
b
7, 38/6, -19/2, -3 1/4, -1.2
c
-19/2, 7, 38/6, -3 1/4, -1.2
d
7, 38/6, -1.2, -3 1/4, -19/2
Answer:
d: 7, 38/6, -1.2, -3 1/4, -19/2.
Step-by-step explanation:
First, divide the fractions to get decimals, this is an easier approach to compare all the numbers.
-19/2 = -9.5
-3 1/4 = 4 x -3 = -12 + 1 = -3.25
38/6= 6.3333 (terminal 3)
The greatest numbers for this list is 6.33, -3.25, and -9.5. The rest of the numbers include -1.2 and 7.
With the entire order, we observe which lists are descending, starting with a positive or a negative number.
1. order can be: 7, 6.33, -1.2, -3.25, and -9.5 or 7, 38/6, -1.2, -3 1/4, -19/2.
2. order commonly confused can be: -9.5, -3.25, -1.2, 6.33, and 7 or -19/2, -3 1/4, -1.2, 38/6, 7.
The only order showing this is d: 7, 38/6, -1.2, -3 1/4, -19/2.
The reason why its not the second order starting with -19/2 is because descending typically refers to a positive number going down to a negative number. However, both orders can be right. For the sake of this problem, the best option is d.
The scores for assessments are displayed in the box-and-whiskers plot below. What is the range of the middle 50% of the data of scores on the assessment?
The range of the middle 50% of the data of scores on the assessment is 10.
Option A is the correct answer.
What is a range in a set of data?The range is the difference between the highest value and the lowest value of a given set of data.
We have,
Median = 80
First quartile = 70
Third quartile = 90
The Middle 50% is from the Median to the First quartile.
Range.
= 80 - 70
= 10
Thus,
The range is 10.
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6 The bottled water industry is currently worth over $200 billion annually. The average
cost of a bottle of water in the United States is 50 cents.
a Determine the equation that represents the cost (v) of buying x bottles of water.
What does the gradient represent in this equation?
b What is the total cost of buying one bottle of water a day for a year (not a leap year)?
c A high-quality, refillable water bottle costs approximately $40. How many bottles of
water would you have to drink in order for this option to be more cost effective?
Id What other factors, apart from cost, might inflence someone's decision whether to
carry their own water bottle or to buy bottles of water?
Answer:
a) The cost of buying x bottles of water is represented by the equation v = 0.50x, where v is the cost in dollars and x is the number of bottles of water. The gradient of this equation, which is 0.50, represents the cost per bottle of water.
b) The total cost of buying one bottle of water per day for a year (365 days) is 365 * 0.50 = $182.50.
c) If a refillable water bottle costs $40, then a person would have to drink 40 / 0.50 = 80 bottles of water in order for the refillable water bottle to be more cost effective.
d) Some factors that might influence someone's decision to carry their own water bottle or to buy bottled water include convenience, availability of clean drinking water, personal preference, and environmental impact.
the security system in a house has two units that set off an alarm when motion is detected. neither one is entirely reliable, but one or both always go off when there is motion anywhere in the house. suppose that for motion in a certain location, the probability that detector a goes off and detector b does not go off is 0.25, and the probability that a does not go off is 0.35. what is the probability that b goes off?
The probability that detector B goes off is 0.75
In this question we have been given the security system in a house has two units that set off an alarm when motion is detected.
Here, the probability that detector A will not go off is 0.35
And the probability that A will go off and B will not go off is 0.25
We need to find the probability that B goes off
The probability that detector A will go off would be,
1 - P( detector A will not go off )
= 1 - 0.35
= 0.65
And the probability that both A and B will go off would be,
= P(A will go off) - P( A will go off and B will not go)
= 0.65 - 0.25
= 0.40
Now we find the required probability.
P(B goes off) = P(both A and B will go off) + P(detector A will not go off)
= 0.40 + 0.35
= 0.75
Therefore, the required probability is 0.75
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Croissants cost 85p each and pain au chocolate cost 95p each. Didier buys 22 pastries and spends a total of £20. How many croissants and how many pain au chocolat did he buy?
Answer:
croissants: 10 pain au chocolat: 12
Step-by-step explanation:
85c + 95p = 2000
c + p = 22
85c + 95p = 2000
-
85c + 85p = 1870
10p = 120
p = 12
c + p = 22
c + 12 = 22
c = 10
Answer:
Step-by-step explanation: Let C be the number of croissants and P be the number of pain au chocolat that Didier buys. We know that C + P = 22 and 0.85C + 0.95P = 20.
We can solve this system of equations using substitution. First, we solve the first equation for P: P = 22 - C. Then, we substitute this expression for P into the second equation: 0.85C + 0.95(22 - C) = 20. Expanding the expression inside the parentheses and combining like terms, we get: 0.85C + 21.1 - 0.95C = 20.
Then, we can solve for C by moving all the terms to one side of the equation: -0.1C = -1.1. Dividing both sides by -0.1, we get: C = 11.
Substituting this value for C back into the equation P = 22 - C, we get: P = 22 - 11 = 11.
Therefore, Didier buys 11 croissants and 11 pain au chocolat.
three less than twice an integer is greater than 1
please help put this in an equation
Answer:
2x-3>1
Step-by-step explanation:
lets say x is the interger
so twice an interger would be 2*x or 2x
and three less than 2x would be 2x-3
and 2x-3 is greater than 1
so 2x-3>1