A town has a population of 2000 and grows at 4.5% every year. To the nearest
tenth of a year, how long will it be until the population will reach 3900?
Answers
Related Questions
130/240 in its simplest form
Answers
Answer:
13/24
Step-by-step explanation:
divide both sides by 10.
pls mark brainliest
Answer:
13/24
Divide the numbers by 10.
\(\frac{130/10}{240/10} = \frac{13}{24}\)
With that information, the answer is 13/24.
Which of the following is equivalent to
4x2y - 2y2x - 5xy
Select one:
a. -2x2y - 5xy + 4xy2
b. 2xy2 - 5xy + 4x2y
c. -2xy2 + 5xy + 4x2y
d. -2xy2 - 5xy + 4x2y
e. 2x2y - 5xy
Answers
Answer:
1 Simplify 4x\times 2y4x×2y to 8xy8xy.
8xy-2y\times 2x-5xy
8xy−2y×2x−5xy
2 Simplify 2y\times 2x2y×2x to 4yx4yx.
8xy-4yx-5xy
8xy−4yx−5xy
3 Simplify.
-xy
−xy
Step-by-step explanation:
The solution to an inequality is graphed on the number line. A number line going from negative 5 to positive 5. A solid circle appears between positive 4 and positive 5. The number line is shaded from the circle to negative 5. What is another way to represent this solution set? {x | x < 4. 5} {x | x ≤ 4. 5} {x | x > 4. 5} {x | x ≥ 4. 5}.
Answers
The solution set for the number line of inequality can be represented as,
{x | x ≤ 4. 5}
What is the number line?The number line is the way of representation of number and digits in a arranged form to understand the data batter.
The meaning of circle in number line,
Open circle-When the value of the variable is equal to the given number, then the graph of the inequality has an open circle.Closed circle or solid circle-When the value of variable is not equal to the given number, then the graph of the inequality has a closed circle.The number line going from negative 5 to positive 5 and a solid circle appears between positive 4 and positive 5. The middle point of 4 and 5 is 4.5.
The solid or closed circle means that the value has less than or equal to 4.5. Thus, the solution set for the number line of inequality can be represented as,
{x | x ≤ 4. 5}
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alan thinks of a number. he squares it, then takes away 1, next multiplies it by 2, takes away 6, divides it by 4 and finally adds 5. his answer is 11. what number did alan start with?
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A number first squares it, then takes away 1, next multiplies it by 2, takes away 6, divides it by 4 and finally adds 5. the answer is 11
then the number is 4
According to the question, given that
A number first squares it, then takes away 1, next multiplies it by 2, takes away 6, divides it by 4 and finally adds 5. the answer is 11
Square of 4 = 16
16 - 1 = 15
15 * 2 = 30
30 - 6 = 24
24 ÷ 4 = 6
then add 5
6 + 5 = 11
Therefore, after solve we get 11 and the number is 4.
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A number is first squared, then multiplied by 2, then divided by 4, then added, before having 1 subtracted from it. The solution is 11.
then 4 is the number.
In response to the query, assuming that
A number is first squared, then multiplied by 2, then divided by 4, then added, before having 1 subtracted from it. The solution is 11.
Square of 4 = 16
16 - 1 = 15
15 * 2 = 30
30 - 6 = 24
24 ÷ 4 = 6
then add 5
6 + 5 = 11
Therefore, after solve we get 11 and the number is 4.
Based on the graph below what is the pressure at a depth of 40 km? At what depth would the pressure be 30kb
Answers
In general, the pressure increases with increasing depth. Due to the weight of the overlying rock and sediment.
What cause pressure increases with increasing depth?The pressure in the Earth's crust is often measured in kilobars (kb), where 1 kb is equivalent to 1000 bars. The relationship between depth (d) in kilometres and.
Pressure (P) in kilobars can be approximated by the following equation:
\(P = 0.03 \times d + 1\) Using this equation, we can calculate the pressure at a depth of 40 km:
\(P = 0.03 \times 40 + 1\)
\(P = 2.2 kb\)
As a result, the pressure at a depth of \(40\) km is approximately \(2.2 kb.\)
To find depth at which the pressure is \(30 kb\), we can rearrange the equation and
solve for d:
\(P = 0.03 \times d + 1\)
\(0.03 \times d = P - 1\)
\(d = (P - 1) / 0.03\)
Substituting \(P = 30 kb\), we get:
\(d = (30 - 1) / 0.03\)
\(d ≈ 966.67 km\)
Therefore, the depth at which the pressure is \(30\) kb is approximately \(966.67\) Km.
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Alishas parents deposited in her bank account PhP 25 O00 00 at an interest at 3.75% compounded yearly on her first birthday and did not withdraw any amount from the account how much money alisha has on her birthday
Answers
Answer:
Php 2593750.00
Step-by-step explanation:
The formula for the amount gotten from a compound interest is given as
A = P(1 + r/n)^nt
Where
A = Amount after t years
P = Initial amount saved or invested = PhP 2500000
R = 3.75
n = Compounding frequency = yearly = 1
t = Time in years = 1
First, convert R percent to r a decimal
r = R/100
r = 3.75%/100
r = 0.0375 per year,
Then, solve our equation for A
A = P(1 + r/n)^nt
A = 2500000.00(1 + 0.0375/1)^(1)(1)
A = Php 2593750.00
The amount Alisha has on her birthday is Php 2593750.00
The amount Alisha has on her birthday is Php 2593750.00
Compound interestThe formula for the amount gotten from a compound interest is given as
A = P(1 + r/n)^nt
Where
A = Amount after t years P = Initial amount saved or invested = PhP 2500000 R = 3.75% = 0.0375 n = Compounding frequency = yearly = 1 t = Time in years = 1
Then, solve our equation for A
A = P(1 + r/n)^nt
A = 2500000.00(1 + 0.0375/1)^(1)(1)
A = Php 2593750.00
The amount Alisha has on her birthday is Php 2593750.00
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what is the domain and range of f(x)=35x
Answers
Answer:
Domain and Range are all real number
Step-by-step explanation:
Answer is above
Mrs. Fry divides 64 gummy
worms among 8 bags. She adds
3 lollipops to each bag. How many
pieces of candy are in each bag?
Answers
Answer: 11 pieces of candy
Step-by-step explanation: First we would have to do 64 ÷ 8 which gives us 8. Then since Mrs. Fry adds 3 lollipops to each bag we would do 8 + 3 which gives us 11.
"Evaluating an Integral In Exercises 3-10, evaluate the integral.
7. S ey y ln x dx, y > 0"
Answers
the solution to the integral ∫ \(e^y\) y ln(x) dx, where y > 0, is y \(e^y\) ln(x) + C.
To evaluate the integral ∫ \(e^y\) y ln(x) dx, where y > 0, we will integrate with respect to x while treating y as a constant.
∫ \(e^y\) y ln(x) dx
Using the property of logarithms, ln(x) can be written as ln(\(e^u\)) where u = ln(x):
∫ \(e^y\) y ln(x) dx = ∫ \(e^y\) y ln(\(e^u\)) dx
Now, we can simplify the integral using the properties of logarithms:
∫ \(e^y\) y ln(\(e^u\)) dx = ∫ \(e^y\) y u dx
Since y is treated as a constant, we can bring it outside the integral:
y ∫ \(e^y\) u dx
Next, we can integrate\(e^y\) u with respect to x. The integral of \(e^y\) u with respect to x is simply \(e^y\) u:
y \(e^y\) u + C
Finally, we substitute u back in terms of x, which is u = ln(x):
y \(e^y\) ln(x) + C
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Answer choices: | Please help!
50 cm; 42 cm2
50 cm; 54 cm2
34 cm; 54 cm2
34 cm; 42 cm2
Answers
The perimeter and area of the given composite figure are:
Area = 50 cm²
Perimeter = 42 cm
How to find the area of the composite figure?To find the total surface area of the composite figure, we will find the area of each individual surfaces and then add them together.
Formula for area of a triangle is:
Area = ¹/₂ * base * height
Formula for area of a rectangle is:
Area = Length * Width
Thus:
T.S.A = 2(¹/₂ * 4 * 5) + (10 * 3)
T.S.A = 20 + 30
T.S.A = 50 cm²
The perimeter will be the sum of the entire boundary length. Thus:
Perimeter = 3 + 10 + 10 + 3 + 3 + 3 + 5 + 5
Perimeter = 42 cm
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can u help me with my work pls?
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Given:
\(f(x)=2x^2-12x+24\)The above expression can be expressed as,
\(undefined\)how many prime numbers are there between 30 and 50
Answers
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. To find out how many prime numbers there are between 30 and 50, we need to check each of the numbers from 30 to 50 to see if it is a prime number.
A prime number is a number that is only divisible by 1 and itself. The prime numbers between 30 and 50 are: 31, 37, 41, 43, and 47.
Therefore, there are 5 prime numbers between 30 and 50.
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a rhombus has side lengths of 10 and a diagonal measuring 12. what is the length of the other diagonal?
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When the other diagonal is 12 inches long and the side is 10 inches long, the diagonal is 16 inches long.
What is rhombus?A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths. A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposing sides of a parallelogram are equal. A quadrilateral with four equal sides that has the shape of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen.
Here,
The length of side=10 inch
The length of diagonal= 12 inch
Let the length of diagonal be x.
6²+(x/2)²=10²
(x/2)²=64
x/2=8
x=16 inch
The length of diagonal is 16 inch when other diagonal measure 12 inch and side measures 10 inch.
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Write the letter of the property, definition, or postulate that justifies each statement.
11. If m/ABC = 90°, then ZABC is a right angle.
12. If m23+ m24 = 180°, then 23 and 24 are
supplementary angles.
13. If m/PQR = m/RST, then ZPQR = ZRST
14. If 21 and 22 form a right angle, then 21 and 22
are complementary angles.
15. If ZX and Y are supplementary and ZX and Z
are supplementary, then 2Y = LZ
16. If ZJ and ZK are vertical angles, then ZJ = ZK
A. Definition of Congruence
B. Definition of Angle Bisector
C. Definition of Complementary Z's
D. Definition of Supplementary Z's
E. Definition of Perpendicular
F. Definition of a Right Angle
G. Angle Addition Postulate
H. Vertical Angles Theorem
I. Complement Theorem
J. Linear Pair (Supplement) Theorem
K. Congruent Complements Theorem
L. Congruent Supplements Theorem
17. If ZPQR and ZSTU are complementary angles, then mZPQR+ m2STU = 90°.
18. If 25 and 26 form a linear, then 25 and 26 are supplementary angles.
Answers
Answer:
Step-by-step explanation:
The difference of a number and 20 is equal to the product of the same number and 6 increased by 15.
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An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 = 500 Number of accidents = 1 80 We are interested in determining if the accident proportions differ between the two age groups. Over Age of 18 m=600 Number of accidents-150 17. Refer to Exhibit 10-11 and let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is a. pu-po S0 d, pu-po-o 18.
Answers
The accident proportions differ between the two age groups is \(\frac{11}{100}\).
We have given that,
number of clients under age of 18 = 500
number of accident = 180
Proportion of client under age of 18 = \(\frac{180}{500}\) = \(\frac{18}{50}\)
number of clients over age of 18 = 600
number of accidents = 150
number of clients over age of 18 = \(\frac{150}{600}\) = \(\frac{15}{60}\) = \(\frac{1}{4}\)
Now we have to find proportion of difference between two age group,
\(\frac{18}{50}\) - \(\frac{1}{4}\) = \(\frac{72 - 50}{200}\)
= \(\frac{22}{200}\)
= \(\frac{11}{100}\)
Therefore the difference between two age groups is \(\frac{11}{100}\) .
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In a rectangle FGHI, diagonals FH and GI intersect at E
What is the length of FH?
Answers
Answer:
The length of \(\overline {FH}\) is;
D. 38 units
Step-by-step explanation:
The given parameters are;
The type of the given quadrilateral FGHI = Rectangle
The diagonals of the quadrilateral = \(\overline {FH}\) and \(\overline {GI}\)
The length of IE = 3·x + 4
The length of EG = 5·x - 6
We have from segment addition postulate, \(\overline {GI}\) = IE + EG
The properties of a rectangle includes;
1) Each diagonal bisects the other diagonal into two
Therefore, \(\overline {FH}\) bisects \(\overline {GI}\), into two equal parts, from which we have;
IE = EG
\(\overline {GI}\) = IE + EG
3·x + 4 = 5·x - 6
4 + 6 = 5·x - 3·x = 2·x
10 = 2·x
∴ x = 10/2 = 5
From which we have;
IE = 3·x + 4 = 3 × 5 + 4 = 19 units
EG = 5·x - 6 = 5 × 5 - 6 = 19 units
\(\overline {GI}\) = IE + EG = 19 + 19 = 38 units
\(\overline {GI}\) = 38 units
2) The lengths of the two diagonals are equal. Therefore, the length of segment \(\overline {FH}\) is equal to the length of segment \(\overline {GI}\)
Mathematically, we have;
\(\overline {FH}\) = \(\overline {GI}\) = 38 units
∴ \(\overline {FH}\) = 38 units.
The volume of a large can of tuna fish can be calculated using the formula
V= π r^2 h. Write an equation to determine the radius of the can.
Answers
The equation that can be used to determine the radius of the can isr = √(v/πh)
What is change of subject of formula?For example, Y is the subject of the following equations. Y = x + 1, Y = 4 + 2x, Y = 2(2x – 3). In the relation v=u + at, v is said to be the subject. When a formula is rearranged so that a different letter becomes the subject, this process is referred to as changing the subject of the relation.
Similar making r the subject in V= π r^2 h
divide both sides by πh
V/πh = r²
r² = V/πh
r = √(V/πh)
therefore the radius of the can be obtained from
r = √(V/πh)
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5 and 4 sevenths times negative 2 and 2 fifths
Answers
Answer:
3/2
Step-by-step explanation:
ugygv
The forward selection procedure starts with ___ independent variable(s) in the multiple regression model Select one: a. no b. two c. all d. one
Answers
The forward selection procedure starts with no independent variables in the multiple regression model.
The purpose of the forward selection procedure is to iteratively add independent variables to the model based on their significance and contribution to the model's predictive power.
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Luis works as a salesperson at an electronics store and sells phones and phone accessories. Luis earns a $14 commission for every phone he sells and a $2 commission for every accessory he sells. On a given day, Luis made a total of $110 in commission from all accessory and phone sales and he sold 4 times as many accessories as phones. Determine the number of phones sold and the number of accessories sold.
Answers
The number of phones sold and the number of accessories sold if Luis earns a $14 commission for every phone he sells and a $2 commission for every accessory he sells and earn a total commission of $110 is 5 and 20 respectively.
What is equation?Equation: a statement stating the equality of two expressions containing variables or numbers. Essentially, equations are questions, and attempt to methodically find the answers to these questions have been the inspiration for the development of mathematics.
Given:
The commission on phone = $14 each,
The commission on accessories = $2 each,
Total commission earned = $110,
Let x is the no of phone sold and y is the no of accessories sold, then,
y = 4x and 14x + 2y = 110,
Solve the above equation by substitution method we get
x = 5 and y = 20
Therefore, the number of phones sold and the number of accessories sold are 5 and 20 respectively.
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If x = √5+2 find the value of x2 + 1/x2
Answers
Answer:
18
Step-by-step explanation:
If we plug (√5+2) into the equation x^2 + 1/x^2, you will get:
(√5+2)^2 + 1/(√5+2)^2
Then just plug it into a calculator and you're golden.
\(\huge\fbox{Answer ☘}\)
x = √5 + 2
\(x {}^{2} + \frac{1}{ x {}^{2} } = ?\\ \\( \sqrt{5} + 2) {}^{2} + \frac{1}{( \sqrt{5} + 2) {}^{2} } \\\\ = > (5 + 4 \sqrt{5} + 4) + ( \frac{1}{5 + 4 \sqrt{5} + 4}) \\\\ = > (4 \sqrt{5} + 9) + ( \frac{1}{4 \sqrt{5} + 9 } ) \\ \\ = > \frac{(4 \sqrt{5 } + 9) {}^{2} +1 }{4 \sqrt{5} + 9} \\\\ = > \frac{80 + 81 + 72 \sqrt{5} + 1}{4 \sqrt{5} + 9} \\\\ = > \frac{162 + 72 \sqrt{5} }{4 \sqrt{5} + 9} \\ \\= > \frac{16 + 72 \sqrt{5} }{4 \sqrt{5} + 9} \times \frac{4 \sqrt{5} - 9}{4 \sqrt{5} - 9} \\\\ = > \frac{64 \sqrt{5 } - 144 + 1440 - 648 \sqrt{5} }{80 - 81} \\ \\ = > \frac{1296 - 584 \sqrt{5} }{ - 1} \\\\\bold\pink{ = > 584 \sqrt{5} - 1296}\)
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Once sales tax is included, a $470 rug ends up costing $517. What is the sales tax percentage?
Answers
Answer:
10%
Step-by-step explanation:
(517-470)/470x100
=10%
Find the difference after tax and divide by the original price and times 100%
can someone please help me?
Answers
Answer:
m<2 = 150
Step-by-step explanation:
m<2 = 150 because of alternate exterior angles
A firm produces two goods in quantities x and y. Its cost function is C(x,y) = 10x + xy + 10y and the prices P, and P, it can charge are, respectively, Ps = 50 - x + y and Py = 50 - x + y. The firm is committed to delivering a total of 15 units. How much should the firm produce of each good to maximize profits?
Answers
To maximize profits, the firm should produce a quantity of goods x = 5 and y = 10, based on the cost function and price constraints.
To maximize profits, the firm needs to find the quantities of goods x and y that will yield the highest profit. The profit function can be defined as the revenue minus the cost. Revenue is calculated by multiplying the quantity of each good produced with their respective prices, while the cost function is given as C(x, y) = 10x + xy + 10y.
The firm is committed to delivering a total of 15 units, which can be expressed as x + y = 15. To determine the optimal production quantities, we need to maximize the profit function subject to this constraint.
By substituting the price expressions Ps = 50 - x + y and Py = 50 - x + y into the profit function, we obtain the profit equation. To find the maximum profit, we can take the partial derivatives of the profit equation with respect to x and y, set them equal to zero, and solve the resulting system of equations.
Solving the equations, we find that the optimal production quantities are x = 5 and y = 10, which maximize the firm's profits.
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At a certain university, students who live in the dormitories eat at a common dining hall. Recently, some students have been complaining about the quality of the food served there. The dining hall manager decided to do a survey to estimate the proportion of students living in the dormitories who think that the quality of the food should be improved. One evening, the manager asked the first 100 students entering the dining hall to answer the following question. Many students believe that the food served in the diniog tall necds improvement. Do you think that the quality of food served here needs improvement, even though that would increase the cost of the meal plant? a. In this setting, explain how bias may have been introduced based on the way this convenience sample was selected and suggest how the sample could have been selected differently to avoid that bias. b. In this setting, explain how bias may have been introduced based on the way the question was worded and suggest how it could have been worded differently to avoid that bias.
Answers
Based on the provided information, a) bias is introduced through convenience sampling there could be specific variable associated with the first hundred students. It can be avoided by simple random sampling. b) bias is introduced through wording as it includes a negative consequence. It can be avoided by just asking for an opinion without any associated reasoning or consequences.
Bias refers to a deviation of feedback which is based on certain influences by the surveyor and respondent. Sampling bias or selection bias refers to a type of bias in which a researcher gathers a sample of respondents for a questionnaire that does not accurately represent the population. Survey bias refers to the way the question is phrased or formatted, leading people to choose a certain answer instead of another. In the given case,
a) A bias may have been introduced based on the way the convenience sample was selected as there could be specific variable associated with each of the first hundred students that walk into the dining room. The first hundred students could possibly like the food and that is the reason why they come early to the dining room. Selecting students at the dining room may also exclude the students who dislike the food and choose to eat elsewhere. A simple random sample can help avoid this bias. By randomly selecting students at the university campus would provide a more inclusive and true representation of the population.
b) A bias may have been introduced based on the way the question is worded is to maintain the current meal plan as it presents a negative consequence to introducing a new meal plan. It states that a new meal plan would result in more cost. In order to avoid bias, the survey should ask students opinion about the food without introducing any external reasoning.
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1.43x -18/35 what is the answer
Answers
Answer:
18/35= 18.35
= 1.43 - 18/35=?
assume that the test scores of a college entrance exam fits a normal distribution. the mean test score is 72, and the standard deviation is 5. what is the percentage of students scoring 84 or more in the exam?
Answers
The percentage of students scoring 84 or more in the exam is 99.18%.
Given, Mean test score = 72,
Standard deviation = 5.
We are supposed to find the percentage of students scoring 84 or more in the exam.
To find the percentage of students scoring 84 or more in the exam, we will use the following steps:
First, we need to find the z-score associated with 84.
Let us assume that z is the z-score corresponding to the value 84, then;
z = (84 - 72) / 5 = 2.4
Now, we have the value of z, we can find the percentage of students scoring 84 or more in the exam using the normal distribution table.
The percentage is the area under the normal distribution curve to the right of the z-score.
To find the area using the normal distribution table, we need to look for the value 2.4 in the z-table. Since 2.4 is not exactly listed in the z-table, we will use the value for 2.4 closest to it.
Using the z-table, the value closest to 2.4 is 0.9918.
Therefore, the percentage of students scoring 84 or more in the exam is;
P(Z > 2.4) = 0.9918 × 100 = 99.18%.
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For the curve given by r(t) = <-3t, -6t,1 + 2t^2>, Find the derivative r'(t) = < _ , _ , _> Find the second derivative r"(t) = < _,_,_> Find the curvature at t =
k(1)=
Answers
To find the derivative of the curve r(t) = <-3t, -6t, 1 + 2t^2>, we differentiate each component with respect to t:
r'(t) = <-3, -6, 4t>
To find the second derivative, we differentiate each component of r'(t):
r"(t) = <0, 0, 4>
The curvature of a curve at a specific point is given by the formula:
k(t) = |r'(t) x r"(t)| / ||r'(t)||^3
Substituting the values:
k(t) = |<-3, -6, 4t> x <0, 0, 4>| / ||<-3, -6, 4t>||^3
The cross product of the vectors is:
<-24, 12t, 0>
The magnitude of the cross product is:
|<-24, 12t, 0>| = sqrt((-24)^2 + (12t)^2 + 0^2) = sqrt(576 + 144t^2) = sqrt(144(4 + t^2))
The magnitude of the vector r'(t) is:
||<-3, -6, 4t>|| = sqrt((-3)^2 + (-6)^2 + (4t)^2) = sqrt(9 + 36 + 16t^2) = sqrt(25(1 + 4t^2))
Plugging these values into the curvature formula:
k(t) = sqrt(144(4 + t^2)) / sqrt(25(1 + 4t^2))^3
To find the curvature at t = 1, we substitute t = 1 into the expression:
k(1) = sqrt(144(4 + 1^2)) / sqrt(25(1 + 4(1^2)))^3
= sqrt(144(4 + 1)) / sqrt(25(1 + 4))^3
= sqrt(144(5)) / sqrt(25(5))^3
= sqrt(720) / sqrt(125)^3
= sqrt(720) / 5^3
= sqrt(720) / 125
= 12sqrt(5) / 125
Therefore, k(1) = 12sqrt(5) / 125.
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There are 16 mathematics majors and 325 computer science majors in a college. Which rule must be used to find out the number of ways that two representatives can be picked so that one is a mathematics major and the other is a computer science major? (You must provide an answer before moving to the next part.) Multiple Choice the subtraction rule the division rule the sum rule the product rule
Answers
Answer is C. product rule
The rule that must be used to find out the number of ways that two representatives can be picked, with one being a mathematics major and the other being a computer science major, is the product rule.
The product rule is used to find the derivative of a product of functions while the quotient rule is for finding the derivative of a quotient of functions.
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