The population of the country was 259 million in 1982 and the continuous exponential growth rate was estimated at 1.6% per year. Assuming that the population of the country continues to follow an exponential growth model, Rounding off the answer to one decimal place, the approximate population in 1992 is 348.2 million.
How to calculate the projected population? We are given, Population in 1982 = 259 millionTime taken = 10 years rate of growth = 1.6% = 0.016 (expressed as a decimal)The formula for exponential growth can be written as; Population = P0ert where, P0 is the initial population, e is the natural logarithmic base, r is the rate of growth and t is the time period We are required to find the projected population in 1992, which means the time period is 10 years (from 1982 to 1992).
Hence, substituting the given values in the formula, we get; P = 259e 0.016 × 10P = 259e0.16P = 259 × 1.185P = 307.215 million Hence, the projected population in 1992 is 307.215 million (rounded off to 1 decimal place, it is 307.2 million).
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The store sells a television for $1000. customers can choose to receive 10% discount and pay it off at a simple interest rate of 4% or they can choose to pay the full price and pay it off in 3 years with no interest. which option is better
Option 1 with the discount and 4% simple interest has a total cost of $972, while Option 2 with no discount and no interest has a total cost of $1000. Option 1 is the better choice as it has a lower total cost.
What is simple interest?Simple interest is a type of interest that is calculated on the original principal amount of a loan or investment. It is a fixed percentage of the principal amount that is paid by the borrower or earned by the lender over a specific period of time.
According to question:To compare the two options, we need to calculate the total cost of each option and compare them.
Option 1: 10% discount and pay off with 4% simple interest
The discount reduces the price of the television to $1000 x 0.9 = $900. If the customer chooses to pay it off at 4% simple interest, the total cost would be:
Total cost = $900 + ($900 x 0.04 x 3) = $972
Option 2: Full price and pay off in 3 years with no interest
The total cost of this option would be simply the full price of $1000 paid over 3 years, so:
Total cost = $1000 / 3 = $333.33 per year x 3 years = $1000
Comparing the two options, we see that Option 1 with the discount and 4% simple interest has a total cost of $972, while Option 2 with no discount and no interest has a total cost of $1000. Therefore, Option 1 is the better choice as it has a lower total cost.
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The complete question is: The store sells a television for $1000. customers can choose to receive 10% discount and pay it off at a simple interest rate of 4% or they can choose to pay the full price and pay it off in 3 years with no interest. which option is better?
Option 1 with the discount and 4% simple interest.
Option 2 with no discount and no interest.
For the value of the sum, enter an expression that gives the exact value, rather than entering an approximation.
A.-12 + 4 – 4/3 +4/9 – 4/27 +4/81 - … = -12/(1+1/3)
B.∑ (1/3)^n = 6*1/3^6(1/3^11-1)/(1/3-1)
a. The exact value of the sum of -12 + 4 – 4/3 +4/9 – 4/27 +4/81 - … = -12/(1+1/3) is 12/7.
b.The exact value of the sum of∑ (1/3)ⁿ = 6*1/3⁶(1/3¹¹-1)/(1/3-1) is 3/2.
A.-12 + 4 – 4/3 +4/9 – 4/27 +4/81 - …
This is an infinite geometric series with first term a = -12 and common ratio r = 4/(-3). The sum of an infinite geometric series is given by:
S = a / (1 - r)
Substituting the values of a and r, we get:
S = (-12) / [1 - (4/(-3))]
Simplify the denominator by multiplying both numerator and denominator by (-3):
S = (-12) / [-3 - 4]
S = (-12) / (-7)
S = 12/7
Therefore, the exact value of the sum is 12/7.
B. 6*1/3⁶(1/3¹¹-1)/(1/3-1)
This is a geometric series with first term a = 1 and common ratio r = 1/3. The sum of a geometric series with n terms is given by:
S = a (1 - rⁿ) / (1 - r)
As n approaches infinity, rⁿ approaches zero and the sum converges to:
S = a / (1 - r)
Substituting the values of a and r, we get:
S = 1 / (1 - 1/3)
S = 3/2
Therefore, an expression that gives the exact value of the sum is 3/2.
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The population of a slowly growing bacterial colony after t hours is given by p(t)=3t^2+24t+200. Find the growth rate after 2 hours.
The growth rate of a bacterial colony after a 2 hours is given by the derivative of its population function with respect to time is 36 .
The growth rate of a bacterial colony is given by the derivative of its population function.
Thus, we need to find the derivative of the population function p(t) with respect to time t, and then evaluate it at t = 2 to get the growth rate after 2 hours.
p(t) = 3t² + 24t + 200
Taking the derivative of p(t) with respect to t, we get:
p'(t) = 6t + 24
Now, evaluating p'(t) at t = 2, we get:
p'(2) = 6(2) + 24 = 36
Therefore, the growth rate of the bacterial colony after 2 hours is 36.
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PLEASE HELP!!! WILL MARK BRANLIEST!!!
Answer:
The point z = 3+4i is plotted as a blue dot, and the two square roots are plotted as a red dot and a green dot. The magnitudes of z and its square roots are shown by the radii of the circles centered at the origin.
Step-by-step explanation:
qrt(z) = +/- sqrt(r) * [cos(theta/2) + i sin(theta/2)]
where r = |z| = magnitude of z and theta = arg(z) = argument of z.
Calculate the magnitude of z:
|r| = sqrt((3)^2 + (4)^2) = 5
And the argument of z:
theta = arctan(4/3) = 0.93 radians
Now, find the two square roots of z:
sqrt(z) = +/- sqrt(5) * [cos(0.93/2) + i sin(0.93/2)]
= +/- 1.58 * [cos(0.47) + i sin(0.47)]
= +/- 1.58 * [0.89 + i*0.46]
Using a calculator, simplify this expression to:
sqrt(z) = +/- 1.41 + i1.41 or +/- 0.2 + i2.8
Halla los números desconocidos de estas operaciones
A)872+. +173=2000
B)9180:. =102
C). -99=706
Con los mismos números y las mismas operaciones podemos obtener diferentes resultados,coloca los paréntesis de manera que se obtengan los resultados indicados. A)3+5x7-2=40
B)3+5×7-2=54
C)3+5×7-2=28
ES PARA HOY PORFAVOR☹,PUEDEN HACER EN UNA HOJA O ESCRIBIR ASI PERO EXPLIQUEN BIEN!!!!!!AYUDA SI NO SABEN NO RESPONDAD
In equation A the missing number is 955, In equation B the missing number is 90 and In equation C the missing number is 805.
A) To find the missing number in the equation 872 + ? + 173 = 2000, we need to subtract 872 and 173 from 2000, which gives us:
2000 - 872 - 173 = 955
Therefore, the missing number is 955.
B) To find the missing number in the equation 9180 ÷ ? = 102, we need to divide 9180 by 102, which gives us:
9180 ÷ 102 = 90
Therefore, the missing number is 90.
C) To find the missing number in the equation ? - 99 = 706, we need to add 99 to 706, which gives us:
706 + 99 = 805
Therefore, the missing number is 805.
To obtain the indicated results with the same numbers and operations, we need to use parentheses to change the order of operations.
A) 3 + (5x7) - 2 = 40
B) (3 + 5) × 7 - 2 = 54
C) 3 + (5 × (7-2)) = 28
Equations are used extensively in various fields of science, engineering, economics, and finance, to name a few. It is formed by placing an equal sign between the two expressions. Equations are used to solve problems and find unknown values.
An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that need to be found, while the constants are known values that are already given. Solving an equation involves manipulating the expressions on both sides of the equal sign using mathematical operations to isolate the variable on one side and constants on the other. The final solution obtained is the value of the variable that satisfies the equation..
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Complete Question: -
Find unknown numbers of these operations
A ) 872 +. + 173 = 2000
B ) 9180:. = 102
C ). -99 = 706
With the same numbers and the same operations we can obtain different results, place the parentheses so that the indicated results are obtained.
A ) 3 + 5 x 7-2 = 40
B ) 3 + 5 × 7-2 = 54
C ) 3 + 5 × 7-2 = 28
IT'S FOR TODAY PLEASE ☹, CAN DO IN A LEAF OR WRITE ASI BUT EXPLAIN WELL!!!!!!HELP IF THEY DON'T KNOW NO RESPOND
find the values of a and b such that
x^2- +5=(x-a)^2+b
The value οf a = 1/2 and b = 19/4 in the equatiοn x² - x + 5 = (x-a)² + b.
What dο yοu mean by algebra?The part οf mathematics in which letters and οther general symbοls are used tο represent numbers and quantities in fοrmulae and equatiοn is called algebra.
x² - x + 5 = (x-a)² + b
x² - x + 5 = x² + a² - 2xa + b
-x + 5 = -2xa + a² + b
By matching cοrrespοnding terms,
2a = 1 and a²+ b = 5
a= 1/2 and a²+ b = 5
Substituting value οf "a"
(1/2)² + b = 5
1/4 + b = 5
b = 5- 1/4
b = 19/4
Thus, a = 1/2 and b = 19/4.
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Mrs banks wants to make 44 quarts of jelly with 70 pounds of fruit if each gallon of jelly costs 6. 5 pounds of fruit will she of enough fruit and will there be extra
Mrs. Banks has enough fruit to make the 44 qt of jelly she wants, but she will have 4 lb of leftover fruit.
Here we have to use the arithmetic operations. First, we need to convert the total quantity of jelly to gallons since we have the amount of fruit needed per gallon. One gallon is equal to 4 quarts, so 44 quarts is equal to 11 gallons.
Next, we can calculate how much fruit is needed for 11 gallons of jelly by multiplying the amount of fruit needed per gallon by the number of gallons
11 gallons x 6 lb of fruit per gallon = 66 lb of fruit needed
Since Mrs. Banks only has 70 lb of fruit, she has enough to make the 44 qt of jelly she wants, but she will have 4 lb of leftover fruit:
70 lb of fruit - 66 lb of fruit needed = 4 lb of leftover fruit
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The given question is incomplete, the complete question is:
Mrs. Banks wants to make 44 qt of jelly with 70 lb of fruit. If each gallon of jelly needs 6 lb of fruit, will
she have enough fruit? How much leftover fruit does she have, or how much extra fruit is needed?
Determine the force in each member of the truss with the method of joints and state if the
members are in tension (T) or compression (C). Set d = 1 m and P = 10 kN. (Hint: Look for zero-
force members to simplify the calculations)
if the members are in tension or compression. Identify all zero force members: Likewise, we can find the reaction force at A by taking minutes about point A: RA x 8m - 5kN x 8m - 5kN x 8m = 0 RA = 5kN
To begin with, we really want to find the reaction forces at An and G.
We can do this by taking minutes about point G.
We realize that the amount of minutes at any point is zero when the framework is in equilibrium.
Consequently, we can compose: 5kN x 8m - RA x 10m = 0 RA = 4kN
Likewise, we can find the reaction force at A by taking minutes about point A: RA x 8m - 5kN x 8m - 5kN x 8m = 0 RA = 5kN
Since we have two distinct qualities for RA, we can presume that the framework isn't in equilibrium.
This really intends that there should be some outside force following up on the framework.
The two obscure forces are at first thought to be ductile (for example pulling away from the joint). In the event that this underlying supposition is mistaken, the registered upsides of the pivotal forces will be negative, meaning pressure.
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the complete question is:
Question l Find the forces in members HE; FH, FE; and FC of the truss as shown in Figure Q1. State if the members are in tension or compression. Identify all zero force members: (10 marks) 8 m 5 KN 8 m 8 m 5 KN 8 m 10 m Figure Q1.
find the percent of the discount: a $30 board game on sale for 21
well, we know the discount is just 30 - 21 = 9, so hmm if we take 30(origin amount) to be the 100%, what's 9 off of it in percentage?
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 30 & 100\\ 9& x \end{array} \implies \cfrac{30}{9}~~=~~\cfrac{100}{x} \\\\\\ 30x=900\implies x=\cfrac{900}{30}\implies x=30[/tex]
Jerry, Jack and Sophie are all hoping to save money! Jerry thinks saving money in a shoe box in his closet every month is a good idea. He decides to start with $125, and then save $50 each month. Jack was given $3520 from his Grandma, and decides to put the money
into an account that has a 6.5% interest rate that is compounded annually. Sophie has earned $3500 working at the movie theater decides to put her money in the bank in an account that has a 7.05% interest rate that is compounded continuously
Part 1: Describe the type of equation that models Jerry’s situation. Create that equation of Jerry’s situation. Using the equation you created, how much money will be in Jerry’s account after 3 years? 10 years?
Think: What do I know and what does it mean? What plan am I going to try?
PLEASE HELP!!!!!
Jerry will have $1825 in his account after 3 years and Jerry will have $6125 in his account after 10 year when compounded.
What is simple interest?Simple interest is computed just using the principle, which is the initial sum borrowed or put into an investment. The interest rate is constant throughout time and solely applies to the principal sum. Short-term loans or investments frequently employ simple interest.
The given situation can be modeled as a linear equation given by:
y = mx + c
For Jerry we have:
y = 50x + 125
For 3 years = 36 months we can substitute x = 36:
y = 50(36) + 125
y = 1825
For x = 10:
y = 50(120) + 125
y = 6125
Hence, Jerry will have $1825 in his account after 3 years and Jerry will have $6125 in his account after 10 year.
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I need help with this
sum area = -3x - 6y + 12 and product area = -36x - 72y.
what is rectangle?
A rectangle is a geometric shape that is defined as a four-sided flat shape with four right angles (90-degree angles) and opposite sides that are parallel and equal in length.
The area of a rectangle is given by the product of its length and width. Assuming that the length of the rectangle is given by -3x - 6y and its width is 12, we can express the area in terms of a sum and a product as follows:
Sum:
Area = length x width
Area = (-3x - 6y) + 12
Area = -3x - 6y + 12
Product:
Area = length x width
Area = (-3x - 6y) x 12
Area = -36x - 72y
Note that the product expression is not equal to the sum expression. This is because we used different assumptions for the length of the rectangle in each case.
Therefore, sum area = -3x - 6y + 12 and product area = -36x - 72y.
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Select all of the following that are linear functions.
x = 5
y
-2
4
0
1
2
-2.
4
5
x + 7 = 4y
A) x = 5 is not a linear function since it is a vertical line and does not have a slope. B) The table description does not provide enough information to determine if it is a linear function. C) x + 7 = 4y is a linear function in slope-intercept form (y = (1/4)x + 7/4).
A linear function is a mathematical function that can be represented by a straight line with a constant slope. The equation of a linear function can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). Option A (x = 5) is not a linear function, as it is a vertical line with an undefined slope. Option B is a linear function, as the table describes points that can be plotted to form a straight line. Option C is also a linear function, but it is in a different form (x + 7 = 4y). This equation can be rearranged to y = (1/4)x + 7/4, which is in the standard form of a linear function.
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Answer: C.) x + 7 = 4y and D
Step-by-step explanation: i hope this helps
what is this pls help
Answer:
x = 45.
Step-by-step explanation:
We know the full angle of this is 180 degrees.
Given: (2x+45) + x = 180
First, collect like terms ( in this case 2x and x, 180 and 45 )
2x + x = 180 - 45
Then calculate:
3x = 135. ( Divide both sides by 3 )
x = 45
PLEASE HELP ME QUICKLY!
Step-by-step explanation:
it would mean that she made 53 batches of soap and 4 batches of lotion.
now, is it a solution ?
then both inequalities must be true with these values.
5×53 + 15×4 <= 325
265 + 60 <= 325
325 <= 325 correct
20×53 + 35×4 <= 1200
remember, 1 hour = 60 minutes.
1060 + 140 <= 1200
1200 <= 1200 correct
so, (53, 4) is the intersection point of both limit lines. and it is as such an extreme point and optimum.
LMN is a straight angle. Find m LMP and m NMP
From the given information provided, the value of angle LMP and angle NMP is 77 and 103 degrees respectively.
Since LMN is a straight angle, it measures 180 degrees.
We are given the measures of LMP and NMP, and we are told that LMP + NMP = LMN. Therefore, we can set up an equation:
LMP + NMP = LMN
(-16x + 13) + (-20x + 23) = 180
Simplifying and solving for x, we get:
-36x + 36 = 180
-36x = 144
x = -4
Now that we have found the value of x, we can substitute it back into the expressions for LMP and NMP to find their measures:
LMP = -16x + 13 = -16(-4) + 13 = 77 degrees
NMP = -20x + 23 = -20(-4) + 23 = 103 degrees
Therefore, the measures of LMP and NMP are 77 degrees and 103 degrees, respectively, and the measure of LMN is 180 degrees.
Question - LMN is a straight angle. LMP = -16x + 13 NMP = -20x + 23 LMP + NMP = LMN What are the measures?
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one hundred students were asked whether they liked certain candy flavors. it was found that liked cherry, liked coconut, and liked both flavors. what's the probability that a randomly selected student...
The probability that a randomly selected student likes coconut is 0.6.
Step-by-step explanation:
Given that,
Now we have to find the probability that a randomly selected student likes coconut.
P (student likes coconut) = the number of students who liked coconut / total number of students
= 60/100
= 0.6
Therefore, the probability that a randomly selected student likes coconut is 0.6.
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why can't we use mean when a data set has one or two values that are much higher than all of the others
The reason we can't use the mean when a data set has one or two values that are much higher than all of the others is that it skews the average, making it not representative of the rest of the data.
What is the mean?The mean is a numerical measure of the central tendency of a data set. It is calculated by dividing the sum of all the values in a data set by the number of data points.
A data set is a collection of observations or measurements that are analyzed to obtain information. It can be represented graphically, in tabular form, or in any other format. The data set may be a sample or the entire population.
If a data set has one or two extremely high or low values, it can significantly impact the mean. These values are known as outliers. The outliers can cause the mean to be higher or lower than the actual middle value of the data.
Hence, in such cases, the median is a better choice for finding the central tendency of the data. The median is the middle value of the data set, and it is less affected by outliers than the mean. The mode, which is the value that occurs most frequently in the data set, is also a measure of central tendency that is less sensitive to outliers than the mean.
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g in acid base reactions, the hydrogen ions from the acid and the hydroxide ions from the base neutralize each other. khp has one ionizable hydrogen; this means that one mole of sodium hydroxide neutralizes one mole of khp. from experiment 1, calculate the exact molarity of the sodium hydroxide. (hint: use the mass of khp and do a stoichiometry problem.....) tip: khp is not the chemical formula. khp stands
In the following question, among the conditions given, the statement is said to be, the exact molarity of the NaOH solution is 0.0960 M.
The question is asking to calculate the exact molarity of the sodium hydroxide from Experiment 1.
KHP stands for potassium hydrogen phthalate, and one mole of sodium hydroxide (NaOH) will neutralize one mole of KHP. To solve the problem, use the mass of KHP and a stoichiometry problem.
First, calculate the number of moles of KHP:
Moles KHP = (Mass KHP (g) / Molar Mass KHP (g/mol))
Then, calculate the moles of NaOH:
Moles NaOH = (Moles KHP * Mole Ratio NaOH/KHP)
Finally, calculate the molarity of NaOH:
Molarity NaOH = (Moles NaOH / Volume NaOH (L))
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what are the roots of 2x^2+10x+9=2x
The roots of the equation 2x² + 10x + 9 = 2x does not exist i.e no real roots
Calculating the roots of the equationTo find the roots of the given quadratic equation 2x² + 10x + 9 = 2x, we can start by rearranging the equation to the standard form of a quadratic equation
2x² + 10x + 9 - 2x = 0
Simplifying the left-hand side, we get:
2x² + 8x + 9 = 0
Now, we can use the quadratic formula to find the roots of the equation:
x = (-b ± √(b² - 4ac)) / 2a
where a = 2, b = 8, and c = 9.
Substituting these values into the formula, we get:
x = (-8 ± √(8² - 4(2)(9))) / 2(2)
Simplifying the expression under the square root, we get:
x = (-8 ± √-8) / 4
The square root of -8 is not a real number
So, the equation has no real root
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Help due soon !!!!!!!!!
An expression for the length of the rectangle in terms of A is [tex]$\boxed{L=x+5}$[/tex]
How to find the expression?We are given that the area of a rectangle is [tex]$A=x^2+x-15$[/tex], and we want to find an expression for the length of the rectangle in terms of A.
Recall that the area of a rectangle is given by the formula: [tex]$A=L\cdot W$[/tex], where L is the length and W is the width. We can use this formula to write L in terms of A and W as [tex]$L=\frac{A}{W}$[/tex].
We know that the rectangle has a length and a width, so we need to find an expression for the width W in terms of A. We can rearrange the given formula for A to solve for W:
[tex]&& \text{(substitute }L=x+5\text{)}[/tex]
[tex]W&=\frac{x^2+x-15}{x+5} && \text{(divide both sides by }x+5\text{)}[/tex]
Now that we have an expression for W in terms of A, we can substitute it into our expression for L to get:
[tex]L&=\frac{A}{W}[/tex]
[tex]&=\frac{x^2+x-15}{\frac{x^2+x-15}{x+5}} && \text{(substitute the expression we found for }W\text{)}\&=x+5[/tex]
Therefore, an expression for the length of the rectangle in terms of A is [tex]$\boxed{L=x+5}$[/tex]
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Analyze the proportion below and complete the instructions that follow. Use a model to find the missing value in the proportion. A. 4 B. 5 C. 10 D. 22 Please select the best answer from the choices provided A B C D
Step-by-step explanation:
The area of a rectangle is 1,872 ft2. The ratio of the length to the width is 9:13. Find the perimeter of the rectangle.
176 ft
You want to make a scale drawing of your bedroom to help arrange your furniture. You decide on a scale of 3 in. = 2 ft. Your bedroom is a 12 ft by 14 ft rectangle. What should the dimensions of your drawing be?
18 in. by 21 in.
If 5/y + 7/x=24 and 12/y + 2/x=24, find the ratio of x to y.
5/7
Simplify the ratio 8ft/12in. Use the conversion 12 in. = 1 ft.
8/1
Analyze the proportion below and complete the instructions that follow.
2x+5/3 = x-5/4
-7
If a+b/2a-b = 5/4 and b/a+9 = 5/9, find the value of b.
30
Analyze the ratio below and complete the instructions that follow.
$30:$6
Simplify the ratio.
5:1
If 14/3 = x/y then 14/x =
3/y
Analyze the diagram below and complete the instructions that follow.
In the diagram, AB:BC is 3:4 and AC = 42. Find BC.
24
Analyze the diagram below and complete the instructions that follow.
If AB:BC is 3:11, solve for x.
9
If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, which of the following is false?
b/a = c/d
Analyze the diagram below and complete the instructions that follow.
Find the ratio of the width to the length of the rectangle, then simplify the ratio. Use the conversion 100 cm = 1 m.
3/4
Simplify the ratio 3 gal./24 qt. Use the conversion 4 qt = 1 gal.
1/2
The area of a rectangle is 4,320 ft2. The ratio of the length to the width is 6:5. Find the length of the rectangle.
72 ft
Analyze the diagram below and complete the instructions that follow.
Given that CB/CA = DE/DF, find BA.
10.5
Analyze the proportion below and complete the instructions that follow.
2/3 = 8/x
3, 8
Analyze the diagram below and complete the instructions that follow.
Are the polygons shown here similar? Justify your answer. The images are not drawn to scale.
Yes, PQR ~TSV with a scale factor of 1:√3
All __________ are similar.
squares
Analyze the diagram below and complete the instructions that follow.
Determine which 2 triangles are similar to each other. The images are not drawn to scale.
GHI ~ JKL
Analyze the diagram below and complete the instructions that follow.
Pentagon PQRST ~ pentagon XYZVW. Find the value of b. The images are not drawn to scale.
3
Analyze the diagram below and complete the instructions that follow.
If ABC ~ XYZ, find XY. The images are not drawn to scale.
24
ABC is a right triangle. The legs of ABC are 9 ft and 12 ft. The shortest side of XYZ is 13.5 ft, and ABC ~ XYZ How long is the hypotenuse of XYZ?
22.5 ft
Subtract the given equation
3x-(4x-11)
Answer:
3x - (4x - 11) = 3x - 4x + 11 = -x + 11
Step-by-step explanation:
I don’t know what I’m doing
Answer:
29.12 square cm
Step-by-step explanation:
Area of equilateral triangle:Side = a = 8.2 cm
[tex]\boxed{\bf Area \ of \ equilateral \ triangle = \dfrac{\sqrt{3}}{4}a^2}[/tex]
[tex]\sf = \dfrac{\sqrt{3}}{4}*8.2*8.2\\\\= \sqrt{3}*4.1 * 4.1\\\\= 1.732 * 4.1 *4.1\\\\= 29.12 \ cm^2[/tex]
smart mugs are the next generations of hot drinks dispensers tha om with built in technology to keep drinks at the perfect temperature for hours on end initial cost of a smart mug was aed 896, because of high demand in market the cost increased by 12% find the new price of the mug
PLS QUICK ITS DUE 1 HOUR!!
With a [tex]12[/tex]% price rise, the smart mug now costs AED [tex]1003.52[/tex].
Price and sell price: what are they?The sale price is the price an user pays to purchase a thing or a commodity. It is a cost that is higher than the market cost and also includes a portion of the profit. The cost price refers to the price paid by the seller for the item or service.
How would you define price?Price is the process of figuring out how much a something or service is worth. Price establishes a customer's cost, although it can or cannot be linked to the price a firm pays to manufacture a good or service.
We need to multiply the initial price by [tex]1.12[/tex] which represents a [tex]12[/tex]% increase in decimal form,
New price [tex]=[/tex] Initial price [tex]*[/tex] (1 [tex]+[/tex] Percent increase in decimal form)
New price[tex]= 896 * (1 + 0.12)[/tex]
New price [tex]= 896 * 1.12[/tex]
New price [tex]= 1003.52[/tex]
Therefore, the new price of the smart mug is AED [tex]1003.52[/tex] after a [tex]12[/tex]% increase.
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A photograph of sides 35cm by 22cm is mounted onto a frame of external dimension 45cm by 30cm.Find the area of the border surrounding the photograph
Dimension of photograph is 35cm and 22cm.
And external dimension of photo frame is 45cm and 30cm
So, the area of the border surrounding the photograph=Area of photo frame−Area of photo.
So, The area of the border surrounding the photograph [tex]=45\times30-35\times22[/tex]
[tex]=1350-770=580cm^2[/tex]
Sophie invested $92,000 in an account paying an interest rate of 6 1/8% compounded
continuously. Damian invested $92,000 in an account paying an interest rate of 6 5/8%
compounded monthly. After 14 years, how much more money would Damian have in
his account than Sophie, to the nearest dollar?
Answer:
Step-by-step explanation:
To solve this problem, we need to use the formula for compound interest:
A = P*e^(rt)
where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm (approximately 2.71828), r is the interest rate (expressed as a decimal), and t is the time (in years).
For Sophie's account, we have:
P = $92,000
r = 6 1/8% = 0.06125 (as a decimal)
t = 14 years
A = 92000*e^(0.06125*14)
A = $219,499.70 (rounded to the nearest cent)
For Damian's account, we have:
P = $92,000
r = 6 5/8% = 0.06625/12 = 0.005521 (as a monthly decimal rate)
t = 14*12 = 168 months
A = 92000*(1+0.005521)^168
A = $288,947.46 (rounded to the nearest cent)
Now we can subtract Sophie's final amount from Damian's final amount to find the difference:
Difference = $288,947.46 - $219,499.70
Difference = $69,447.76
Therefore, Damian would have about $69,448 more in his account than Sophie, to the nearest dollar.
Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks. If Terri does not make any calls, what would her bill be?
Answer:
$10
Step-by-step explanation:
We Know
Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks.
Let C be the total cost, and x be the number of minutes she talks; we have the equation.
C = 0.05x + 10
If Terri does not make any calls, what would her bill be?
C = 0.05(0) + 10
C = $10
So, her bill will be $10
Question 9(Multiple Choice Worth 2 points)
(Irrational Numbers LC)
Describe in words where √63 would be plotted on a number line.
O Between 3 and 4, but closer to 3
O Between 3 and 4, but closer to 4
O Between 2 and 3, but closer to 2
O Between 2 and 3, but closer to 3
A local winery wants to create better marketing campaigns for its white wines by understanding its customers better. One of the general beliefs has been that higher proportion of women prefer white wine as compared to men. The company has conducted a research study in its local winery on white wine preference. Of a sample of 400 men, 120 preferred white wine and of a sample of 500 women, 170 preferred white wine. Using a 0.05 level of significance, test this claim.INPUT Statistics required for computation170 = Count of events in sample 1500 = sample 1 size120 = Count of events in Sample 2400 = sample 2 size0.05 = level of significance0 = hypothesized differenceOUTPUT Output valuesSample 1 Proportion 34.00%Sample 2 Proportion 30.00%Proportion Difference 4.00%Z α/2 (One-Tail) 1.645Z α/2 (Two-Tail) 1.960Standard Error 0.031Hypothesized Difference 0.000One-Tail (H0: p1 − p2 ≥ 0)Test Statistics (Z-Test) 1.282p-Value 0.900One-Tail (H0: p1 − p2 ≤ 0)Test Statistics (Z-Test) 1.282p-Value 0.100Two-Tail (H0: p1 − p2 = 0)Test Statistics (Z-Test) 1.276p-Value 0.202Group of answer choicesThis is a one-tail test and the data does support the claim that higher proportion of women prefer white wine as compared to men.This is a one-tail test and the data does not support the claim that higher proportion of women prefer white wine as compared to men.This is a two-tail test and the data does support the claim that higher proportion of women prefer white wine as compared to men.This is a two-tail test and the data does not support the claim that higher proportion of women prefer white wine as compared to men.Question 2. Based on the study results presented in the last question, what is the upper bound for the proportion differences between women and men for a 95% confidence interval?(Note: Please enter a value with 4 digits after the decimal point. For example, if you computed an upper boundary of 23.456% or .23456, you would enter it here in decimal notation and round it to four digits, thus entering .2346).
Answer:
235.65
Step-by-step explanation:
Given the triangle, find the length of X. Give your answer in simpliest radical form.
Answer:
x = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the cosine ratio in the lower right triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} } }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = 4[tex]\sqrt{2}[/tex]
