Answer:
y>= -27/16
Step-by-step explanation:
I just put in the calculator
The population of a city is P(t) = 4e^0.03t(in millions), where t is measured in years.(a) Calculate the doubling time of the population.(b) How long does it take for the population to triple in size?(c) How long does it take for the population to quadruple in size?
a) Doubling time of the population.
Initial population = 4
Doubling = 2 x 4 = 8
[tex]8=4e^{0.03t}[/tex]Then, solve for t:
[tex]\begin{gathered} \frac{8}{4}=\frac{4e^{0.03t}}{4} \\ 2=e^{0.03t} \end{gathered}[/tex]Apply the exponent laws:
[tex]\begin{gathered} \ln 2=0.03t \\ \frac{\ln2}{0.03}=\frac{0.03t}{0.03} \\ t=23.1\approx23 \end{gathered}[/tex]Answer a: 23 years
b) Initial population = 4
Triple the population = 3 x 4 = 12
Therefore:
[tex]\begin{gathered} 12=4e^{0.03t} \\ \frac{12}{4}=\frac{4e^{0.03t}}{4} \\ 3=e^{0.03t} \\ \ln 3=0.03t \\ \frac{\ln 3}{0.03}=\frac{0.03t}{0.03} \\ t=36.6\approx37 \end{gathered}[/tex]Answer b: 37 years
c) Initial population = 4
Quadruple the population = 4 x 4 = 16
So:
[tex]\begin{gathered} 16=4e^{0.03t} \\ \frac{16}{4}=\frac{4e^{0.03t}}{4} \\ 4=e^{0.03t} \\ \ln 4=0.03t \\ \frac{\ln 4}{0.03}=\frac{0.03t}{0.03} \\ t=46.2\approx46 \end{gathered}[/tex]Answer c: 46 years
Rewrite 7.25 as a mixed number in lowest terms.
A)7 2/5
B)7 1/4
C)7 25/100
D)7 1.5
Answer:
B
Step-by-step explanation:25 as a percent is 1/4 of 100 and the seven is the whole number since they are full numbers not decimals
The volume of a cylinder is 225pi cmand its radius is 5 cm.What is the length of the cylinder's height?o 9 cmo 5 cmo 10 cmo 7 cm
The formula for the volume of the cylinder is given by:
[tex]V=\pi\cdot r^2\cdot h[/tex]Where:
r = radius
h = length of height
Substitute the given values:
[tex]225\pi=\pi\cdot(5)^2\cdot h[/tex]And solve for h:
[tex]\begin{gathered} 225\pi=\pi\cdot25\cdot h \\ \frac{225\pi}{25\pi}=\frac{25\pi h}{25\pi} \\ h=9 \end{gathered}[/tex]Answer: 9 cm
S varies inversely as G. If S is 4 when G is 1.8, find S when G is 6.
Given that "S" varies inversely as "G", it is an Inverse Variation Relationship. Then, it has this form:
[tex]S=\frac{k}{G}[/tex]Where "k" is the Constant of Variation.
Knowing that:
[tex]S=4[/tex]When:
[tex]G=1.8[/tex]You can substitute values and solve for "k":
[tex]\begin{gathered} 4=\frac{k}{1.8} \\ \\ (4)(1.8)=k \\ \\ k=7.2 \end{gathered}[/tex]Then, the equation that models the situation is:
[tex]S=\frac{7.2}{G}[/tex]Substituting this value of "G" into the equation and evaluating:
[tex]G=6[/tex]You get:
[tex]S=\frac{7.2}{6}=1.2[/tex]Hence, the answer is:
[tex]S=1.2[/tex]If tan 0= 15/8 and cos 0= -8/17, then what is sin 0?
Enter the answer as a fraction.
Work Shown:
[tex]\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\\\\\sin(\theta) = \tan(\theta)*\cos(\theta)\\\\\sin(\theta) = \frac{15}{8}*\left(-\frac{8}{17}\right)\\\\\sin(\theta) = \boldsymbol{-\frac{15}{17}}[/tex]
Side note: theta is in quadrant III since sin(theta) < 0 and cos(theta) < 0.
A cylinder has a radius of 15 millimeters and a height of 17 millimeters.
What is the approximate volume of the cylinder?
O 3,004 cubic millimeters
O 3,405 cubic millimeters
O 12,017 cubic millimeters
O 13,619 cubic millimeters
Answer:
O 12,017 cubic millimeters
Step-by-step explanation:
Volume of cylinder = height x cross-section area(in this question, it's a circle) = hpr^2
17ml x (15ml)^2 x p(ill calculate it in calculator, not as 3.14)
= (approximately) 12017ml^3
Show that(x+1)(x+3)(x+5)can be written in the form ax^3+bx^2+cx+d where a,b,c and d are all positive integers.
The given expression : (x + 1)(x + 3)(x + 5) can be written as (x³ + 9x² + 23x + 15)
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following expression -
(x + 1)(x + 3)(x + 5)
We have -
(x + 1)(x + 3)(x + 5)
x{(x + 3)(x + 5)} + 1{(x + 3)(x + 5)}
x(x + 3)(x + 5) + (x + 3)(x + 5)
(x² + 3x)(x + 5) + (x + 3)(x + 5)
x²(x + 5) + 3x(x + 5) + x(x + 5) + 3(x + 5)
x³ + 5x² + 3x² + 15x + x² + 5x + 3x + 15
x³ + 9x² + 23x + 15
which is same of the form
ax³ + bx² + cx + d
Therefore, the given expression : (x + 1)(x + 3)(x + 5) can be written as (x³ + 9x² + 23x + 15)
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Find two supplementary angles if the measure of the first is four times the second. Helpful hint: supplementary angles have a sun of 180 degrees
Answer:
I denoted angle a by x and angle b by 4x .Hope it helps
What is the difference in the y values? 62 70 72
When we look for the constant rate of change, we subtract the first two y-values in the first place:
[tex]216-144=72[/tex]Hence, the difference is 72.If Jalen had 109 inches of string and Kelly had 3 yards of string, who had more string?
Answer: Jalen has more string then Kelly
Step-by-step explanation:
Converting Kelly's string from yards, to inches to match up with Kelly's length of string we use the formula:
#yd = (# × 36) = total amount of "
Inputting the information in the formula, It'd look like this:
5 yd = (5 × 36) = 108"
therefore, from this information the answer to the question, is Jalen.
Measurement and conversion (d = rt) Mackenzies bike can go 12 mph. She needs to be at a store at 10:00 A.M.. Of the store is 20 miles away, what time will she need to leave?
We have to use the equation
[tex]d=rt[/tex]Where r = 12 mph, d = 20 miles, let's find t.
[tex]\begin{gathered} 20=12t \\ t=\frac{20}{12}=\frac{10}{6}=\frac{5}{3} \end{gathered}[/tex]She'll take 5/3 hours to get there which is equivalent to 1 2/3 hours.
Let's transform 2/3 hours to minutes to find the exact time she has to leave.
We know that 1 hour is 60 minutes.
[tex]\frac{2}{3}hr\cdot\frac{60\min}{1hr}=\frac{120}{3}\min =40\min [/tex]So, she will take exactly 1 hour and 40 minutes.
If you have to get there at 10:00 A.M., then she has to leave at 8:20 A.M.Part A:
Solve this equation 1/2x-7=1/3(x-12)
Part B:
Explain or show your reasoning.
x = 18 in the equation given in the question that is 1/2x-7=1/3(x-12).
Simple equations is a linear equation involving variables with degree one. It contains mainly one variable.
Part A -
⇒ 1/2x-7=1/3(x-12)
⇒ 1/2x-7 = x/3 - 4
⇒ x/2 - x/3 = -4 + 7
⇒ 3x - 2x/6 = 3
⇒ x/6 = 3
⇒ x = 18
Part B -
According to equation 1/2x-7=1/3(x-12) we need to find x . So, first we open the brackets on the right hand side and then bring the variables to the l.h.s and the constants to the r.h.s . After that we take the lcm of x/2 and x/3 and equate it to 3. Then we get the value of x as 18.
Hence, x = 18 in the equation 1/2x-7=1/3(x-12).
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Quadrilateral ABCD has vertices A(-3,6), B(6,0),C(9,-9), and D(0, -3). Prove that ABCD isa) a parallelogramb) not a rhombus
We have the following vertices given:
A(-3,6), B=(6,0), C(9,-9), D=(0,-3)
a) We can begin find the distance between two points using this formula:
[tex]d=\text{ }\sqrt{(x_2-x_1)^2+(y_{2\text{ }}-y_1)^2}[/tex]For this case we need to find the distance between AD and BC and using the formula given we have:
[tex]AD=\text{ }\sqrt{(0+3)^2+(-3-6)^2}=\text{ }\sqrt{90}=\text{ 3}\sqrt{10}[/tex][tex]BC=\text{ }\sqrt{(9-6)^2+(-9-0)^2}=\text{ }\sqrt{90}=\text{ 3}\sqrt{10}[/tex]We see that both distances are equal. Now we can calculate the slopes for AD and BC and we got using this formula:
[tex]m=\text{ }\frac{y_2-y_1}{x_{2\text{ }}-x_1}[/tex][tex]_{}m_{AD}=\text{ }\frac{-3-6}{0+3}=\text{ }-3[/tex][tex]m_{BC}=\frac{-9-0}{9-6}=-3[/tex]Then we can conclude that the quadrilateral is a paralellogram because it has one pair of opposite sides that both congruent and parallel
b) For this problem is not a rhombus because not all the distances AB, AC, AD, BC and CD are equal
Which statement best explains whether y = 2x -3 is a linear function or a nonlinear function
y= 2x-3 is a linear function because the graph contains the points (0, −3), (1, −1), (2, 1), which are on a straight line.
Which statement best explains whether y = 2x − 3 is a linear function or a nonlinear function?
it is a linear function because the graph contains the points (0, −3), (1, −1), (2, 1), which are on a straight line.
It is a nonlinear function because the graph contains the points (0, −3), (1, −1), (2, 1), which are not on a straight line.
It is a linear function because the graph contains the points (−3, 0), (−1, 1), (1, 2), which are on a straight line.
It is a nonlinear function because the graph contains the points (−3, 0), (−1, 1), (1, 2), which are not on a straight line.
A linear equation has the following form:
y = mx + b
where
m is the slope
b is the y-intercept.
Given:
y = 2x - 3
by comparing it with linear equation,
y = y
m = 2
x = x
b = -3
so by this we can conclude that
y = 2x -3 is a linear function because the graph contains the points (0, −3), (1, −1), (2, 1), which are on a straight line
You can also perform a vertical line test. If the line touches your graphed function in more than one spot, it is not a function.
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I know this is discreet but unsure of the second part, of the question.
Integers are whole numbers, either positive or negative. In this scenario, the time can include fractions like 2.5. The values can range from 0 upwards
Thus, the correct option is the first one
m1=_
50
90
70
s
P
A
C
E
Answer:
50
Step-by-step explanation:
Use the formula: m<1 = 1/2(140-40) = 50
See attachment
AN ENGLISH EXAM CONSISTS OF TEN ESSAY QYESTIONS. IF A STUDENT MUST CHOOSE 4 OF THE 10 QUESTIONS HOW MANY DIFFERENT SETS OF 4 QUESTIONS ARE AVAILABLE?
Given
Number of questions in an english exam = 10
Find
Number of different sets of 4 questions are available.
Explanation
as we have given that a student must choose 4 of the 10 questions.
so , number of different set of 4 questions are available =
[tex]^{10}C_4[/tex]so ,
[tex]\begin{gathered} ^{10}C_4=\frac{10!}{4!(10-4)!} \\ \\ ^{10}C_4=\frac{10!}{4!6!} \\ \\ ^{10}C_4=\frac{10\times9\times8\times7\times6!}{4\times3\times2\times1\times6!} \\ \\ ^{10}C_4=\frac{5040}{24} \\ \\ ^{10}C_4=210 \end{gathered}[/tex]Final Answer
Hence , the number of different sets of 4 questions are available are 210
(25xy^2+75xyz+125x^2yz) / (-5x^2y)
(long division)
The answer of the long division is( -5/x)(y+3a+5x).
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
(25xy^2 + 75xyz +125x^2yz)]/(-5x^2y)[(25xy)(y+3z+5x)]/(-5x^2y)=[-5(y+3a+5x)]/x=(-5/x)(y+3a+5x)hence,The answer of the long division is( -5/x)(y+3a+5x).
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−9−5x>-1
2
-5
-10
Or none
Which of the following values are solutions to the inequality
Answer
If my answer is ok for you rate my answer
Answer:
-5 and -10
Step-by-step explanation:
-9-5(-5)
-9+25
=16
-9-5(-10)
-9+50
=41
Hey sorry, I just need an answer and an explanation of how you did your work. I'm having trouble on this topic but there aren't many math videos that can help me at the moment. Please be as detailed as possible with your explanation so I can get a sense of how you came to your conclusion, thank you.
After using the linear regression we would have the value for a and b. a and b represent the slope (a) of a line and the y-intercept (b).
To find the values of the equation we must round the results of the linear regression to the nearest integer
a would be equal to -2 as the number -1.96341463 is nearer to -2 than -1.
b would be equal to 19 as the number 19.09756098 is nearer to 19 than 20.
The final equation would be:
y= -2x + 19
Shaia has been monitoring her weight. In December, she weighed 167.5 pounds; by June the following year, she weighed 142.3 pounds. Calculate the absolute and relative change in Shaia's weight from December to June.
Step 1
Given; Shaia has been monitoring her weight. In December, she weighed 167.5 pounds; by June the following year, she weighed 142.3 pounds. Calculate the absolute and relative change in Shaia's weight from December to June.
[tex]\begin{gathered} new\text{ value=142.3} \\ reference\text{ value=167.5} \end{gathered}[/tex]Step 2
[tex]Absolute\text{ change=142.3-167.5=-25.2}[/tex][tex]\begin{gathered} relative\text{ change=}\frac{142.3-167.5}{167.5}=-\frac{252}{1675}\times100 \\ relative\text{ change=-}\frac{1008}{67}\text{ \%} \\ \end{gathered}[/tex]Answer;
[tex]\begin{gathered} Absolute\text{ change=-25.2} \\ Relative\text{ change=-15.04\%} \end{gathered}[/tex]in an art room there are three easels for every five children if there are 25 children how many easels are there
Given 3 easels for every 5 children
So, there are x easels for 25 children
Using the ratio and the proportional
3 : 5 = x : 25
[tex]\frac{3}{5}=\frac{x}{25}[/tex]so, solve for x
[tex]x=\frac{3\cdot25}{5}=\frac{75}{5}=15[/tex]So, the number of easels for 25 children = 15 easels
Can you explain to me why this question is wrong, and what are the right answers?
Answer:
cos(25) = sin(65)
sin(25) = cos(65)
tan(45) = tan(45)
Explanation:
To know which are the true statements, we will use the following identities
sin(θ) = cos(90 - θ)
cos(θ) = sin(90 - θ)
Therefore,
sin(25) = cos(90 - 25)
sin(25) = cos(65)
cos(25) = sin(90 - 25)
cos(25) = sin(65)
Additionally, tan(45) is equal to itself, so
tan(45) = tan(45)
Therefore, the true statements are
cos(25) = sin(65)
sin(25) = cos(65)
tan(45) = tan(45)
housing uses 3 cups of sugar to make 36 muffins how many cups of sugar will she need to make 60 muffins
housing uses 3 cups of sugar to make 36 muffins how many cups of sugar will she need to make 60 muffins
3 per 36
36 / 3 = 12
_______________
1 cups per 12 muffins
5.32 rounded to the nearest whole number
Answer:
5
Step-by-step explanation:
Example: Anything 0.49 and under rounds to 0. Anything 0.5 and up rounds to 1.
Brainliest, Please!Given:
The number 5.32.
To find:
Its approximate value when rounded to the nearest whole number.
Explanation:
In the number: 5.32. To round it to the nearest whole number means to remove the decimal part but following the rules of approximation.
When rounding to the nearest whole number:
If the number after the decimal point is 0,1,2,3, and 4, we write the result as it is.If the number after the decimal point is 5 and above, we add 1 to the whole number part.In this case, the number after the decimal point is 3, therefore: 5.32=5
Answer: The number 5.32 rounded to the nearest whole number is 5.
A shoe store marks up the price of shoes by 35%. Jill wants to buy a pair of shoes that cost $135. What was the wholesale price?
The wholesale price of the pair of shoe Jill bought is 100 dollars.
How to find the wholesale price of the shoe?Mark up is the difference between a product's selling price and cost as a percentage of the cost.
The shoe store marks up the price of shoes by 35%. Jill wants to buy a pair of shoes that cost $135. The wholesale price of the of the shoe can be calculated as follows:
mark up % = 135 - x / x × 100
where
x = wholesale price35 = 13500 - 100x / x
cross multiply
35x = 13500 - 100x
35x + 100x = 13500
135x = 13500
divide both sides by 135
x = 13500 / 135
x = 100 dollars
Therefore,
whole sale price = 100 dollars
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Caley is trying to find the best deal on a flight from New York to Orlando. She checks the price each week and tracks how much it changes.
After 3 weeks she pay $208.10.
From the question, we have
After 3 weeks she pay =
$211.30+$22.50-$17-$8.70 = $208.10
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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SOMEONE PLSS HELP FOR QUESTION 1
Answer:
triangle abc is has same degres of angles with triangle def, but def is smaller in 3 times. it's only what i know, sorry if i not help
i think yea, they has a same angles, but def smaller in 3 times so i think yes
Find the magnitude and direction angle of the resultant of each pair of vectors.
1) m =(-15, 16) n = (2, -6)
2) t = (12, 16) u =(-12, 16)
3) m =(-17, 3) n = (8, 15)
4) a = (-6, 8) b = (19, 14)
5) t=(-12, -16) u = (15, 2)
6) a =(-8, 15) b = (16, -9)
AnsweStep-by-step explanation:
9134
Question 9 (1 point)Your new T-shirt shrank slightly when it was washed and dried. What scale factor below could best describe this dilation?abOcOd1.31.00.90.1←QX
Solution
- The shirt shrank a little. This implies that when you take the ratio of the dimensions of the shrunk shirt, and that of the original shirt.
- This would mean that the scale factor (the result from the above ratio), would be less than 1. But it would not be that much less than 1.
- Thus, the possible scale factor is 0.9