Given:
The initial population is p = 26 million.
The decreasing percentage is r = 15% each year = 0.15.
The objective is to write the sequence of population after 4 years.
Explanation:
The general formula of population decrease is,
[tex]A=P(1-r)^t\text{ . . . . .(1)}[/tex]The population in the 1st-year can be calculated by substituting t=1 in equation (1).
[tex]\begin{gathered} A_1=26(1-1.15)^1 \\ =26(0.85) \\ =22.1\text{million} \end{gathered}[/tex]The population in the 2nd year can be calculated by substituting t=2 in equation (1).
[tex]\begin{gathered} A_2=26(1-0.15)^2 \\ =26(0.85)^2 \\ =18.785million \end{gathered}[/tex]The population in the 3rd year can be calculated by substituting t=3 in equation (1).
[tex]\begin{gathered} A_3=26(1-0.15)^3 \\ =26(0.85)^3 \\ =15.967255million \end{gathered}[/tex]Hence, the population for the first 4 years will be,
26million,
22.1million,
18.785million,
15.967255million.
Plssss help!
Geometry A
Brainliest
Answer:
18 ft.
Step-by-step explanation:
Please help topic is geometry
Image of point O(-2,-1) after two reflections , first across the line y=5 and then across the line x = 2 is (6,11) .
What do you mean by reflection in coordinate plane?
A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context.
Given point is O(-2,-1)
It is given that point O has reflected twice,
Firstly point O has reflected across the line y= 5
So, it become ,
(-2,11)
Secondly, it is reflected across the line x = 2
So, it become,
(6,11)
Hence, image of point O(-2,-1) after two reflections , first across the line y=5 and then across the line x = 2 is (6,11) .
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Use the line of best fit to make a
conjecture about the value of
Heather's portfolio at the end of
year 8.
Answer: 25
Step-by-step explanation:
Write the coefficient of x in the following terms
3. xy
1. 24x
4. x
2. abx
5. 3xy
6. xyz
Answer:
1. 1
2. 24
3. 1
4. 1 [ab]
5. 3
6. 1
Step-by-step explanation:
Every variable or alphabet's coefficient is the number on the left of it.
e. g coefficient of x is 1.
or coefficient of 83x is 83
HELP ME PLEASE. i need this math project done and there's an hour left on the deadline!! find the volume of air in the lungs 4 seconds into the reparatory cycle
Answer:
The volume of air that is coming in and going out is 500 ml. A single respiratory cycle takes 4 seconds to complete. The residual volume of air left in the lungs after the completion of the cycle is 2000 ml.
Im an older lady not the best at this type of math please help
We need to first find the intersection between Q and R, which is the common elements between both groups. We have:
[tex]Q\cap R=\mleft\lbrace r,e,x\mright\rbrace[/tex]Now we need to determine the union between them:
[tex]P\cup(Q\cap R)=\mleft\lbrace e,x,a,c,t,r,e,x\mright\rbrace[/tex]- 6(x - 2) = 36 or 4 + x < 14 Step 3 of 4: Using your answers from the previous steps, solve the overall inequality problem and express your answer in interval notation. Use decimal form for numerical values.
Question:
Solution:
Consider the following inequalities system :
Inequality 1:
[tex]-6(x-2)\text{ }\leq36[/tex]or
Inequality 2:
[tex]4+x<14[/tex]Applying the distributive property in inequality 1, we obtain:
[tex]-6x+12\text{ }\leq36[/tex]this is equivalent to:
[tex]-6x\text{ }\leq36-12\text{ = 24}[/tex]that is:
[tex]-6x\leq24[/tex]this is equivalent to:
[tex]6x\ge-24[/tex]solving for x, we get:
[tex]x\text{ }\ge-\frac{24}{6}\text{ = -4}[/tex]that is:
[tex]x\text{ }\ge\text{ -4}[/tex]Then inequality 1 is equivalent to the following solution
[tex]x\text{ }\ge\text{ -4}[/tex]On the other hand, for inequality 2 solving for x, we get:
[tex]x<14-4\text{ = 10}[/tex]that is:
[tex]x<10[/tex]so that, the solution to the inequality system is
[tex]x\text{ }\ge\text{ -4}[/tex]or
[tex]x<10[/tex]now, this is equivalent to say:
[tex]x\text{ }\ge\text{ -4 U x<10}[/tex]or in interval notation:
[tex]\lbrack-4,+\infty)\text{ U (-}\infty\text{,10) }[/tex]one step equations z/4=12
To solve;
z/4=12
Multiply both-side of the equation by 4
That is;
[tex]\frac{z}{4}\text{ }\times\text{ 4 = 12 }\times4[/tex]At the left-hand side of the equation 4 will cancel-out 4 leaving us with just z
z = 48
William is 4 years older than three times Alex's age . William is 31 years old . How old is Alex
Answer:
13
Step-by-step explanation:
.
Answer:
Alex is 14 years old.
Step-by-step explanation:
You can take William's age and divide it by 3, because William is 3 times the age of Alex:
31 divided by 3 = 10.33.
So, we will just say 10 for now.
Now, we add 4 to the 10 because WIlliam is 4 years older than three times his age.
So, in conclusion, Alex is 14 years old.
May I have Brainliest please? I am so close to getting my next ranking! I just need 2 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
110.4 ÷4 step bye step show me pictures
we ahve
110.4 ÷4
so
110.4/4
Multiply by 10/10 the expression
1104/40
simplify
1104/40=552/20=276/10=27.6
the answer is 27.6
how do you divide a number into a number with an exponent?
To divide a number into a number with an exponent
So, factor the number then put it to the power of (how many will appear)
for example :
8 = 2 * 2 * 2
so, there are 3 of the number 2
So,
8 = 2^3
An element with a mass of 990 grams decays by 27.8% per minute. To the nearest minute, how long will it be until there are 50 grams of the element remaining?
It will take 9.21 minutes until 50 grams.
What is decay?
"Decay" means "decrease". If the rate of decrease of a quantity is proportional to its current value, then we say that it is subject to exponential decay.
Formula of decay,
f(t) = a(1-r)^t
f(t) is the value after decay.
r is rate
t is time and a is initial value
Given,
initial mass was 990.
rate = 0.278
after decay = 50 gram.
We get,
50 = 990(1-0.287)^t
50/990 = (0.723)^t
taking log on both side.
t = 9.21
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Drag each number to the correct location on the image.
Classify the real numbers below as rational or irrational numbers.
AWNSER GETS BRAIN
Answer:
Step-by-step explanation:
1. Square root of 8 is not a rational number.
2. 1/4 is a rational number.
3. Square root of 90 is not a rational number.
4. 2/3 is a rational number.
5. Square root of 4 is not a rational number.
6. /2 is not a rational number.
7. is not a rational number.
I think these are right, please give me brainliest.
4.
The coordinates of the vertices of a rectangle are A (5, 3),
B (5,-9), C (-1,-9), and D (-1, 3).
D
Which measurement is closest to the distance between point B and
point D in units?
The distance between the points B (5 , -9) and D (-1 , 3) is 13.491 units.
Given, the coordinates of the vertices of a rectangle
A (5, 3), B (5,-9), C (-1,-9), and D (-1, 3)
Now we have to find the distance between B and D
On using the distance formula, we get
Distance = √((x1 - x2)² + (y1 - y2)²)
Distance = √(5 - (-1))² + (-9 - 3)²
Distance = √(6)² + (-12)²
Distance = √36 + 144
Distance = √180
Distance = 13.491 units
Hence, the distance between the points B (5 , -9) and D (-1 , 3) is 13.491 units.
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Why is it difficult to solve one verr two minus one over eight without using a common denominator
To substract two fractions, we have to have common denominators.
For example, if we want to substract 1/3 from 1/2, we have to convert the fractions so they have a common denominator of 6.
The denominators are the ones that give sense to the fraction. In fact, when we substract whole numbers, we can consider we are substracting "fractions of one".
Then, for example, 5 - 4 could have been written as 5/1 -4/1.
If the numbers have different denominators, we can not perform additions or substractions until we express the fractions with the same denominator.
Trying to substract two fractions with different denominators is like substracting two things that are not expressed in the same units and it will yield an incorrect result.
What is the volume of a hemisphere with radius 3 ft? What is the volume of a hemisphere with diameter 13 cm?
The volume of a sphere is given by
[tex]V_s=\frac{4}{3}\pi r^3[/tex]Since a hemisphere is half sphere, its volume is given by
[tex]\begin{gathered} V_{}=\frac{4}{6}\pi r^3 \\ \text{which is equivalent to} \\ V_{}=\frac{2}{3}\pi r^3 \end{gathered}[/tex]where r is the radius.
Case a.
In this part r=3 ft, then by substituting this values into our last formula we get
[tex]V=\frac{2}{3}(3.1416)(3^3)[/tex]which gives
[tex]V=56.55ft^3[/tex]Case b.
In this part r=(13/2) cm, then by substituting this values into our last formula we get
[tex]V=\frac{2}{3}(3.1416)(6.5^3)[/tex]which gives
[tex]V=287.59cm^3[/tex]Solve the system using the substitution technique:(−6, −3.6)(0.6, 0.8)(6, 4.4)(−0.6, 0)
Given
The system of equations,
[tex]\begin{gathered} -2x+3y=1.2\text{ \_\_\_\_\_}(1) \\ -3x-6y=1.8\text{ \_\_\_\_\_}(2) \end{gathered}[/tex]To find the solution using substitution technique.
Explanation:
It is given that,
[tex]\begin{gathered} -2x+3y=1.2\text{ \_\_\_\_\_}(1) \\ -3x-6y=1.8\text{ \_\_\_\_\_}(2) \end{gathered}[/tex]That implies,
[tex]\begin{gathered} (1)\Rightarrow-2x+3y=1.2 \\ \Rightarrow3y=1.2+2x \end{gathered}[/tex]And,
[tex]\begin{gathered} (2)\Rightarrow-3x-6y=1.8 \\ \Rightarrow-3x-2(3y)=1.8 \end{gathered}[/tex]Substitute 3y=1.2+2x in the above equation.
That implies,
[tex]\begin{gathered} -3x-2(1.2+2x)=1.8 \\ -3x-2.4-4x=1.8 \\ -7x=1.8+2.4 \\ -7x=4.2 \\ x=\frac{4.2}{-7} \\ x=-0.6 \end{gathered}[/tex]And, substitute x=-0.6 in (1).
That implies,
[tex]\begin{gathered} (1)\Rightarrow-2(-0.6)+3y=1.2 \\ \Rightarrow1.2+3y=1.2 \\ \Rightarrow3y=1.2-1.2 \\ \Rightarrow3y=0 \\ \Rightarrow y=0 \end{gathered}[/tex]Hence, the solution is (-0.6,0).
7. Compare Ann and Barry Lindale's expenses for renting versus owning a home inthe table below.a. Complete each table.b. Is it less expensive for them to buy or rent a home, and what is the difference?
To complete the tables, we multiply the given numbers:
First table:
[tex]\begin{gathered} Rent:\text{ 850}\times12=10200, \\ Phone,\text{ Internet \& Cable TV: }99\times12=1188. \end{gathered}[/tex]Second table:
[tex]Phone,\text{ Internet \& Cable TV: }99\times12=1188.[/tex]Now, to determine which option is less expensive we compute the total annual expenses for each case:
1.-Rental:
[tex]10200+45+180+1560+2400+1188=15,573.[/tex]2.- Homeowner:
[tex]6600+3600+480+1710+2400+1188+570+960+1180=18,688.[/tex]From the above calculations, we can conclude that the cheaper option based on the given annual expenses is to rent.
Answer:Renting is less expensive.
Ava ,cole and Zane have a total of 175 stickers.the ratio of the number of stickers Ava has to the number of stickers cole has is 5:3. The ratio of the number of the number of stickers cole has to the number of stickers Zane has in 2:3. How many stickers do Ava have?
Ava has 70 stickers.
Given that the ratio of the number of stickers Ava has to the number of stickers Cole has = 5:3 = 10:6
Also, the ratio of the number of stickers Cole has to the number of stickers Zane has = 2:3 = 6:9
Thus, the compounded ratio of the number of stickers Ava, Cole and Zane has is = 10:6:9
Let the numbers of stickers of Ava has be = 10x
The number of stickers of Cole has, is = 6x
The number of stickers of Zane has, is = 9x
According to question, the total number of stickers they have is 175. So,
10x+6x+9x = 175
25x = 175
x = 175/25
x = 7
Hence Ava has = 10x = 10*7 = 70 stickers.
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Exercise #99) g(x) = x3 + x f(x) = 2x-3 - 3 Find (gof)(x)
Given two functions f(x) and g(x), its composition will be:
[tex](g\circ f)=g(f(x))[/tex]It is read g compound f or simply said to g we are going to fill it with f. So, you have
[tex]\begin{gathered} (g\circ f)=g(f(x)) \\ (g\circ f)=(2x-3)^3+(2x-3) \end{gathered}[/tex]To expand the binomial, apply the binomial formula to the cube, that is:
[tex](a-b)^3=a^3-3a^2b+3ab^2-b^3[/tex]So, you have
[tex]\begin{gathered} (g\circ f)=(2x-3)^3+(2x-3) \\ (g\circ f)=(2x)^3-3(2x)^2(3)+3(2x)(3)^2-(3)^3+(2x-3) \\ (g\circ f)=2^3x^3-3(2^2x^2)(3)+3(2x)9-27+(2x-3) \\ (g\circ f)=8x^3-3(4x^2)(3)+54x-27+(2x-3) \\ (g\circ f)=8x^3-36x^2+54x-27+2x-3 \end{gathered}[/tex]Finally, operate similar terms
[tex](g\circ f)=8x^3-36x^2+56x-30[/tex]If you know that 84 is 70% of the whole, how can you use proportional reasoning to determine the whole?
70100 shows 70% as a ratio. The ratio 84x compares 84 to the whole, x. Write an equation so that the first ratio is equal to the second ratio. Solve for x : x = 120.
70100 shows 70% as a ratio. The ratio 84x compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 58.8.
70100 shows 70% as a ratio. The ratio x84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.
70100 shows 70% as a ratio. The ratio x84 compares 84 to the whole, x. Write an equation so that the first ratio is equal to the second ratio. Solve for x : x = 58.8.
The value of x is 120.
70/100 shows 70% as a ratio. The ratio x : 84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.
Given, that 84 is 70% of the whole.
Let the whole be x,
According to the question,
(70/100) × x = 84
On multiplying both the sides by 100/70, we get
x = 84×100/70
Now, on solving the expression, we get
x = 120
Hence, 70/100 shows 70% as a ratio. The ratio x : 84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.
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Statement: A fitness club advertises a special for new members. Each month, m, of membership is $19, with an initial enrollment fee of $75. Write an expression for the cost of membership. Then, find the cost of 8 months of membership
Given:
Monthly membersihp fee is, m = $19.
Initial enrollment fee is, i = $75.
The objective is to write a cost expression and to fnd the cost for 8 months of membership.
From the given data, the enrollment fee is an one time payment. But the monthly membership fee is a variable cost with respect to number of months x.
Then, the expression can be represented as,
[tex]y=19x+75[/tex]Here, y stands for cost, x stands for number of months.
Thus, the required cost expression is obtained.
To find the cost for 8 months, substitute x = 8 in the cost expression.
[tex]\begin{gathered} y=19(8)+75 \\ y=152+75 \\ y=227 \end{gathered}[/tex]Hence, the cost for 8 months is $227.
Caleb wants to buy a pair of shoes that cost $49.95. He also wants to buy a T-shirt, but he cannot spend more than $60. He needs to calculate how much he can spend on a T-shirt. Which inequality models this situation?
Answer:
C) x + 49.95 ≤ 60Step-by-step explanation:
Let the cost of T-shirt is x.
The cost of pair of shoes is $49.95 and the total should be no more than $60.
This can be modeled as:
x + 49.95 ≤ 60The matching choice is C.
The Associative Property applies to which operations? Check all that apply.
Hello! First, let's remember what is Associative Property:
It is a mathematical rule who says that the order of the factors doesn't change the final result of a calculus.
We have the associative property in two mathematical operations, I'll show you some examples:
If we want to sum three numbers, 5, 10 and 15, how is the right way? We have some ways to do it:
(5+10)+15 = (15)+15 = 30
(5+15)+10 = (20)+10 = 30
5+(10+15) = 5+(25) = 30
So, no matter the order of the numbers, we will always get the same result.
An example with the other operation now:
If we want to multiply three numbers, 2, 3 and 5:
(2*3)*5 = (6)*5 = 30
(2*5)*3 = (10)*3 = 30
2*(3*5) = 2*(15) = 30
Also, no matter the order of the factors, we'll always obtain the same result.
However, in the subtraction and in the division we have to follow the right order, according to the precedence, so we can't use the Associative Property on these operations.
Right answer: C and D.
Please help me solve for X, I am including a picture
Answer:
x = 14
Explanation:
To get the value of x, we wll be using the SOH CAH TOA identity
Using sin theta = opposite/hypotenuse
[tex]\begin{gathered} sin45\text{ = }\frac{h}{7\sqrt[]{6}} \\ h\text{ =7}\sqrt[]{6}\text{ sin45} \\ h\text{ = 7}\sqrt[]{6}\times\frac{1}{\sqrt[]{2}} \\ h\text{ = 7}\sqrt[]{3} \end{gathered}[/tex]h is the vertical height of the triangles.
Next is to get the value of x;
Similarly;
[tex]\begin{gathered} \sin \text{ 60 = }\frac{h}{x} \\ \text{ sin60 = }\frac{7\sqrt[]{3}}{x} \\ x\text{ = }\frac{7\sqrt[]{3}}{\sin 60} \\ x\text{ = }\frac{7\sqrt[]{3}}{\frac{\sqrt[]{3}}{2}} \\ x\text{ = 7}\sqrt[]{3}\times\frac{2}{\sqrt[]{3}} \\ x\text{ = 7}\cdot2 \\ x\text{ =14} \end{gathered}[/tex]Hence the value of x required is 14
help with this one to
Answer:
D
Step-by-step explanation:
even
4(-x^3) = 4x^3
-4x^3 = 4x^3 (false)
odd
-4x^3 = 4(-x^3)
-4x^3 = -4x^3
A store manager paid $44.00 for a shirt. She marked up the price of the shirt by 80% and then sold the shirt what was the selling price of the shirt
Cost price = $44
mark up percent = 80% = 80/100 = 0.8
selling price = ?
The markup formula:
[tex]markup=\text{ }\frac{selling\text{ price - cost price}}{\cos t\text{ price}}[/tex][tex]\begin{gathered} 0.8=\text{ }\frac{selling\text{ price - 4}4}{44} \\ \text{cross multiply:} \\ \text{0.8(44) }=\text{ selling price - 44} \\ \end{gathered}[/tex][tex]\begin{gathered} 35.2\text{ = selling price - 44 } \\ 35.2\text{ + 44 = selling price } \\ \text{selling price = \$79.2} \end{gathered}[/tex]Follow the steps to solve the equation.
Given equation is
[tex] \sqrt[3]{x {}^{2} - 7 } = \sqrt[3]{2x + 1} [/tex]
to solve this equation we first need to cube both the sides . As this would remove the cube root on both the sides ,
[tex]\longrightarrow (\sqrt[3]{x^2-7})^3 = (\sqrt[3]{2x+1})^3[/tex]
This would become ,
[tex]\longrightarrow x^2-7=2x+1 \\[/tex]
[tex]\longrightarrow x^2-2x-7-1=0\\[/tex]
[tex]\longrightarrow x^2-2x-8=0\\[/tex]
[tex]\longrightarrow x^2 -4x +2x -8=0\\[/tex]
[tex]\longrightarrow x(x-4)+2(x-4)=0\\ [/tex]
[tex]\longrightarrow (x+2)(x-4)=0\\[/tex]
[tex]\longrightarrow \underline{\underline{ x = 4,-2}} [/tex]
And we are done!
Answer:
[tex]\textsf{To solve the given equation, $\boxed{\sf cube}$ both sides}.[/tex]
Step-by-step explanation:
Given equation:
[tex]\sqrt[3]{x^2-7} =\sqrt[3]{2x+1}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies (x^2-7)^{\frac{1}{3}}=(2x+1)^{\frac{1}{3}}[/tex]
Cube both sides of the equation:
[tex]\implies \left( (x^2-7)^{\frac{1}{3}}\right)^3= \left((2x+1)^{\frac{1}{3}}\right)^3[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies (x^2-7)^{\frac{3}{3}}=(2x+1)^{\frac{3}{3}}[/tex]
[tex]\implies (x^2-7)^{1}=(2x+1)^{1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]
[tex]\implies x^2-7=2x+1[/tex]
Subtract 2x from both sides:
[tex]\implies x^2-2x-7=1[/tex]
Subtract 1 from both sides:
[tex]\implies x^2-2x-8=0[/tex]
Rewrite -2x as (-4x + 2x):
[tex]\implies x^2-4x+2x-8=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-4)+2(x-4)=0[/tex]
Therefore:
[tex]\implies (x+2)(x-4)=0[/tex]
Apply the zero-product property:
[tex]x+2=0 \implies x=-2[/tex]
[tex]x-4=0 \implies x=4[/tex]
Subtract 7x minus 8 from 2x^2- minus 1
Expression 2x²-(-1) - [7x-8] is equal to 2x² - 7x +9
Expression is combination of math operations , numbers and unknown variables.
Math operation can be subtraction , addition , multiplication or division.
There are two types of expression : numerical expression and algebraic expression . Expression consists of only numbers are numerical where expression containing numbers and variables are algebraic expression.
Subtract 7x-8 from 2x²-(-1)
2x²-(-1) - [7x-8]
product of two minus is plus
2x²+1 -[7x-8]
open the bracket and change the minus sign
2x²+1 - 7x + 8
there is no x² and x term so,
2x² - 7x +1+8
2x² - 7x +9 is our required expression
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Fence A is 1 1/2 yards long but is 1 4/5 inches long on the blueprint. What is the unit rate per yard on this blue print? If fence B is 10 yard king,how long is fence B on the blueprint
The unit rate per yard is 0.03yards per unit
The length of fence B is 0.3yards
What is unit rate?A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. In fact, unit rate is said to be the amount of something in each unit or per unit.
Fence A which is 1 1/2yards but 1 4/5inches on blueprint. 1 inch = 0.0278 yards
blueorint reading = 9/5×0.0278=0.05=5/100yards
therefore the scale is 3/2 : 5/100 = 3/2÷5/100
= 3/2×100/5= 1:30 = 0.03 :1
therefore the unit rate / yard = 0.03yardperunit
if a fence B is 10yards then on the blueprint it will be 10×0.03= 0.3yards
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