2 x 2 is two times two
answer: 4
The population P of a city is given by P = 115600e^0.024t, where t is the time in years. According to this model, after how many years will the population be 130,000?4.29 years4.89 years5.19 years4.49 years
Given:
The population P of a city is given by,
[tex]P=115600e^{0.024t,}[/tex]To find:
The time taken for the population to reach 130,000.
Explanation:
Substituting P = 130,000 in the given function, we get
[tex]\begin{gathered} 130000=115600 \\ e^{0.024t}=\frac{130000}{115600} \\ e^{0.024t}=1.1245 \\ 0.024t=\ln1.1245 \\ 0.024t=0.1174 \\ t=4.891 \\ t\approx4.89years \end{gathered}[/tex]Therefore, the number of years required for the population to reach 130,000 is 4.89years.
Final answer:
The number of years required is 4.89years.
1 - The Le Mans car race is a 24-hgur race. The longest distance erertraveled by a car in the race is 3,315 miles. What is the distancerounded to the nearest ten?2- The longest river in the world is the Nile. It is 4,184 miles long.What is the length of the Nile River rounded to the nearesthundred miles?3- Frank rounds 846,025 to the nearest hundred thousand and to the nearest ten thousand.Part A What is 846,025 rounded to the nearest hundred thousand?Part B What is 846,025 rounded to the nearest ten thousand?Part C Which rounded number is greater? Explain.
1. To find the nearest ten of 3315.
Since 15 is midway between 10 and 20.
So, the nearest ten of 3315 is 3320.
2. To find the nearest hundred miles of 4,184 miles:
184 is closest to 200.
Hence, the nearest hundred miles of 4,200 miles.
3.
A) To find the nearest hundred thousand of 846,025:
846,025 is closest to 800,000.
Hence, nearest hundred thousand of 846,025 is 800,000.
B) To find the nearest ten thousand of 846,025:
46,025 is closest to 50,000.
Hence, nearest ten thousand of 846,025 is 850,000.
C) Comparing the results of Part A and Part B,
The rounded number of Part B is greater.
how do I have to search x in a triangle??
1) the value of x is 7
Explanation:1) From the diagram, the angles with the red ink are equal.
SInce the two angles at the base are equal, we call the triangle an isosceles triangle.
This triangle have two sides and two angle equal.
As a result, the sides opposite the angles given in the triangle are equal to each other.
The sides opposite the angles are x and 7. So, x is equal to 7.
Hence, the value of x is 7
The same principle or procedure can be applied to question number 2.
5x + 4y = 12Step 1 of 2: Determine the missing coordinate in the ordered pair (0) so that it will satisfy the given equation,
Answer:
Explanations:
Given the equation;
[tex]5x+4y=12[/tex]In order to get the missing coordinate in the ordered pair (0, ?), we will substitute x = 0 into the equation and get the corresponding y-value as shown:
[tex]\begin{gathered} 5(0)+4y=12 \\ 0+4y=12 \\ 4y=12 \end{gathered}[/tex]Divide both sides of the equation by 4;
[tex]\begin{gathered} \frac{4y}{4}=\frac{12}{4} \\ y=3 \end{gathered}[/tex]Therefore, the missing coordinate will be 3 to have (0, 3)
simplify the expression tan (3 x+ 2pi) as the tangent of a single angle
tan(3x)
Explanation
[tex]\tan (3x+2\pi)[/tex]Step 1
remember some property
[tex]\tan (a+b)=\frac{\tan a+\tan b}{1-\tan a\tan b}[/tex]then
[tex]\begin{gathered} \tan (3x+2\pi)=\frac{\tan 3x+\tan 2\pi}{1-\tan 3x\tan 2\pi}\text{ Equation(1)} \\ \tan \text{ 2}\pi=0 \\ so \\ \tan (3x+2\pi)=\frac{\tan 3x+0}{1-\tan 3x\cdot0}\text{ } \\ \tan (3x+2\pi)=\frac{\tan \text{ 3x}}{1-0}=\frac{\tan \text{ 3x}}{1} \\ \tan (3x+2\pi)=\tan (3x) \end{gathered}[/tex]I hope this helps you
A college had 5,000 students in 2018. The number of students decreased by 10% in 2019 andanother 5% in 2020. How many students did the college have in 2020? (1 point)
Okay, here we have this:
Inicially we have 5000 students, let's calculate how many were left in 2019:
Students in 2019=5000*0.9
Students in 2019=4500
Now, let's finally calculate how many were left in 2020:
Students in 2020=4500*0.95
Students in 2020=4275
Finally in 2020 they were 4275 students
Which integer represents this scenario? a fish grows 4 inches a) -4" b) 4” 6.NS.5
as it is about growth, the integer is positive, therefore
answer is b) 4"
The student Fun Club plans to go to the movies. At the matinee, tickets cost $6 and popcorn is $3. At evening shows, tickets cost $9 and popcorn is $4. The Fun Club attends a matinee and spends less than $60, and then attends an evening show and spends more than $36. If they purchased the same number of tickets and popcorns at each show, which of the following is a possible solution for the number of tickets and popcorns purchased?
Matinee
Cost of each ticket: $6
Cost of popcorn: $3
Evening:
Ticket: $9
Popcorn: $4
Number of tickets: x
Number of popcorns : y
The Fun Club attends a matinee and spends less than $60
6x + 3y < 60
Then attends an evening show and spends more than $36
9x+ 4y < 36
We have the system:
6x + 3y < 60 (a)
9x+ 4y >36 (b)
Graph each inequality:
The intersection of red and blue is the solution.
7 tickets and 5 popcorns (7,5) is inside the intersection, So, it is the solution.
10 Natalie uses a 15% off coupon when she buys a camera. The original price of the camera is $45.00. How much money does Natalie save by using the coupon.?
Given data:
The given discount through coupon is d=15%.
The original price of camera is c=$45.00.
The discount on the given amount is,
[tex]\begin{gathered} d=(\frac{15}{100})(45) \\ =6.75 \end{gathered}[/tex]Thus, the amount saved is $6.75.
The United States Pentagon building is modeled on the coordinate plane as regular pentagon ABThe vertices of the pentagon are A(-7.42,2.42), B(0,7.88),C(7.42,2.42),D(4.605,-6.35), and E(-4.605-6.35) what is the approximate perimeter in feet of the us pentagon building
Given,
The coordinates of the vertices of the pentagon is,
A(-7.42,2.42), B(0,7.88), C(7.42,2.42),D(4.605,-6.35), and E(-4.605-6.35)
Required
The approximate perimeter of the pentagon.
The perimeter of the pentagon is calculated as,
The length of side AB is,
[tex]AB=\sqrt{(-7.42-0)^2+(2.42-7.88)^2}=\sqrt{84.868}=9.2124[/tex]The length of side BC is,
[tex]AB=\sqrt{(7.42-0)^2+(2.42-7.88)^2}=\sqrt{84.868}=9.2124[/tex]The length of side CD is,
[tex]CD=\sqrt{(4.605-7.42)^2+(-6.35-2.42)^2}=\sqrt{84.8371}=9.211[/tex]The length of DE is,
[tex]DE=9.21[/tex]The length of AE is,
[tex]CD=\sqrt{(4.605-7.42)^2+(-6.35-2.42)^2}=\sqrt{84.8371}=9.211[/tex]The perimeter of the pentagon is,
[tex]Perimeter=9.2124+9.2124+9.211+9.211+9.21=46.0568[/tex]Hence, the perimeter of the pantagon is 46.0568.
Solve each equation by using the square root property. X^2–6x+9=4
We have the following:
[tex]\begin{gathered} x^2-6x+9=4 \\ \end{gathered}[/tex]solving by the square root property
[tex]\begin{gathered} x^2-6x+9=4 \\ x^2-6x+9-9=4-9 \\ x^2-6x=-5 \\ x^2+2ax+a^2=\mleft(x+a\mright)^2 \\ 2ax=-6x \\ 2a=-6\rightarrow a=-3 \\ x^2-6x+(-3)^2=-5+(-3)^2 \\ (x-3)^2=-5+(-3)^2 \\ (x-3)^2=-5+9 \\ x-3=\pm\sqrt[]{4} \\ x=\sqrt[]{4}+3=2+3=5 \\ x=-\sqrt[]{4}+3=-2+3=1 \end{gathered}[/tex]which of the following equations is a direct variation equation that has the ordered pairs 12.5, 5 as a solutiona. y=7.5xb. y=x-7.5c. x=y+7.5d. y=2.5x e. y= -2.5x f. (2/5)x
The ordered pair given is 12.5, 5
This means that
When x = 12.5, y = 5
Looking at the given equations, if we substitute the values of x and y, the correct option would be C
The equation is expressed as
x = y + 7.5
By substituting, it becomes
12.5 = 5 + 7.5
12.5 = 12.5
The correct option is C
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 7z
Answer:
(-3, 4)(5, 0)=====================
Given systemx + 2y = 5 x² + y² = 25Rearrange the first equationx = 5 - 2y Substitute the value of x into second equation(5 - 2y)² + y² = 254y² - 20y + 25 + y² = 255y² - 20y = 0y² - 4y = 0y(y - 4) = 0y = 0 and y = 4Find the value of xy = 0 ⇒ x = 5 - 2*0 = 5y = 4 ⇒ x = 5 - 2*4 = -3Answer:
[tex](x,y)=\left(\; \boxed{-3,4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{5,0} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}\;x+2y=5\\x^2+y^2=25\end{cases}[/tex]
To solve by the method of substitution, rearrange the first equation to make x the subject:
[tex]\implies x=5-2y[/tex]
Substitute the found expression for x into the second equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}x=5-2y \implies (5-2y)^2+y^2&=25\\25-20y+4y^2+y^2&=25\\5y^2-20y+25&=25\\5y^2-20y&=0\end{aligned}[/tex]
Factor the equation:
[tex]\begin{aligned}5y^2-20y&=0\\5y(y-4)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for y:
[tex]5y=0 \implies y=0[/tex]
[tex]y-4=0 \implies y=4[/tex]
Substitute the found values of y into the first equation and solve for x:
[tex]\begin{aligned}y=0 \implies x+2(0)&=5\\x&=5\end{aligned}[/tex]
[tex]\begin{aligned}y=4 \implies x+2(4)&=5\\x+8&=5\\x&=-3\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{-3,4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{5,0} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
2/7 in reduced terms
2/7 is in reduced terms already
no simplification can be made over this fraction.
hope it is clear
Generalize Two data sets have the same number of values. The first data set has a mean of 7.2 and a standard deviation of 1.25. The second data set has a mean of 7.2 and a standard deviation of 2.5. Which data set is more spread out?
ANSWER
The second data set is more spread out
EXPLANATION
The standard deviation measures the spread of a data distribution. The more spread out a data distribution is, the greater its standard deviation.
In this problem, the second data set has twice the standard deviation of the first data set, so it's more spread out.
7/8 = 7/16 =Reduce your answer to the lowest terms.
012Explanation34BCheck5Use the figure and the table to answer the parts below.67(a) Find the probability that a real number between 4 and 6 is picked.08(b) Find the probability that a real number between 4 and 7 is picked.0RegionABCXArea0.320.560.12 I need help with this math problem
Given:
The graph is:
Find-:
(a)
Find the probability that a real number between 4 and 6 is picked.
(b)
Find the probability that a real number between 4 and 7 is picked.
Explanation-:
The area of the region
[tex]\begin{gathered} \text{ Region }\rightarrow\text{ Area} \\ \\ A\rightarrow0.32 \\ \\ B\rightarrow0.56 \\ \\ C\rightarrow0.12 \end{gathered}[/tex]The probability is:
[tex]P(A)=\frac{\text{ Favorable outcome}}{\text{ Total outcome}}[/tex]The total outcomes is:
[tex]\begin{gathered} =0.32+0.56+0.12 \\ \\ =1 \end{gathered}[/tex](a)
Probability to the 4 and 6
The 4 to 6v region is B
[tex]\begin{gathered} P(B)=\frac{\text{ favorable outcomes for B}}{\text{ Total outcomes}} \\ \\ P(B)=\frac{0.56}{1} \\ \\ P(B)=0.56 \end{gathered}[/tex](B)
Probability for 4 to 7
The region B and C
[tex]\begin{gathered} 1. \\ \\ P(B\text{ and }C)=\frac{0.56+0.12}{1} \\ \\ =0.68 \end{gathered}[/tex]10x + 50 + 6x = 58 if x is the solution to the given equation, what is the value of 32x
The solution to the given equation is;
[tex]\begin{gathered} 10x+50+6x=58 \\ \text{Collect all like terms,} \\ 10x+6x=58-50 \\ 16x=8 \\ \text{Divide both sides by 16} \\ \frac{16x}{16}=\frac{8}{16} \\ x=\frac{1}{2} \end{gathered}[/tex]Therefore, the value of 32x shall be;
[tex]\begin{gathered} 32x \\ =32(\frac{1}{2}) \\ =\frac{32}{2} \\ =16 \end{gathered}[/tex]The answer is 16
please help me I really need help in my math work
we need to know the formula of the area of a rectangle
[tex]A=l\cdot w\text{ }[/tex]we already know A and l we need to clear w
[tex]w=\frac{A}{l}=\frac{2x^2+5x-12}{2x-3}[/tex]we need to do the division
[tex]undefined[/tex]Marie requires 2 gallons of paint to cover an area of 400 square feet. Identify the graph that shows the relationship between the quantity of paint and the area covered and the parent function that best describes it. Then use the graph to estimate how many gallons of paint Marie requires to paint an area of 2,400 square feet.
Given:
x = 2 gallons of paint
y = 400 square feet of area
The graph representing the given point (x,y) = (2, 400) is number 4: linear 12 gallons.
Then, to estimate how many gallons of paint Marie requires to paint an area of 2,400 square feet.
We locate the point y = 2400 and find the corresponding x value. This is:
x = 12
Answer:
* the graph is the fourth one
* 12 gallons
IQ is normally distributed with a mean of 100 and a standard deviation of 15.a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95.Write your answer in percent form. Round to the nearest tenth of a percent.P(10 greater than 95) =%b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125.Write your answer in percent form. Round to the nearest tenth of a percent.P(IQ less than 125) =%c) In a sample of 800 people, how many people would have an IQ less than 110?peopled) In a sample of 800 people, how many people would have an IQ greater than 140?peopleCheck Answer
To answer this questions we need to remember the standard score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the value we are looking for, mu si the mean and sigma is the standard deviation.
a.
We need the probability:
[tex]P(IQ>95)[/tex]using the standard score this is equivalent to:
[tex]\begin{gathered} P(IQ>95)=P(z>\frac{95-100}{15}) \\ =P(z>-0.3333) \end{gathered}[/tex]Using a normal distribution table we have:
[tex]P(z>-0.3333)=0.6306[/tex]Therefore the probability to select a person with more than 95 IQ points is 63.1%.
b.
Following the same reasoning as before we have:
[tex]\begin{gathered} P(IQ<125)=P(z<\frac{125-100}{15}) \\ =P(z<1.6667) \\ =0.9522 \end{gathered}[/tex]Therefore the probability to select a person with less than 125 IQ points is 95.2%
c.
To find how many people of this sample have more less than 110 points we need to find that probability:
[tex]\begin{gathered} P(IQ<110)=P(z<\frac{100-110}{15}) \\ =P(z<-0.666) \\ =0.7475 \end{gathered}[/tex]Multiplying this value with the sample size we have
[tex](800)(0.7475)=598[/tex]Therefore 598 people will have an IQ less than 110.
d.
By the same reasoning as before we have:
[tex]\begin{gathered} P(IQ>140)=P(z>\frac{140-100}{15}) \\ =P(z>2.6667) \\ =0.0038 \end{gathered}[/tex]Multiplying this value with the sample size we have
[tex](800)(0.0038)=3[/tex]Therefore 3 people will have an IQ greater than 140.
Let the random variable x be the number of rooms in a randomly chosen owner- occupied housing unit in a certain city. The distribution for the units is given below.
(a)
Since X can only assume whole values, it is a discrete random variable.
(b)
The sum of all probabilities in the table must be equal to 1, so we have:
[tex]\begin{gathered} 0.07+0.22+0.41+0.2+0.05+0.03+0.01+P(10)=1\\ \\ 0.99+P(10)=1\\ \\ P(10)=1-0.99\\ \\ P(10)=0.01 \end{gathered}[/tex](c)
The values of x smaller than 5 in the table are 3 and 4, so we have:
[tex]P(X<5)=P(3)+P(4)=0.07+0.22=0.29[/tex](d)
For x between 4 and 6, we have:
[tex]P(4\leq x\leq6)=P(4)+P(5)+P(6)=0.22+0.41+0.2=0.83[/tex](e)
Looking at the table, for x = 3 we have:
[tex]P(3)=0.07[/tex]1. If triangle ABC is congruent to triangle DEF, DE=17, EF =13, DF =9, and BC = 2x-5, then which of the following is the correctvalue of x?(1) 5(3) 9(2) 7(4) 11
If both trianlges are congruent, we get that:
[tex]BC=DE[/tex]This way,
[tex]2x-5=17[/tex]Solving for x :
[tex]\begin{gathered} 2x-5=17 \\ \rightarrow2x=17+5 \\ \rightarrow2x=22 \\ \Rightarrow x=11 \end{gathered}[/tex]This way, we get that x = 11
Answer: Option 4
If f(5)=3, write an ordered pair that must be on the graph of y = f(x + 1) + 2
(4, 5)
Explanations:The given function is:
y = f(x + 1) + 2
There are many ordered pairs that can be on the graph of y = f(x + 1) + 2, but with the information given will can look for one of them.
Let x = 4
y = f(x + 1) + 2
y = f(4 + 1) + 2
y = f(5) + 2
Since it is given that f(5) = 3, the equation above can be simplified to get the value of y.
y = f(5) + 2
y = 3 + 2
y = 5
Therefore, an ordered pair that must be on the graph of y = f(x+1) + 2 is (4, 5)
Can you help Turn this equation to the other equation
3x-y=-27
x+2y=16
y=_x+_
y=_x+_
Answer:
y=3x+27
2y= x+16or,
or,y= x+16/2
Do anyone know the answer to these questions? Please explain as well
given data:
[tex]\begin{gathered} \frac{7}{21}\text{ and }\frac{21}{24} \\ \end{gathered}[/tex]to find whether they form an proposition.
using cross product,
[tex]\begin{gathered} \frac{7}{21}\cdot\frac{21}{24} \\ 24\cdot7=21\cdot21 \\ 168\ne441 \end{gathered}[/tex]the cross product are not equal.
Thus, they donot form a proposition.
Find the absolute value of | 2x+ z | + 2y x = 2.1, y = 3, z = -4.2
6
Explanations:The given absolute value expression is:
| 2x+ z | + 2ySubstitute x = 2.1, y = 3, z = -4.2 into the given expression:
[tex]|2(2.1)+(-4.2)|+2(3)[/tex]This can be simplifed as:
[tex]|2(2.1)-4.2|+6[/tex][tex]|4.2-4.2|+6[/tex]Since |4.2-4.2| = 0, the expression above becomes:
0 + 6
= 6
Therefore, the absolute value of the expression, after simplification, is 6
Use the box method to distribute and simplify (-3x – 3)(5 + 4x²). Drag and drop the terms to the correct locations of the table.
Looking at the diagram, the box method has already been applied. The simplified answer would be gotten by adding up each term in the boxes while taking into consideration, the signs of each term. It becomes
- 15x - 15 - 12x^2 - 12x^3
Rearranging the terms in descending order of the exponents, it becomes
- 12x^3 - 12x^2 - 15x - 15 15x - 15 - 12x
Math Lab A - Section 203B Notebook Home Insert Draw View Class Notebook U abe А. = = A Styles ☆ ? The table shows the average mass, in kilograms, of different sizes of cars and trucks. Size Small Car Average Mass (kilograms) 1,354 1,985 Large Car Large Truck 2,460 Part A To the nearest hundred, how much greater is the mass of a large truck than the mass of a small car? Fill in the blanks to answer the question. To the nearest hundred, a large truck has a mass of kilograms, and a small car has a mass of kilograms. So, a large truck has a mass about kilograms greater than a small car.
Given:
Round the mass of the large car to the nearest thousand.
Because 1985 is between 1,000 and 2,000 and closer to 2,000 ,the number should round up to 2,000.
Option D is the correct answer.
Can you show me how to solve this and graph?
The points (x,y) whose values satisfy the equation -5y=13 belong to the graph of that equation.
First, isolate y by dividing both sides of the equation by -5 and simplifying:
[tex]\begin{gathered} -5y=13 \\ \Rightarrow\frac{-5y}{-5}=\frac{13}{-5} \\ \Rightarrow y=-\frac{13}{5} \end{gathered}[/tex]Then, the points (x,y) belon to the graph of the equation -5y=13 whenever the value of y is -13/5, regardless of the value of x. Then, choose two different values of x to find two points that belong to the graph. For example, x=0 and x=2. Then, this two points belong to the graph:
[tex]\begin{gathered} (0,-\frac{13}{5}) \\ (2,-\frac{13}{5}) \end{gathered}[/tex]Notice that -13/5=-2.6,
Plot the points (0,-2.6) and (2,-2.6) in a coordinate plane:
Since the given equation is linear, the graph of the equation is a straight line. We can draw a straight line between any two points given. Draw a line between (0,-2.6) and (2,-2.6) to find the graph of the equation -5y=13: