Match each expression to the correct number of significant figures.194.9-4.922,0002127.7
Hello
For the first expression, we have
[tex]194.9-4.9=190[/tex]This have a 2 significant value
[tex]2000[/tex]This have a 1 significant value.
[tex]27.7[/tex]This have a 3 significant value
A certain forest covers an area of 2300 km^2. Suppose that each year this area decreases by 7.75%. What will the area be after 8 years?Use the calculator provided and round your answer to the nearest square kilometer.
EXPLANATION:
Given;
We are told that a forest covers an area of 2300 square kilometers.
Next we are told that this forest area decreases by 7.75% each year.
Required:
We are required to calculate the area remaining after 8 years.
Step-by-step solution:
To solve this math problem, take note that what we have is an exponential decay problem. The initial size decreases (decays) at a constant rate every year.
The formula for an exponential growth/decay is given as shown below;
[tex]f(x)=a(1-r)^x[/tex]Where the variables are as follows;
[tex]\begin{gathered} a=initial\text{ }value \\ r=rate\text{ }of\text{ }decay \\ x=number\text{ }of\text{ }years \end{gathered}[/tex]With the values given, we can substitute and we'll have the following;
[tex]f(8)=2300(1-0.0775)^8[/tex][tex]f(8)=2300(0.9225)^8[/tex][tex]f(8)=2300(0.524482495947)[/tex][tex]f(8)=1206.3097...[/tex]Rounded to the nearest square kilometer, we would now have;
ANSWER:
[tex]Area\text{ }after\text{ }8\text{ }years=1206km^2[/tex]using the set of numbers find the mean rounded to the nearest tenth , median , mode and range.98 , 98 , 90 , 82 , 89 , 87
The median is defined as the sum of all the values divided by the total number of data, then in this case:
[tex]\begin{gathered} \mu=\frac{98+98+90+82+89+87}{6} \\ \mu=\frac{544}{6} \\ \mu=90.7 \end{gathered}[/tex]To find the median we need to order the data:
[tex]82,\text{ 87, 89, 90, 98, 98}[/tex]The median is the number that divides all the data in half, since we have an even number of data we need to take the mean between the middle data, that is, the median is:
[tex]\frac{89+90}{2}=89.5[/tex]The mode is the number that repeats itself more on the data set, then in this case we the mode is 98.
The range is the difference between the lowest and highest data, then:
[tex]98-82=16[/tex]Summing up we have:
mean: 90.7
median: 89.5
mode: 98
Range: 16
1. Given the points Al-1, 2) and B(7, 8), find the coordinates of the polnt P on the directed line segment JB that partitions AB in the ratio 1:3. Plot P along with segment AB. 10 B 6 (x,y) = (x1+k(x2 - x2),y. +k(y2-y) 2 210182632 2 68 110 2 24 6 8 -10 2. Find the coordinates of P so that P partitions AB in the ratio 5.1 with A(2, 4) and B(8, 10). L 3. Find the coordinates of P so that P partitions AB in the ratio 1 to 3 with A(-5, 4) and B(7,-4). 4. Find the coordinates of P so that P partitions AB in the ratio 3:4 with A(-9, -9) and B(5,-2).
We can find the point with help of the end points and the ratio so:
[tex]\begin{gathered} x=-1+\frac{1}{1+3}(7-(-1)) \\ x=-1+\frac{1}{4}8 \\ x=-1+2 \\ x=1 \end{gathered}[/tex]now for y:
[tex]\begin{gathered} y=2+\frac{1}{1+3}(8-2) \\ y=2+\frac{1}{4}6 \\ y=3.5 \end{gathered}[/tex]So now we can graph it so:
1. Smoesnail crawls at 3/25 m.p.h. At this rate, how far can he get in 1 2/3 hours?
Answer:
[tex]\frac{1}{5}\text{ miles}[/tex]Explanation:
Here, we want to get the distance the snail can go in the given time
Mathematically, we have it that:
[tex]\text{Distance = sp}eed\text{ }\times\text{ time}[/tex]speed = 3/25 mph
Time = 1 2/3 hours = 5/3 hours
Thus, we have it that:
[tex]\text{Distance = }\frac{3}{25}\text{ }\times\frac{5}{3}\text{ = }\frac{1}{5}\text{ miles}[/tex]24. Cree la gráfica aproximada de la función cuadrática con intersecciones en x en (-5, 0) y (3,0) y una intersección en y en (0, -7.5). 1. Seleccione un botón para elegir el tipo de gráfico. 2. Arrastre los dos puntos a la posición correcta.
Archanged2. A student used a random number generator with the digits 1 to 20 to simulate the total number of questions she might guess correctly on atrue/false exam that had 20 questions. The dot plot below show the results of 100 trials.Based on the data, which number of correct answersmost likely, and what percentage of the 100 trials does this represent?Guessed 9 correctly on 30% of the trialsGuessed o correctly on 100% of the trialsGuessed 9 correctly on 25% of the trialsGuessed 10 correctly on 30% of the trials
The following observation are derived from the graph shown relating number of guesses against the number of trials
+) Guessed 6 correctly on 2% of the trials
+) Guessed 7 correctly on 8% of the trials
+) Guessed 8 correctly on 25% of the trials
+) Guessed 9 correctly on 30% of the trials
+) Guessed 10 correctly on 19% of the trials
+) Guessed 11 correctly on 12% 0f the trials
+) Guessed 12 correctly on 3% of the trials
+) Guessed 13 correctly on 1% of the trials
From the options provided, it can be concluded that:
He guessed 9 correctly on 30% of the trials. The first option is the correct option
What is the equation to solve: if the sim of four consecutive integers is 26, what is the value of the first integer?
ANSWER:
5
STEP-BY-STEP EXPLANATION:
We set up the equation as follows:
Let x be the first integer
[tex]x+x+1+x+2+x+3=26[/tex]We solve for x:
[tex]\begin{gathered} 4x+6=26 \\ \\ 4x=26-6 \\ \\ x=\frac{20}{4} \\ \\ x=5 \end{gathered}[/tex]The value of the first integer is 5
Identify the Sampling Method. Identify the sampling method (simple randomsampling, systematic sampling, convenience sampling, or stratified sampling) in the followingstudies. study of the use of antidepressants selects 50 participants between the ages of 20 and 29,50 participants between the ages of 30 and 39, and 50 participants between the ages of 40 and49.
Step 1
Analyze the Sampling method
In stratified sampling, the population is divided into two or more groups called strata according to some criterion such as geographic location, grade level, age, income, etc. Subsamples are randomly selected from each stratum. Elements within each stratum are homogenous but are heterogeneous across the strata. For example;
From this question, the general study is on the use of antidepressants. This is the strata, each stratum of 50 participants each based on age cuts across. They are homogenous in their individual stratum of age grades( 20-29), (30-39), (40-49) but are homogenous in the sense that 50 participants were chosen across all stratum and the study is generally about antidepressants.
Hence, the right answer is stratified sampling.
I need help with my math ASAP
33,200 sq units (option A)
Explanation:Surface area of triangular prism = base × height + length ×perimeter of triangle
base = j = 150 units
height = h = 40 units
length = k = 85 units
m = 85 units
Perimeter of triangle = j + m + m
Perimeter of triangle = 150 + 85 + 85 = 320 units
Surface area of triangular prism = 150(40) + 85(320)
Surface area of triangular prism = 6000 + 27200
Surface area of triangular prism = 33,200 sq units (option A)
Match the term on the left with its figure on the right.
Question:
Solution:
1. Equilateral triangle:
An equilateral triangle is a triangle in which all three sides have the same length.
This is the case of the following figure (D) :
2. A Scalene right triangle:
A scalene right triangle is a triangle in which all three sides are in different lengths and one of its angles is 90 degrees.
This is the case of the following figure (A):
3. Isosceles right triangle:
An isosceles right triangle has two equal sides and one angle of 90 degrees, as the following figure (C):
4. Isosceles obtuse triangle:
An isosceles obtuse triangle has two equal sides with any angle greater than 90 degrees, as in the following figure (B):
anyone that knows about cos, tan, and csc please help!
Consider the following polynomial function.f(x) = (x + 2)²(x-4)³(x − 3)Step 2 of 3: Find the x-intercept(s) at which f crosses the axis. Express the intercept(s) as ordered pair(sAnswerSelect the number of x-intercept(s) at which f crosses the axis.Selecting an option will display any text boxes needed to complete your answer.none023
Given
The polynomial function,
[tex]f\mleft(x\mright)=(x+2)²\left(x-4\right)³\left(x−3\right)[/tex]To find: The x-intercepts.
Explanation:
It is given that,
[tex]f\mleft(x\mright)=(x+2)²\left(x-4\right)³\left(x−3\right)[/tex]That implies,
The x-intercept is determined by setting f(x)=0.
Then,
[tex]\begin{gathered} f\mleft(x\mright)=0 \\ (x+2)²\left(x-4\right)³\left(x−3\right)=0 \\ (x+2)^2=0,\text{ }(x-4)^3=0,\text{ }x-3=0 \\ x+2=0,\text{ }x-4=0,\text{ }x-3=0 \\ x=-2,\text{ }x=4,\text{ }x=3. \end{gathered}[/tex]Hence, the x-ntercepts are (-2,0), (4,0), (3,0).
Rewrite 0.00384 in scientific notation.
Given:
There are given the decimal number:
[tex]0.00384[/tex]Explanation:
According to the question:
We need to write the given decimal number in the form of scientific notation.
Then,
To write into the scientific notation, we will use their properties.
So,
From the given decimal number,
[tex]0.00384[/tex]Then,
The scientific notation is:
[tex]0.00384=3.84\times10^{-3}[/tex]Final answer:
Hence, the answer is shown below:
[tex]\begin{equation*} 3.84\times10^{-3} \end{equation*}[/tex]Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 36.25°. What is the measure of ∠Q?
143.75°
107.5°
71.875°
36.25°
Answer:
71.875
Step-by-step explanation:
p = q
180 - 36.25 = 143.75
p + q = 143.75
143.75 ÷ 2 = 71.875
Which equation represents a circle centered at (3.5) and passing through the point (-2.91?OA (+3)2 + (y + 5)² = 17OB. (-3)²+(y-5)² = 17OC. (x+3)²+(y+ 5)² = 41OD. (-3)2 + (y-5)² = 41ResetNext
ANSWER
[tex](x-3)^2+(y-5)^2=41[/tex]EXPLANATION
Given;
[tex]\begin{gathered} center=(3,5) \\ points=(-2,9) \end{gathered}[/tex][tex]\begin{gathered} (x-a)^2+(y-b)^2=(r)^2 \\ (x-3)^2+(y-5)^2=(\sqrt{41})^2 \\ \end{gathered}[/tex]The table below represents a linear function f(x) and the equation represents a function (x)f(x)-1-12g(x)09(x) = 2x + 610Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x), (6 points)Part B: Which function has a greater y-intercept? Justify your answer (4 points)I
Answer:
(a)The slope of f(x) is greater than the slope of g(x).
(b)g(x) has a greater y-intercept.
Explanation:
Part A
From the table of f(x), we have the pairs:
(-1,-12),(0,-6) and (1,0).
First, we find the slope of f(x).
[tex]\begin{gathered} \text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{-6-0}{0-1} \\ =-\frac{6}{-1} \\ =6 \end{gathered}[/tex]Given the function g(x) defined as follows:
[tex]g(x)=2x+6[/tex]Comparing g(x) with the slope-intercept form (y=mx+b), the slope of g(x) is m=2.
Sentence: The slope of f(x) is greater than the slope of g(x).
Part B
The y-intercept is the point in a function where x=0.
In f(x), When x=0, f(x)=-6
• The y-intercept of f(x) is -6.
Comparing g(x) with the slope-intercept form (y=mx+b), the y-intercept of g(x), b=6.
Therefore, g(x) has a greater y-intercept.
What is the probability of rolling a sum of six on a standard pair of six sided dice
The probability of rolling a sum of six on a standard pair of six sided dice is 0.139.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
When we rolled two dice, there were 36 possible results. Of those 36 results, 5 of them added up to 6, and they were: {1, 5}, {2, 4}, {3, 3}, {4, 2}, and {5, 1}.
Therefore, P(sum 6) = 5/36 = 0.1388888
With a typical pair of six-sided dice, the likelihood of rolling a sum of 6 is 0.139.
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solving systems with subtraction y=7txy=3x+9
y = 7 + x
y = 3x + 9
To solve the simulataneous equation with subtraction,
Step 1: name the equations
y = 7 + x ---- equation 1
y = 3x + 9 ----- equation 2
Step 2: subtract equation 1 from 2
so that
y - y = (3 x -x ) + (9 - 7)
0 = 2x + 2
2x = - 2
divide oth sides by 2
x = -2/2
x = -1
To get y, substitute the value for x into equation 1
y = 7 + x
y = 7 + (-1)
y = 7-1 = 6
y = 6
hence the solution is (-1, 6)
1 and In an experiment, the probability that event A occurs is –, the probability that event B occurs is 5 1 the probability that events A and B both occur is What is the probability that A occurs given that B occurs? Simplify any fractions. Submit
Solution
We have the following info given:
P(A) = 4/5
P(B)= 1/7
P(A and B) = 1/9
We want to find this probability:
P(A|B)= P(A and B)/P(B)
Replacing we got:
[tex]P(A|B)=\frac{\frac{1}{9}}{\frac{1}{7}}=\frac{7}{9}[/tex]
if in 3 minutes you can do 45 sit-ups, how much can you do in 1 minutes?
First let's determine the number of squats per minute by finding the ratio of the number of squats per minute.
[tex]r=\frac{45\text{ sit ups}}{3\text{ min}}=15\text{ sit-up per minute }[/tex]This means that you can do 15 sit-ups in one minute.
Suppose that a certain fortunate person has a net worth of $76.0 billion ($ 7.60×1010 ). If her stock has a good year and gains $3.20 billion ( 3.20×109 ) in value, what is her new net worth? THE NEW NET WOTH IS 7.92×10^10 Suppose that this individual now decides to give one-eighth of a percent (0.125 % ) of her new net worth to charity. How many dollars are given to charity?
Find the 0.125% of 7.92x10^10: Multiply the amount by 0.125 and then divide into 100 or multiply the amount by 0.125/100
[tex]\begin{gathered} \frac{0.125}{100}=1.25\times10^{-3} \\ \\ 7.92\times10^{10}*1.25\times10^{-3}=(7.92*1.25)\times10^{10-3}=9.9\times10^7 \end{gathered}[/tex]Then, $9.9x10^7 are given to charityFind the value of x 6 : 9 = x : 72
To find x we write the proportion as a fraction:
[tex]\begin{gathered} \frac{6}{9}=\frac{x}{72} \\ x=\frac{72\cdot6}{9} \\ x=48 \end{gathered}[/tex]Therefore x=48
Riley work 5 1/4 hours on Monday 3 3/8 hours on Tuesday and 2 and 5/6 hours on Wednesday he rounded the hours to 5,3,and two before adding them together to get 10 hours did he make a high or low estimate
First, let's convert the mixed numbers to fractions:
5 1/4 = 21/4 = 5.25
3 3/8 = 27/8 = 3.375
2 5/6 = 17/6 = 2.83333
5.25 + 3.375 + 2.83333 = 11.45833333
Therefore he made a low estimate
Find the first six terms of the sequence.a = 2n² - 2
We are given the nth term of a sequence:
[tex]a_n=2n^2\text{ - 2}[/tex]We are required to find the first six terms.
For each term, we substitute for n and evaluate.
First term (n =1)
[tex]\begin{gathered} a_1\text{ = 2 }\times(1)^2\text{ - 2} \\ =\text{ 2 -2 } \\ =\text{ 0} \end{gathered}[/tex]Second term (n = 2)
[tex]\begin{gathered} a_2\text{ =2 }\times(2)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 4 -2} \\ =\text{ 8 - 2} \\ =\text{ 6} \end{gathered}[/tex]Third term (n = 3)
[tex]\begin{gathered} a_3\text{ = 2 }\times(3)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 9 - 2} \\ =\text{ 18 - 2} \\ =\text{ 16} \end{gathered}[/tex]Fourth term (n =4)
[tex]\begin{gathered} a_4\text{ = 2}\times(4)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 16 - 2} \\ =\text{ 32 - 2} \\ =\text{ 30} \end{gathered}[/tex]Fifth term ( n = 5)
[tex]\begin{gathered} a_5\text{ = 2 }\times(5)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 25 - 2} \\ =\text{ 50 - 2} \\ =\text{ 48} \end{gathered}[/tex]Sixth term ( n = 6)
[tex]\begin{gathered} a_6\text{ = 2 }\times(6)^2\text{ - 2} \\ =\text{ 2 }\times\text{ 36 - 2} \\ =\text{ 72 - 2} \\ =\text{ 70} \end{gathered}[/tex]Hence, the first six terms of the sequence are : 0, 6, 16, 30, 48 and 70
In the parallelogram below, if AP = 45 and PC = 3x + 15, find x.
One of the properties of a parallelogram is that its diagonals bisect each other. This means that one diagonal cuts the second diagonal in equal length.
This means that AP = PC. If AP = PC, then 45 = 3x + 15.
[tex]45=3x+15[/tex]We can now find the value of x using the equation above.
First, subtract 15 on both sides of the equation.
[tex]45-15=3x+15-15[/tex][tex]30=3x[/tex]Then, divide both sides of the equation by 3 to isolate x.
[tex]\frac{30}{3}=\frac{3x}{3}[/tex][tex]10=x[/tex]Therefore, the value of x is 10. (Option B)
(X^2+8x+12)/(x+2) que
Given:
[tex]\frac{x^2+8x+12}{x+2}[/tex]Let's divide the polynomials.
To divide, let's factorize the polynomial in the numerator.
Factorize using the AC method.
Find a pair of numbers whose product is 12 and whose sum is 8.
Thus, we have the numbers:
2 and 6
The factors of the polynomial in the numerator are:
(x+2) and (x+6)
We have:
[tex]\frac{(x+2)(x+6)}{x+2}[/tex]Now, cancel the common factors:
Therefore, the quotient after dividing the polynomials is = x + 6
ANSWER:
[tex]x+6[/tex]Which of the following is equivalent to the expression below? 196 - 54 +24
Given the follow:
Root96 - root54 + root24
We are to find the expression that is equivalent.
root96 = root16 x root6
root54 = root9 x root6
root24 = root4 x root6
(root16 x root6) - (root9 x root6) + (root4 x root6)
= 4root6 - 3root6 + 2root6
= (4 - 3 + 2)root6
= (1 + 2)root6
= 3root6
Therefore, the correct option is C which is 3root6
Solve for q.
-18q+ 18q+ 2q + 14 = 4
q=
Answer:
-18q+18q+2q+14=4Step-by-step explanation:
Data:find "q'
first take 2 as common
solution .
2(-9q+9q+q+7)=4
Now divided 2 by both sides.
2(-9q+9q+q+7) ÷2
=4÷2
-9q+9q+q+7 =2
q+7=2
q=2-7
q=-5 Answer.
harlyne deposited $3400 into a savings account that has an annual simple interest rate of 0.2%. Find the amount in the savings account after each number of years.
2 years $
5 years $
8 years $
The simple interest after 2, 5 and 8 years on a principal of $3400 at 0.2% are $3413.6, $3434 and $3454.4 respectively
SIMPLE INTERESTSimple interest is a quick and easy method to calculate interest on the money, in the simple interest method interest always applies to the original principal amount, with the same rate of interest for every time cycle.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r(%) and is to be written as r/100.
Principal: The principal is the amount that initially borrowed from the bank or invested. The principal is denoted by P.Rate: Rate is the rate of interest at which the principal amount is given to someone for a certain time, the rate of interest can be 5%, 10%, or 13%, etc. The rate of interest is denoted by R.Time: Time is the duration for which the principal amount is given to someone. Time is denoted by T.Amount: When a person takes a loan from a bank, he/she has to return the principal borrowed plus the interest amount, and this total returned is called Amount.Using the data given;
S.I = P × R × T
When T = 2 years
S.I = 3400 * 0.002 * 2
S.I = 13.6
The amount after 2 years = 3400 + 13. 6 = $3413.6
When T = 5 years
S.I = 3400 * 0.002 * 5
S.I = 34
The amount after 5 years = 34 + 3400 = $3434
When T = 8 years
S.I = $3454.4
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