Answer:
13
Explanation:
The explicit formula of a sequence is given below:
[tex]f\mleft(n\mright)=5+4\mleft(n-1\mright)[/tex]When n=3
[tex]\begin{gathered} f\mleft(3\mright)=5+4\mleft(3-1\mright) \\ =5+4(2) \\ =5+8 \\ =13 \end{gathered}[/tex]The 3rd term of the sequence is 13.
divide 406 by -14 A) -29B) -34C) 34D) 44
The correct answer is -29 (option A)
You stand 40 feet from a tree. The anlge of elevation from the ground tothe top of the tree is 47 degrees. How tall is the tree? (round to the nearesttenth)0 42.9 feet0 27.3 feet29.3 feetO 40 feet
The first step is to draw the picture.
We want to find the opposite side.
We know the adjacent side
The trig function with opposite and adjacent is tangent
tan 47 = opp / adjacent
tan 47 = opp/40
40 * tan 47 = opp side
42.8947484 = opp side
Rounding to the nearest tenth
42.9 ft
A storage container is 3 feet long, 5 feet wide, and 6 feet tall. if the diameter of a baseball is about 1.43 inches, approximately how many basketballs fit in the container? ( volume of a sphere is V = 4/3pi^3)
First, let's find the volume of the storage container:
Vs = 3*5*6 = 90 ft³
Now, let's do a conversion:
1.43 in * 1ft/12in = 0.119 ft
The radius is the diameter divide by 2:
r = 0.119/2 = 0.059583 ft
Let's find the volume of the baseball:
V = 4/3 π r³ = 4/3 π (0.059583)³ = 0.000886 ft³
Now divide the volume of the storage container by the volume of the baseball:
90/0.000886 ≈ 101573
Approximately 101573 balls fit in the container
state the equation of the axis of symmetry of the function f(x) = 3x^2 + 6x - 2
The given function is:
[tex]f(x)=3x^2+6x-2[/tex]Complete the square and factor as follows:
[tex]\begin{gathered} f(x)=3(x^2+2x+1)-2-3 \\ f(x)=3(x+1)^2-5_{} \end{gathered}[/tex]Compare with:
[tex]f(x)=a(x-h)^2+k[/tex]To get:
[tex](h,k)=(-1,-5)[/tex]Since the parabola is vertical the axis of symmtery is vertical which is x=-1.
PLS HELP DUE TODAY!Find the mean, median, mode, and range of each set of data round answers to the nearest hundredth 0,3,2,1,7,4,3,2,1,1,1,0,2,3,0,2,6,2Second question:Find the mean, median, mode, and range of each set of data round answers to the nearest hundredth 3,2,2,1,0,0,5,3,1,0,1,0,2,6,3,2,3
To answer this question, we (first) need to order the data from the least to the greatest element of this set:
[tex]l=\mleft\lbrace0,3,2,1,7,4,3,2,1,1,1,0,2,3,0,2,6,2\mright\rbrace[/tex]If we order in that mentioned way, we have (this is done, mostly to find the median):
[tex]l=\mleft\lbrace0,0,0,1,1,1,1,2,2,2,2,2,3,3,3,4,6,7\mright\rbrace[/tex]MedianTo find the median of this data, we need to find the value for which 50% of the data are below this value, and above this value - it is a central value. We have 18 elements:
0,0,0,1,1,1,1,2,2,2,2,2,3,3,3,4,6,7
Since we have an even number of elements, we need to find the "average" of both central numbers:
[tex]Median=\frac{2+2}{2}\Rightarrow Median=2[/tex]Therefore, the median is equal to 2.
ModeThe mode is the element that is more founded into the set of numbers. In this case, if we look carefully at the data, we have that this value is 2 because we have 5 cases in which 2 appears in that set of data.
MeanTo find the mean, we need to sum each of the elements in the set of data, and then divide that result by the number of data - in this case, we have 18 elements. Then, we have:
[tex]Mean=\frac{(0+0+_{}0+1+1+1+1+2+2+2+2+2+3+3+3+4+6+7)}{18}[/tex][tex]\text{Mean}=\frac{40}{18}\Rightarrow Mean=2.22222222222\ldots[/tex]If we round the mean to the nearest hundredth, we have that the mean = 2.22.
RangeThe range is the difference between the maximum value and minimum value of the set of data, and we have:
Minimum = 0
Maximum = 7
Therefore, the range is equal to R = (7 - 0) ---> Range = 7.
In summary, for this set of data, we have that:
• Mean = 2.22 (rounded to the nearest hundredth)
,• Median = 2 (2.00 rounded to the nearest hundredth)
,• Mode = 2 (2.00 rounded to the nearest hundredth)
,• Range = 7 (7.00 rounded to the nearest hundredth)
Solve for k in 2 - (k+4) = 3a.) What is the variable?b.) What is happing to the variable? (list the operations from the first thing to the last thing)c.) What is the inverse (opposite) of the last thing that happened to the variable. (Make a list of the steps to solve)
We have the equation 2-(k+4)=3.
The variable is k, because is the only unknown number. Solving for k:
[tex]\begin{gathered} 2-(k+4)=3 \\ 2=3+(k+4)=3+4+k=7+k \\ 2-7=k \\ -5=k \end{gathered}[/tex]The variable has the following operations:
• Add 4
,• Multiply by (-1)
,• Add 2
The inverse of the last thing is Subtract 2, subtract is the opposite of add.
State the null and alternative hypotheses for the claimThe average score of high school basketball games is less than 88.
N5 pointsSketch the graph of the piecewise function below. Make sure your graph is cle-4,4% -3f(x) = -x + 3, - 3 341 Dra5
We are asked to plot the piecewise function given by:
SO we notice two points where the function graph is going to change:
x = -3 , and x = 3
We plot it in pieces :
Notice the endpoints of the different segments as "solid dots" or "empty dots" depending on the retrictions of the domain as given in the instructions.
any letters or words in your answer! Ciera works at a day care center. Her job is to make sure there are always enough adult workers. Last month, there were 7 adults for 56 children, which is the minimum ratio allowed under state law. This month, 74 children are expected to enroll. How many adults will there need to be at the center? Your answer
10 adults
Explanation
Step 1
find the unit rate
[tex]\text{unit rate=}\frac{Number\text{ of Children}}{\text{Number of adults}}[/tex]Let
number of children=56
number of adults=7
replace,
[tex]\begin{gathered} \text{unit rate=}\frac{Number\text{ of Children}}{\text{Number of adults}}= \\ \text{unit rate=}\frac{56\text{ Children}}{7\text{ adults}} \\ \text{unit rate= 8 Children per adult} \end{gathered}[/tex]Step 2
Let x represents the adults needed for 74 children
find the unit rate:
[tex]\begin{gathered} \text{unit rate=}\frac{Number\text{ of Children}}{\text{Number of adults}} \\ \text{unit rate=}\frac{74}{x} \end{gathered}[/tex]as the unit rate must be the same
[tex]\begin{gathered} 8\frac{Children}{\text{adult}}=\frac{74}{x} \\ 8=\frac{74}{x} \\ cross\text{ multiply} \\ 8x=74\cdot1 \\ 8x=74 \\ \text{divide both sides by 8} \\ \frac{8x}{8}=\frac{74}{8} \\ x=9.25 \\ \text{hence, we n}eed\text{ 10 adults at the center} \end{gathered}[/tex]For the following situation, (a) write an equation in the form y=mx+b, (b) find and interpret the ordered pair associated with the equation for x=5, and (c) answer the question.A health club membership costs $80, plus $48 per month. Let x represent the number of months and y represent the cost in dollars. How much does the first year’s membership cost?
Based on the question, a health club membership costs $80, plus $48 per month. This can be written as $80 + $48 per month = health membership cost.
If x = month and y = cost, then we can rewrite the equation as:
[tex]\begin{gathered} 80+48x=y \\ or \\ y=48x+80 \end{gathered}[/tex]a. This is our equation in the form of y = mx + b. (y = 48x + 80).
b. If the number of months is 5 or x = 5, we can solve for the total cost of membership by replacing "x" with "5" in the equation.
[tex]\begin{gathered} y=48x+80 \\ y=48(5)+80 \\ y=240+80 \\ y=320 \end{gathered}[/tex]The ordered pair is (5, 320).
This ordered pair indicates that the cost for 5-month membership is $320.
c. Since there are 12 months in 1 year, replace "x" in the equation with 12 and then, solve.
[tex]\begin{gathered} y=48x+80 \\ y=48(12)+80 \\ y=576+80 \\ y=656 \end{gathered}[/tex]Therefore, the first year's membership cost is $656.
Write a piecewise function describing your weekly pay P, in terms of the number of hours worked, h.
SOLUTION
the wage for less that 40 hours of work is
[tex]12h[/tex]The wage for more than 40 hours is:
[tex]1.5\times12=18h[/tex]Therefore the piecewise function is
[tex]\begin{cases}12h{,0\lt h\le40} \\ 18h{,h\gt40}\end{cases}[/tex]
What’s the answer to which expression is larger 5^3 or 4^4
5^3 = 5 x 5 x 5 = 125
4^4 = 4 x 4 x 4 x 4 = 256
256 > 125
4^4 is larger than 5^3
the hikers received more fruit then they brought on the hike?
When the fruit in question was shared. They each got 14/4 = 3 and half ( 3.5 )
Those who brought less than 3 and half are those who we need to find
Baxter brought 3, Hendrick = 2, Mary = 4, Kendra = 5.
So those who brought less than they got ( 3 and half ) are Baxter and Hendrick
Thr sum of 2 numbers is 97.The greater number is three less then four times the lesser number.Find the numbers
need answer soon PLEASE!!!!
Answer:
Greater number: 77 Lesser number: 20
Step-by-step explanation:
Sooo
20 × 4 is 80
80 - 3 = 77
77 + 20 = 97
Answer:
77 & 20
Step-by-step explanation:
x+y=97
x=4y-3
4y-3+y=97
5y=97+3
5y=100
5 5
y=20
x=4y-3
x=4(20)-3
x=80-3
x=77
don't forget to follow , rate & like
17) Determine if the number is rational (R) or irrational (I)
Given the number:
[tex]71.\bar{5186}[/tex]You can identify that there is a line about the first four decimal digits. That indicates that is a Repeating Decimal or Recurring Decimals.
Repeating Decimals are defined as those numbers whose decimal part becomes periodic.
By definition, Rational Numbers are those numbers that can be written as a simple fraction whose numerator and denominator are both integers.
By definition, Repeating Decimals are Rational Numbers.
Hence, the answer is: It is a Rational Number.
Which of thhr following liner equations have a negitive y-intercept?circle all that apply
Select all prime numbers 2,4,6,7,9,5
The Solution:
Given the set of numbers below:
[tex]2,4,6,7,9,5[/tex]We are asked to select all the prime numbers in the set.
A prime number is a number that can only be divided by 1 and itself. That is, it is a number that has only two factors.
So, the prime numbers in the set are:
[tex]2,7,5[/tex]Since these numbers only have two factors each.
Therefore, the correct answer is {2,7,5}
Answer:
The prime numbers would be 2, 5, and 7.
Step-by-step explanation:
Prime numbers are numbers that can only be multiplied by 1 and itself.
Here is a list of the common factors of each number:
2: 1, 2
4: 1, 2, 4
6: 1, 2, 3, 6
7: 1, 7
9: 1, 3, 9
5: 1, 5
So, our prime numbers are 2, 5, and 7.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Abha is hosting a party at a place that can hold up to 125 people. Seventy eight people have said they are coming. How many more people can Abha invite?Inequality: ?Solution: ?
Since 78 people said they are coming already, and the place can hold a maximum of 125 people. Abha can invite a certain number of people (say x) such that the total number of attendees, ie x + 78 does not exceed 125.
In inequality form;
[tex]x+78\leq125[/tex]We can go for the solution;
[tex]\begin{gathered} x+78\leq125 \\ x\leq125-78 \\ x\leq47 \end{gathered}[/tex]Thus the inequality is
[tex]\begin{gathered} x+78\leq125 \\ \text{and the solution is} \\ x\leq47 \end{gathered}[/tex]What is the missing step in this proof?A.Statement: 24 25, and 21 23.Reason: Alternate Interior Angles TheoremB.Statement: DÈ is parallel to AC.Reason: AB is a transversal cutting De and AC.C.Statement: 2124, and 23 25.Reason: Alternate Interior Angles TheoremD.Statement: 2124, and 23 25.Reason: 21 and 24, and 23 and 25 are pairs of supplementary angles.
Answer
Option C is correct.
Explanation
The alternate interior angles theorem explains that when two parallel lines are cut by a transversal, the alternate interior angles are congruent.
Hope this Helps!!!
real exponential equation the base B must be positive. graph the equation using basis that are less than one or greater than one to determine any differences. what differences are there if any?
Let's graph the following functions.
[tex]\begin{gathered} f(x)=2^x \\ g(x)=(\frac{1}{2})^x \end{gathered}[/tex]The image below shows the graph.
According to the graph, the difference between the function is that f(x) is increasing and g(x) is decreasing, this behavior is caused by the base of the powers, the base 1/2 (between 0 and 1) gives a decreasing exponential function, and the base 2 (greater than 1) gives an increasing exponential function.
Hence, C is the right answer.a bowling alley charges its customers an hourly rate to bowl plus shoe rental. The hourly rates are per Lane. a linear model of this situation contains the values (2,39) and (3, 56.25), where x represents the number of hours bowled on one lane, and why represents the total cost for bowling.
Answer:
[tex]\$17.25[/tex]Explanation: We have to find the hourly rate to bowl, provided the following information:
[tex]\begin{gathered} (x_1,y_1)=(2,39) \\ (x_2,y_2)=(3,56.25) \end{gathered}[/tex]Where x is the number of hours and y is the total cost.
[tex]\begin{gathered} y(x)=mx \\ m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{56.25-39}{3-2} \\ m=\frac{56.25-39}{3-2}=\frac{\$17.25}{1hr} \\ m=\frac{\operatorname{\$}\times17.25}{1hr} \\ \therefore\rightarrow \\ y(x)=17.25x \end{gathered}[/tex]Therefore it costs $17.25 for an hour to bowl.
2) A scuba diver descends to a location that is -12 1/3 m relative to sea level. He then descends another 8 1/4 M. What is the scuba divers final location relative to sea level.
NUMBERS ONLY
Answer:
-26 m
Step-by-step explanation:
you take away 8 1/4 from original
Type the correct answer in each box. Use numerals instead of words In the figure, lines BD and QS are parallel
..Given: Two parallel lines BD and QS and a transversal AT
To Determine: The measure of CRQ and CRS
Solution
From the image given, angle DCR and CRQ are alternate angles
Also angle DCR and angle CRS are each pair of the same interior angles
Please note that alternates angles are equal and each pair of same-side interior angles are supplementary
Apply the theorem above
[tex]\begin{gathered} \angle CRQ=\angle DCR(alternate-angles) \\ \angle CRQ=77^0 \end{gathered}[/tex]Also
[tex]\begin{gathered} \angle DCR+\angle CRS=180^0(same-ineterior-angles) \\ 77^0+\angle CRS=180^0 \\ \angle CRS=180^0-77^0 \\ \angle CRS=103^0 \end{gathered}[/tex]Hence:
∠CRQ = 77⁰
∠CRS = 103⁰
find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -12 and 768 respectively
ANSWER:
[tex]a_n=3\cdot(-4)^{n-1}[/tex]STEP-BY-STEP EXPLANATION:
We have the following formula for nth terms
[tex]a_n=a_1\cdot r^{n-1}^{}[/tex]we replace for each point and we are left
[tex]\begin{gathered} a_2=-12 \\ -12=a_1\cdot r^{2-1}\rightarrow-12=a_1\cdot r^{}\text{ (1)} \\ a_5=768 \\ 768=a_1\cdot r^{5-1}\rightarrow768=a_1\cdot r^4\text{ (2)} \end{gathered}[/tex]We solve the system of equations that remains like this:
[tex]\begin{gathered} a_1=\frac{-12}{r}\text{ (3)} \\ a_1=\frac{768}{r^3}\text{ (4)} \\ \text{we equalize (3) and (4)} \\ -\frac{12}{r}=\frac{768}{r^4} \\ r^3=\frac{768}{-12} \\ r=\sqrt[3]{-64} \\ r=-4 \end{gathered}[/tex]Now, for a1
[tex]\begin{gathered} a_1=\frac{-12}{-4} \\ a_1=3 \end{gathered}[/tex]For the equation −2 + 3 = 6 a. Find y when x is 3b. Find x when y is 4
Given equation,
[tex]-2x+3y=6[/tex](a) Find y when x is 3.
[tex]\begin{gathered} -2\times(3)+3y=6 \\ -6+3y=6 \\ 3y=12 \\ y=4 \end{gathered}[/tex](b) Find x when y is 4.
[tex]\begin{gathered} -2x+3y=6 \\ -2x+3\times4=6 \\ -2x+12=6 \\ -2x=-6 \end{gathered}[/tex]Thus, the value of x is
[tex]\begin{gathered} 2x=6 \\ x=3 \end{gathered}[/tex]What are the new coordinates of the point (-2,1) after undergoing the transformation?
Given the following rule of a transformation:
[tex]P(x,y)\rightarrow P^{\prime}(x+2,2y)[/tex]We will find the new coordinates of the point (-2,1) after undergoing the transformation.
[tex](-2,1)\rightarrow(-2+2,2(1)=(0,2)[/tex]So, the answer will be the last option (0, 2)
can you please help me
The formula for the area of a circle is:
[tex]A=\pi\cdot r^2[/tex]also the diameter can be written in function of the radius
[tex]D=2\cdot r[/tex]from this equation we can find the radius
[tex]r=\frac{D}{2}[/tex]this transforms the formula for the area into
[tex]\begin{gathered} A=\pi\cdot(\frac{D}{2})^2 \\ A=\frac{\pi}{4}\cdot D^2 \end{gathered}[/tex]since the diameter is equal to 26cm, then the area will be
[tex]\begin{gathered} A=\frac{\pi}{4}\cdot676cm^2 \\ A=169\pi(cm^2)\approx530.93cm^2 \end{gathered}[/tex]A floor tile is 2 feet wide. Convert the width to inches.
Solution
- The conversion from feet to inches is given below:
[tex]1ft\to12inches[/tex]- We are told that the tile is 2ft wide. Thus, we can convert the width to inches using the above conversion as follows:
[tex]\begin{gathered} \frac{12\text{ in}}{1\text{ ft}}=\frac{x\text{ in}}{2\text{ ft}} \\ \\ \text{ Multiply both sides by 2} \\ x=\frac{12\times2}{1} \\ \\ \therefore x=24inches \end{gathered}[/tex]Final Answer
The answer is 24 inches
The owners of a recreation area are filling a small pond with water. Let W be the total amount of water in the pond (in liters). Let T be the total number of minutes that water has been added. Suppose that w= 35T +300 gives W as a function of T during the next 70 minutes.Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.
Given:
[tex]W=35T+300[/tex]To find:
The domain and the range when t = 70 minutes.
Explanation:
When t = 70, we get
[tex]\begin{gathered} W=35(70)+300 \\ W=2750l \end{gathered}[/tex]The ordered pair of the solution is,
[tex](70,2750)[/tex]As the domain is the set of all input values, so the domain will be,
[tex][0,70][/tex]As the range is the set of all output values, so the range will be,
[tex][300,2750][/tex]Final answer:
The domain is,
[tex][0,70][/tex]The range is,
[tex][300,2750][/tex]Given f(x)= 1/x+6, find the average rate of change of f(x) on the interval [8,8+h]. Your answer will be an expression involving h
Function:
[tex]f(x)=\frac{1}{x+6}[/tex]Interval: [ 8, 8+h ]
Average rate of change:
[tex]A(x)=\frac{f(b)-f(a)}{b-a}[/tex]where a = 8 and b = 8 + h...
[tex]\begin{gathered} f(b)=\frac{1}{b+6} \\ f(8+h)=\frac{1}{8+h+6}=\frac{1}{h+14} \\ f(8+h)=\frac{1}{h+14} \end{gathered}[/tex][tex]\begin{gathered} f(a)=\frac{1}{a+6} \\ f(8)=\frac{1}{8+6}=\frac{1}{14} \end{gathered}[/tex]Then:
[tex]\begin{gathered} A(x)=\frac{\frac{1}{h+14}-\frac{1}{14}}{8+h-8}=\frac{\frac{1}{h+14}-\frac{1}{14}}{h}=-\frac{1}{14\cdot(h+14)} \\ A(x)=-\frac{1}{14h+196} \end{gathered}[/tex]