basically they are the negative multiples of 6, so:
[tex]a_n=-6n[/tex]Determine the solution to the given equation.4 + 3y = 6y – 5
Answer:
[tex]y=3[/tex]Explanation:
Step 1. The expression we have is:
[tex]4+3y=6y-5[/tex]And we are required to find the solution; the value of y.
Step 2. To find the value of y, we need to have all of the terms that contain the variable on the same side of the equation. For this, we subtract 6y to both sides:
[tex]4+3y-6y=-5[/tex]Step 3. Also, we need all of the numbers on the opposite side that the variables are, so we subtract 4 to both sides:
[tex]3y-6y=-5-4[/tex]Step 4. Combine the like terms.
We combine the terms that contain y on the left side of the equation, and the numbers on the right side of the equation:
[tex]-3y=-9[/tex]Step 5. The last step will be to divide both sides of the equation by -3 in order to have only ''y'' on the left side:
[tex]\begin{gathered} \frac{-3y}{-3}=\frac{-9}{-3} \\ \downarrow\downarrow \\ y=3 \end{gathered}[/tex]The value of y is 3.
Answer:
[tex]y=3[/tex]In 1990, the cost of tuition at a large Midwestern university was $104 per credit hour. In 1998, tuition had risen to $184 per credit hour.
We have to find the linear relationship for the cost of tuition in function of the year after 1990.
The cost in 1990 was $104, so we can represent this as the point (0, 104).
The cost in 1998 was $184, so the point is (8, 184).
We then can calculate the slope as:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{184-104}{8-0} \\ m=\frac{80}{8} \\ m=10 \end{gathered}[/tex]We can write the equation in slope-point form using the slope m = 10 and the point (0,104):
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-104=10(x-0) \\ y=10x+104 \end{gathered}[/tex]We can then write the cost c as:
[tex]c=10x+104[/tex]We then can estimate the cost for year 2002 by calculating c(x) for x = 12, because 2002 is 12 years after 1990.
We can calculate it as:
[tex]\begin{gathered} c=10(12)+104 \\ c=120+104 \\ c=224 \end{gathered}[/tex]Now we have to calculate in which year the tuition cost will be c = 254. We can find x as:
[tex]\begin{gathered} c=254 \\ 10x+104=254 \\ 10x=254-104 \\ 10x=150 \\ x=\frac{150}{10} \\ x=15 \end{gathered}[/tex]As x = 15, it correspond to year 1990+15 = 2005.
Answer:
a) c = 10x + 104
b) $224
c) year 2005.
Determine whether 17y = 3x − 19 is quadratic or not. Explain.No; there is no x2 term, so a = 0.No; there is no x-term, so b = 0.No; there is no constant term, so c = 0.Yes; it can rewritten in the form y = ax2 + bx + c.
The standard form of quadratic equation is given as,
[tex]ax^2+bx\text{ + c = 0 where a }\ne\text{ 0}[/tex]The equation is given as,
[tex]17y\text{ = 3x - 19}[/tex]Therefore,
[tex]\text{From the given equation x}^2\text{ is not present and also a = 0.}[/tex]Thus the given equation is not a quadratic equation.
In a recent year, 26.3% of all registered doctors were female. If there were 47,400 female registered doctors that year, what was the total number of registered doctors? Round your answer to the nearest whole number.
From the problem statement we can write:
47,400 is 26.3% of total registered doctors
We need to convert this word equation to algebraic equation noting that,
• "is" means "="
,• "of" means "x"
Also, remember to convert the percentage to decimal by dividing by 100,
[tex]\frac{26.3}{100}=0.263[/tex]The algebraic equation, thus, is:
[tex]47,400=0.263\times\text{total}[/tex]We let total be "t" and solve :
[tex]\begin{gathered} 47,400=0.263t \\ t=\frac{47,400}{0.263} \\ t=180228.14 \end{gathered}[/tex]Rounding to the nearest whole number,
Total Registered Doctors = 180,228
Answer:
180,228A fisherman drops a fishing line into the sea. The end of the fishing pole is at an elevation of 5 feet. The hook that is in the water is at an elevation of -2 feet.cessmentThe number line shows their heights. Sea level is represented by 0.1. Write an absolute value expression telling how many feet the end of the fishingpole is above sea level. Evaluate the expression.2. Write an absolute value expression telling how many feet the hook is below sealevel. Evaluate the expression. 3. If the fishing line goes straight down into the water, what is the distance betweenthe end of the pole and the hook? Explain how you found this distance.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
sea level = 0 ft
end of fishing pole = 5 ft
hook = -2 ft
Step 02:
absolute value:
distance between sea level and the end of fishing pole:
| 5 - 0| = | 5 | = 5 ft
distance between hook and sea level:
|0 - (-2)| = | 0 + 2| = |2| = 2 ft
distance between hook and the end of the fishing pole:
| 5 - (-2)| = | 5 + 2| = |7| = 7 ft
To find out the distance we must consider the entire interval.
That is the full solution.
Answer:
Given a fishing line acting as number line, find the asked distances
Explanation:
given a fishing line having its one end of the fishing pole above the water. Let this distance be denoted by 'a'.
given that the hook of this fishing line is in the water hence, below the sea level. Let this depth be denoted by 'b'.
let the height of pole from sea-level be denoted by , height of the hook from sea level be denoted by and the length between pole end and hook be
since, this fishing line is acting as a number line with sea level as . The depth of fishing hook is negative and the elevation of the pole end is positive .
hence we get expressions,
for given values the evaluation of the expressions is,
Step-by-step explanation:
Find the 100-th term of the following sequence
3, 10, 17, 24, …
Also find the sum of the first 100 terms.
Answer:
696
Step-by-step explanation:
*nth term = 7n - 4
n = 100
7 × 100 - 4 = 696
So the 100th term of the following sequence is: 696
*To find the nth term:
They all increase by 7 so it is 7n3 - 7 = -4 so then it is 7n - 4Answer:
Below in bold.
Step-by-step explanation:
This is an arithmetic sequence with a1 = 3 and d = 7.
So, 100th term
= a1 + d(n - 1)
= 3 + 7(100-1)
= 696.
Sum (100) =
(n/2)[2a1 + d(n - 1)]
= 50(6 + 99*7)
= 50 * 699
= 34950.
Write the tangent ratios for LP and 4Q. If needed, reduce!P12R160Not drawn to scaletan P=tan Q =
Given: The right triangle PQR as shown
To Determine: The tangents of P and Q
Solution
Given a right triangle, the tangent of any angle can be determine
Note that the side facing the right angle is the hypothenuse, the side facing the angle is the opposite and the other side is the adjacent.
Determine the opposite and the adjacent for angle P in the triangle PQR given
[tex]\begin{gathered} Note; \\ tan\theta=\frac{opposite}{adjacent} \\ tanP=\frac{16}{12} \\ tanP=\frac{4}{3} \end{gathered}[/tex]State the rational number represented by each letter on the number line as a decimal.
The rational number represented by the letter D is -43/100 and by the letter R is -46/100.
What is rational number?
A rational number is one that can be written as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.
Here the number line is divided into 10 division with equal distance.
Each division is of the distance 0.01
So, the decimal number represented by letter D is -0.43 and by the letter R is -0.46.
To convert decimal number into rational number,
-0.43 = -43/100
-0.46 = -46/100
Therefore, the rational number represented by each letter on the number line as a decimal are D = -43/100 and R = -46/100.
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Solve for x. Write the reasons next to each step.Submit723x+10
x = 26/3
Explanation:We would apply the mid-segment theorem:
The base of the smaller triangle = 1/2 (the base of the bigger triangle)
The base of the smaller triangle = 3x + 10
the base of the bigger triangle = 72
3x + 10 = 1/2(72)
Reason: Mid segment is parallel to the base of the large triangle. And it is equal to half the length of the base of the large triangle
simplifying:
3x + 10 = 72/2
3x + 10= 36
subtract 10 from both sides:
3x + 10 - 10 = 36 - 10
3x = 26
DIvide both sides by 3:
3x/3 = 26/3
x = 26/3
or x = 8 2/3
Liam's monthly bank statement showed the following deposits and withdrawals.If Liam's balance in the account was $62.45 at the beginning of the month, what was the account balance at the end of the month?
First, let's take the inital balance and add all the deposits:
[tex]62.45+32.35+63.09+98.79=256.68[/tex]Then, we'll take this amount and substract all the withdrawals:
[tex]256.68-114.95-79.41=62.32[/tex]This way, we can conclude that the account balance at the end of the month was $62.32
Enter an equation that represents the data in the table. 3 5 10 8 16 10 20 у 6 An equation is y = 6
Given data:
The given table is shown.
The expression for the equation passing through the points (3, 6) and (5, 10) is,
[tex]\begin{gathered} y-6=\frac{10-6}{5-3}(x-3) \\ y-6=\frac{4}{2}(x-3) \\ y-6=2(x-3) \\ y=2x \end{gathered}[/tex]Thus, the equation of the line is y=2x.
Question 5
< >
A research group needs to determine a 99% confidence interval for the mean repair cost for all car insurance
small claims. From past research, it is known that the standard deviation of such claims amounts to $146.91.
a. What is the critical value that corresponds to the given level of confidence?
Round your answer to two decimal places.
b. If the group wants their estimate to have a maximum error of $16, how many small claims should they
sample?
Round your answer up to the next integer.
Submit Question Jump to Answer
A standard deviation is a measure of how widely distributed the data is in relation to the mean. The critical value is z = 1.645 and the should sample at least 228.13638 small claims.
What is meant by standard deviation?A standard deviation (or) is a measure of how widely distributed the data is in relation to the mean. A low standard deviation indicates that data is clustered around the mean, whereas a high standard deviation indicates that data is more spread out.
The square root of the average of all squared deviations is the standard deviation. A region defined by one standard deviation, or one sigma, plotted above or below the average value on that normal distribution curve would include 68 percent of all data points.
Explanation in detail:
We can calculate our ∝ level by subtracting 1 from the confidence interval and dividing it by 2. So:
[tex]$\alpha=\frac{1-0.99}{2}=0.05[/tex]
Now we must locate z in the Stable, as z has a p value of [tex]$1-\alpha$[/tex]
So z with a p value of 1-0.05=0.95 equals z=1.645, implying that the answer to question an is z=1.645.
Determine the margin of error M as follows:
[tex]M=z * \frac{\sigma}{\sqrt{n}}[/tex]
In which ∝ is the standard deviation of the people and n is the size of the sample.
b)
[tex]$16=1.645 \cdot \frac{146.91}{\sqrt{n}}[/tex]
Expand
[tex]$1.645 \cdot \frac{146.91}{\sqrt{n}}: \quad \frac{241.66695}{\sqrt{n}}$$$[/tex]
[tex]$16=\frac{241.66695}{\sqrt{n}}$$[/tex]
Square both sides:
[tex]$\quad 256=\frac{58402.91472 \ldots}{n}$[/tex]
[tex]$256=\frac{58402.91472 \ldots}{n}[/tex]
Solve
[tex]$256=\frac{58402.91472 \ldots}{n}: \quad n=228.13638 \ldots$[/tex]
Verify Solutions: [tex]$n=228.13638 \ldots$[/tex] True
The solution is
n=228.13638...
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I wanted to know if this is the right answer
Notice that angles 6 and 4 are alternate exterior angles, therefore:
[tex]m\measuredangle4=m\measuredangle6.[/tex]Answer: m<4=66.
What is the most precise name for quadrilateral ABCD with vertices A(−5,7), B(6,−3), C(10,2), and D(−1,12)?A. rectangleB. parallelogramC. squareD. rhombus
Answer:
A. Rectangle
Step-by-step explanation:
I need help with a question
8c + 3 = 5c + 12
5c is adding on the right, then it will subtract on the left
3 is adding on the left, then it will subtract on the right
8c - 5c = 12 - 3
3c = 9
3 is multiplying on the left, then it will divide on the right
c = 9/3
c = 3
While reviewing the previous day’s arrest report, a police sergeant that seven suspects were arrested, all of whom had either one or two previous arrests. Including yesterday arrests, there were 16 total among them. How many suspects had had less than two prior arrests?
ANSWER :
EXPLANATION :
Help meeeee4) Consider the equation z(x)=(x-5,x s101-x+8, x > 10Note that for this problem, you do not actually have to evaluate the results. Just make sure that youexplain your choices.a. If you are trying to evaluate Z(3), which equation would you choose, and why?b. If you are trying to evaluate Z(11), which equation would you choose, and why?c. If you are trying to evaluate Z(10), which equation would you choose, and why?
4). a. If you are trying to evaluate Z(3) in order to know which equation would you choose we would have to make the following calcuations:
So, if Z(3), then:
substitute the x with the number 3
[tex]z\left(3\right)=3-5=-2,3\leq10,\text{ 1-3=-2, 3}>10[/tex]Therefore, the equation to choose if Z(3) would be x>10, because by substitute the x with the number 3 would be the largest function with a positive number and sign.
Blackgrass black graph is the of y=f(x) chose the equation for the red graph
The Solution:
The correct answer is [option A]
Given:
Required:
To determine the equation of the red graph if the black graph function is y = f(x).
The correctb
A 13-feet ladder is placed 5 feet away from a wall. What is the height at which the top of the ladder reaches the wall?
Draw the situation for a better understanding:
To find the height at which the top of the ladder reaches the wall use pythagorean theorem:
[tex]\begin{gathered} h=\sqrt[]{13^2-5^2} \\ h=\sqrt[]{169-25} \\ h=\sqrt[]{144} \\ h=12 \end{gathered}[/tex]The height at which the top of the ladder reaches the wall is 12 ft.
Graph the inequality on a plane. Shade a region below or above. Y < - 1
In order to graph the inequality on the coordinate plane, we first need to find it's border, which is delimited by the line below:
[tex]y=-1[/tex]This line is a straight line parallel to the x-axis and that passes through the y-axis at the point (0, -1). Since the original inequality has a "less" sign, we need to make this boundary line into dashes.
Now we can analyze the inequality:
[tex]y<-1[/tex]Since the signal is "<", we need to shade all the region of the coordinate plane for which y is below -1, this means that we have to paint the region below the line. The result is shown below:
Add the equation below:-9p=3p + 18Hint: We can isolate the variable by dividing each side by factors that don't contain the variable.
We have the next given equation:
[tex]9p=3p+18[/tex]Now, we can subtract both sides by 3p:
[tex]\begin{gathered} 9p-3p=3p-3p+18 \\ 6p=18 \end{gathered}[/tex]Then, divide both sides by 6:
[tex]\begin{gathered} \frac{6p}{6}=\frac{18}{6} \\ p=3 \end{gathered}[/tex]Hence, the answer is p=3
In a film, a character is criticized for marrying a woman when he is three times her age. He wittily replies, "Ah, but in 21 years time I shall only be twice her age." How old are the man and the
woman?
Write a linear function that models the total monthly costs for each option for x hours of court rental time.
The age of man is 63 years and the age of women is 21 years.
Given that, a character is criticized for marrying a woman when he is three times her age.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Let age of man be x and the age of women be y.
Now, x=3y ---------(1)
In 21 years time man will be twice her age.
x+21=2(y+21)
⇒ x+21=2y+42
⇒ x-2y=21 ---------(2)
Substitute equation (1) in (2), we get
3y-2y=21
⇒ y = 21
So, x=3y=63
Therefore, the age of man is 63 years and the age of women is 21 years.
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Write an equation for the description.Two-thirds a number x plus 6 is 10.
We have the next description:
- Two-thirds a number x plus 6 is 10.
To represent the description we can use the next equation:
[tex]\frac{2}{3}x+6=10[/tex]Find the surface area of the cylinderA). 188.4 ft^2B). 226.08 ft^2C). 244.92 ft^2D). 282.6 ft^2
To solve this problem, we will use the following formula for the surface area of a cylinder:
[tex]A=2\pi rh+2\pi r^2,[/tex]where r is the radius of the base, and h is the height of the cylinder.
Substituting h= 10 ft, and r = 3 ft in the above formula, we get:
[tex]A=2\pi(3ft)(10ft)+2\pi(3ft)^2.[/tex]Simplifying, we get:
[tex]A=244.92ft^2.[/tex]Answer: Option C.
8. Factor ()=63−252++60 completely given that x=3 is a zero of p(x). Use only the techniques from the lecture on 3.3 (synthetic division). Other methods will receive a score of zero. Be sure to show all your work (including the synthetic division).
Factor the polynomial
[tex]\begin{gathered} p(x)=6x^3-25x^2+x+60 \\ \text{Given that, }x=3\text{ is a zero} \end{gathered}[/tex]Using the synthetic division method to factorize the polynomial completely,
The resulting coefficients from the table are 6, -7, -20, 0
Thus the quotient is
[tex]6x^2-7x-20[/tex]Factorizing the quotient completely,
[tex]\begin{gathered} 6x^2-7x-20 \\ =6x^2-15x+8x-20 \\ =3x(2x-5)+4(2x-5) \\ =(3x+4)(2x-5) \end{gathered}[/tex]Therefore, the other two zeros of the polynomial are:
[tex]\begin{gathered} (3x+4)(2x-5)=0 \\ 3x+4=0 \\ x=-\frac{4}{3} \\ 2x-5=0 \\ x=\frac{5}{2} \\ \\ Therefore,t\text{he factors of the polynomial are:} \\ (x-3)(3x+4)(2x-5) \end{gathered}[/tex]HELP ASAP 15 POINTS Determine which integer will make the equation true.
4x + 7 = 23
S = {3, 4, 5, 6}
3
4
5
6
Answer:
S = 4
Step-by-step explanation:
23-7 = 16
16/4 = 4
4x4+7 = 23
Answer: S = 4
Step-by-step explanation:
23 - 7 = 16
16 / 4 = 4
4 x 4 + 7 = 23
A group of 38 people are going to an amusement park together. They decide to carpool to save fuel. If seven people can fit in each car, how many cars do they need to take on the outing? [?] cars 3
So, the number of people = 38
7 people can fit in a one car
so, to find the number of cars divide 38 by 7
So, the number of cars = 38/7 = 5.4
But the number of cars must be integer
so, the number of cars = 6 cars
The answer is 6 cars
Expand the following using the suitable identity.(-x + 2y - 3z)^2
Given the expression (-x + 2y - 3z)², we are to expand it using a suitable identity.
Using the square of the sum of trinomial identity expressed as:
[tex](a+b+c)^2=a^2+b^2+c^2+2\text{ab+2ac+2bc}[/tex]From the given expression;
[tex]\begin{gathered} a=-x \\ b=2y \\ c=-3z \end{gathered}[/tex]Substitute the parameters into the identity to expand as shown:
[tex](-x+2y-3z)^2=(-x)^2+(2y)^2+(-3z)^2+2(-x)(2y)+2(-x)(-3z)_{}+2(2y)(-3z)[/tex]
Simplify the result to have:
[tex](-x+2y-3z)^2=x^2+4y^2+9z^2-4xy+6xz_{}-12yz[/tex]This gives the correct expansion using a suitable identity
Please help me with my calc hw, I'd be more than happy to chip in albeit with my limited knowledge.
Given:
[tex]F(x)=\int_0^x\sqrt{36-t^2}dt[/tex]Required:
To find the range of the given function.
Explanation:
The graph of the function
[tex]y=\sqrt{36-t^2}[/tex]is upper semicircle with center (0,0) and radius 6, with
[tex]-6\leq t\leq6[/tex]So,
[tex]\int_0^x\sqrt{36-t^2}dt[/tex]is the area of the portion of the right half of the semicircle that lies between
t=0 and t=x.
When x=0, the value of the integral is also 0.
When x=6, the value of the integral is the area of the quarter circle, which is
[tex]\frac{36\pi}{4}=9\pi[/tex]Therefore, the range is
[tex][0,9\pi][/tex]Final Answer:
The range of the function is,
[tex][0,9\pi][/tex]CD is the midsegment of trapezoid WXYZ. you must show your work to all the parts below
Given that CD is the midsegment of the trapezoid WXYZ
From the properties of Midsegment of trapezoid we have :
0. The midsegment of a trapezoid is parallel to each base.
,1. The length of the midsegment of a trapezoid is equal to half the sum of the lengths of its bases.
[tex]\text{length of mid segment =}\frac{a+b}{2}[/tex]In the given figur, the mid segement CD= 22
length of parallel side is WZ=x+3
and the length of another side XY = 4x+1
so apply the mid segment length formula :
[tex]\begin{gathered} CD=\frac{WZ+XY}{2} \\ 22=\frac{x+3+4x+1}{2} \\ 5x+4=44 \\ 5x=40 \\ x=8 \end{gathered}[/tex]x=8,
For, XY :
Substitute x=8 into the given length expression of XY
XY =4x+1
XY=4(8)+1
XY=33
For, WZ :
Substitute x=8 into the given expression length of WZ
WZ=x+3
WZ=8+3
WZ=11
Answer :
a). x = 8
b). XY = 33
c). WZ = 11