In order to calculate the first four terms of this sequence, let's use the values of n = 1, 2, 3 and 4 in the expression for An:
[tex]\begin{gathered} n=1\colon \\ A_1=42-7(1-1)=42 \\ \\ n=2\colon \\ A_2=42-7(2-1)=35 \\ \\ n=3\colon \\ A_3=42-7(3-1)=28 \\ \\ n=4\colon \\ A_4=42-7(4-1)=21 \end{gathered}[/tex]Therefore the first four terms are 42, 35, 28 and 21.
How is 600:450 and 60:45 equivalent
How is 60:45 and 4:3 equivalent
How is 600:450 and 4:3 equivalent
Four friends are playing a game. 36 cards are dealt out between the friends. Which equation can be used to find how many cards each person receives
Given
Four friends are playing a game.
36 cards are dealt out between the friends.
To find: Which equation can be used to find how many cards each person receives.
Explanation:
It is given that,
Four friends are playing a game.
36 cards are dealt out between the friends.
Let x be the number of cards received by each person.
Then,
[tex]\begin{gathered} 4x=36 \\ x=\frac{36}{4} \\ x=9 \end{gathered}[/tex]Hence, each person receives 9 cards.
Thus,
[tex]undefined[/tex]slove equations with variables on both sides-4 + 9z = 10z
Dakota fills a measuring cup 5/8 cup of sugar 2 times to make a cake. Which multiplication equation shows the total amount of sugar Dakota uses?
We have that Dakota fills a measuring cup 5/8 cup of sugar two times. The multiplication equation that shows the total amount of sugar is:
[tex]2\cdot\frac{5}{8}=\frac{10}{8}=\frac{8}{8}+\frac{2}{8}=1+\frac{2}{8}=1\frac{2}{8}[/tex]We needed to multiply the fraction 5/8 by 2, and then solve for the given operations.
Therefore, the answer is the last option:
2 x 5/8 = 10/8 = 1 2/8 cups of sugar
Find the exact value and the approximate value of the area of the triangle
From the big triangle we know that:
[tex]\begin{gathered} x^2+y^2=12^2 \\ x^2+y^2=144 \end{gathered}[/tex]From the triangle on the right we also know that:
[tex]h^2+9^2=y^2[/tex]From the triangle on the left we know:
[tex]3^2+h^2=x^2[/tex]Adding the last two equations we have that:
[tex]\begin{gathered} x^2+y^2=h^2+9^2+h^2+3^2 \\ x^2+y^2=2h^2+90 \end{gathered}[/tex]Equating the last equation with the first one we have that:
[tex]\begin{gathered} 2h^2+90=144 \\ 2h^2=144-90 \\ 2h^2=54 \\ h^2=\frac{54}{2} \\ h^2=27 \\ h=\sqrt[]{27} \end{gathered}[/tex]Then, the height of the triangle is the squared root of 27.
Once we know the height we can calculate the area.
[tex]\begin{gathered} A=\frac{1}{2}bh \\ =\frac{1}{2}12\sqrt[]{27} \\ =6\sqrt[]{27} \end{gathered}[/tex]Therefore the exact value of the area is:
[tex]6\sqrt[]{27}[/tex]This can be approximated to (rounding on the hundreths):
[tex]31.18[/tex]A cube is partially filled with 4 mmof water. If the water is 1 mm high, what is the length of one side of the cube?O 1 mmVx02 mmO 3 mm04 mmSave and ExitNextSubmitMark this and returnA cube is partially filled with 4 mm cubed of water. If the water is 1mm high, what is the length of one side of the cube?
Given:
a.) A cube is partially filled with 4 mm of water.
b.) The water is 1 mm high
Let's draw the scenario to better understand the problem,
help me pleasee!!
thank you
The equation of the revenue is y = -500/3x + 3000 and the daily sales for $7.50 is $1750
How to determine the equation of the line?The points are given as
(6, 2000) and (8, 1000)
Calculate the slope of the points using the following slope formula
m= (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (6, 2000) and (8, 1000)
Slope = m
So, we have
m = (1000 - 2000)/(8 - 2)
Evaluate the expression
m = -500/3
The equation of the line is then calculated using the line equation formula
y = m(x - x₁) + y₁
Where
(x₁, y₁) = (6, 2000)
So, we have
y = -500/3(x - 6) + 2000
Expand
y = -500/3x + 3000
The daily sales for $7.50This means that
x = 7.50
Recall that
y = -500/3x + 3000
Substitute x = 7.50
y = -500/3 x 7.50+ 3000
Evaluate
y = 1750
So, the daily sales is $1750
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What is X for
3(2x + 11) + 4(2x + 3) = 9(2x + 13) - 3x
Answer:
x = -72
Step-by-step explanation:
3(2x + 11) + 4(2x + 3) = 9(2x + 13) - 3x
(6x + 33) + (8x + 12) = (18x + 117 ) - 3x
14x + 45 = (18x + 117) - 3x
14x + 45 = 15x + 117
-45
14x = 15x + 72
-15x
-1x = 72
/-1
x = -72
Using the prototype oblique triangle shown below and the information given, find the measure of the remaining sides and angles in the triangle.
find:
beta:
a:
b:
Using the law of sines, the remaining angles and sides of the triangle are given as follows:
[tex]\beta = 20^\circ[/tex]a = 8.2.b = 6.What is the law of sines?Suppose we have a triangle in which:
Side with a length of a is opposite to angle A.Side with a length of b is opposite to angle B.Side with a length of c is opposite to angle C.The lengths and the sine of the angles are related according to the equation presented as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The remaining angle measure is given as follows:
[tex]\beta = 180 - (132 + 28) = 20^\circ[/tex]
(this is because the sum of the internal angles of a triangle is of 20º).
Then side a is calculated from the law of sines as follows:
sin(28º)/a = sin(132º)/13
a = 13sin(28º)/sin(132º)
a = 8.2.
Side b is also calculated from the law of sines, as follows:
sin(20º)/b = sin(132º)/13
b = 13sin(20º)/sin(132º)
b = 6.
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Original price $30; Markup 7.5$The retail price is $ ?
Retail price = $37.5
Explanation:Original price = $30
Markup = $7.5
Retail price = cost price + markup
cost price = Original price = $30
Retail price = $30 + $7.5
Retail price = $37.5
Jessica used 2/3 yard of fabric to make scarf can she make 2 of these scarfs with 1 3/4 yards of fabric, and why?
SOLUTION:
Step 1;
In this question, we are given the following;
Jessica used 2/3 yard of fabric to make scarf can she make 2 of these scarfs with 1 3/4 yards of fabric, and why?
Step 2:
The details of the solution are as follows;
Use this description to write the quadratic function in vertex form:The parent function f(x)=x^2 is vertically stretched by a factor of 2 and translated 14 units right and 6 units up.
The vertex form is given by:
[tex]y=a(x-h)^2+k[/tex]The parent function is:
[tex]f(x)=x^2[/tex]The function is vertically stretched by a factor of 2 :
[tex]2f(x)=2x^2[/tex]and translated 14 units right:
[tex]2f(x-14)=2(x-14)^2[/tex]and 6 units up:
[tex]2f(x-14)+6=2(x-14)^2+6[/tex]Answer:
[tex]g(x)=2(x-14)^2+6[/tex]indicate the equation of the given line in standard form show all your work for full creditthe line containing the diagonal ,BD,of a square whose vertices areA(-3,3) B(3,3) C (3,-3) and D (-3,-3)find two equations one for each diagonal
ANSWER:
x + y = 0
x - y = 0
EXPLANATION:
Given the coordinates:
A(-3,3)
B(3,3)
C(3,-3) and
D (-3,-3)
One diagonal is line AC.
Find the slope of AC:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\text{ }\frac{-3-3}{3-(-3)}=\frac{-6}{6}=\text{ -1}[/tex]Solpe of AC = -1
Using the slope intercept form, y = mx+b, we have:
y = -1x + b
y = -x + b
The equation for AC:
y = -x
The other diagonal is BD.
find the slope of BD:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\text{ }\frac{-3-3}{-3-3}=\frac{-6}{-6}=\text{ 1}[/tex]Slope of BD = 1
The equation of BD:
y = 1x
y = x
Therefore the equation of both lines in standard form will be:
AC ==> x + y = 0
BD ==> x - y = 0
A={1,2,3,4,5} and B={6,7,8,9}. Find A∪B
Answer:
{1, 2, 3, 4, 5, 6, 7, 8, 9}
Step-by-step explanation:
[tex]A \cup B[/tex] represents the set of all elements in [tex]A[/tex] or [tex]B[/tex].
A set of data has a normal distribution with a mean of 56 and a standard deviation of 9. Find the percent of data within the following interval. from 29 to 83 The percent of data within the given interval is ____%.
Solution
We are given
[tex]\begin{gathered} \mu=56 \\ \sigma=9 \end{gathered}[/tex]First, we will find the probability p(29 < x-bar < 83)
Note: z score formula
[tex]z=\frac{\bar{x}-\mu}{\sigma}[/tex]To find the probability
[tex]\begin{gathered} p(29<\bar{x}<83)=p(\bar{x}<83)-p(\bar{x}<29) \\ p(29<\bar{x}<83)=p(z<\frac{83-56}{9})-p(z<\frac{29-56}{9}) \\ p(29<\bar{x}<83)=p(z<3)-p(z<-3) \\ p(29<\bar{x}<83)=0.99865-0.0013499 \\ p(29<\bar{x}<83)=0.9973001 \\ p(29<\bar{x}<83)=0.9973\text{ \lparen to four decimal places\rparen} \end{gathered}[/tex]Therefore, the percentage within the given interval will be
[tex]0.9973\times100=99.73\%[/tex]The answer is
[tex]\begin{equation*} 99.73\% \end{equation*}[/tex]What is (5x)(-2x) in words but I don’t need the answer (can give if u want to)?
(5x)(-2x) in words is Five times x multiplied by negative two times x
Define algebraic expression.Using variables, constants, and algebraic operations, an expression can be described as an algebraic expression in mathematics (addition, subtraction, etc.). Terms are used to construct expressions. Any combination of a number, a variable, and operation symbols is considered an expression. Two expressions are combined to form an equation, which is joined by the equal sign. Example of a word: The product of 8 and 3. Word illustration: 11 is the result of adding 8 and 3.
Given Data
Expression
(5x)(2x)
Translating algebraic expression into verbal expression:
Five times x multiplied by negative two times x
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Find the value of z.
x
y
1089
400
w
N
z = [? ]°
Answer:
34 degrees
Explanation;
Using the theorem below to solve the problem;
Angle at the vertex is equal to to half of the difference of angles of its intercepted arcs
Angle at the vaertex = z
difference of angles of its intercepted arcs = 108 - 40
difference of angles of its intercepted arcs = 68
Using the theorem
z = 1/2(108-40)
z = 1/2 * 68
z = 34 degrees
Hence the value of z is 34 degrees
An inverse variation includes the points (-4, 3) and (-1, n). Find n.
In a inverse variation you have two variables, in this case (x,y) x and y, and a constant value k in the form:
[tex]y=\frac{k}{x}[/tex]When x increase y decreases and when x decreases y increases (inverse variation)
As you have two (x,y) data;
(-4, 3 ) and (-1 , n)
And both have the same constant k.
[tex]\begin{gathered} 3=\frac{k}{-4} \\ \\ n=\frac{k}{-1} \end{gathered}[/tex]Solve in the first equation the k:
[tex]\begin{gathered} k=-4\cdot3 \\ k=-12 \end{gathered}[/tex]Use the value of k= -12 to find n in the second equation:
[tex]n=\frac{-12}{-1}=12[/tex]Then , the value of n is 12The ages of rocks in an isolated area are known to be approximately normally distributed with a mean of 7 years and a standard deviation of 1.8 years. Using the normalcdf function on your graphing calculator, what percent of rocks are between 5.8 and 7.3 years old?
The answer is B: 31.4%
Using a graphic calculator you have:
Mean: 7
SD: 18
Lower bound: 5.8
Upper bound: 7.3
What is the surfacearea, in square inches,of the square pyramidbelow?
hi, for solve this question we need to use the formula below:
[tex]\text{Area of each triangle + area of the quadrangular base = Total area}[/tex]First, the area of the base:
[tex]\begin{gathered} \text{area base = side }\cdot\text{ side} \\ \text{area base = 4in }\cdot\text{ 4in} \\ \text{area base = 16in}^2 \end{gathered}[/tex]Now, the area of each triangular side:
we have the base as 4in, and the height as 9in.
So, using the formula:
[tex]\begin{gathered} \text{area = }\frac{\text{ base }\cdot\text{ height}}{2} \\ \text{area = }\frac{\text{ 4 }\cdot9}{2} \\ \text{area = }\frac{\text{3}6}{2}=18in^2\text{ each triangular side} \end{gathered}[/tex]Now, let's sum all of the values:
4 triangular sides + 1 quadrangular side
(4 * 18in) + (1 * 16in)
72in² + 16in² = 88in²
Answer: ALTERNATIVE NUMBER 2. 88in²
What is the volume of the prism that is 5 meters wide, 4 meters high, and 8 meters long?A. 160 m³B. 180 m³C. 120 m³D. 200 m³
12. A basketball teams wins 4/7 of their games. What is the probability that in a season of 15games they will win exactly 8 games. (circle one answer)A.,C,(4/7)*(3/7) B. S, (3/7)477' c. S.(4/7 (377)C*())* D. C, (4/7) (3/7)
A basketball game does not end in a tie. This means that it is either the team wins the game or they draw the game. These outcomes are independent becuase winning one game has no effect on the outcome of the next game. This means that we have a binomial distribution here. the formula for binomial distribution is expressed as
P(x) = nCx * p^x * q^(n - x)
where
n is the number of trials
x is the number of successess
p is the probability of success
q is the probability of failure
We are concerned with the outcome of winning. This means that success is when the team wins. Thus,
p = 4/7
q = 1 - p = 1 - 4/7 = 3/7
n = 15
x = 8
We want to find P(x = 8)
By applying the binomial distribution formula,
P(x = 8) = 15C8 * (4/7)^8 * (3/7)^(15 - 8)
P(x = 8) = 6435 * (4/7)^8 * (3/7)^7
P(x = 8) = 0.194
The probability that in a season of 15 games they will win exactly 8 games is
0.194
Solve
-21 < 3x - 12 < 6
Answer:
-3 < x < 6
Step-by-step explanation:
-21 < 3x - 12 < 6
first lets add 12 to everything
-9 < 3x < 18
now lets divide everything by 3
-3 < x < 6
related rates need help calculus
Answer:
0.1468 ohms per second
Step-by-step explanation:
You want the rate of change of R when ...
1/R = 1/r1 +1/r2r1 = 70 Ωr2 = 120 Ωr1' = 0.3 Ω/sr2' = 0.2 Ω/sDerivativeThe desired rate of change is the derivative of R with respect to time. Implicitly differentiating the given relation with respect to time, we have ...
-R'/R² = -r1'/r1² -r2'/r2²
R' = R²(r1'/r1² +r2'/r2²)
Using the given relation and values, we have ...
1/R = 1/70 +1/120 = 190/(70·120)
R = (840/19)
R' = (840/19)(0.3/70² +0.2/120²) = 53/361 ≈ 0.1468
The rate of change of R is about 0.1468 ohms per second.
Additional comment
Most graphing calculators can figure this value for you.
16. What is the average of the following numbers? 7, 4, 6, 11, 10, 17, 15? (a) 14 (b) 9 (c) 10 (d) 12 (e) 20
Answer:
C: 10
Step-by-step explanation:
Help answer please. The graph of g and the graph of fare shown. Which of the following describes a single transformation that compares the graph of g with the graph of f?
Select all that apply.
The options that describes a single transformation that compares the graph of g with the graph of f are;
B) The graph of g is shifted 3 units right.
C) The graph of g is shifted 3 units up.
What is the Graph Transformation?Transformation is a method required to resize or change the orientation of a given shape or figure. The types of transformation are translation, reflection, rotation, and dilation.
Translation is a method of transformation that involves moving an object or shape from one point to another without changing any dimension.
Reflection is a method of transformation that involves flipping a given figure about a given reference point or line. In order words, a mirror image of the original object.
Rotation is a method of transformation that involves turning a given figure at an angle about a reference point.
Dilation is a method of transformation whereby the length of the sides of the figure is either increased or decreased.
Now, looking at the given graph, we see that the line showing the graph g is clearly shifted by either 3 units to the right or 3 units upwards to get the function line f.
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Write the list of integers in increasing order from left to right.12, -4, -9,2, -2.
we have the list
12, -4, -9,2, -2
rewrite in increasing order from left to right
The answer is
-9,-4,-2,2,12Divide x^2+x-4 by (x+3)
The resulting value of the division of x²+x-4 by (x+3),
Quotient = x - 2
Remainder = 2
Division:
The process of division means the process of breaking a number up into equal parts, and finding out how many equal parts can be made.
Given,
Here we have the expression x²+x-4.
Now, we need to divide by the expression (x + 3).
Here we have to use the long division method in order to solve it.
The following steps are followed to solve this:
1. Divide the first term of the dividend by the first term of the divisor
2. Write down the calculated result x in the upper part of the table.
3. Multiply it by the divisor
4. Subtract this result from the dividend
This steps is repeated until no further division.
Thus process will be showed on the attached figure.
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Find the missing side of this righttriangle.Х.911x= [?]✓Enter the number that belongs in the green box.
Using pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ _{\text{ }}where\colon \\ a=11 \\ b=9 \\ c=x \\ x=\sqrt[]{9^2+11^2}^{} \\ x=\sqrt[]{202} \end{gathered}[/tex]Answer:
[tex]x=\sqrt[]{202}[/tex]Identify the slope and y-intercept from the graph, and then write the equation of the line. YA 3) 1. slope = y-intercept= y =
As shown on the graph:
y-intercept is the value of y at which x = 0
so, from the graph when x = 0 , y = -3
To find the slope use two points to calculate it
Using the points (0 , -3) and ( 4 , 4 )
the slope = Rise/Run
Rise = 4 - (-3) = 4 + 3 = 7
Run = 4 - 0 = 4
so, the slope = 7/4
The slope intercept form of the line is y = mx + c
Where m is the slope and c is y-intercept
Slope = m = (7/4)
y-intercept = c = -3
So,
y = (7/4) x - 3
