Answer:
[tex]2.0806 * 10^{2}[/tex]
Step-by-step explanation:
Standard notation, also known as scientific notation, is when the whole number can only be [tex]1\leq 0 < 10[/tex]. The rest of the number is behind the decimal point.
1,1,2,6,24,_,_,_,_,Explain and fill the sequence, write the explicit and recursive formula for the sequence
Given the sequence:
1, 1, 2, 6, 24
Let's fill in the sequence.
Here, we can see that the nth term is equal to the pprevious term multiplied by n.
First term: 1 x 1 = 1
Second term: 1 x 2 = 2
Third term: 2 x 3 = 6
Fourth term: 6 x 4 = 24
Fifth term: 24 x 5 = 120
Sixth term: 120 x 6 = 720
Seventh term: 720 x 7 = 5040
8th term: 5040 x 8 =40320
Hence, the sequence is:
1, 1, 2, 6, 24, 120, 720, 5040, 40320
The explicit formula of the sequence is:
[tex]a_n=a_{n-1}\ast n[/tex]For example to find the 6th term, we have:
[tex]\begin{gathered} a_6=a_{6-1}\ast6 \\ \\ a_6=a_5\ast6 \\ \\ a_6=120\ast6 \\ \\ a_6=720 \end{gathered}[/tex]We can see the 6th term is 720.
For the recursive formula, we have:
[tex]\begin{cases}a_1=1 \\ \\ n\ge2_{} \\ \\ a_n=a_{n-1}\ast n\end{cases}[/tex]ANSWER:
Sequence: 1, 1, 2, 6, 24, 120, 720, 5040, 40320
Explicit formula:
[tex]a_n=a_{n-1}\ast n[/tex]
Recursive formula:
[tex]\begin{cases}a_1=1 \\ \\ n\ge2_{} \\ \\ a_n=a_{n-1}\ast n\end{cases}[/tex]
Some help I will mark Brain liest
Answer:
-2.86, -0.37, 0.19, 0.91, 1.46
Step-by-step explanation:
the negatives will always be the least, hope this helps!
Find the value of the following expression: (3^8•2^-5•9^0)^-2•(2^-2/3^3)^4•3^28 Write your answer in simplified form.
Answer:
4
Step-by-step explanation:
Given expression:
[tex](3^{8} \cdot 2^{-5} \cdot 9^{0})^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
Any number to the power of zero is 1:
[tex]\implies (3^{8} \cdot 2^{-5} \cdot 1)^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\implies (3^{8} \cdot 2^{-5})^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b \cdot c^d)^p=a^{bp}\cdot c^{dp}:[/tex]
[tex]\implies 3^{(8 \cdot -2)} \cdot 2^{(-5 \cdot -2)} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{\left(2^{-2}\right)^{4} }{\left(3^{3}\right)^{4} } \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{2^{(-2 \cdot 4)}}{3^{(3\cdot 4)}} \cdot 3^{28}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{2^{-8}}{3^{12}} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot 2^{-8} \cdot 3^{-12} \cdot 3^{28}[/tex]
Gather like terms:
[tex]\implies 2^{10} \cdot 2^{-8} \cdot3^{-16} \cdot 3^{-12} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 2^{(10-8)}\cdot3^{(-16-12+28)}[/tex]
[tex]\implies 2^{2}\cdot3^{0}[/tex]
Any number to the power of zero is 1:
[tex]\implies 2^{2}\cdot 1[/tex]
[tex]\implies 2^2[/tex]
Therefore, the solution is:
[tex]\implies 2^2=2 \times 2=4[/tex]
a wildfire organization wants to fence off an area of a beach. The organization can only fence 100 yd². what length (x) and width (y) should the organization use the Least amount of fencing as possible
It is given that the total area of the beach is 100 yd².
We have to find the length x and the width y that the organization shoul use to use the least amount of fencing as possible. it means that we have to find the dimensions for which parameter is leasr.
The perimeter of a rectangle is:
[tex]P=2\times(l+w)[/tex]In option 1, the length is 50 yards and the width is 20 yards. then the perimeter will be (using the previous formula) equal to 140.
In option too the perimeter will be 130.
in option 3 the perimeter will be 134.44
and, in option 4 it will be 146.36
therefore the least perimeter is 130 when the length is 40 yd and the width is 25 yd.
Solve the system by the substitution method. *8x – 3y = -22y = 5x + 19 (-5,6) (4,-3) (0,-5) (-3,4)
8x - 3y = -22
y = 5x + 19
Substituting the second equation into the first one:
8x - 3(5x + 19) = -22
8x - 3*5x - 3*19 = -22
8x - 15x - 57 = -22
-7x = -22 + 57
x = 35/(-7)
x =
Find the points on
y = x³ + 6x² - 15x + 1 at which the
gradient is zero.
Answer:
(-5, 101) or (1, -7)
Step-by-step explanation:
The gradient of a function is zero when its first differential is zero
Taking first derivative of y = x³ + 6x² - 15x + 1
we get
[tex]\dfrac{dy}{dx} = \dfrac{d}{dx}(x^3+6x^2-15x\:+\:1)[/tex]
[tex]= \dfrac{d}{dx}(x^3)+ \dfrac{d}{dx}(6x^2) - \dfrac{d}{dx}(15x)\:+\: \dfrac{d}{dx}(1)\\\\[/tex]
[tex]= 3x^2 + 2(6x) - 15 + 0\\\\\\= 3x^2 + 12x - 15x\\[/tex]
Set this first differential to 0, find the solution set for x
[tex]3x^2 + 12x - 15x =0[/tex]
This is a quadratic equation which will have 2 solutions for x.
First divide throughout by 3
[tex]= > x^2 + 4x - 5 = 0[/tex]
Factor the term:
[tex]= > x^2 + 4x - 5 = 0\\\\== > (x -1)(x + 5) = 0\\== > x - 1 =0 \text { or } x + 5 =0\\\\[/tex]
This means x = 1 or x = -5 is the solution set
To find the y value corresponding to these values of x, plug in each of these x values in the original equation and solve for y
Plug in x = 1 into equation x³ + 6x² - 15x + 1
=> 1³ + 6(1)² - 15(1) + 1
=> 1 + 6 - 15 + 1
=> -7
So one point is (1, -7)
Looking at the choices we can eliminate the first and last choices
Looking at choices 2 and 3 we see that only one of them has x = -5 which is the other solution value. This is the second choice
So the correct answer is second choice
(-5, 101) or (1, -7)
Note we did not have to go through the pain of computing y for x = -5
Which value of a will make the following equation true?
(p²)4p³ = pll
a=0
a=2
O No value of a will work.
O a = 1
so u need to know
[tex] {p}^{a} \times {p}^{b} = {p}^{a + b} [/tex]
and
[tex] { ({p}^{a} )}^{b} = \: {p}^{a \times b} [/tex]
question :
[tex] { ({p}^{a} )}^{4} \times {p}^{3} = {p}^{11} [/tex]
so we can tell :
[tex] {p}^{(a \times 4) +3 } = {p}^{11} [/tex]
then
[tex](a \times 4 )+ 3 = 11[/tex]
[tex]a = 2[/tex]
the answer is a=2
Not sure I’m doing this correctly or I’m missing something please help ! The wheel has a radius of 32 feet and the distance from the center of the Ferris wheel to the ground is 40 feet.
a)
From the information given, the ferris wheel makes a complete rotation in 16 minutes.
A complete rotation is 360 degrees. This means that each angle is
360/12 = 30 degrees
Lets us assume that the starting point is A. As the ferris wheel move towards the highest point at D, the angle covered is 30 + 30 + 30 = 90 degrees
We have the following equations
360 = 16
90 = (90 x 16)/360 = 4
b) Recall, 1 minute = 60 seconds
Thus, 16 minutes = 16 x 60 = 960 seconds
It x
Solving a percent makes your prom using a system of linear equations
Water :60 ounces
Salt solution:60 ounces
Explanation
Step 1
set the equations
Let x represent the amoun of water forthe solution
let y represents the amount of solution ( 40% salt)
so
a)the scientific mixes water with the solution to obtain 120 ounces, so
[tex]x+y=120\Rightarrow equation\left(1\right)[/tex]b)the mixture is 20% salt
so
salt fromwater+salt from solution( 40%) = salt in the solution (20%)
so
[tex]\begin{gathered} 0+0.4y=120*0.2 \\ 0.4y=24 \\ divide\text{ both sides by 0.4} \\ \frac{0.4y}{0.4}=\frac{24}{0.4} \\ y=60 \end{gathered}[/tex]hence, the amount of salt solution is 60 ounces
,now to find x, replace the y value in equation (1)
[tex]\begin{gathered} x+y=120\Rightarrow equation\left(1\right) \\ x+60=120 \\ subtract\text{ 60 in both sides} \\ x+60-60=120-60 \\ x=60 \end{gathered}[/tex]so, water : 60 ounces
therefore, the answer is
Water :60 ounces
Salt solution:60 ounces
I hope this helps you
solve for k=prt for p
What is 1+1? Express in number form.
The number form of (1 + 1) will be (1 + 1) only.
What is number form?When a person who experiences number forms thinks of numbers, a mental map of the numbers automatically and unconsciously appears. Numbers are translated into specific spatial locations, and this translation may vary from person to person. In his book The Visions of Sane Persons, Sir Francis Galton first described and named number forms (Galton 1881a). They have been classified as a type of synesthesia in later studies (Seron, Pesenti, and Nol 1992; Sagiv et al. 2006).So, 1 + 1 in number form:
Given (1 + 1) is 2 when we do the sum of it, the number form of 2 will be:
1 + 1Therefore, the number form of (1 + 1) will be (1 + 1) only.
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For a normal distribution, it is known that the mean is zero and the standard deviation is 1. Be sure to draw and label a normal distribution for each problem. Find the probability that a z score is between -1.15 and 1.98.
To find the probability between two z-scores on a normal distribution, we can use a z-score table.
A z-score table gives the probability of a data less than the corresponding z-score, like in the picture:
So, if we want the probability between 1.98 and -1.15, we need to do the following:
[tex]P(-1.15However, usually z-score tables go only from z = 0 and above, so we need a way to consult the negative z.Since the normal distribution in symmetric around z = 0, we have that:
[tex]P(z<-1.15)=P(z>1.15)[/tex]And since the whole distribution give a 100% probability, or an area of 1, we have that:
[tex]\begin{gathered} P(z<1.15)+P(z>1.15)=1 \\ P(z>1.15)=1-P\mleft(z<1.15\mright) \end{gathered}[/tex]So, in the end, we have:
[tex]\begin{gathered} P(-1.151.15) \\ P(-1.15So, we can consult the values for the probabilities of z < 1.98 and z < 1.15 on the z-score table:[tex]\begin{gathered} P(z<1.98)\approx0.9761 \\ P(z<1.15)\approx0.8749 \end{gathered}[/tex]So, the total probability is:
[tex]\begin{gathered} P(-1.15So, the probability is approximately 0.8510.The pentagonal prism below has a cross-sectional area of
27 cm² and a length of 3 cm.
Calculate the volume of the prism.
Give your answer in cm³.
Answer:
81 cm³
Step-by-step explanation:
1. Classify each angle pair as corresponding, alternate interior, alternate exterior,
same side interior, linear pair.
a) <1 and <5
b) <15 and <7
c) <11 and <1
d) <4 and <10
e) <8 and <13
f) <3 and <4
∠1 and ∠5 are a pair of corresponding angles.
∠15 and ∠7 are corresponding angles.
∠4 and ∠10 are a pair of alternate interior angles.
∠8 and ∠13 are a pair of co-interior angles.
∠3 and ∠4 are a pair of linear angles.
What are corresponding angles?
When two parallel lines are intersected by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).
What are alternate interior angles?
When a transversal connects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines. At two different locations, the transversal passes through the two lines that are coplanar. These angles indicate whether or not the two provided lines are parallel to one another. When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairings of that transversal. Alternate interior angles are what they are termed.
What are alternate exterior angles?
The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles.
What are linear pair of angles?
When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.
Following the above literature,
∠1 and ∠5 are a pair of corresponding angles since angles are created in matching corners or corresponding corners with the transversal.
∠15 and ∠7 are corresponding angles since angles are created in matching corners or corresponding corners with the transversal.
∠4 and ∠10 are a pair of alternate interior angles.
∠8 and ∠13 are a pair of co-interior angles.
∠3 and ∠4 are a pair of linear angles since pair's total angles are always equal to 180°.
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What is the slope of the line passing through the points (-1, 7) and (4, -1)? 0 2 0-2 please answer quickly if you can
Answer:
answer in image
Step-by-step explanation:
Figure NN is the result of a transformation on Figure MM. Which transformation would accomplish this?
The transformation that is used is a translation of 3 units upwards.
Numerous different coordinate systems can be used to describe geometrical figures.
The connection between several systems is defined by coordinate transformations, which offer formulas for the coordinates in one system in terms of the coordinates in another system. For example, if the polar axis on a plane is the positive x axis and the origins of the Cartesian coordinates (x, y) and the polar coordinates (r), respectively, are the same. The transformation of the coordinates from the polar to the Cartesian coordinate system is x = r cos α and y = r sin α.From the diagram of the graph we can see that the transformation that is used is translation of 3 units upwards.
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Fill in the missing amounts (do not use commas or decimal points.)
A$
B$
C$
D$
E$
F$
The missing amount is A. 790 B. 20 C. 90 D. 75 E. 20 F. 275
Subtract non-cash assets from total current assets. This number represents the cash amount on the balance sheet. Below is a simple way to calculate income, capital, and total cost of income: Net Income = Ending Equity Starting Equity from the Balance Sheet Total Expenses = Net Income Net Income.
Everything a company owns must come from debt-equity owners or equity so the equation must be balanced. Equity equals the balance sheet total minus all liabilities. All these figures are on the company's balance sheet. For homeowners, equity is the value of the home minus any outstanding mortgage debt or liens.
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6. A newborn baby eats 8 times a day. At each feeding, he
eats 2.5 ounces of formula. How many ounces would the
baby eat in 1 week?
Answer:
140 ounces
Step-by-step explanation:
(8)(2.5)(7) = 140 ounces
What does x equal?
x(x + 10) = 0
Answer:
x=-10, you would get this by fixing the equation like this (x+10) (x+) =0 then you would have to -10 on both sides and you get -10 as your answer
Simplify: qp - 8m - m +1 - m; usee m= -3, p = 9, and q = 570-297616None of these answers are correct.
Answer:
76
Step-by-step explanation:
We are given the following expression:
qp - 8m - m + 1 - m
It can see simplified combining commom terms as:
qp + m(-8 - 1 - 1) + 1
Which is
qp - 10m + 1
Replacing m by -3, q by 5 and p by 9
5*9 - 10*(-3) + 1 = 45 + 30 + 1 = 76
The sum of measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 21 more than the second. Let x,y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
The measure of all the three angles of a triangle will be 45°, 57° and 78° respectively.
What is Triangle?
A triangle is a three sided polygon , which has three vertices and three angles, whose sum is equal to 180 degree.
Given that;
The sum of measures of the angles of a triangle is 180.
The sum of the measures of the second and third angles is three times the measure of the first angle.
The third angle is 21 more than the second.
Now,
Let the measures of all the three angles are x , y and z.
Since, The sum of measures of the angles of a triangle is 180.
So, we can formulate;
x + y + z = 180° .... (i)
The sum of the measures of the second and third angles is three times the measure of the first angle.
So, we can formulate;
y + z = 3x ... (ii)
The third angle is 21 more than the second.
So, we can formulate;
z = 21 + y ... (iii)
Substitute value of z in equation (ii);
y + 21 + y = 3x
3x = 2y + 21
x = 2/3 y + 7
So, We can substitute x = 2/3y + 7 , y = y and z = 21 + y in equation (i), we get;
x + y + z = 180°
2/3 y + 7 + y + 21 + y = 180
2/3y + 2y + 28 = 180
8/3 y = 180 - 28
8/3 y = 152
y = 152 × 3 / 8
y = 57°
Hence, x = 2/3y + 7
x = 2/3 × 57 + 7
x = 2 × 19 + 7
x = 45°
And, z = 21 + y
z = 21 + 57
z = 78°
Thus, The measure of all the three angles of a triangle will be 45°, 57° and 78° respectively.
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Betty's Auto Wash earns revenues of $14 per customer. After serving 6 customers, how much revenue will Betty's Auto Wash have?
Given data:
The given revenue earn per customer is $14.
The expression for the given statement is,
1 customer= $14
Multiply the above expression by 6 on both sides.
6(1 customer)=6($14)
6 customers=$84
Thus, revenue earn by 6 customers is $84.
6 ft
11 ft
How do I solve this problem
Answer:
the answer is 66
Step-by-step explanation:
multiply
The approximate volume in milliliters, y, for a volume of x fluid ounces is equal to 29.57 times the value of x. Which table represents this relationship?
Step-by-step explanation:
volumes of liquor because these are the ones which have volume and cm can be changed to millimeters
determine the number of different ways the given number can be written as the sum of 2 primes? 50
the prime numbers smaller than 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
let's find the sums that give us 50:
3+47=50
7+43=50
13+37=50
19+31=50
so the answer is four different ways.
find the intervals for the function Y=f(x) whose graph is given below is increasing and where it is decreasing and find the value of the absolute minimum
In this problem we have a vertical parabola open upward
the vertex represents the absolute minimum
Looking at the graph
the vertex is the point (1,-3)
therefore
the function is increasing at the interval (1, infinite)
the function is decreasing at the interval (-infinite, 1)
the absolute minimum is (1,-3)
Find the area of the figure given to the right. The hexagon is regular. Round to the nearest whole number.
We can divide the hexagon into 6 equilateral triangles, and call the side 'x'. I will draw the situation:
Every line is x because the hexagon is regular (all sides have the same length). Therefore we can find x, because two times x is 18'':
[tex]2x\text{ = 18}[/tex][tex]x\text{ = 9 inches}[/tex]The hexagon has the same area of 6 equilateral triangles with the side equal to x. The formula of the area of an equilateral triangle is:
[tex]Area\text{ = }\frac{x^2\sqrt[]{3}}{4}[/tex]Therefore the area of the hexagon will be:
[tex]\text{AreaHexagon = 6}\times\frac{x^2\sqrt[]{3}}{4}^{}[/tex][tex]\text{AreaHexagon = 6}\times\frac{9^2\sqrt[]{3}}{4}^{}[/tex][tex]\text{AreaHexagon }\cong210.44\text{ square inches}[/tex]Rounding it will be 210 square inches.
Theo is saving $8 per week for a vacation he is taking. He started off with some money in savings, but less than $8. At the end of his weeks savings, he had a total of $52. How much money did theo start of with?
To find the money at start let us use an equation
Since he puts $8 per week
Then his rate is 8
Since he has a total of $52 after some weeks
We must find the nearest number to 52 in table 8
Since 6 * 8 = 48 the nearest number to 52 in table 8
Then he did that for 6 weeks
52 = 8(6) + x
Let us find x
52 = 48 + x
Subtract 48 from both sides
52 - 48 = 48 - 48 + x
4 = x
He started with $4
Which value of x is in the domain of f(a)V-14?A. X = 13B. X=0C. X = 20D. X= -1SUBMIT
the answer is C x=20
Write an equation of the line passing through (4,-2) that is parallel to the line -3x minus 4y =5
Answer:
Step-by-step explanation:
y=4x3
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
First, rearrange -3x - 4y = 5 into y = mx + c form.
-3x - 4y = 5
-4y = 3x + 5
y = -3/4x - 5/4
Since parallel lines have the same gradient, equation of line is y = -3/4x + c.
Substitute (4,-2) into the equation to find c.
-2 = -3/4(4) + c
c = 1
Hence, equation of line is y = -3/4x + 1.
