Mathematical expressions with the form, where x is the base and n is the exponent, are called powers. In powers, the base is the integer or variable that is continually multiplied, and the exponent designates how many times to multiply the base by itself.
Exponents should be subtracted when dividing powers by the same base, according to the quotient rule. For instance, dividing h(6) by h(2) yields h(6-2) = h(4). A quick and simple technique to make the problem simpler is to subtract the exponents.
Use the Quotient of Powers Rule to reduce the number of terms when splitting like terms with exponents. According to this rule, to determine the solution while dividing terms with the same base, simply remove their exponents. The trick is to only take out exponents with matching bases.
This means that every number raised to the power of zero is one because it is simply the result of no numbers at all, which is the multiplicative identity, or 1.
Hence we made the clear conclusions.
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Kari wins 1,282 tickets at an arcade. For each group of 65 tickets, she will receive a prize. Kari solves the problem 1,282 ÷ 65 and determines that she has enough tickets right now for 19 prizes. What is the least number of additional tickets that Kari needs to win to have enough tickets for a 20th prize?and i need a step by step explanation.
Answer:
18 more tickets
Step-by-step explanation:
What we know:
We know that 65 Tickets is 1 Prize.
We know we have 1,282 tickets.
So if 65 tickets is one prize
then to figure out how many for twenty then we:
65 x 20 = 1300
Now to figure out how many more she needs at the least we:
1300 - 1282 = 18
So for 1 more prize she needs 18 more tickets.
You are one of the retirement counselors at the Valley View Bank. You have been asked to give a presentation to a class of high school seniors about the importance of saving for retirement. Your boss has designed an example for you to use in your presentation. The students are shown five retirement scenarios and are asked to guess which yields the most money. Note: All annuities are ordinary annuities. Also, although some people stop investing, the money remains in the account and receives 10% interest compounded annually. Look over each scenario and make an educated guess as to which investor will have the largest accumulation of money invested at 10% over the next 40 years. Then for your presentation, calculate the final value for each scenario, how much each person actually contributed, and how much interest was earned. • Adam invests $1,200 per year and stops after 15 years (remember, the balance will remain in this account, earning 10% interest compounded annually for the remaining 25 years. • Becky waits 15 years, invests $1,200 per year for 15 years, and then stops (balance will earn int • Clare waits 15 years, then invests $1,200 per year for 25 years. • David waits 10 years, then invests $1,500 per year for 15 years, and then stops (balance will earn interest for the remaining 15 years). • Ellen waits 10 years, then invests $1,500 per year for 30 years.
The retirement counselors at the Valley View Bank$454404.05 > $129818.11 > $108780.71, then the Venus have the largest accumulation.
[tex](1+10)^{15}[/tex]Venus invests $1,200 per year and stops after 15 years.
He can get money : [tex]1200*[/tex] [tex](1+10)^{15}[/tex] at the first year,
We can use ,
Compound interest formula, S = [tex]P*(1+i)^{n}[/tex]
Where,
P means the Principal
I means the interest
n means the year
S means the principal and interest
At the second year he can get,
= 1200 * [(1+[tex]\frac{10degrees}{1}[/tex]) + ([tex]1+[\frac{10degrees}{1} ]^{2}[/tex])
The money of first year has two years interest,
The money of second year has one year interest.
So, we can calculate the 15th year he can get :
= 1200 * [[tex](1+\frac{10degrees}{1}] ^{1}) +(1+(\frac{10degrees}{1} )^{2} )+......(1+(\frac{10degrees}{1})^{15} )[/tex]
= 1200 * [tex]\frac{(1*1)*(1-1*1^{15} )}{1-1*1}[/tex]
The sum of geometric progression,
[tex]S_{n} =\frac{a*(1-q)^{n} }{1-q}[/tex] , q≠1
= $ 41939.67
The rest of years he can get money :
= 41939.67 * ([tex](1+10percent))^{40-15}[/tex]
= $ 454404.053
Kevin can get money 1200* [[tex](1+(\frac{10degrees}{1}) ^{1} )+.......(1+(\frac{10degrees}{1} )^{15} )[/tex]
= 41939.67 at 30th year
Finally he can get money = 41936.67 [tex](1+\frac{10degrees}{1}) ^{40-15*0}[/tex]
= $ 108780.71
Rafael can get money : 1200 * [[tex](1+(\frac{10degrees}{1}) ^{1} )+.......(1+(\frac{10degrees}{1} )^{25} )[/tex]
= $ 129818.11
$454404.05 > $129818.11 > $108780.71
Therefore,
The retirement counselors at the Valley View Bank$454404.05 > $129818.11 > $108780.71, then the Venus have the largest accumulation.
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solve using distributive property ASAP
8(x+2)
The equation 8(x+2) can be expressed using the distributive property as 8x + 16.
What is distributive property?The distributive property can be described as the as the multiplication system of solving a particular expressions easily through the process of distributing another number within the given brackets.
The expression that was given as 8(x+2) , if it so be solved using the distributive property the we will have 8x + 16 because this result means that it has been shared in to part, because the multiplication operation has been performed on the given expression.
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Is 47/8 less then 23/4
Answer:
no
Step-by-step explanation:
Generally you can't really compare two functions with a different denomination, and you want to multiply the fractions by some fraction: [tex]\frac{a}{a}[/tex] which simplifies to one so we're not changing the value of the fraction at all but it helps so we have the same denominator.
You'll notice we can multiply 4 by 2 to get 8, which would give us the same denominator as 8.
[tex]\frac{23}{4}*\frac{2}{2}=\frac{46}{8}[/tex]
Now it's much easier to compare: [tex]\frac{47}{8}\text{ and }\frac{46}{8}[/tex] and here all we have to compare is the numerators, and obviously 47 is greater than 46 so the 47/8 is greater than the 23/4. This means 47/8 is not less than 23/4
Find the length of the third side. If necessary, write in simplest radical form.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{4}\\ b=\stackrel{opposite}{2}\\ \end{cases} \\\\\\ c=\sqrt{4^2 + 2^2}\implies c=\sqrt{16 + 4}\implies c=\sqrt{20}[/tex]
Find the scale factor from triangle A to triangle B:
Answer:
Step-by-step explanation:
x=3?
Answer:
3
Step-by-step explanation:
If you multiply 1 by 3 it gives you 3, the side of triangle B. Using that scale factor. you can then take the side of triangle B that is 9 and divide it by 3. That gives you the missing side of triangle A.
Hope this helps! :)
The point Q lies on the segment PR.
Find the coordinates of Q so that PQ is
Check
17/0 of PR.
P(-3,4)
Coordinates of Q: D
Q (?, ?)
R (24,-32)
X
Save For Later
Submit
Answer:
Step-by-step explanation:
it would be 42,32 i know
(1 point) Find the slope of the line containing the points f(-3) = 9 and f(9) = -10.
The most appropriate choice for slope of a line will be given by-
Slope of the line = [tex]\frac{-19}{12}[/tex]
What is slope of a line?
At first it is important to know about line.
Line is a geometrical object that has only length but no breadth and no height.
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta\\[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by
m = [tex]tan\theta[/tex]
If the line passes through ([tex]x_1,y_1[/tex]) and ([tex]x_2, y_2[/tex]) , then
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Here,
[tex]x_1 = -3, y_1 = 9. x_2 = 9, y_2 = -10[/tex]
Slope = [tex]\frac{-10 - 9}{9 - (-3))}[/tex]
= [tex]\frac{-19}{12}[/tex]
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A genetic experiment with peas resulted in one sample of offspring that consisted of 434 green peas and 153 yellow peas.
a. Construct a 90% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
a) The 90% confidence interval to estimate the percentage of yellow peas is (23.09%, 29.03%.)
b) Based on the confidence interval, the results of the experiment do not appear to contradict the expectation that 25% of the offspring peas would be yellow.
Given:
Confidence level,c = 90% = 0.90
Number of successes, x = 153
Sample size,n = 434 + 153 = 587
a) The sample proportion is the number of successes divided by the sample size is,
p = x/n
p = 153/587
p ≅ 0.2606
For confidence level 1 - α = 0.90, determine [tex]z_{\alpha /2} = z_{0.05}[/tex] utilizing the normal probability table in the appendix
[tex]z_{\alpha /2} = 1.64[/tex]
The margin of error is calculated as:
[tex]E = z_{\alpha /2} \sqrt{\frac{p(1-p)}{n} }[/tex]
[tex]E = 1.64\sqrt{\frac{0.2606(1 -0.2606)}{587} }[/tex]
E ≅ 0.0297
Therefore, the boundaries of the confidence interval are:
p - E = 0.2606 - 0.0297 = 0.2309 = 23.09%
p + E = 0.2606 + 0.0297 = 0.2903 = 29.03%
We are 90% confident that the true percentage of yellow peas is between 23.09% and 29.03%.
b) As 25% is between 23.09% and 29.03%, and 25% of the offspring are expected to be yellow peas and thus the results do not contradict expectations.
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what is the equation of a line that goes through the points 2, -2 and 0,2
it is vital that we first find the gradient/slope between the points .
⇒[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{2-(-2)}{0-2} \\m=\frac{4}{-2} \\m=-2[/tex]
The general equation of a straight line is given by y=mx+c I will use the points (0,2) to find the value of y since the other variables are found already.
[tex]2=-2(0)+c\\\\c=2[/tex]
⇒This tells us that the equation of the line is y=-2x+2
Pls help with number 20
The lengths 8 cm, 14 cm, 15 cm can form a triangle
Explanation:Given 8 cm, 14 cm, 15 cm
These can form a triangle if the sum of any two sides of the triangle is greater than the third side.
8 + 14 > 15
14 + 15 > 8
8 + 15 > 14
Since all the above are true, we conclude that they can form a triangle
Multiply using the FOIL method.
(8z + 7)(9z-1)
Answer: [tex]72z^{2} +55z-7[/tex]
Step-by-step explanation:
We multiply each component with each other:
8z * 9z = 72z^2
8z * -1 = -8z
9z * 7 = 63z
7 * -1 = -7
We then add it all together, 63z + -8z = 55z and get
[tex]72z^{2} +55z-7[/tex]
What 2 2/4 x 3 5/6
I need an answer quick because i need this answer.
[tex] \frac{10}{4} \times \frac{23}{6} \\ = \frac{230}{24} \\ = \frac{115}{12} \\ = 9 \frac{7}{12} [/tex]
ATTACHED IS THE SOLUTION
i needed help with the problem. didn't understand it.
Answer:
a
Step-by-step explanation:
as all the other points had inflection
Write an equation for the function graphed below. The y intercept is at (0,0.2)
Equation for the function graphed is f(x) = -0.6 (x - 1)² ÷ (x + 1)(x + 3)
Given, the y-intercept is at (0, 0.2).
From the given graph, it can be deduced the vertical asymptotes are at x = -1, x = 1 and x = -3.
Which implies denominator is 0 and the function is undefined for x = -1, x = 1 or x = -3.
So, -1 and -3. are the roots of the denominator. As a result, the denominator equation has the form: (x + 1)(x + 3).
For finding the equation of the function f(x) = a(x - 1)² ÷ (x + 1)(x + 3)
Put f(0) = 0.2
f(0) = a(0 - 1)² ÷ (0 + 1)(0 + 3) = 0.2
a = - 0.6
∴ Equation is f(x) = -0.6(x - 1)² ÷ (x + 1)(x + 3) for y-intercept is at (0,0.2).
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log 2 8 = 3 can be written in the form 2 A = B where
The equation written in exponential form is (a) 2³ = 8
What are exponents?A symbol used to denote the action of raising to a power that is written above and to the right of a mathematical phrase.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given equation is
㏒₂ 8 = 3
㏒ₐx = b
x = aᵇ
㏒₂8 = 3
8 = 2³
Hence, (a) 2³ = 8
Therefore, the equation written in exponential form is (a) 2³ = 8.
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What is the slope of the line represented by the equation 2x+3y=-12
Answer:
-2/3
Step-by-step explanation:
I graphed it
equations with parenthesis
Answer:b=6
Step-by-step explanation:
In exercises 11-14 ,find m<1,m<2, and m<3.explain your reasoning ?
The measure of angles 1, 2, and 3 in exercise 11. are 100°, 80°, and 100°.
The measure of angles 1, 2, and 3 in exercise 12. are 47°, 133°, and 47°.
The measure of angles 1, 2, and 3 in exercise 13. are 80°, 80°, and 100°.
The measure of angles 1, 2, and 3 in exercise 14. are 94°, 86°, and 94°.
For 11. part:
Considering a transversal p that cuts two parallel lines l and m,
Each pair of internal angles on the same side of a transversal that intersects two parallel lines are supplementary.
m∠1 + 80° = 180°
m∠1 = 180° - 80°
m∠1 = 100°
Similarly, m∠1 + m∠2 = 180°
⇒ 100° + m∠2 = 180°
⇒m∠2 = 180° - 100°
⇒m∠2 = 80°
and also, m∠2 + m∠3 = 180°
⇒ 80° + m∠3 = 180°
⇒m∠3 = 180° - 80°
⇒m∠3 = 100°
Therefore, m∠1 = 100°, m∠2 = 80° and m∠3 = 100°.
For 12. part:
m∠3 + 133° = 180°(interior angles are supplementary)
m∠3 = 180° - 133°
⇒m∠3 = 47°
m∠2 = 133°(alternate interior angles)
The angle vertically opposite to 133° would also be 133°.
So, 133° + m∠1 = 180°( interior angles are supplementary)
m∠1 = 47°
Therefore, m∠1 = 47°, m∠2 = 133° and m∠3 = 47°.
For 13. part:
m∠3 = 100° (vertically opposite angle)
Let's assume the angle adjacent to ∠3 is x.
m∠3 + m ∠x = 180° (Linear pair property)
100° + m ∠x = 180°
m ∠x = 180° - 100°
m ∠x = 80°
Therefore, m∠1 = m∠2 = m ∠x = 80°(Corresponding angles are equal.)
For 14. part:
m∠1 + 86° = 180°(co-interior angles are supplementary)
m∠1 = 180°- 86° = 94°
The angle vertically opposite to m∠1 is also equal to 94°.
94° + m∠1 = 180°(co-interior angles are supplementary)
m∠2 = 86°
Similarly, the angle vertically opposite to m∠2 is also equal to 86°.
86° + m∠3 = 180°(co-interior angles are supplementary)
m∠3 = 94°
Therefore, m∠1 = 94°, m∠2 = 86° and m∠3 = 94°.
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How many
inches are in 3.5 miles
Answer:
221 760 inches
Step-by-step explanation:
So, 3.5miles * 63360= 221760 inches.
Formula: multiply the value in miles by the conversation factor '63360'.
Write an equation in slope-intercept form for the line with slope -4/3 and y-intercept 3
I got that but I’m not sure if it’s right.
Answer:
[tex]y=-\frac{4}{3}x+3[/tex]
help meeeeeeeeeeeeee
Answer:
74.44
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.065(10)+55.190 \\ \\ =74.44[/tex]
BAсThe sum of m AB and mBC is equal to:O 360° - MAC240" - MAC180т АС120
The sum of mAB and mBC is equal
360 - mAC
which makes otion A the correct answer
PLS ANSWER THIS MATH PROBLEM!!
Answer:
48[tex]units^{2}[/tex]
Step-by-step explanation:
A set of average city temperatures in April are normally distributed with a mean of 19.7 Celsius in a standard deviation of two Celsius the average temperature of Kabul is 15 Celsius what proportion of the average city temperatures are lower than that of Kabul?
Answer:
There is a proportion of 0.94% cities with average city temperatures lower than that of Kabul
Step-by-step explanation:
In this question, we are to calculate the proportion of average city temperatures lower than that of Kabul.
Firstly, we shall calculate the z score
Mathematically;
z = (value - mean)/standard deviation = 15 - 19.7/2 = -4.7/2 = -2.35
so we are to calculate the probability of; P(z< -2.35) = 0.0094
This means there is a proportion of 0.94% cities with average city temperatures lower than that of Kabul
Which value of xis in the domain of f(x) = √x – 7?
We are looking for values of x that will not make the equation undefined .Obviously the function has restrictions we have to make sure that x-7 is always ≥0 because it is under a square root
[tex]x-7\geq 0\\x\geq 7[/tex]
The domain of the function is all the real numbers greater or equal to 7 .
x≥7 ε R
I would appreciate it if anyone could help?
:)
The most appropriate choice for corrosponding angle will be given by-
x = 2 is the correct answer
What is corrosponding angle?
At first we need to understood what is angle, parallel lines and transversal
Angle
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
Parallel lines
Two lines are said to be parallel if on extending them indefinitely, they will never intersect
Transversal
Transversal is a line that intersects two or more parallel lines
Corrosponding angle
The angles formed in the same position on the same side of transversal when a transversal cuts two or more parallel lines
Here,
(7x + 3)° and (8x + 1)° are corrosponding angles.
Lines m and n are parallel.
So corrosponding angles are equals
By the problem,
(7x + 3) = (8x + 1)
8x - 7x = 3 - 1
x = 2
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If the ratio of red objects to blue objects is 3 : 1, what precent of the objects are red?
Answer:
75%
Step-by-step explanation:
If the ratio of red:blue is 3:1, then there are 4 (some multiple of 4) in all.
The ratio of red:total is 3:4
3/4 is .75, times by 100 to convert to a percent.
.75 × 100 is 75%
Find the sample standard deviation.
15 42 53 7 9 12 14 28 47
The answer to your question is s. sqrt (316.9) = 17.8 when you take the square root of that number. As a result, the correct response is 17.8.
This is further explained below.
What is the sample standard deviation?Generally, Because you need to calculate the sample standard deviation to answer the question, use the following formula:
[tex]s = \sqrt {{ \sum of x - \bar x}{(n - 1} }[/tex]
There are 9 numbers, there, so n - 1 = 8
find the mean
[tex]\bar x[/tex]: 15 + 42 + 53 + . . . + 47 = 227. 227 / 9
x= 25.2
After that, deduct one from each number and then square the output, as seen here:
(15 - 25.2) = 104.0 (42 - 25.2)²
= 282.2 (53 - 25.2)²
= 772.8
After that, total up all of those values. The response to this, using this illustration as an example, is
[tex]x=\frac{ 2,535.2}{ 8}[/tex]
x= 316.9.
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express the final answer in terms of log x, and log y
log x^3y^2
The logarithmic function log ( x³ y² ) when expressed in terms of log x and log y is 3 log ( x ) + 2 log( y).
The opposite of exponentiation is the logarithm. In other words, the exponent to which a fixed number, the base a, must be raised in order to create a specific number x, is represented by the logarithm of that number.
Consider the logarithmic function log x³ y⁴
Using the logarithmic formula,
log ( a b ) = log (a) + log (b)
We have,
log( x³ y² ) = log ( x³ ) + log( y² )
By applying the logarithmic property:
log ( xⁿ ) = n log x
We have,
log x³ y² = log ( x³ ) + log( y² )
log x³ y² = 3 log ( x ) + 2 log( y)
Therefore, the function log ( x³ y² ) in terms of log x and log y is 3 log ( x ) + 2 log( y).
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