We want the answer in exponential form:
[tex]h(x)=a\cdot b^x[/tex]where a and b are the constants to be determined. We can find a and b by substituting the given points and construct a system of equatons, that is, by replacing point (1,16) we have
[tex]\begin{gathered} 16=a\cdot b^1 \\ so \\ 16=a\cdot b \end{gathered}[/tex]and by substituting point (5,1296), we get
[tex]1296=a\cdot b^5[/tex]Then, we have 2 equations in 2 unknonws:
[tex]\begin{gathered} a\mathrm{}b=16 \\ a\mathrm{}b^5=1296 \end{gathered}[/tex]By isolating a from the first equation and substituting this result into the second one, we get
[tex]\begin{gathered} (\frac{16}{b})b^5=1296 \\ \end{gathered}[/tex]which gives
[tex]\begin{gathered} 16b^4=1296 \\ b^4=\frac{1296}{16} \\ b^4=81 \\ b=\sqrt[4]{81} \\ b=3 \end{gathered}[/tex]Then, by substituting this result into the first equation of our system, we obtain
[tex]\begin{gathered} a\cdot3=16 \\ \text{then} \\ a=\frac{16}{3} \end{gathered}[/tex]Therefore, the answer is
[tex]h(x)=\frac{16}{3}\cdot(3)^x[/tex]evaluate
x3+x0 for x=2
Answer:
6
Step-by-step explanation:
You replace the x’s with 2 and then solve the problem like you would do with any other problem.
2(3)+2(0)
2(3)=6
2(0)=0
6+0=6
Please correct me if i’m wrong. I just finished this lesson!
The correct answer is: " 9 " .
_______
Step-by-step explanation:
Given: " x³ + x⁰ " ; Evaluate for "x = 2 ".
Plug in 2 for the x values; and solve:
" 2³ + 2⁰ " ;
Note: " 2³ = 2 * 2 * 2 = 8 " ;
" 2⁰ = 1 " .
Note: Any 'non-zero' value, raised to the 'zeroth' [0°]' exponential power, is equal to 'one' [ 1 ].
So: " x³ + x⁰ = 2³ + 2⁰ = 8 + 1 = 9 ."
The answer is: " 9 ".
_______
Hope this is helpful! Best wishes to you!
_______
1. In one brand of frozen dinner, there are 22 grams of fat. Each gram of fat is 9 calories. Each frozen dinner has 945calories. What percent of these calories is from fat?
There are 22 grams of fat and each gram of fat is 9 calories, then
[tex]22\text{ grams }\cdot9\frac{calories}{gram}=198\text{ calories from fat}[/tex]945 calories represents 100%, then 198 represents:
[tex]\begin{gathered} \frac{945\text{ calories}}{198\text{ calories}}=\frac{100\text{ \%}}{x\text{ \%}} \\ 945\cdot x=100\cdot198 \\ x=\frac{19800}{945} \\ x=21\text{ \%} \end{gathered}[/tex]21% of the calories are from g
The table below shows the educational attainment of a country's population, aged 25 and over. Use the data in the table, expressed in millions, to find the probability that a randomly selected citizen, aged 25 or
over, had 4 years of college.
Male
Female
Total
Less Than
4 Years
High School
15
19
34
4 Years
High School
Only
25
32
57
Some College
(Less Than
4 Years)
18
26
44
4 Years
College
(or More)
24
20
44
Total
82
97
179
The probability that a randomly selected citizen, aged 25 or
over, had 4 years of college : 0.2458
From the table
Total number of citizens aged 25 or above = 179 million.
number of citizens aged 25 or above, had 4 years of college = 44 million
Therefore, probability = 44/179 = 0.2458
What is probability ?Probability is a branch of mathematics that deals with calculating the probability of a given event, expressed as a number between 1 and 0. An event with a probability of 1 can be considered certain: for example, the probability of a coin toss. a toss that results in either "heads" or "tails" is 1 because there are no other options, assuming the coin lands flat. An event with probability 0.5 can be considered equally likely to occur or not to occur: for example, the probability that a coin toss results in heads is 0.5, because the toss is equally likely to result in tails." An event with probability 0 can be considered impossible: for example, the probability that the a coin lands (uniformly) without both sides up is 0, because either "heads" or "tails" must be up.
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math question #12solve for the missing value x 1/2: 4 = 1/3 : x
To find the value of x we need to write the equation in another form that tells us what to do; both sides of the equations are ratios then we have:
[tex]\begin{gathered} \frac{1}{2}:4=\frac{\frac{1}{2}}{4} \\ \text{ and} \\ \frac{1}{3}:x=\frac{\frac{1}{3}}{x} \end{gathered}[/tex]Then the equation is:
[tex]\frac{\frac{1}{2}}{4}=\frac{\frac{1}{3}}{x}[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{\frac{1}{2}}{4}=\frac{\frac{1}{3}}{x} \\ \frac{1}{8}=\frac{1}{3x} \\ 3x=8 \\ x=\frac{8}{3} \end{gathered}[/tex]Therefore, the value of x is 8/3
need help asappppppp
a.
Consider that the volume (V) of a cone with radius 'R' and height 'H' is given by,
[tex]V=\frac{1}{3}\pi R^2H[/tex]Substitute the values,
[tex]\begin{gathered} V=\frac{1}{3}\pi(4)^2(3) \\ V=16\pi \end{gathered}[/tex]Therefore, option b is the correct choice.
b.
Consider that the volume (V') of a cylinder with radius 'R' and height 'H' is given by,
[tex]V^{\prime}=\pi R^2H[/tex]Solve for the ratio of volume of cone to that of cylinder as,
[tex]\frac{V}{V^{\prime}}=\frac{(\frac{1}{3}\pi R^2H)}{(\pi R^2H)}=\frac{1}{3}[/tex]Therefore, option c is the correct choice.
Expand using binomial theorem(4x-7y)^4
Answer:
Recall that the binomial theorem states that:
[tex](a+b)^n=\sum ^n_{k=0}{\binom{n}{k}}a^{n-k}b^k\text{.}[/tex]Then:
[tex](4x-7y)^4=\sum ^4_{k=0}{\binom{4}{k}}(4x)^{4-k}(-7y)^k\text{.}[/tex]Therefore:
[tex]\begin{gathered} (4x-7y)^4={\binom{4}{0}(4x)^{4-0}(-7y)^0}+{\binom{4}{1}(4x)^{4-1}(-7y)^1}+{\binom{4}{2}(4x)^{4-2}(-7y)^2} \\ +{\binom{4}{3}(4x)^{4-3}(-7y)^3+{\binom{4}{4}(4x)^{4-4}(-7y)^4\text{.}}} \end{gathered}[/tex]help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
function of f(-5) is equal to the same value of y in an equation y= f(x).
therefore x value is -5 on x-axis and on this point it gives the value of y-axis which is -2
Determine the number of solutions to the given system remember to use the format(x,y) to type in your points and do not use spaces if there is only one type the point and one space and none in the other if there’s none type none in both of the boxes
Remember that
when solving a system by graphing, the solution is the intersection point both graphs
Looking at the graph
The intersection point is (5,6)
therefore
The solution is the point (5,6)Find the length of arc RS. Use 3.14 for .Round to the nearest tenth.P6.48 inS7391500 650R[? ]inEnter
Given:
[tex]\theta=150^o[/tex]The radius of the circle is 6.48 in.
To find:
We need to find the arc length of RS.
Explanation:
Consider the formula to find the length of the arc.
[tex]undefined[/tex]Hello! Need some help on parts a,b, &c. The question and rubric is linked below. Thank you!
Part A: -5/9, 6/10, -7/11, 8/12
Part B:
[tex]f(n)=(-1)^{n}(\frac{n}{n+4})[/tex]Part C: Positive
Explanation:The given sequence is:
[tex]-\frac{1}{5},\frac{2}{6},-\frac{3}{7},\frac{4}{8},....[/tex]As seen above the sequence is an alternating sequence because it changes in sign
Also, neglecting the sign chnages, we will observe, a common diffference of 1 in the numerator and denominator
a) Therefore, if the pattern continues, the next 4 terms in the sequence are:
-5/9, 6/10, -7/11, 8/12
b)
Without the sign, the explicit equation representing the numerator is calculated below:
1, 2, 3, 4......
The first term, a = 1
The common difference, d = 1
This is an arithmetic sequence
N(n) = a + (n - 1)d
N(n) = 1 + (n - 1)(1)
N(n) = 1 + n - 1
N(n) = n
The explicit equation representing the denominator is calculated below
5, 6, 7, 8........
The first term, a = 5
The common difference, d = 1
D(n) = a + (n - 1)d
D(n) = 5 + (n - 1)(1)
D(n) = 5 + n - 1
D(n) = n + 4
The alternating sequence will include the term below:
[tex](-1)^n[/tex]Therefore, the explicit equation for f(n) representing the sequence is:
[tex]f(n)=(-1)^n(\frac{n}{n+4})[/tex]Part C) The sign of f(56) will be:
(-1)^56 = 1
Since this gives us a positive value, the sign of f(56) is positive
In developing her science project, Leigh learned that light travels at a constant rateand that it takes 500 seconds for light to travel the 93 million miles from the Sun toEarth. Mars is 142 million miles from the Sun. About how many seconds will it takefor light to travel from the Sun to Mars?A. 235 secondsB. 327 secondsC. 642 secondsD. 763 seconds
D. 763 seconds
Explanation:
Data:
Seconds light travels distance between Sun and Earth : 500 seconds
Distance between Sun and Earth: 93 million miles
Distance between Sun and Mars: 142 million miles
Formula: (see image below)
Solution:
From Sun to Mars the light takes (142 * 500) / 93 = 763 seconds
NB:
The tactic is to first put the data given in a table like in the image above, to first multiply diagonally then divide horizontally. (starting from the data that his paired data).
Here the paired data missing is the time it takes for the light to travel from the Sun to Mars, therefore you'll multiply the distance between the Sun to Mars (known data missing a pair) by the time it takes light to travel from the Sun to Earth (known data with its pair), then divide the result by the distance between the Sun and earth (pair of the former mentioned known data)
MATRECIES: Suppose ={u,v,w}⊆R3 is linearly independent. Determine if the set 4 ={u, v, v−w, u+v+w} is linearly independent or linearly dependent.
The set is linearly dependent.
To explicitly prove this, we need to show there is at least one choice of constants [tex]c_1,c_2,c_3,c_3\in\Bbb R[/tex] such that
[tex]c_1 u + c_2 v + c_3(v-w) + c_4(u+v+w) = 0[/tex]
or equivalently,
[tex](c_1 + c_4) u + (c_2 + c_3 + c_4) v + (-c_3 + c_4) w = 0[/tex]
which is the same as solving the system of equations
[tex]\begin{cases} c_1 + c_4 = 0 \\ c_2 + c_3 + c_4 = 0 \\ -c_3 + c_4 = 0 \end{cases}[/tex]
From the first and last equations, we have [tex]c_1=-c_4[/tex] and [tex]c_3=c_4[/tex]. Substituting these into the second equation leaves us with [tex]c_2-2c_1=0[/tex], and so the overall solution set is
[tex]c_1 = \dfrac12 c_2 = -c_3 = -c_4[/tex]
for which there are infinitely many not-all-zero solutions.
3. Pentagon PENTA with P(0, 2), E(4,6), N(8,-1), T(6,-3), and A(2,-4); reflect across y-axis. /1a. What is the "arrow rule" to show this transformation? 15 b. What are the vertices of the image after the transformation?
1a) The arrow will be (-x,y) for reflection
1b)The vertices are P(-(0),2), E(-4,6), N(-8,-1), T(-6,-3), A(-2/-4) = P(0,2), E(-4,6), N(-8,-1),T(-6,-3), A(-2,-4)
I need help with this question please and thank you
Answer:
[tex]x(x+3)[/tex]Step-by-step explanation:
The least common denominator of a and b is the smallest multiplier that is divisible by both a and b. In this case, for:
[tex]\begin{gathered} \frac{x+4}{x}+\frac{x}{x+3}=\frac{(x+3)(x+4)+x\cdot x}{x(x+3)} \\ \end{gathered}[/tex]simplify.
rewreit the expression in the form [tex]5^{n}[/tex].
The expression in the form of 5ⁿ is 5⁻¹³
What is the expression?An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.
Given:
F(x) = 5⁻⁵/5⁸
F(x) = 5⁻⁵⁻⁸
F(x) = 5⁻¹³
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the function f(x)=600-100x models the value, f(x), of a video game system x years after purchase
Complete question is:
The function f(x) = 600 - 100x models the value, f(x), of a video game system x years after purchase. Which choice represents the most appropriate domain of the function?
Answer and explanation:
The domain of a function is the values you can plug into the function, the possible values for x.
While x could take any value, there are a range of apropiate values that it can take.
For example, since x represents years after purchase, x can not be a negative number, because that would represent negative years, thus x must be greater or equal to 0.
Domain:
[tex]\lbrack0,\infty)[/tex]Diagram LabelValueUnitsRadius of the Pool Cover9feetDiameter of the Pool Cover18feetCircumference of the Pool CoverfeetArea of the Pool Coversquare feet
Step1: Write out the given parameters
[tex]\begin{gathered} \text{Diameter}=18\text{feet} \\ \text{Radius}=\frac{diameter}{2}=\frac{18}{2}=9feet \end{gathered}[/tex]We are to find the area of the pool cover and it circumference
Step2: write out the formula
[tex]\begin{gathered} \text{Area of pool cover=}\pi r^2 \\ \text{where }\pi=3.14 \end{gathered}[/tex][tex]\text{Area of pool cover=3.14}\times9^2=254.34square\text{ f}eet[/tex]Hence the area of the pool cover is 254.34 square feet
The circumference of the pool cover is given by
[tex]\begin{gathered} 2\pi r \\ 2\times3.14\times9 \\ 56.52 \end{gathered}[/tex]Therefore the circumference of the pool cover is 56.52 feet
What is what is 156.4÷23
Answer:
156.4 ÷ 23 = 6.8
Step-by-step explanation:
hope this helps
() Organic sugar used to be sold at a bulk price of $3.70 per pound. The price was recently increased by 20%. What is the current price per pound?
It is given that an item used to be sold for $3.70 per pound.
It is required to find the current price per pound if the price was increased by 20%.
A 20% increase in the price, $3.70 is calculated as:
[tex]\frac{100+20}{100}\cdot3.70=\frac{120}{100}\cdot3.70=4.44[/tex]Hence, the current price of the item is $4.44 per pound.
The current price of the item is $4.44 per pound.
Find the y-intercept of the line on the graph.
Answer:
-2
Step-by-step explanation:
This is where the line crosses the y axis. It is at point (0,-2)
Question 2 of 10 What is the slope formula? O A. A. 12-1 xz - X OB. Kz - x /2 - 4 OC. c. * + x, x2 + y OD. 1/2-X Kez - V
The slope is calculated by findidng the ratio of the vertical change (change in y) to the horizontal change (change in x) between any two distinct points.
Then the slope formula is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]Lines a and b are parellel.If the slope of a line a is 1/4 , what is the slope of the line b?
Answer:
D. 1/4
Explanation:
By definition, two lines are parallel if they have the same slope.
Given that lines a and b are parallel; and the slope of line a = 1/4, then:
The slope of line b = 1/4.
The correct choice is D.
Write an algebraic expression for the sum of 3 coins and c coins.
Oc+3
Oc/3
O3c
Oc-3
Answer:
c+3
Step-by-step explanation:
The word 'sum' means addition, so the equation would be c+3
find the probability of rolling a die five times and getting no threes 
Answer:
5/5
Step-by-step explanation:
since its 5 times u re rolling the dice and u have 5 chances or 5 possibilities of getting 5
Answer:
Step-by-step explanation:
1) Set an equation
Getting a three on the dice is 1/6. So the opposite is 5/6.
5/6 * 5/6 * 5/6 * 5/6 * 5/6
2) Solve
3125/7776
0.4018
40.18%
8=6+a/4 how do I solve this
6 is adding on the right, then it will subtract on the left
[tex]\begin{gathered} 8-6=\frac{a}{4} \\ 2=\frac{a}{4} \end{gathered}[/tex]4 is dividing on the right, then it will multiply on the left
[tex]\begin{gathered} 2\cdot4=a \\ 8=a \end{gathered}[/tex]
Every month, Michael pays $5 plus $0.10
per text message for phone service.
Which equation represents the amount
Michael pays for phone service each
month, y, if he sends and receives x text
messages?
A. y = 0.1x + 5.
B. y = 0.2x + 10
C. y = 0.1x
D.
y = 5x
Answer:
y = 0.1x + 5
Step-by-step explanation:
0.1x = the amount he pays for all his texts and 5 is a fixed amount so add them up to get y
can you please help me with this
The image of the point P(x, y) = (4, 2) by means of a translation formula is point P'(x, y) = (- 1, 4).
What is the image of a given point after making a translation?
In this question we find the coordinates of a point set on Cartesian plane which is modified by using a translation, a kind of rigid transformation. Rigid transformations are transformations applied on geometric loci such that Euclidean distances are conserved.
Vectorially speaking, translations are described by the following formula:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vectorIf we know that P(x, y) = (- 9, - 3) and P'(x, y) = (- 14, - 1), then the translation vector is:
T(x, y) = P'(x, y) - P(x, y)
T(x, y) = (- 14, - 1) - (- 9, - 3)
T(x, y) = (- 5, 2)
Then, the image of the point (4, 2) is:
P'(x, y) = (4, 2) + (- 5, 2)
P'(x, y) = (- 1, 4)
The image of the point (4, 2) by using a translation formula is (- 1, 4).
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estion 5 (1 point)Given the two images below. What is the scale used to transform GHI to G'HI?Scale Factor -->GHIGHBlank 1:SubmitSaved at
We can see the upper vertix of the triangle in the first figure is at the point (0,6) and after the shrink is at (0,2). So what's the number I can divide 6 to get a 2? It's 3. So the scale factor is 1/3
The test scores for the analytical writingsection of a particular standardized test canbe approximated by a normal distribution, asshown in the figure.(a) What is the maximum score that can be inthe bottom 10% of scores?(b) Between what two values does the middle80% of scores lie?
Solution:
Given:
Recall that the z-value is expressed as
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \text{where} \\ \mu\Rightarrow\operatorname{mean}\text{ value} \\ \sigma\Rightarrow s\tan dard\text{ deviation} \end{gathered}[/tex]Thus,
[tex]z=\frac{x-3.7}{0.91}\text{ ---- equation 1}[/tex]A) maximum score that can be in the bottom 10% of scores
using the table of z-values,
for the bottom 10% scores, we have
[tex]z=-1.28155156554[/tex]To evaluate x, substitute the value of z into equation 1.
Thus,
[tex]\begin{gathered} -1.28155156554=\frac{x-3.7}{0.91}\text{ } \\ \Rightarrow x=2.5337895 \end{gathered}[/tex]Thus, the maximum score that can be in the bottom 10% of scores is 2.5
B) Two values for which the middle 80% of scores lie.
From the z score values shown below:
The z scores of the value are
[tex]\begin{gathered} z_1=-1.28 \\ z_2=1.28 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \text{when z=-1.28, we have} \\ -1.28=\frac{x-3.7}{0.91}\text{ } \\ \Rightarrow x=2.5352 \\ \text{when z=1.28, we have} \\ 1.28=\frac{x-3.7}{0.91} \\ \Rightarrow x=4.8648 \end{gathered}[/tex]Thus, the two values for which the middle 80% of scores lie are 2.5 and 4.86.
The art teacher mixed 12 ounces of yellow paint with 5 ounces of blue paint to make green. How many ounces of blue would be needed if you used 20 ounces of yellow ?
The relation is 12 ounces of yellow paint with 5 ounces of blue paint. To find how many ounces of blue would be needed if you used 20 ounces of yellow, we can use the next proportion:
[tex]\frac{12\text{ ounces of yellow}}{20\text{ ounces of yellow}}=\frac{5\text{ ounces of blue}}{x\text{ ounces of blue}}[/tex]Solving for x,
[tex]\begin{gathered} 12\cdot x=5\cdot20 \\ 12\cdot x=100 \\ x=\frac{100}{12} \\ x=\frac{25}{3} \end{gathered}[/tex]You would need 25/3 ounces of blue paint
