The exponential equation that matches the coordinate is 3(2)^x while the linear equation is y = 6x
Exponential equationThe standard exponential equation is expressed as y= ab^x
where
a is the base
x is the exponent
Given the coordinates (2, 12) and (4, 48)
12 = ab^2
48 = ab^4
Find the ratio
4 = b^2
b = 2
Sice ab^2 = 12
4a = 12
a = 3
The exponential equation that matches the coordinate is 3(2)^x
For the linear equation
The standard form is y = mx + b
m is the slope = 48-12/4-2
Slope = 12/2
Slope = 6
For the y-intercept
12 = 6(2) + b
b = 0
Hence the required linear equation is. y = 6x
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Find the area of the convex polygon with vertices (0,5), (-1,2), (4,4), (-3,-4) and (2,0).
The area of the convex polygon is 43/2 square units
How to determine the area of the convex polygon?The vertices are given as:
(0,5), (-1,2), (4,4), (-3,-4) and (2,0)
The area is then calculated as:
[tex]A = \frac 12(\left[\begin{array}{cc}x_1&x_2\\y_1&y_2\end{array}\right] + \left[\begin{array}{cc}x_2&x_3\\y_2&y_3\end{array}\right] + ....+\left[\begin{array}{cc}x_n&x\\y_n&y\end{array}\right] )[/tex]
So, we have:
[tex]A = \frac12 * (|-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 + 2 * -4 - 0 * -3 -3 * 2 + 4 * 1|)[/tex]
Evaluate
[tex]A = \frac12 * (|-43|)[/tex]
Remove the absolute bracket
[tex]A = \frac12 * 43[/tex]
This gives
[tex]A = \frac{43}2[/tex]
Hence, the area of the convex polygon is 43/2 square units
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Multiply the following numbers. Reduce the answer to lowest terms.
Answer:
B 4 1/3
Step-by-step explanation:
if 4200 men have sufficient food for 32 days at the rate of 12 hectogram per person , how many men may leave so that the same food is sufficient for 42 days at the rate of 16 hectogram per person
Using proportions, it is found that 66 men can leave so there will still be enough food.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the situation described, the rule of three is given as follows:
4200 men - 32 days - 12 hectogram per person.
x men - 42 days - 16 hectogram per person.
Considering that the amount per person and the number of people is inverse proportional, we have that:
[tex]\frac{4200}{x} = \frac{32}{42} \times \frac{16}{12}[/tex]
[tex]\frac{4200}{x} = \frac{512}{504}[/tex]
Applying cross multiplication:
512x = 504 x 4200
x = 504 x 4200/512
x = 4134.
The amount of men that can leave is:
4200 - 4134 = 66.
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20% of a number is 17 . find the number
Answer:
x = 85Step-by-step explanation:
20% of a number is 17 . find the number
divide 17 by 20 and you find 1%, multiply by 100 and you get 100%
x = 17 : 20 * 100
x = 0.85 * 100
x = 85
PLS HELP ITS DUE IN 9 MIN AND IM CONFUSED AND I DON’T WHAT TO DO ANSWER ASAP ILL GIVE BRAINIESTTTTT
A financial planner has three portfolios: A, B, and C. Because investors have different tolerances for risks, 20% of people are likely to invest in portfolio A, 30% are likely to invest in B, and 50% are likely to invest in C. Each portfolio has both stocks and bonds, and investors are equally likely to choose either.
This is a tree diagram that represents the probability of investors choosing the different financial products.
What is the probability of an investor choosing either stocks or bonds from portfolio C?
Considering the given tree diagram, there is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
At each node, the sum of the probabilities is of 1, hence:
0.2 + 0.3 + Z = 1.
Z = 0.5.
There is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.
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Describe the following expressions in words: x+4
ales volume last weekend for four samples, each consisting of five car dealerships, were as follows: Data Point 1 2 3 4 5 Sample 1 37 15 43 25 21 Sample 2 38 31 12 19 28 Sample 3 16 21 45 32 25 Sample 4 19 10 45 37 22 What is the standard deviation of the distribution of sample means
The sample standard deviation of sample 1 is 11.54, of sample 2 is 10.21, of sample 3 is 11.25, of sample 4 is 14.15.
Given
Data point sample 1 sample 2 sample 3 sample 4
1 37 38 16 19
2 15 31 21 10
3 43 12 45 45
4 25 19 32 37
5 21 28 25 22
We have to find the sample standard deviation of each sample.
We have to first mean of each sample.
Sample mean of 1=141/5=28.2
Sample mean of 2=128/5=25.6
Sample mean of 3=139/5=27.8
Sample mean of 4=133/5=26.6
Sample standard deviation=[tex]\sqrt{}[/tex]∑[tex](x-x bar)^{2}/n-1[/tex]
∑[tex](x-x bar)^{2}[/tex] is calculated in the figure.
Sample standard deviation of sample 1=[tex]\sqrt{532.8/4}[/tex]
=[tex]\sqrt{133.2}[/tex]
=11.54
Sample standard deviation of sample 2=[tex]\sqrt{417.2/4}[/tex]
=[tex]\sqrt{104.3}[/tex]
=10.21
Sample standard deviation of sample 3=[tex]\sqrt{506.8/4}[/tex]
=[tex]\sqrt{126.7}[/tex]
=11.25
Sample standard deviation of sample 4=[tex]\sqrt{801.2/4}[/tex]
=[tex]\sqrt{200.3}[/tex]
=14.15.
Hence the sample standard deviation of sample 1 is 11.54, sample standard deviation of sample 2 is 10.21, sample standard deviation of sample 3 is 11.25, sample standard deviation of sample 4 is 14.15.
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A potato was launched in the air using a potato gun. the function for the situation was h(t) = -16t2 + 100t + 10, where t was the time in seconds and h(t) was the height in feet. (3 points each) a. what was the maximum height of the potato? b. what was the lowest height of the potato? c. what was the lowest time that applies to the actual situation? d. what is the greatest time that applied to the actual situation? e. using your answers to parts a through d, what are the domain and range of the function, as they apply to this situation? use set builder notation.
The answers to all the parts are given below.
To find the answers using a function:The height equation is:
h(t) = - 16t^2 + 100t + 10
A) To find the maximum height, we must find the time where the velocity is 0, so we must derive it with respect to the time.
v(t) = - 2 * 16 * t + 100 = 0
t = 100/(2*16) = 3.125s
Now we put this time in our height equation:
h(3.125s) = -16*3.125^2 + 100*3.125 + 10 = 166.25 ft.
B) The lowest height of the potato will be h = 0ft when the potato hits the ground.
C) the lowest time that works for that function is t = 0s when the potato is fired by the gun.
D) the maximum time can be found when the potato hits the ground, after that point the equation does not work anymore, let's find it,
h(t) = 0 = -16t^2 +100t+10
we can solve it using Bhaskara's equation:
[tex]t=\frac{-100+-\sqrt{100^{2} +4*16*10} }{-2*16} =\frac{-100+-103.2}{-32}[/tex]
So the two solutions are:
t = 6.3s
t = -0.1s
We need to choose the positive time, as we already discussed that the minimum time that works for the equation is t = 0s.
so here the answer is t = 6.3s
E) the domain is 0s ≤ t ≤ 6.3s
The range is 0ft ≤ h ≤ 166.25 ft.
Therefore, the answers to all the parts are shown.
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The line plot (shown in the attached image) shows the prices of sunglasses at a department store.
a. Find the mean, median, and mode.
b. Which measure best describes the data? Why?
c. Which measure might be misleading in describing the average price of sunglasses? Explain your reasoning.
Please help!! show all work and be sure to give final responses in complete sentence form in context of the problem, and explain your reasoning.
a. Mean is 70.8, median is 70, and mode is 60
b. Mean describes the data best
c. Mean can be a misleading central measure in case of outliers
Calculating Mean, Median and Mode
Mean = Total sum of pries / Total number of sunglasses
Mean = (20 + 20 + 50 + 50 + 50 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 70 + 70 + 80 + 80 + 80 + 80 + 90 + 90 + 90 + 90 + 100 + 100 + 130) / 25
Mean = 70.8
Median = (n/2 + 1)th term
Here, n is the number of sunglasses.
Median = (25/2 + 1)th term
Median =13th term
Median = 70
Mode = Most occurring data
Mode = 70
Why is mean the best central measure to describe the data?
When your data distribution is continuous and symmetrical, such as when your data are normally distributed, the mean is typically the best measure of central tendency to utilize. Thus, mean describes the average price of the sunglasses here
Mean Being Misleading
In case there are outliers, the mean of the data gets highly affected. Hence, it can be misleading for analyzing average price of the data.
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Find the value of f(4)?
From the given graph, we can see by tracing that f(4) is -3.5
Graph of a quadratic functionThe given graph is a graph of a quadratic function with a parabola opening upwards.
According to the question, we are to find the value of y where the value of x is 4. From the given graph, we can see by tracing that f(4) is -3.5
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A printing company charges a fixed rate to set up the printing press, plus a cost of $3.50 for every 100 copies. If 800 copies cost $64.00, how much will it cost to print 1500 copies?
Answer:
88.5
Step-by-step explanation:
3.5 * 8 = 28, this is how much was spent on copies printed. If 800 copies cost $64 and 28 of that was on the 3.5 fee per 100, then the flat rate must be:
64-28 = 36.
Now, let's do 1500. For 1500 copies, you will get charged $3.5 15 times. This amounts to 52.5, then adding the fixed fee of 36 dollars, you get
88.5
Find the quotient: look at pic
Answer:
2y+6
Step-by-step explanation:
first, pull out the 2 from the top to separate the equation
second, factor out y
third, cancel out the common factor of y-1
fourth, remove the parenthesis from 2(y+3)
answer = 2y+6
HELP ASAP PLS
Select the correct answer from each drop-down menu.
Quadratic function f is shown on the graph.
I don't know what the options are in the drop-down menu but the function f is symmetric around the point (4,–1) which is called the axis of symmetry. (4,–1) is the minimum of the graph.
How do I put the pairs for the values in the domain
Answer:
Step-by-step explanation: use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded.
Write two expressions that have a solution of x = 4.
ASAP!! Ty
Answer:
X multiplied by 2 is 8
X divided by 2 is 4
Step-by-step explanation:
This is the quickest thing i can give you
What information is needed to shoe ABC~EDC
Answer:
I guess the first one is correct........
24. Which measurement is equivalent to 10 g?
a. 1 dag
b. 1 dg
c. 1 cg
d. 1 hg
Answer:
a. 1 dag
Step-by-step explanation:
The list of SI prefixes is attached. Each has an abbreviation that can be used with the abbreviation for the SI unit of interest.
ApplicationA factor of 10 is signified by the prefix deka-, abbreviated "da". Then 10 grams is 1 dekagram, or 1 dag.
PLEASE HELP ASAP
List these numbers from SMALLEST TO LARGEST
29.94
28.15
27.068
28.08
28.3
Answer:
Step-by-step explanation:
27.068
28.08
28.15
29.94
The sum of all but one interior angle of a heptagon is 776°. What is the measure of the final interior angle? 42º 56º 124º 304º
The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)
What is the measure of the missing interior angle in a heptagon?
Heptagons are polygons with seven sides, seven vertices, seven interior angles and seven central angles. Herein we know the value of the sum of six interior angles and we need to know the measure of the seventh interior angle. We can determine the measure of the seven interior angles by using the following expression:
θ = (n - 2) · 180°, where n is the number of sides of the polygon. (1)
If we know that n = 7, then sum of the internal angles in the heptagon is:
θ = (7 - 2) · 180°
θ = 900°
And the measure of the final interior angle is found by subtraction:
θ₇ = 900° - 776°
θ₇ = 124°
The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)
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Explain why the following form linearly dependent sets of vectors. (solve this problem by inspection.)
u1 = (3, -l), u2 = (4, 5), u3 = (-4, 7) in r2
A set of vectors {v1,v2,...,vk} is linearly independent if the vector equation x1v1 + x2v2 + .......... + xkvk = 0 has only the trivial solution
x1 = x2 = .... = xk =0. Then the set {v1,v2,...,vk} is linearly dependent otherwise.
So putting in the formula we get
x1u1 + x2u2 + x3u3 = 0
x1u1 + x2u2 = -x3u3
au1 + bu2 = u3 ∵ (-x1/x3 = a & -x2/x3 = b)
On putting in the values
a(3,-1) + b(4,5) = (-4,7)
(3a+4b,-a+5b) = (-4,7)
On comparing we get
3a + 4b = -4 -(1)
-a + 5b = 7 -(2)
on solving these equations we get
b = 17/19 and a= -48/19
which is non trivial.
Thus the following form linearly dependent sets of vectors.
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If you substitute 12 2x for y in the second equation, how is the resulting equation written in standard form?
The resulting equation written in standard form is 16x² - 22x + 6 = 0.
What is equation in standard form?Quadratic Equation in Standard Form: ax² + bx + c = 0
a, b and c are known values. a can't be 0.
"x" is the variable or unknown (we don't know it yet).
The "solutions" to the Quadratic Equation are where it is equal to zero.
They are also called "roots", or sometimes "zeros"
We can Factor the Quadratic (find what to multiply to make the Quadratic Equation)
Or we can Complete the SquareOr we can use the special Quadratic Formula:Quadratic Formula: x = [ -b (+-) √(b² - 4ac) ] / 2a, Just plug in the values of a, b and c, and do the calculations.Calculation for the given equation-
Now, y=-16x²+24x+6
Substitute, y = 12+2x in y = -16x²+24x+6.
=> 12+2x = -16x²+24x+6
=> 16x²-24x-6+12+2x = 0
=> 16x²-22x+6 = 0
Therefore, the quadratic equation given in the standard form is 16x²-22x+6 = 0.
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The complete question is-
The two equations are given below;
Y = 12 + 2x linear equation
Y = -16x² + 24x + 6 quadratic equation
If you substitute 12 + 2x for y in the second equation how is the resulting equation written in standard form?
I need help with this!!
Answer: $18.51
Step-by-step explanation:
1015cm^3/7.95cm^3/g = 127.67g
127.67g/1000g = .128
.128*$.29 = $.037
$.037*500 = $18.51
Answer:
$1170
Step-by-step explanation:
1. We know that each steel part has a volume of 1015 cubic centimeters, and the machinist wants to make 500 of these. Then the total volume of the steel part the machinist will make will be 1015 x 500.
--> 1015 x 500
--> 507500 cubic centimeters.
2. The density of the steel part is 7.95 grams per one cubic centimeter. Then the total density of the 500 steel parts will be 507500 x 7.95.
--> 507500 x 7.95
--> 4,034,625 grams.
3. For every kilo of steel part, the cost is $0.29. We should first change the 4,034,625 gram to kilo. Since 1000 grams is a kilo, we divide 4,034,625 by 1000.
--> 4,034,625 grams / 1000 = 4034.625 kilograms.
Now we multiply 4034.625 by 0.29 to find the total cost.
--> 4034.625 x 0.29
--> 1170.04125.
Since the question specifically asked to round it to the nearest dollar, our final answer becomes $1170.
A math class consists of 25 students, 14 female and 11 male. Two students are selected at random to
participate in a probability experiment. Compute the probability that
a) a male is selected, then a female.
b) a female is selected, then a male.
c) two males are selected.
d) two females are selected.
e) no males are selected.
The probability that a male is selected, then a female is 0.26
The probability that a female is selected, then a male is 0.26
The probability that two males are selected is 0.18
The probability that two females are selected is 0.30.
The probability that no males are selected is 0.30.
What are the probabilities?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that a male is selected, then a female = (11/25) x (14 / 24) = 0.26
The probability that a female is selected, then a male = (14/25) x (11 / 24) = 0.26
The probability that two males are selected = (11/25) x (10/24) = 0.18
The probability that two females are selected = (14/25) x (13 / 24) = 0.30
The probability that no males are selected = (14/25) x (13 / 24) = 0.30
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Ilean works as a welder and
web designer. As a welder, she earns $18 per hour. Last week she
worked x hours as a welder and her friend paid her $75 to design a web page. Write an
expression to represent the total amount llean earned last week.
The expression which can be used to represent the total amount llean earned last week is 75 + 18x
EquationAmount llean earns per hour welding = $18Number of hours worked as welder = xAmount earned as a web page designer = $75An expression to represent the total amount llean earned last week = Amount earned as a web page designer + (Amount llean earns per hour welding × Number of hours worked as welder)
= 75 + (18 × x)
= 75 + 18x
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What is the slope of a line passing through (-5, 5) and
(-4, 10)?
Answer:
5
Step-by-step explanation:
Formula for finding slope:
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
Slope of line passing through (-5,5) and (-4,10)
=
[tex] \frac{5 - 10}{ - 5 - ( - 4)} \\ = \frac{ - 5}{ - 5 + 4} \\ = \frac{ - 5}{ - 1} \\ = 5[/tex]
Answer:
Slope = 5
Step-by-step explanation:
Slope:(-5,5) ; x₁ = -5 & y₁ = 5
(-4, 10) ; x₂ = -4 & y₂ = 10
[tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{10-5}{-4-[-5]}\\\\ =\dfrac{10-5}{-4+5}\\\\=\dfrac{5}{1}\\\\= 5[/tex]
Q.estimate the area of each polygon in square units.
i cant understand the question can someone help me and provide detailed explanation with the solution. please provide reasons so i can grasp the concept.
The area of the polygon is 12 square units. In mathematics and everyday life, an estimate is an approximate calculation or guess that is close to the actual value but may not be exact.
To make an estimate or guess, you can square off the parallelogram and create a rectangle and add your squares (or multiply 3x4) to = 12": This part explains a method for estimating the area of a parallelogram. It suggests that if you take a parallelogram and "square it off" (convert it into a rectangle by drawing a perpendicular line), you can then find the area of the rectangle, which is easier to calculate. In this case, the dimensions of the rectangle are given as 3 units for the base and 4 units for the height, and the estimated area is 12 square units.
You can use the formula for the exact area using base x height (3x4) you get the same answer of 12 square units": This part emphasizes that the estimation method used in step 2 (multiplying 3 by 4) produces the same result as the exact formula for finding the area of a parallelogram, which is base times height. In this case, both the estimation and the formula give an area of 12 square units.
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A box contains 65 balls numbered from 1 to 65. If 11 balls are drawn with replacement, what is the probability that at least two of them have the same number?
Using the binomial distribution, there is a 0.265 = 26.5% probability that at least two of them have the same number.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are:
p = 1/65 = 0.0154, n = 65.
The probability that at least two of them have the same number is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which:
P(X < 2) = P(X = 0) + P(X = 1)
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{65,0}.(0.0154)^{0}.(0.9846)^{65} = 0.3647[/tex]
[tex]P(X = 1) = C_{65,1}.(0.0154)^{1}.(0.9846)^{64} = 0.3703[/tex]
So:
P(X < 2) = P(X = 0) + P(X = 1) = 0.3647 + 0.3703 = 0.735.
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.735 = 0.265[/tex]
0.265 = 26.5% probability that at least two of them have the same number.
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To fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm. Which inequality can be used to represent the lengths of the glass that will fit in the frame?
12 < x ≤ 12.2
12 > x ≤ 12.2
x > 12 or x ≤ 12.2
x < 12 or x ≤ 12.2
Considering the definition of an inequality, the inequality that expresses the previous relationship is 12 < x ≤ 12.2
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that to fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm.
It means that the length has to be strictly greater than 12 cm but less than or equal to 12.2 cm. In other words, length of frame must be longer than 12 cm means that x>12, while ength of frame not longer than 12.2 cm means x≤12.2
Finally, the inequality that expresses the previous relationship is
12 < x ≤ 12.2
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Volume=
Help me please!! Asap! Thanks so much
The volume of the oblique prism is 16261 cubic units
How to determine the volume?The given parameters are:
Height = 23
Base area = 707
The volume is calculated as:
V = base area * height
So, we have:
V = 707 * 23
Evaluate
V = 16261
Hence, the volume of the oblique prism is 16261 cubic units
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Outside a home, there is a 4-key keypad numbered 1 through 4. The correct six-digit code will open the garage door. The numbers can be repeated in the code
(a) How many codes are possible?
(b) What is the probability of entering the correct code on the first try, assuming that the owner doesn't remember the code?
(a) The number of possible codes is
(Type an integer or fraction. Simplify your answer)
(b) The probability that the correct code is given on the first try, assuming that the owner doesn't remember it is
(Type an integer or fraction Simplify your answer.)
Using the Fundamental Counting Theorem, it is found that:
a) 256 codes are possible.
b) The probability is [tex]\frac{1}{256}[/tex].
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
There are 4 keys, each with 4 options, hence the parameters are:
[tex]n_1 = n_2 = n_3 = n_4 = 4[/tex].
Then the number of codes is:
[tex]N = 4^4 = 256[/tex]
And the probability is:
[tex]p = \frac{1}{256}[/tex].
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