Answer:
y = 5*2ˣStep-by-step explanation:
Exponential function:
y = abˣOrdered pairs given:
(1, 10) and (4, 80)Substitute x and y values to get below system:
10 = ab80 = ab⁴Divide the second equation by the first one and solve for b:
80/10 = b³b³ = 8b = ∛8b = 2Use the first equation and find the value of a:
10 = a*2a = 5The function is:
y = 5*2ˣAnswer:
\(y=5 \cdot 2^x\)
Step-by-step explanation:
An exponential function is written in the form:
\(y=ab^x\)We can use the given points that the exponential function passes through to solve for a and b.
Create a system of equations by substituting (1, 10) and (4, 80) into the exponential form of a function.
\(\text{I}:\ 10=ab^1\) \(\text{II}: \ 8 0=ab^4\)Divide Equation I by Equation II in order to cancel out variable a.
\(\displaystyle \frac{80=ab^4}{10=ab}\)\(8=b^3\)\(b=2\)Now we can solve for a by substituting b back into either equation from the system of equations.
\(10=ab\) \(10=a(2)\) \(a=5\)Substitute 5 for a and 2 for b into the form of an exponential function to find the exponential function that passes through (1, 10) and (4, 80).
\(y=5 \cdot 2^x\)y = 5 · 2ˣ is the exponential function that describes the graph.
2x2 – 8x = 10
Complete the square
Answer:
this equation has no solution
Step-by-step explanation:
jesuseduardomontiel0 avatar
jesuseduardomontiel0
3 days ago
Mathematics
High School
Daniel has 4.8 pounds of ground beef. He makes 8 burgers of equal amounts. Daniel draws this model to show how much each burger will weigh. Daniel's model correct? Why or why not?
WOW JIMMY. THATS A BIG . BIG. BIG. NUT SACK
At a meeting for math enthusiasts, two entrance fees are charged. Anyone who knows the code word “algemath” only pays 2 euros. Those who are unlucky and do not know the code word pay three euros more. You know that 7338 people were present and that the cashier received 17487 euros. How many people knew the password?
Number of People who knows the Code are 6401
What is Linear Equation in Two Variable?
A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Solution:
Let, Number of People who kows the Code be x
Number of Peoplee who do not know the Code be y
According to the Question:
x + y = 7338 ----------(i)
2x + 5y = 17487 ----------(ii)
Multiplying Equation (i) by 2
2x + 2y = 14676 ---------(iii)
Substracting Equation (iii) from Equation (ii)
3y = 2811
y = 937
This means x = 6401
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Find the measurement of m
The measure of the inscribed angle G in the circle is 85 degree.
What is the measure of angle G?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
Since the circle equals 360 degrees, we can determine the intercepted arc DF.
Hence:
Arc DF = 360 - ( 70 + 120 )
Arc DF = 360 - 190
Arc DF = 170°
Now, plug the value into the above formula:
Inscribed angle = 1/2 × intercepted arc.
Inscribed angle G = 1/2 × 170°
Inscribed angle G = 85°
Therefore, angle G has a measure of 85 degree.
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math help mee i hate math om fg
Answer:
4
Step-by-step explanation:
it is technically 4.5625 bc thats 73 divided by 16 but to make it even that would have to be 4.
Answer:Easy 4.5
Step-by-step explanation:
That’s bc 73 dvided by 16 = 4.5
Solve the equation on the
interval [0, 2pi).
3 sin x = sin x + 1
Answer:
π/6 , 7π/6
Step-by-step explanation:
3sinx = sinx + 1 ⇒ 2sinx = 1 ⇒ sinx = 1/2
At which value(s) of x does sinx equal 1/2?
x = arcsin(1/2) at π/6 and 5π/6
what is the raito 40 to 18
Answer:
20:9
Step-by-step explanation:
Here we will simplify the ratio to 40:18 for you and show you how we did it.
To simplify the ratio 40:18, we find the greatest common divisor of 40 and 18, and then we divide 40 and 18 by the greatest common divisor.
The greatest common divisor that you can use to simplify 40:18 is 2. This means the answer to ratio 40:18 simplified is:
20:9
Write an equation in slope-intercept form (-5,-7);y=-2x+4
Answer:
Step-by-step explanation:
First, let us substitute x and y values: -7 = -2(-5) + 4
Next, let us simplify using the substitution property of equality: 14 = -7 (SEE BELOW MORE INFO).
Now, this does not make sense yet because 14 cannot possibly equal -7. Therefore, we must add a b value, therefore leading us to the equation:
14 + b = -7
by simplifying, we can conclude that b = -21
Finally, we can plug in the b-value into our original equation:
y = -2x + 4 - 21
After simplifying, we get y = -2x - 17. When this is graphed, we can see that -2x - 17 intersects (-5, -7).
Writing ratios as a percentage
In the past year Heather watched 16 movies that she thought were very good. She watched 50 movies over the whole year. Of the movies she watched, what percentage did she rate as very good?
She rated 32% percent of the movies very good
2) In order to receive a passing grade in your math class, you must attain an average of at least 65. If your scores on 5 exams were 90, 65, 50, 78 and 82, did you receive a passing grade?
Answer:
73
Step-by-step explanation:
to get the average you add all five together and divide by the number of scores, which is five
The map shows an obstacle course at a school fair. The units are given in yards.
What is the total distance of
the obstacle course?
? yards
Start
(-40, -10)
Tire
Race
(-40, -30)
Finish
(10, 20)
Monkey
Bars
(40,20)
Rope
Climb
(40,-30)
The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).
Using this formula, we can calculate the distances between each pair of consecutive points as follows:
Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards
Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards
Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards
Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards
Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.
Can someone please Help me ?
Cesar drove his car to Mexico to visit relatives. The speed limit sign on the Freeway said 110 kilometers per hour, but the speedometer on Cesar's car is calibrated in miles per hour. How fast should Cesar's drive his car to avoid va speeding ticket if 1 kilometer is about 0.62 miles? Please also show how you got the work.
Please help it is Due Today!!!!!
based on the graph how many tiles are im figure 0
For figure {0}, the number of tiles will be equal to 2.
What is a mathematical function, equation and expression?Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is a graph as shown in the image.
The line passes through point -
(3, 8) and (4, 10)
So, the slope of the line will be -
m = (10 - 8)/(4 - 3)
m = 2
y = 2x + c
For the point (3, 8), we can write -
8 = 6 + c
c = 2
For figure {0}, the number of tiles will be equal to 2.
Therefore, for figure {0}, the number of tiles will be equal to 2.
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Which are rational numbers? (A) -9 (B) 5/8 (C) 0 (D) all of the above
Answer:
D. All of the above
Step-by-step explanation:
all numbers are considered rational numbers
what type of sequence is shown: 1,2,4,7,10A) Arithmetic sequenceB) geometric sequence C) neithernote this is not graded its practice
Given Sequence:
\(1,2,4,7,10\)If the sequence is arithemetic sequence the difference between to consicutive elements will be same.
\(\begin{gathered} d_1=2-1=1 \\ d_2=4-2=2 \end{gathered}\)Since,
\(d_1\ne d_2\)The sequence is not a arithmetic sequence.
If the sequence is a geometric sequence the ratio between two succesive elements will be same.
\(\begin{gathered} r_1=\frac{2}{1}=2 \\ r_2=\frac{4}{2}=2_{} \\ r_3=\frac{7}{4}=1.75 \end{gathered}\)Since,
\(r_2\ne r_3\)The sequence is not a geometric sequence.
Thus, the correct option is option (C) neither. The sequnce is neither arithmetic sequence nor a geometric sequence.
A group of 66 randomly selected students have a mean score of 22.4 with a standard deviation of 2.8 on a placement test. What is the 90% confidence interval for the mean score, μ, of all students taking the test? 21.5 < μ < 23.3 21.8 < μ < 23.0 21.6 < μ < 23.2 21.7 < μ < 23.1
The 90% confidence interval for the mean score, μ, of all students taking the test is B. 21.8<u<23.0
How to illustrate the information?Given a=0.1, Z(0.05)=1.645 (from standard normal table)
So 90% confidence interval is
xbar+/-Z*s/vn
= 22.4+/-1.645*2.8/sqrt(66)
= (21.83304, 22.96696)
Therefore, the 90% confidence interval for the mean score, μ, of all students taking the test is 21.8<u<23.0.
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Floyd builds rectangles using matches, as shown below. When the length of the rectangle is 3 matches, he used 8 matches. When the length of the rectangle is 7 matches, he used 16 matches. How many matches does Floyd need to make a rectangle with length 20 matches? [Type in only o numeric digit as your answer with no spaces Answer: Search Q
Floyd needs 33 matches to make a rectangle with a length of 20 matches.
To find out how many matches Floyd needs to make a rectangle with a length of 20 matches, we can observe a pattern in the given information.
From the given data, we can see that as the length of the rectangle increases by 4 matches, the number of matches used increases by 8. This means that for every additional 4 matches in length, Floyd requires 8 more matches.
Using this pattern, we can calculate the number of matches needed for a rectangle with a length of 20 matches.
First, we need to determine the number of 4-match increments in the length of 20 matches. We can do this by subtracting the starting length of 3 matches from the target length of 20 matches, which gives us 20 - 3 = 17.
Next, we divide the number of 4-match increments by 4 to determine how many times Floyd needs to add 4 matches. In this case, 17 ÷ 4 = 4 with a remainder of 1.
Since Floyd requires 8 matches for each 4-match increment, we multiply the number of increments by 8, which gives us 4 × 8 = 32 matches.
Finally, we add the remaining matches (1 match in this case) to the total, resulting in 32 + 1 = 33 matches needed to reach a length of 20 matches.
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how to solve this separable differential equation?
The solution to the differential equation \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\) is,
\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).
What is a differential equation?Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation.
The given differential equation is \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\).
Now, multiplying both sides by dx we,
\(2^{\sqrt{x}}dy = cosce(ln(y))dx\).
Dividing both sides by \(2^{\sqrt{x}}\) we have,
\(sin(ln(y))dy = \frac{dx}{2^{\sqrt{x}}}\).
\(\[ \int sin(ln(y))dy = \int \frac{dx}{2^{\sqrt{x}}}\).
\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).
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What does the x coordinate of a point tell you?
Answer:
X is for the height
Step-by-step explanation:
Arcodding to the coordinate table , this chart has x and y. We measure the y first then we measure the x.
the y coordinate show the length and the y measure the height
I hope it'll help you much
Thank you for asking
Find the area of the shaded region.
f(x)=x4-12x³ +48x², g(x) = 44x+105
340-
(-1,61)
(5,325)
co.
8
Q
Answer:
Step-by-step explanation:
To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:
x^4 - 12x^3 + 48x^2 = 44x + 105
x^4 - 12x^3 + 48x^2 - 44x - 105 = 0
We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:
x = -1.932, x = 0.695, x = 4.149
Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.
The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:
A = ∫3^4 [g(x) - f(x)] dx
A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx
A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx
We can integrate term by term using the power rule:
A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4
A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]
A = 347.2
Therefore, the area of the shaded region is approximately 347.2 square units.
the sum of 2 numbers which are in a ratio 2:5 is 21 what are the numbers
Ratio = 2 : 5
Numbers = 2x & 5x
\(2x + 5x = 21 \\ 7x = 21 \\ x = 21 \div 7 \\ x = 3\)
Numbers :-
2x = 2 × 3 = 6
5x = 5 × 3 = 15.
The numbers are 6 & 15.
A bag of the same size balls contains six blue balls firebrand balls five yellow balls and four green balls what is the probability of selecting a blue or green ball on the first draw
The probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.
What is probability ?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur. If an event has a probability of 0.5, it means that the event is equally likely to occur or not occur. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability is an important concept in mathematics, statistics, and many other fields, as it allows us to make predictions and decisions based on the likelihood of certain outcomes.
According to the question:
The total number of balls in the bag is:
6 blue balls + 5 yellow balls + 4 green balls = 15 balls
The probability of selecting a blue or green ball on the first draw can be found by dividing the number of blue and green balls by the total number of balls:
P(blue or green) = (number of blue balls + number of green balls) / (total number of balls)
P(blue or green) = (6 + 4) / 15
P(blue or green) = 10 / 15
P(blue or green) = 2/3
Therefore, the probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.
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Quadrilateral ABCD is a square and the length of BD¯¯¯¯¯ is 10 cm.
What is the length of AE¯¯¯¯¯ ?
Enter your answer in the box.
the length of AE¯¯¯¯¯ =
cm
The length of AE¯¯¯¯¯ is 5√2 cm.
Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.
Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.
Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.
In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the diagonal (the hypotenuse) is the same as the side length, s.
Applying the Pythagorean theorem:
s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2
10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2
100 = 2 * AE¯¯¯¯¯^2
AE¯¯¯¯¯^2 = 50
Taking the square root of both sides:
AE¯¯¯¯¯ = √50
Simplifying the square root:
AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm
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Simplify the polynomial, then evaluate for x = 2.
x+3x²+2x-3-4x²+6
x² + 3x + 9; 19
x² + 3x + 3; 5
-x² + 3x + 9; 11
O
O
-x² + 3x + 3; 13
Answer:
x^2 + 3x + 9 = (x + 3)(x + 3)
When x = 2, we have:
(2 + 3) * (2 + 3)
5 * 5
25
Please gimme the variables to define the sytem and 2 system of equations
Answer:
\(8.5x+4y=99.5,\ x+y=17\)
Step-by-step explanation:
\(\mathrm{System\ of\ equations:}\\8.5x+4y=99.5\\x+y=17\\\mathrm{where,}\ x\ \mathrm{is\ the\ number\ of\ popcorns\ and\ }y\mathrm{\is\ the\ number\ of\ candies}\)
This model represents 9,015 ÷ 4.
What is the solution to 9,015 ÷ 4?
Answer:
2253.75
Step-by-step explanation:
It would have a decimal because these numbers are not equal :D
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer.
Part B: Write a function to represent the data. Show your work.
Part C: Determine the average rate of change between station 2 and station 4. Show your work.
Answer:
She will need a time of 1024 units to complete the 10th station.
Step-by-step explanation:
A. As the quotient between consecutive terms is the same, the data is a geometric sequence.
B. The recursive formula is:
C. She will need a time of 1024 units to complete the 10th station.
In a sequence, if the difference between consecutive terms is the same, the sequence is arithmetic.
If the quotient between consecutive terms is the same, the sequence is geometric.
Item a:
When x increases by 1, y is multiplied by 2, hence, as the quotient between consecutive terms is the same, the data is a geometric sequence.
Peanut allergies are becoming increasingly common in Western countries. Some evidence points to the timing of peanuts! first introduction in the diet as an influential factor, raising the question of whether pediatricians should recommend early exposure or avoidance. A study enrolled infants with a diagnosed peanut allergy and randomly assigned them to either completely avoid peanuts or consume peanuts in small amounts regularly until they reached 60 months of age. At the end of the study, 18 of the 51 infants who had avoided peanuts were still allergic to peanuts. In contrast, 5 of the 47 infants who had consumed peanuts were still allergic to peanuts. Do the data indicate that one approach is more beneficial? Follow the four‑step process.
STATE: What is the question we are asking?
A. Does early exposure to peanuts better reduce peanut allergy in children with a known allergy to peanuts?
B. Does early exposure to peanuts in small amounts or complete avoidance of peanuts better reduce peanut allergy in children with a known allergy to peanuts?
C. Should all children under the age of 60 months avoid peanuts or only eat them in small amounts?
D. Should all children under 60 months eat peanuts regularly in small amounts?
Answer:
B. Does early exposure to peanuts in small amounts or complete avoidance of peanuts better reduce peanut allergy in children with a known allergy to peanuts?
Step-by-step explanation:
Remember we are told there's already a question whether pediatricians should recommend early exposure or avoidance. Thus, the research question should answer these two issues (early exposure or avoidance).
Hence, the question we are asking is: Does early exposure to peanuts in small amounts or complete avoidance of peanuts better reduce peanut allergy in children with a known allergy to peanuts?
Inverse of f(x)=-2x-5/-4x+9
Answer:
Step-by-step explanation:
7
4.Find the missing length indicated. Leave your answer in simplest radical form.
The missing length indicated in the triangle is; x = 16
How to use Pythagoras Theorem?We are given a right angle triangle. From the given right angle triangle, we can see that the length of the hypotenuse of the biggest triangle is x.
Now, using Pythagoras theorem, we can find the length of the altitude of the bigger triangle as;
a = √((8√3)² - 12²)
a = √(192 - 144)
a = √48
a = 4√3
12/(8√3) = cos θ
cos θ = 0.8660
θ = 30°
(8√3)/x = cos 30
x = (8√3)/cos 30
x = 16
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