The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.
In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:
((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)
Now, we can combine the two terms in the equation by finding a common denominator:
(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)
Next, we can combine the terms in the numerator by factoring out (y-b):
[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)
Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:
(y-b)(y-b+1)/(y-b+1) = y-b
Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1) after being simplified, is equivalent to the polynomial y-b.
Learn more about polynomials :
https://brainly.com/question/30127172
#SPJ4
write the hypotheses to test if the success rate for art at this clinic is significantly higher than the success rate reported by the cdc.
In contrast to the CDC's reported success rate, the success rate for art at this clinic is substantially greater.
what is null hypothesis ?A claim or assumption that there is no statistically significant difference between two populations or sets of data is known as the null hypothesis. It serves as the beginning point for statistical hypothesis testing and is typically indicated as H0. According to the null hypothesis, any observed difference between the populations or data sets is the result of sampling error or random chance rather than a genuine difference.
given
The success rate for art at this clinic is not statistically different from the CDC's claimed success rate.
In contrast to the CDC's reported success rate, the success rate for art at this clinic is substantially greater.
To know more about null hypothesis visit
https://brainly.com/question/28920252
#SPJ1
Write the equation of. the circle graphed below
Answer:
[tex](x+2)^{2} +(y+2)^{2} =9[/tex]
Step-by-step explanation:
the equation of circle:
center:(-2,-2)
The distance between the center and the side:3
So, the radius is 3
(x-h)^2+(y-k)^2=r^2
[tex](x - - 2)^{2} +(y- - 2)^{2} =3^{2}[/tex]
[tex](X+2)^{2} +(y+2)^{2} =9[/tex]
7. What is the greatest whole number that satisfies the inequality
3x - 1 < 8 ?
Answer:
2
Step-by-step explanation:
3(2)-1<8
6-1<8
5<8
if you go up to 3 as the whole number then the equation ends up 8<8, and the sign is less than (<) not less than or equal to.
So 2 would be the answer.
1. Find the sine of angle in the triangle below.
3
8
To solve the question asked, you can say: So the other side of the triangle will be as [tex]A = \sqrt73[/tex].
What precisely is a triangle?A triangle is a closed two-dimensional geometric object consisting of three line segments, called edges, that intersect at three places called vertices. Triangles are distinguished by their sides and angles. A triangle can be equilateral (all sides equal), isosceles, or odd, depending on the sides. Triangles are classified as acute (any angle less than 90 degrees), right (angles equal to 90 degrees), or obtuse (any angle greater than 90 degrees). The area of a triangle can be calculated using the formula A = (1/2)bh. where A is the area, b is the base of the triangle, and h is the height of the triangle.
here in the triangle we have sides that are 3 and 8
we can use
[tex]A^2 = B^2 + C^2\\A^2 = 3^2 + 8^2\\A^2 = 9+64\\A^2 = 73\\A = \sqrt73[/tex]
So the other side of the triangle will be as [tex]A = \sqrt73[/tex].
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
How much would it cost to buy a sheet of a metal 4m by 75cm which cost E90 to a metal of 5m by 2m
It would cost €27 to buy a sheet of area 4 meters by 75 centimeters.
We solve this problem easily by employing the unitary method. To answer this question, we need to first calculate the area of the metal sheet being sold and the area of the metal sheet being purchased.
The area of the metal sheet being sold is:
5 meters × 2 meters = 10 square meters
The area of the metal sheet being purchased is:
4 meters × 0.75 meters = 3 square meters
Now we can calculate the price per square meter of the metal sheet being sold:
€90 ÷ 10 square meters = €9 per square meter
Finally, we can calculate the cost of the metal sheet being purchased:
3 square meters × €9 per square meter = €27. Therefore, the cost to buy a sheet of area 4 meters by 75 centimeters which costs €90 to a metal of area 5 meters by 2 meters would be €27.
Learn more about the unitary method on
https://brainly.com/question/14793162?referrer=searchResults
#SPJ4
Identify the circumference of a circle with a diameter of 34 feet. Use 3.14 for π.
Circumference= diameter × 3.14
C= 34 feet× 3.14= 106.76 feet
A whale is swimming due north at a speed of 30 miles per hour. Just 5 miles away, a whale-watching tour boat is traveling south, directly toward the whale, at a speed of 46 miles per hour. How long will it be before they meet?
If necessary, round your answer to the nearest minute.
The equation that relates distance, rate (speed), and time is d=rt.
When two bodies are moving toward each other or away from each other, r is the sum of the rates.
The best solution will mark you brain list
The time it will take both the boat and whale to meet is 18 minutes(nearest minutes).
What is a displacement?Displacement is defined as the change in position of an object in a specified direction. It is measured in meters and it's a vector quantity.
[tex]\text{Since velocity} = \bold{displacement/time}[/tex]
[tex]\bold{displacement} = \text{velocity} \times \bold{time}[/tex]
The total space between the boat and the whale is 5 miles.
Using addition of vectors
[tex]5= v2t - v1t[/tex]
[tex]5= 46t - 30t[/tex]
[tex]5 = 16t[/tex]
[tex]t= 5\div16 = 0.3 \ hrs[/tex]
To minutes, = 0.3 × 60 = 18minutes(nearest minutes)
Therefore it will take the boat and the whale 18minutes to meet.
learn more about displacement from
https://brainly.com/question/14422259
vertical bar chart that shows frequency on the y-axis [ choose ] population is divided into groups, some groups are selected and all observations from each selected group are included in the sample [ choose ] collection of all data that is of interest [ choose ] a subset or part of a population [ choose ] a sample where the population is divided into groups and several are randomly sampled form each group [ choose ] consists of attributes, labels, or nonnumerical entries [ choose ]
A vertical bar chart that shows frequency on the y-axis is called a histogram. It is a graph showing the distribution of continuous data.
Histograms are used to give an estimate of the probability distribution of a continuous variable sample. Additionally, a subset or part of a population is called a sample. A population is divided into groups, and some groups are selected, and all observations from each selected group are included in the sample. This is called stratified random sampling.
A collection of all data that is of interest is known as the universe.
A collection of attributes, labels, or nonnumerical entries is known as categorical data. This type of data is descriptive in nature, as it allows us to identify what features the data has or belongs to. For instance, age group, gender, and occupation are examples of categorical data. A sample where the population is divided into groups and several are randomly sampled from each group is called a cluster sample. Cluster sampling is an excellent method for conducting a survey when the population is widespread and heterogeneous.
To know more about the "Histogram": https://brainly.com/question/25983327
#SPJ11
g a second unit vector which is also orthogonal to both 8,-8,8 and 0,5,5 is the unit vector which points in the direction opposite to u1 -2/6.-1/6,1/6 this is the vector u2
The vector u2 is (0, √3/3, 2/3). It is a unit vector that is orthogonal to both 8,-8,8 and 0,5,5.
Given two vectors 8,-8,8 and 0,5,5, we need to find another unit vector that is orthogonal to both the given vectors. Let's call this vector u1.The vector u1 can be obtained by taking the cross product of the two given vectors:u1 = (8,-8,8) × (0,5,5)u1 = (-40,-40,40)
To get a unit vector, we need to normalize u1 by dividing it by its magnitude:|u1| = √((-40)² + (-40)² + 40²) = 60u1 = (-40/60, -40/60, 40/60) = (-2/3, -2/3, 1/3)Now we need to find another unit vector that is orthogonal to u1.
One way to do this is to take the cross product of u1 with another vector, and then normalize the result. We can choose any vector that is not parallel to u1. For example, we can choose the vector (1,0,0).u2 = u1 × (1,0,0)u2 = (-2/3, -2/3, 1/3) × (1,0,0)u2 = (0,1/3,2/3)
To get a unit vector, we need to normalize u2 by dividing it by its magnitude:|u2| = √(0² + (1/3)² + (2/3)²) = 1/√3u2 = (0, √3/3, 2/3)
Learn more about Unit Vector
brainly.com/question/30279109
#SPJ11
16 A function is given.
f(x)= (2x-2)(x − 3)
-
Use the Add Point tool to plot the zeros and the maximum or minimum value of the function.
The zeros of the function are x=1 and x=3, and the minimum value of the function is at x=2.
What is the polynomial function?
A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.
To find the zeros, we set the function equal to zero and solve for x:
(2x-2)(x-3) = 0
This equation is true when either 2x-2=0 or x-3=0. Solving for x in each case, we get:
2x-2=0 => x=1
x-3=0 => x=3
So the zeros of the function are x=1 and x=3.
To find the maximum or minimum value of the function, we can take the derivative of the function and set it equal to zero:
f'(x) = 4x - 8
4x - 8 = 0 ----> x = 2
So the critical point of the function is x=2. To determine if this point is maximum or minimum, we can use the second derivative test:
f''(x) = 4
Since f''(2) > 0, the function has a minimum at x=2.
Therefore, the zeros of the function are x=1 and x=3, and the minimum value of the function is at x=2.
To learn more about the polynomial function visit:
https://brainly.com/question/2833285
#SPJ1
Caleb observed the costumes that people wore to a costume party. The themes of the costumes and the number of people who wore them are shown in the following table.
Costume Theme Superhero Decades Scary TV & Movie Characters Animals Career
Number of People 128 96 72 52 24 28
A circle graph was drawn from the data in the table. What percentage would be on the Decades slice of the circle graph?
24%
26.7%
86.4%
96%
Question 4(Multiple Choice Worth 2 points)
Answer: 24
Step-by-step explanation:
Consumer Reports magazine presented the following data on the number of calories in a hot dog for each of 17 brands of meat hot dogs:
173 191 182 190 172 147 146 139 175 136 179 153 107 195 135 140 138 Fill in the blanks as the data for the five-number summary:
Min = [min] Q1 = [Q1] M = [Median] Q3 = [Q3] Max = [Max]
The five-number summary for the given data is Min = 107, Q1 = 138, M = 175, Q3 = 190, and Max = 195.
How to find the minimum, maximum?In statistics, the five-number summary is a set of descriptive statistics that provide a summary of the distribution of a dataset. The five-number summary consists of the minimum value, the first quartile (Q1), the median (M), the third quartile (Q3), and the maximum value.
To find the five-number summary for the given data on the number of calories in a hot dog for each of 17 brands of meat hot dogs, we need to order the data from smallest to largest.
107 135 136 138 139 146 147 153 172 173 175 179 182 190 191 195
The minimum value is the smallest value in the dataset, which is 107.
The first quartile (Q1) is the value that is greater than or equal to 25% of the data and less than or equal to 75% of the data. To find Q1, we take the median of the lower half of the data:
Q1 = median(107, 135, 136, 138, 139, 146, 147, 153) = 138
The median (M) is the value that is in the middle of the dataset when the data is ordered from smallest to largest. For the given data, there are 17 values, so the median is the 9th value:
M = median(107, 135, 136, 138, 139, 146, 147, 153, 172, 173, 175, 179, 182, 190, 191, 195) = 175
The third quartile (Q3) is the value that is greater than or equal to 75% of the data and less than or equal to 25% of the data. To find Q3, we take the median of the upper half of the data:
Q3 = median(172, 173, 175, 179, 182, 190, 191, 195) = 190
The maximum value is the largest value in the dataset, which is 195.
Therefore, the five-number summary for the given data is Min = 107, Q1 = 138, M = 175, Q3 = 190, and Max = 195.
To know more about Median visit:
brainly.com/question/1153198
#SPJ1
I don’t know what I’m doing
Answer:
29.12 square cm
Step-by-step explanation:
Area of equilateral triangle:Side = a = 8.2 cm
[tex]\boxed{\bf Area \ of \ equilateral \ triangle = \dfrac{\sqrt{3}}{4}a^2}[/tex]
[tex]\sf = \dfrac{\sqrt{3}}{4}*8.2*8.2\\\\= \sqrt{3}*4.1 * 4.1\\\\= 1.732 * 4.1 *4.1\\\\= 29.12 \ cm^2[/tex]
An arch of a bridge is made up by bending a steel beam into the shape of a semi circle 20m
the length of the steel beam is approximately 31.4 meters to the nearest meter.
The length of the steel beam is equal to the circumference of the semi-circle formed by bending the beam into the shape of an arch.
The formula for the circumference of a circle is:
C = πd
Where C is the circumference, π is the value of pi, and d is the diameter of the circle.
Since the arch is a semi-circle, the diameter is equal to the span of the arch, which is 20m. So we can calculate the circumference of the arch as follows:
C = πd/2
= 3.14 x 20m / 2
= 31.4m
Therefore, The steel beam measures, to the nearest meter, 31.4 meters in length.
To learn more about circumference click here
brainly.com/question/28757341
#SPJ4
Complete Question
An arch of a bridge is made by bending a steel beam into the shape of a semi circle, if the span (diameter) of the arch in 20m, use the value 3.14 for pi to find the length of the steel beam to the nearest meter.
Help please & thanks
The function f(t)=−5t^2+20t models the approximate height of an object t seconds after it is launched. Which of the following equations correctly shows the quadratic formula being used to determine the number of seconds it will take for the objects to be at a height of 18 feet after launch?
The equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.
What is trigοnοmetric equatiοns ?Trigοnοmetric equatiοns are equatiοns that invοlve trigοnοmetric functiοns such as sine, cοsine, tangent, etc. These equatiοns usually invοlve finding values οf the unknοwn angle(s) that satisfy the given equatiοn. They can be sοlved using algebraic techniques οr by using the prοperties οf trigοnοmetric functiοns.
Accοrding tο the given infοrmatiοn:
The given functiοn is [tex]f(t) = -5t^2 + 20t[/tex], which mοdels the height οf an οbject in feet as a functiοn οf time in secοnds.
Tο find the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch, we need tο sοlve the equatiοn [tex]-5t^2 + 20t = 18[/tex].
Tο sοlve this quadratic equatiοn using the quadratic fοrmula, we first identify the values οf a, b, and c frοm the general fοrm οf a quadratic equatiοn, [tex]ax^2 + bx + c = 0[/tex].
In this case, a = -5, b = 20, and c = -18. Substituting these values intο the quadratic fοrmula, we get:
[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]
Plugging in the values οf a, b, and c, we get:
[tex]t = (-20 \± \sqrt{+(20^2 - 4(-5)(-18)})) / 2(-5)[/tex]
Simplifying this expressiοn, we get:
[tex]t = (-20 \± \sqrt{(400 - 360))} / (-10)[/tex]
[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]
[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]
[tex]t = 2 \± 0.632[/tex]
Therefοre, the twο pοssible values οf t are:
t = 2 + 0.632 = 2.632 secοnds
t = 2 - 0.632 = 1.368 secοnds
Therefοre, the equatiοn that cοrrectly shοws the quadratic fοrmula being used tο determine the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch is:
[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]
[tex]t = (-20 \± \sqrt{(20^2 - 4(-5)(-18))}) / 2(-5)[/tex]
[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]
[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]
t = 2 ± 0.632
Therefοre, the equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.
To know more about trigonometric equations visit :
brainly.com/question/30710281
#SPJ1
When a researcher draws conclusions about a population based on the results of a test on a sample, he or she is most likely using which of the following? a) inductive statistics b) deductive statistics c) descriptive statistics d) inferential statistics
When a researcher draws conclusions about a population based on the results of a test on a sample, he or she is most likely using inferential statistics. Therefore Option A is correct.
Inferential statistics: It involves using sample data to make inferences or draw conclusions about a population. In this case, the researcher is using the results from the sample to make inferences about the population from which the sample was drawn.
Deductive statistics, inductive statistics, and descriptive statistics are other branches of statistics that are used for different purposes.
Deductive statistics:Deductive statistics involves starting with a general principle or theory and testing it with data, Inductive statistics:Inductive statistics involves starting with data and using it to develop a theory or principle. Descriptive statistics: Descriptive statistics involves summarizing and describing data using measures such as mean, median, and standard deviation.Therefore the researcher draws a conclusion to use inferential statistics about a population based on test of sample.Option A is correct.
To Learn more about the 'statistics':
https://brainly.com/question/14724376
#SPJ11
please answer i have 5 minutes i need an answer FAST!!!
(8.15x4 divided by 5) x 3.2 = _____.
Answer:
20.864
Step-by-step explanation:
8.15 x 4 is 32.6. I used a calculator but what I would do if I were solving on paper would be to double it, and then double it again.
Then, we divide 32.6 by five to get 6.52. I did this with a calculator, but if I were solving on paper, I would divide by 10 (move decimal point), and then double it.
Finally, we muliply 6.52 by 3.2. I did this with a calculator and got 20.864, but if I was doing this on paper, I would just solve using standard form!
Let me know if this helped by hitting brainliest! If you have any questions, comment and I'll get back to you ASAP.
rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?
Answer:
3 pounds of coffee.
Step-by-step explanation:
Equation
y = -7.37x + 80
substitute 57.89 for y
57.89 = -7.37 + 80 Subtract 80 from both sides
57.89 - 80 = -7.37 + 80 - 80
-22.11 = -7.37x Divide both sides by -7.37
3 = x
3 pound of coffee
Helping in the name of Jesus.
Answer:
rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?
Step-by-step explanation:
Let's first find out how much money Rita spent on coffee:
$80 (initial balance) - $57.89 (remaining balance) = $22.11 spent on coffee
Now, let x be the number of pounds of coffee that Rita bought. Since the coffee costs $7.37 per pound, we can set up the equation:
$7.37x = $22.11
Solving for x, we can divide both sides by $7.37:
x = 3
Therefore, Rita bought 3 pounds of coffee.
Suppose that a fair, 6 sided die is rolled. Let X indicate the event that an odd number is rolled in other words, X = 1 if an odd number is rolled and X = 0 otherwise). Let Y indicate the event that 3, 4, or 5 is rolled (in other words, Y = 1 if 3, 4 or 5 is rolled and Y = 0 otherwise). Find P(X = 0, y = 1). a. 2/3 b. 176 C.1/3 d. 5/6 e. 1/2
Option (c) 1/3 is the correct answer.Let us first understand the given problem,It is given that the fair 6-sided die is rolled and let X indicates the event that an odd number is rolled and Y indicates the event that 3,4, or 5 is rolled.
P(X=0,Y=1)Solution:When an odd number is not rolled, then an even number is rolled. So, the possible even numbers that can be rolled on a die are 2,4 and 6. Therefore,X = 0, when an even number is rolledY = 1, when 3, 4 or 5 is rolledLet's find P(X=0,Y=1).P(X = 0, Y = 1) = P(rolling 4) = 1/6The sample space for a fair die will be {1,2,3,4,5,6}.
The odd numbers are {1,3,5}. Therefore,P(X = 1) = probability of getting an odd number= 3/6 = 1/2 (3 possible odd numbers out of 6)P(X = 0) = probability of getting an even number= 3/6 = 1/2 (3 possible even numbers out of 6)P(Y = 1) = probability of getting 3, 4, or 5= 3/6 = 1/2 (3 possible numbers out of 6)P(Y = 0) = probability of getting 1, 2, or 6= 3/6 = 1/2 (3 possible numbers out of 6)P(X = 0, Y = 1) = P(rolling 4) = 1/6. Therefore, P(X=0, Y=1) = 1/6Therefore, option (c) is correct.
Learn more about odd number:
https://brainly.com/question/31057068
#SPJ11
two fifths of 60 is what number
Answer:
I hope this helps please rate my answer
Step-by-step explanation:
2/5×60
2×12=24
The number of employees for a certain company has been decreasing each year by 5%. If the company cumently has 860 employees and this rate continues, find the number of employees in 10 years
The number of employees in 10 years will be approximately
(Round to the nearest whole number as needed)
Based on the exponential decay equation, the number of employees for the company that has been decreasing yearly by 5%, will in 10 years be approximately 515.
What is exponential decay equation?The exponential decay equation or function gives the value in t years that has a constant ratio of decrease.
Exponential decay equation is one of the two exponential functions. The other is the exponential growth equation.
The annual decrease in the number of employees = 5%
The current number of employees in the company = 860
The expected time = 10 years.
The exponential decay equation is as follows, y = 860 x 0.95^10.
y = 860 x 0.95^10 = 515
Learn more about exponential functions at https://brainly.com/question/30127596
#SPJ1
a clock has an hour, minute, and second hand, all of length $1$. let $t$ be the triangle formed by the ends of these hands. a time of day is chosen uniformly at random. what is the expected value of the area of $t$?
The expected value of the area of t is 1/12.
The length of the hands of the clock is 1. If a time of day is chosen uniformly at random, what is the expected value of the area of t?
The area of the triangle is given by the formula
A=1/2 ab sinC.
Here, we use Law of cosines to determine the angle C, which is enclosed by the hour and minute hands.
[tex](\cos C)_{h,m}=\frac{h^2+m^2-1}{2hm}[/tex]
So, we can write the expected value of the area of t as
[tex]\begin{aligned}E[A]&=\int_{0}^{2\pi}\frac{1}{2}(1)(1)sinC\left(\frac{1}{12}+\frac{1}{720}((Cos C)_{h,m})^2\right)dC \\ &=\frac{1}{24\pi}\int_{0}^{2\pi}(sinC+sin(11C))dC \\ &=\frac{1}{12}\end{aligned}[/tex]
Hence, the expected value of the area of t is 1/12.
To know more about area: https://brainly.com/question/27843019
#SPJ11
QS and TV areparallellines. P Q R S T U V W Which angles are vertical angles?
The required angles ∠SRP and ∠TUW are alternate exterior angles.
What is alternate exterior angles?Alternate exterior angles are a pair of angles that lie on opposite sides of a transversal line that intersects two other lines. Specifically, the angles are exterior to the two intersecting lines and lie on opposite sides of the transversal.
More formally, if two parallel lines are intersected by a transversal, then alternate exterior angles are the pair of angles that are:
On opposite sides of the transversal line.
Outside of the two parallel lines.
Congruent to each other.
These angles are called "alternate" because they are on opposite sides of the transversal and "exterior" because they are outside of the two parallel lines. The congruence of the angles is a result of the parallel lines creating equal corresponding angles.
So,∠SRP and ∠TUW are alternate exterior angles.
To know more about Angles visit:
brainly.com/question/28451077
#SPJ1
5x - 16xy +16y to the power of 2* +7x + 17y to the power of 2*
(16y and 17y are both to the power of 2)
The value of variable x for the given equation, 5x - 16xy +16y² +7x + 17y² is −33 y²/ 4(3 − 4y).
Give a brief account on algebraic expression.An algebraic expression is the idea of using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here. An algebraic expression said to be a combination of variables and constants. Any multiplied value that is prefixed to a variable is a factor. An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.).
5x - 16xy +16y² +7x + 17y²
= 12x - 16xy + 33y²
Using the Quadratic Formula, we have:
x = −33 y²/ 4(3 − 4y)
To know more about Quadratic Formula, visit:
https://brainly.com/question/22364785
#SPJ1
Ted is five times as old as Rosie was when Ted was Rosie's age. When Rosie
reaches Ted's current age, the sum of their ages will be 72. Find Ted's current age.
Answer:
45 yo
Step-by-step explanation:
Let's start by defining some variables to represent the ages of Ted and Rosie:
- Let's call Ted's current age "T"
- Let's call Rosie's current age "R"
From the problem statement, we know that:
- Ted is five times as old as Rosie was when Ted was Rosie's age. Written as an equation, this becomes:
T = 5(R - (T - R))
Simplifying this equation, we get:
T = 5(R - T + R)
T = 10R - 5T
- When Rosie reaches Ted's current age, the sum of their ages will be 72. Written as an equation, this becomes:
R + T = 72 - T
We now have two equations with two variables. We can use substitution to solve for T.
Substitute the second equation into the first equation to eliminate R:
T = 10R - 5T
T = 10(72 - T) - 5T
T = 720 - 15T
16T = 720
T = 45
Therefore, Ted's current age is 45.
You construct three 88% confidence intervals as follows: A) A t-interval with 6 degrees of freedom. B) A t-interval with 2 degrees of freedom. C) A z-interval Assuming the mean and standard deviation are the same for all three intervals, write the three intervals (A, B, and C) in order, from narrowest to widest.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. A low standard deviation means data are clustered around the mean, and a high standard deviation indicates data are more spread out.
A) A t-interval with 6 degrees of freedom: Mean +/- 0.76 * Standard Deviation
B) A t-interval with 2 degrees of freedom: Mean +/- 1.82 * Standard Deviation
C) A z-interval: Mean +/- 1.645 * Standard Deviation
Therefore, the intervals in order from narrowest to widest are:
A) A t-interval with 6 degrees of freedom,
C) A z-interval, and
B) A t-interval with 2 degrees of freedom.
The order from narrowest to widest is:
C) z-interval
A) t-interval with 6 degrees of freedom
B) t-interval with 2 degrees of freedom
Also,
The z-interval will be the narrowest because the z-distribution has a smaller variance than the t-distribution. The t-interval with 6 degrees of freedom will be wider than the z-interval because the t-distribution has a larger variance than the z-distribution.
Finally, the t-interval with 2 degrees of freedom will be the widest because the t-distribution has the largest variance when degrees of freedom is low.
To learn more about “Standard Deviation” refer to the: https://brainly.com/question/475676
#SPJ11
12x + 376; 15x + 280.
When would they have the same amount
Answer: 32,760
Step-by-step explanation
12x+376
15x+280
when you put it in demos both of the line cross and you can see you answer when you click were the lines cross.if you use the giving value it would be 750
Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.x2+y2=100a) Find dy/dt when x=6, y=8 given that dx/dt=4.b) Find dx/dt when x=8, y=6 given that dy/dt=-2.
a) When x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.
Using implicit differentiation, we have:
2x(dx/dt) + 2y(dy/dt) = 0
Solving for dy/dt, we get:
dy/dt = -(x/y)(dx/dt)
Substituting x = 6, y = 8, and dx/dt = 4, we get:
dy/dt = -(6/8)(4) = -3
Therefore, when x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.
b) Using implicit differentiation again, we have:
2x(dx/dt) + 2y(dy/dt) = 0
Solving for dx/dt, we get:
dx/dt = -(y/x)(dy/dt)
Substituting x = 8, y = 6, and dy/dt = -2, we get:
dx/dt = -(6/8)(-2) = 1.5
Therefore, when x = 8 and y = 6, and dy/dt = -2, the value of dx/dt is 1.5.
To find the values of dy/dt and dx/dt, we used implicit differentiation, which is a technique used to find the derivative of an equation that is not expressed in the form y = f(x).
In this case, we had the equation x^2 + y^2 = 100, and we differentiated both sides of the equation with respect to t. Then, we solved for the required derivative using the given values of x, y, and the other derivative.
For more questions like Function click the link below:
https://brainly.com/question/12431044
#SPJ11
The simple interest on a certain sum at 5% per annum for 3 years and 4years differ by rupees 82 find the sum
The principal sum is Rs. 1640 if the difference in simple interest between 3 years and 4 years is Rs. 82 at a rate of 5% per annum.
Let x be the principal sum. According to the problem, the difference in simple interest between 3 years and 4 years is Rs. 82. This means that the interest earned in the fourth year is Rs. 82 more than the interest earned in the third year.
Using the formula for simple interest, we can calculate the interest earned in each year:
Simple interest for 3 years = (x * 5% * 3) = 0.15x
Simple interest for 4 years = (x * 5% * 4) = 0.2x
The difference between the two is:
0.2x - 0.15x = 0.05x
We are given that this difference is equal to Rs. 82, so:
0.05x = 82
Solving for x, we get:
x = 82 / 0.05 = 1640
Therefore, the principal sum is Rs. 1640.
Learn more about the simple interest here: brainly.com/question/25845758
#SPJ4
13x • 4x^2y
Does it equal 52x^2y? Or can you not combine them?
We can simplify the expressiοn tο [tex]52x^3y,[/tex] nοt [tex]52x^2y[/tex].
In math, hοw dο yοu sοlve expressiοns?Yοu must substitute a number fοr each variable and perfοrm arithmetic οperatiοns tο evaluate an algebraic expressiοn. Because 6 + 6 = 12, the variable x in the preceding example is equal tο 6. We can evaluate the expressiοn after replacing the variables with their values if we knοw their values.
We can use expοnent prοperties tο simplify the expressiοn [tex]13x[/tex]• [tex]4x^2y[/tex]:
[tex]13x[/tex]•[tex]4x^2y = 13[/tex] • [tex]x^1[/tex]• 4 • [tex]x^2[/tex]•[tex]y^1[/tex]
[tex]= 52[/tex]• [tex]x^3[/tex]•[tex]y^1[/tex]
As a result, we can simplify the expressiοn tο [tex]52x^3y[/tex] rather than[tex]52x^2y.[/tex]
To know more about Expression visit:
brainly.com/question/28170201
#SPJ1