Answers
Answer:
A and B the top two
Step-by-step explanation:
3/(x - 4) = (x - 5)/x Cross Multiply
3x = (x - 4)(x - 5) Remove the brackets
3x = x^2 - 5x - 4x + 20 Combine the right
3x = x^2 - 9x + 20 Subtract 3x from both sides
0 = x^2 - 9x - 3x + 20 Combine
0 = x^2 - 12x + 20 The right side factors
(x - 10)(x - 2)
x - 10 = 0
x = 10
x - 2 = 0
x = 2
Related Questions
There are 200 kids in the 7th grade at smith middle school. If 25% of them purchase a school t-shirt that costs $20, how much money did the 7th grade spend on t-shirts?
Answers
Answer:
$1,000.
Step-by-step explanation:
200 kids divided by 25% or 4 = 50 then 50 x 20 = 1,000.
The table shows the number of students graduating from a university in selected years. Use a calculator to write a cubic model for the number of graduates in a given year since 1990. Then use the model to estimate the number of graduates in 2001.
P(x) ≈ 27.13x3 − 473.44x2 + 2829.33x − 4381.69
The estimated the number of graduates in 2001 is 5,565.
P(x) ≈ −473.44x2 + 2829.33x − 4381.69
The estimated the number of graduates in 2001 is 4,133.
P(x) ≈ 473.44x2 − 2829.33x + 4381.69
The estimated the number of graduates in 2001 is 3,535.
P(x) ≈ −27.13x3 + 473.44x2 − 2829.33x + 4381.69
The estimated the number of graduates in 2001 is 2,504.
Answers
The cubic regression equation is y = 27.13x^3 - 473.44x^2 + 2829.33x - 4381.69 and the estimated the number of graduates in 2001 is 5565
How to determine the cubic regression equationFrom the question, we have the following parameters that can be used in our computation:
See attachment
Using a graphing calculator, we have the following summary:
a = -4381.6892b = 2829.3314c = -473.4406d = 27.1349Standard Error of Regression: 81.5267Coefficient of determination R²: 0.9978The model from the above summary is
y = 27.1349x^3 - 473.4406x^2 + 2829.3314x - 4381.6892
Approximate
y = 27.13x^3 - 473.44x^2 + 2829.33x - 4381.69
In the year 2001, we have
x = 11
So, we have
y = 27.13 * 11^3 - 473.44 * 11^2 + 2829.33 * 11 - 4381.69
Evaluate
y = 5565
The estimated the number of graduates in 2001 is 5565
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Use the graph below to determine the equation of the circle in (a) center-radius form and (b) general form.
Answers
9514 1404 393
Answer:
(x +5)² +(y -3)² = 25x² +y² +10x -6y +9 = 0Step-by-step explanation:
The "center-radius" form is ...
(x -h)² +(y -k)² = r² . . . . . . . circle with center (h, k) and radius r
The graphed circle has its center at (-5, 3) and a radius of 5. Putting these numbers into the above form gives the equation ...
(x +5)² +(y -3)² = 25 . . . . center-radius form
Expanding the parentheses, we get ...
x² +10x +25 +y² -6y +9 = 25
Subtracting 25, and putting in general form, the equation becomes ...
x² +y² +10x -6y +9 = 0 . . . . general form
_____
Additional comment
General form is f(x, y) = 0, where the terms of f(x, y) are lexicographical order and decreasing degree.
x=1÷81 p=1÷4 and q=3,find the value of xqp
Answers
The value of xqp as required in the task content is: 3 / 32.
What is the value of xqp?As evident in the task content;
x = 1 ÷ 81 p = 1 ÷ 4 and q = 3.
Therefore, x = 1 / 8, p = 1 / 4 and q = 3.
Hence, it follows that the value of xqp can be determined as follows;
xqp = 1/8 × 1/4 × 3
xqp = 3 / (8 × 4)
xqp = 3 / 32.
Ultimately, the value of xqp is; 3 / 32.
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A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce.
Give the answers correct to four decimals.
a) What is the probability the contents of a single cup will be greater than 12.1 ounces?
b) If a sample of 9 cups is selected, what is the probability that the mean of the sample will be greater than 12.1 ounces?
Answers
a) The probability is 0.308538.
b) The probability is 0.066807.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
mean= 12 ounce
standard deviation = 0.2 ounce
a) The probability the contents of a single cup will be greater than 12.1 ounces
P( x> 12.1 ounce) = P( x \(- \mu_x/ \sigma_x\) > (12.1- 12)/ 0.2)
= P( z< 0.1/ 0.2)
= P( z< 0.5)
= 0.308538
b) If a sample of 9 cups is selected
then, P( x> 12.1) = P( x \(- \mu_x/( \sigma_x/ \sqrt{n} )\) > (12.1- 12)/ (0.2/ √9))
= 0.066807
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using the table find the value of y when x=2
Answers
Answer:
y = 8 when x = 2
Step-by-step explanation:
y = 4x
The type of experimental design where the assignment of experimental units to treatment and control groups is random is called a(n) __________.
Answers
The type of experimental design where the assignment of Experimental units to treatment and control groups is random is called a randomized controlled trial (RCT).
The type of experimental design where the assignment of experimental units to treatment and control groups is random is called a randomized controlled trial (RCT).
Randomized controlled trials are widely used in various fields of research, including medicine, psychology, and social sciences. They are considered the gold standard for evaluating the effectiveness of interventions or treatments. The key feature of an RCT is the random assignment of participants or experimental units to either the treatment group or the control group.
Randomization helps to ensure that the treatment and control groups are similar in terms of both observed and unobserved characteristics, reducing the potential for bias and confounding variables. By randomly assigning participants, researchers can make causal inferences about the effects of the treatment, as any observed differences between the groups can be attributed to the intervention.
In an RCT, experimental units can be individuals, groups, organizations, or any other defined units depending on the research context. The random assignment process involves using a randomization procedure, such as coin flipping, random number tables, or computer-generated randomization, to assign participants to the treatment and control groups.
By comparing the outcomes or responses of the treatment and control groups, researchers can determine the effectiveness or impact of the intervention being studied. Statistical techniques, such as hypothesis testing and analysis of variance, are commonly used to analyze the data collected from the RCT and draw conclusions.
a randomized controlled trial is the type of experimental design where the assignment of experimental units to treatment and control groups is random. It is a rigorous approach to evaluating the effects of interventions and minimizing biases, providing robust evidence for decision-making and policy development.
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A coach divided his team into two groups of equal size.
.
of the first group drinks at least 2 glasses of water a day
• 75% of the second group drinks at least 2 glasses of water a day.
What fraction of the team drinks at least 2 glasses of water a day?
Answers
Applying the percentages, and considering that 70% of the first group drinks at least 2 glasses of water a day, it is found that 0.725 = 72.5% of the team drinks at least 2 glasses of water a day.
The team is divided into two equal groups, hence, each represents 50%.
The percentages associated with drinking at least 2 glasses of water a day is:
70% of 50%(first group)75% of 50%(second group)Hence, applying the weighed percentage, the total percentage is:
\(T = 0.7(0.5) + 0.75(0.5) = 0.725\)
0.725 = 72.5% of the team drinks at least 2 glasses of water a day.
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A painting crew bought 30 gal of paint for a job. The crew members used 3 gal of paint per hour until they used all the paint.
Which sketch represents this situation?
Answers
Answer:
Top top right graph is the correct answer.
Step-by-step explanation:
If the crew bought 30 gallons of paint and used 3 gallons per hour, they would run out in 10 hours. The only graph that shows this is the top right graph.
Check
3 x 10 = 30
^^My answer is correct ;)
Find a solution to the linear equation 6x+y=6
Answers
Answer:
y = -6x + 6
Step-by-step explanation:
Unless you are asking for solving the linear equation itself, the answer would be y = -6x + 6.
If you were trying to set up systems and then solve for actual solutions, you would need two equations. I will go with solving the linear equation, but if you meant solving systems, the answer cannot be found.
determine if the graph is symmetric above the x-axis the y-axis or the originr=-5-5costheta
Answers
Step 1: Test for symmetry about the x-axis by Replacing θ with -θ in the equation
The curve r=f(θ) is symmetrical about the x-axis if the equation r=f(θ) is unchanged by replacing θ with -θ
\(r=5-5\cos (-\theta)=5-5\cos \theta\text{ (}\cos (-\theta)=\cos \theta)\)Hence, the curve is symmetrical about the x-axis
Step 2 Test for symmetry about the y-axis by Replacing θ with -θ and r with -r in the equation
The curve r=f(θ) is symmetrical about the x-axis if the equation r=f(θ) is unchanged by replacing θ
with -θ and r with -r
\(\begin{gathered} -r=5-5\cos (-\theta)=5-5\cos \theta \\ \text{ Therefore} \\ r=-5+5\cos \theta \\ \text{ Since } \\ -5+5\cos \theta\ne5-5\cos \theta \\ \text{ then there is no symmetry about the y-axis} \end{gathered}\)Step 2 Test for symmetry about the origin by replacing r with -r in the equation
The curve r=f(θ) is symmetrical about the origin if the equation r=f(θ) is unchanged by replacing r
with -r
\(\begin{gathered} -r=5-5\cos \theta \\ \text{this implies that} \\ r=-5+5\cos \theta \\ \text{ Since} \\ -5+5\cos \theta\ne5-5\cos \theta \\ \text{ then there is no symmetry about the origin} \end{gathered}\)
Therefore, the curve is symmetrical only about the x-axis.
Hence, the right option is the first one.
Beth is considering two job offers. One has an annual salary of $61.1K and the other has an annual salary of $63.4K. What is the difference in the weekly pay for these two job? (K means $1,000, so $61.1K is $61,100 for example) *
Answers
Answer: The difference is approximately $44. Remember that is not an exact amount because the weeks are approximated and the second offer was also approximated.
Step-by-step explanation:
If one has $61,100 and the other has 63,400 annually which means that is the amount they will be offered a year. So first we need to determine how many weeks are in a year.There are approximately 52 weeks in one year so we will divide the salaries by 52 to find how much they each offer in one week.
First Offer: 61,100 / 52 = 1175
Second Offer: 63,400/52= approximately 1219
Now find the difference between the numbers
1219. - 1175 = $44
The difference in weekly pay for these two job will be around $0.04k.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Number of weeks in 1 year = number of weeks in 1 month × 12
Number of weeks in 1 year = 4 × 12 = 48
Annual salary in the first job = $61.1k
So weekly salary of first job =$1.28k
Annual salary in the second job = $63.4k
So weekly salary of second job = $1.32k per week
Difference between weekly pay = 1.32 - 1.28 = 0.04k
Hence "The difference in weekly pay for these two job will be around $0.04k".
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Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run?
A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by.
Select all that apply.
You know the difference in the distances the boys ran, so this is a subtraction problem.
You are finding the total distance the boys ran, so this is an addition problem.
Dean ran part of the distance Sam ran, so this is a multiplication problem.
The correct equation is s + 2.3 = 6.8.
The correct equation is s – 2.3 = 6.8.
The correct equation is 2.3s = 6.8.
Answers
Answer:
A,E
Step-by-step explanation:
Operation: Minus
To find how far Sam ran, we need to subtract 2.3 from Dean's distance of 6.8 km.
6.8 km - 2.3 km = 4.5 km
Therefore, Sam ran 4.5 km, since Dean ran 2.3 km fewer than Sam.
Answer:
a and e
Step-by-step explanation:
got it right on homework
Line segment AB Is 8 cm. Find the circumference. Use 3.14 for pi
Answers
Calculate 1 + 3 + 5 +...+ (2n - 1) for several natural numbers n.
Answers
Answer:
The solutions for 1 + 3 + 5 +...+ (2n - 1), for the first 10 natural numbers are given in the explanation section below.
Step-by-step explanation:
To calculate 1 + 3 + 5 +...+ (2n - 1) for several natural numbers n, we will use several natural numbers to represent n.
For n= 1,
2n - 1 = 2(1) - 1 = 2 - 1 = 1
Hence, 1 = 1
For n = 2,
2n - 1 = 2(2) - 1 = 4 - 1 = 3
Hence, 1 + 3 = 4
For n = 3,
2n - 1 = 2(3) - 1 = 6 - 1 = 5
Hence, 1 + 3 + 5 = 9
For n = 4,
2n - 1 = 2(4) - 1 = 8 - 1 = 7
Hence, 1 + 3 + 5 + 7 = 16
For n = 5,
2n - 1 = 2(5) - 1 = 10 - 1 = 9
Hence, 1 + 3 + 5 + 7 + 9 = 25
For n = 6,
2n - 1 = 2(6) - 1 = 12 - 1 = 11
Hence, 1 + 3 + 5 + 7 + 9 + 11 = 36
For n = 7,
2n - 1 = 2(7) - 1 = 14 - 1 = 13
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
For n = 8,
2n - 1 = 2(8) - 1 = 16 - 1 = 15
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64
For n = 9,
2n - 1 = 2(9) - 1 = 18 - 1 = 17
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81
For n = 10,
2n - 1 = 2(10) - 1 = 20 - 1 = 19
Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100
Alberto left the airport and traveled toward the capital. One hour later Danielle left traveling 10 km/h faster in an effort to catch up to him. After five hours Danielle finally caught up. What was Alberto's average speed?
Answers
Answer:
Step-by-step explanation:
Alberto traveled v km/h.
After 1 hour they are v km apart.
Danielle travels (v+10) km/h.
The distance between them decreases by 10 km/h.
They meet in 5 hours, after Danielle has traveled 5v+50 km and Alberto has traveled 6v km.
6v = 5v+50
v = 50 km/h
Alberto travels 50 km/h
Use the t-distribution to find a confidence interval for a mean mu given the relevant sample results. Give the best point estimate for mu, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A 95% confidence interval for mu using the sample results x-bar equals 76.4, s = 8.6, and n = 42.
Point estimate = ?
Margin of error = ?
Answers
Answer:
Point estimate = 76.4
Margin of Error = 2.680
Step-by-step explanation:
Given that distribution is approximately normal;
The point estimate = sample mean, xbar = 76.4
The margin of error = Zcritical * s/√n
Tcritical at 95%, df = 42 - 1 = 41
Tcritical(0.05, 41) = 2.0195
Margin of Error = 2.0195 * (8.6/√42)
Margin of Error = 2.0195 * 1.327
Margin of Error = 2.67989
Margin of Error = 2.680
Find the circumference of a circle with a diameter of meters. Use as an approximation for . Round your answer to the nearest whole meter. Enter only the number.
Answers
Solution:
The circumference of a circle is expressed as
\(\begin{gathered} circumference=\pi\times d \\ where\text{ d}\Rightarrow diameter\text{ of the circle} \end{gathered}\)Given that the diameter of the circle is 13 meters, we have
\(d=13\)By substitution, we have
\(\begin{gathered} circmference=\pi\times13 \\ where\text{ }\pi=3.14 \\ thus, \\ circumference=3.14\times13 \\ =40.82 \\ \therefore \\ circumference\approx41\text{ meters} \end{gathered}\)Hence, the circumference of the circle, to the nearest meter, is
\(41\)+83--95 x + 7+72÷-9 what is the answer
Answers
Answer:
7.4
Step-by-step explanation:
Not completely sure because that equation is really hard to read. You might have put it in wrong.
Answer:
-95x + 91
Step-by-step explanation:
72/9 = 8
83 - 95x + 8
91 - 95x or -95x + 91
a 3 foot wide wood deck will be built around a rectangular shaped pool that measures 15 feet by 30 feet. the resulting deck shape is also rectangular. if the lumbar cost is $10 square yard. what is the cost of the wood for the deck?
Answers
Answer:
she has some big feet
Step-by-step explanation:
do u know th
Tina pet sits to earn extra money. She charges a flat service fee of $20, plus $15 per day. If one of her customers spent less than $125, which of the following inequalities could be used to solve for x, the number of days the customer paid for pet sitting?
Answers
Therefore, **x < 7** is the inequality that may be utilized to find x
What is inequality?A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).
For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".
Let x represent how many days the client paid for pet sitting.
$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.
We are aware that the customer's purchase was under $125. Consequently, we can write:
20 + 15x < 125
Putting this disparity simply:
15x < 105
x < 7
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As part of an environmental impact study, a power company wants to estimate the difference in mean water temperature between the discharge of its plant and the offshore waters. How many sample measurements must be taken at each site to estimate the true difference between means to within .2°C with 95% confidence? Assume that the standard deviation in readings is about 1.5°C at each site and the same number of readings will be taken at each site.
Answers
Using the z-distribution, it is found that 217 sample measurements should be taken at each site.
The margin of error of a z-confidence interval is given by:
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which:
z is the critical value. \(\sigma\) is the population standard deviation. n is the sample size.The first step is finding the critical value, which is z with a p-value of \(\frac{1 + \alpha}{2}\), in which \(\alpha\) is the confidence level.
In this problem, \(\alpha = 0.95\), thus, z with a p-value of \(\frac{1 + 0.95}{2} = 0.975\), which means that it is z = 1.96.
Estimate of the standard deviation of 1.5, thus, \(\sigma = 1.5\).
We want the sample for a margin of error of 0.2ºC, thus, we have to solve for n when \(M = 0.2\).
\(M = z\frac{\sigma}{\sqrt{n}}\)
\(0.2 = 1.96\frac{1.5}{\sqrt{n}}\)
\(0.2\sqrt{n} = 1.96(1.5)\)
\(\sqrt{n} = \frac{1.96(1.5)}{0.2}\)
\((\sqrt{n})^2 = (\frac{1.96(1.5)}{0.2})^2\)
\(n = 216.1\)
Rounding up:
217 sample measurements should be taken at each site.
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Given: △ABC, m∠A=60°
m∠C=45°, AB = 9
Find: Perimeter of △ABC
Area of △ABC
Answers
Answer:
Hope this helps
Step-by-step explanation:
Dina wants to earn money to save for a car so she decided to make beaded bracelets to sell at a local Farmer’s Market. She rented a table for $15 and set up her shop. Each bracelet that she makes cost approximately $1.75 for materials. She sells each bracelet for $6.00.
How much profit will she make from each bracelet, not including the table rental?
(A.) $1.75
(B.) $6.00
(C.) $4.25
(D.) $7.75
Answers
Set up a proportion and solve the following!
Two out of five students in the ninth grade have braces. If there are 325 students in the ninth grade, how many have braces?
Answers
Which is the quotient for
2
.
21
÷
0
.
34
?
A.
0.65
B.
6.05
C.
6.5
D.
65
Answers
Answer:
The answer is 6.5
Step-by-step explanation:
What is 65% written as a decimal?
A. 0.065
B. 0.65
C. 6.5
D. 65
Answers
Answer:
b.0.65
Step-by-step explanation:
i think it is I'm sorry if it's not
Answer:
b. 0.65
Step-by-step explanation:
Find the domain of the rational expression: 6-x/4x+20
Answers
The domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.
To find the domain of a rational expression, we need to identify any values of x that would result in division by zero. Division by zero is undefined in mathematics
In this case, we need to set the denominator, 4x+20, equal to zero and solve for x:
4x + 20 = 0
Subtract 20 from both sides:
4x = -20
Divide both sides by 4:
x = -5
Therefore, the value x = -5 makes the denominator zero.
Now, we need to consider the values of x for which the denominator is not zero. Since the denominator is a linear expression (a polynomial of degree 1), it is defined for all real numbers except x = -5.
So, the domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.
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If an investment over eight years at a rate of $160.00 results in a final balance of $660.00, what was the original investment?
Answers
How did you do this question?
Answers
Answer:
R = ∞
I = (-∞, ∞)
Step-by-step explanation:
Use the ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│
lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] / [xⁿ⁺⁵ / (2n!]│
lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] × (2n! / xⁿ⁺⁵)│
lim(n→∞)│x 2n! / (2(n+1)!)│
lim(n→∞)│n! / (n+1)!││x│
lim(n→∞) (1 / (n+1))│x│
0
The series converges if the limit is less than 1.
The limit is always less than 1, so the radius of convergence is infinite.
So the interval of convergence is (-∞, ∞).