Answer:
Step-by-step explanation:
Area of rectangle = Length × Width
The given rectangle has a length if x meters
The width of the triangle is (x-3) meters
The area of the rectangle is given as 10 square meters.
Area if rectangle = x(x-3) = 10
Multiplying each term in the parentheses,
x^2 -3x = 10
x^2 -3x -10 = 0
This is a quadratic equation
We will look for two numbers such that when they are multiplied, it will give us -10x^2 and when they are added, it will give -3x. It becomes
x^2 + 2x - 5x -10 = 0
x(x+2)-5(x+2) =0
( x + 2)(x-5) = 0
x = -2 or x = 5
The length of the rectangle cannot be negative so the length is 5 meters
Widith = x+3 = 5-3 = 2 meters
Final answer:
The dimensions of the rectangle are found by solving the quadratic equation derived from the area. The length is 5 meters, and the width is 2 meters, as negative dimensions are not possible.
Explanation:
To find the dimensions of the rectangle with an area of 10 square meters and the sides defined as x and x
- 3, we have derived a quadratic equation x^2 - 3x - 10 = 0 which factors down to (x + 2)(x - 5) = 0. This gives us two possible solutions for x: either x + 2 = 0 or x - 5 = 0. Solving these equations, we find x = -2 or x = 5. Since a rectangle cannot have a negative dimension, we disregard x = -2. Therefore, the length of the rectangle is x = 5 meters and the width is x - 3 = 2 meters.
In a certain carnival game the player selects two balls at random from an urn containing 3 red balls and 9 white balls. The player receives $4 if he draws two red balls and $1 if he draws one red ball. He loses $2 if no red balls are in the sample. Determine the probability distribution for the experiment of playing the game and observing the player's earnings.
The probability to draw two red balls is __, to draw one red ball is __, and to draw zero red balls is __.
Answer:
The probability to draw two red balls = 1/22
The probability to draw one red ball = 9/22
The probability to draw no red ball = 12/22
Step-by-step explanation:
Number of Red balls = 3
Number of White balls = 9
If the player draws two red balls, he receives $4
If the player draws one red ball, he receives $1
If the player draws no red ball, he looses $2
The total number of balls = 3+9
= 12
Let R represent Red balls
Let W represent White balls
The probability that the player earns $4 by picking two red balls is represented as Pr(R1 n R2)
Pr(R1 n R2) = Pr(R1) * Pr(R2)
Pr(R1) = 3/12
= 1/4
Pr(R2) = 2/11(we assume he draws without replacement)
Pr(R1 n R2) = 1/4*2/11
= 2/44
= 1/22
The probability of earning $4 is 1/22
The probability of drawing one red ball is Pr(R1 n W2) or Pr(W1 n R2)
Pr(R1) = 3/12
= 1/4
Pr(W2) = 9/11
Pr(W1) = 9/12
= 3/4
Pr(R2) = 3/11
Pr(R1 n W2) or Pr(W1 n R2) =
(1/4 * 9/11) + (3/4 * 3/11)
= (9/44) + (9/44)
= 18/44
= 9/22
Therefore, the probability of earning $1 is 9/22
The probability that no red ball is chosen is Pr(W1nW2)
Pr(W1) = 9/12
= 3/4
Pr(W2) = 8/12
Pr(W1nW2) = 3/4 * 8/11
= 24/44
= 12/22
therefore. the probability of loosing $2 is 12/22
The probability to draw two red balls is [tex]\(\frac{1}{22}\)[/tex], to draw one red ball is [tex]\(\frac{9}{22}\)[/tex], and to draw zero red balls is [tex]\(\frac{15}{22}\)[/tex].
To find the probability distribution, we need to calculate the probabilities of drawing two red balls, one red ball, and no red balls from the urn containing 3 red balls and 9 white balls. We use combinations to determine these probabilities.
1. Total Possible Combinations:
The total number of ways to choose 2 balls out of 12 is given by the combination formula:
[tex]\[ \binom{12}{2} = \frac{12!}{2!(12-2)!} = \frac{12 \times 11}{2 \times 1} = 66 \][/tex]
2. Probability of Drawing Two Red Balls:
To draw 2 red balls, we select 2 out of the 3 red balls:
[tex]\[ \binom{3}{2} = \frac{3!}{2!(3-2)!} = \frac{3 \times 2}{2 \times 1} = 3 \][/tex]
The probability is:
[tex]\[ P(\text{2 red balls}) = \frac{\binom{3}{2}}{\binom{12}{2}} = \frac{3}{66} = \frac{1}{22} \][/tex]
3. Probability of Drawing One Red Ball:
To draw 1 red ball and 1 white ball, we select 1 out of the 3 red balls and 1 out of the 9 white balls:
[tex]\[ \binom{3}{1} = 3 \quad \text{and} \quad \binom{9}{1} = 9 \][/tex]
The number of ways to draw 1 red and 1 white ball is:
[tex]\[ \binom{3}{1} \times \binom{9}{1} = 3 \times 9 = 27 \][/tex]
The probability is:
[tex]\[ P(\text{1 red ball}) = \frac{\binom{3}{1} \times \binom{9}{1}}{\binom{12}{2}} = \frac{27}{66} = \frac{9}{22} \][/tex]
4. Probability of Drawing Zero Red Balls:
To draw 0 red balls (i.e., both balls are white), we select 2 out of the 9 white balls:
[tex]\[ \binom{9}{2} = \frac{9!}{2!(9-2)!} = \frac{9 \times 8}{2 \times 1} = 36 \][/tex]
The probability is:
[tex]\[ P(\text{0 red balls}) = \frac{\binom{9}{2}}{\binom{12}{2}} = \frac{36}{66} = \frac{18}{33} = \frac{6}{11} = \frac{15}{22} \][/tex]
5. Probability Distribution for Earnings:
Now, we summarize the probabilities and corresponding earnings
- Drawing two red balls: [tex]\(\frac{1}{22}\)[/tex], earning $4
- Drawing one red ball: [tex]\(\frac{9}{22}\)[/tex], earning $1
- Drawing zero red balls: [tex]\(\frac{15}{22}\)[/tex], losing $2
Thus, the correct probability distribution for the experiment of playing the game and observing the player's earnings is:
- Probability to draw two red balls: [tex]\(\frac{1}{22}\)[/tex]
- Probability to draw one red ball: [tex]\(\frac{9}{22}\)[/tex]
- Probability to draw zero red balls: [tex]\(\frac{15}{22}\)[/tex]
2. A stone is an English measure of weight. There are 14 pounds in 1 stone and 2.2 pounds in 1 kilogram. A certain person weighs 9 stone.
(a) If you wanted to convert the person’s weight to kilograms, what conversion factor should you use? Round the conversion to the nearest hundredth. Show your work.
(b) What is the person’s weight in kilograms rounded to the nearest tenth?
Answer:
The answer to your question is 57.3 kg
Step-by-step explanation:
a)
[tex]X stones \frac{14 pounds}{1 stone} \frac{1 kilogram}{2.2 pounds}[/tex]
= [tex]\frac{14}{2.2}[/tex]
= 6.36 X stones
b) Weight = 6.36 (x)
x = 9 stones
Weight = 6.36 (9)
= 57.3 kg
You have a gift card for a coffee shop worth $90. Each day you use the card to get a coffee for $4.10. Write an explicit formula to represent the amount of money available as an arithmetic sequence. What is the value of the card after you buy your 8th coffee?
Answer: The value of the card after you buy your 8th coffee will be $61.3
Step-by-step explanation:
The worth of the gift card for the coffee shop is $90. Each day you use the card to get a coffee for $4.10. This means that the worth of the gift card is reducing by $4.10 each day. This rate is in arithmetic progression.
The formula for the nth term of an arithmetic sequence, Tn is expressed as
Tn = a + (n-1)d
Where a is the first term
d is the common difference
n is the number of days
From the information given,
a = $90
d = - $4.1
The explicit formula representing the amount of money available will be
Tn = 90 - 4.1(n - 1)
The value of the card after you buy your 8th coffee will be
T8 = 90 - 4.1(8 - 1) = T8 = 90 - 4.1×7
T8 = 90 - 28.7
T8 = $61.3
I’d appreciate the help!
Answer:
[tex]\displaystyle 1\frac{119}{250}\:liter[/tex]
[tex]\displaystyle 7,5\:sleps[/tex]
[tex]\displaystyle 37,3\:sleps [/tex]
Step-by-step explanation:
[tex]\displaystyle 1\frac{119}{250} = \frac{1476}{1000}[/tex]
[tex]\displaystyle 1\frac{1}{13} \times 7 = 7\frac{7}{13} ≈ 7,538461538 ≈ 7,5[/tex]
[tex]\displaystyle \frac{41}{1\frac{1}{10}} = 37\frac{3}{11} ≈ 37,3[/tex]
I am joyous to assist you anytime.
Given a central angle of 100 in a circle with a radius of 7 in., what is the intercepted arc length of the central angle?
**Use 3.14 for π and round to ONE decimal place.
Answer:
12.2 inches
Step-by-step explanation:
Write and solve a proportion.
Arc length / circumference = central angle / 360°
x / (2π × 7) = 100° / 360°
x = 12.2
The arc length is 12.2 inches
A cylinder has a volume of 33 cubic inches. What is the volume of a cone with the same radius and height?
A: 44 cubic inches
B: 33 cubic inches
C: 11 cubic inches
D: 99 cubic inches
C
Step-by-step explanation:
The volume of a cylinder = πr²h
= 33 cubic inches
The volume of a cone = ¹/3 πr²h
If the cylinder and come share the same radius and height then ‘πr²h’ part of the formulas is the same for both;
It means the difference in proportionality is ¹/3 (because even π is the same across board). The volume of the cone is therefore;
¹/3 (33)
= 11
= 11 cubic inches
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A rope, attached to a weight, goes up through a pulley at the ceiling and back down to a worker. The worker holds the rope at the same height as the connection point between the rope and weight. The distance from the connection point to the ceiling is 40 ft. Suppose the worker stands directly next to the weight (i.e., a total rope length of 80 ft) and begins to walk away at a constant rate of 2 ft/s. How fast is the weight rising when the worker has walked: 10 feet? Answer = 30 feet? Answer =
The weight rises at the same constant rate of 2ft/s that the worker walks away, regardless of how far the worker has travelled. When the worker walks away, the length of the rope attached to the weight decreases and thus raises the weight. Therefore, at both distances, 10ft and 30ft, the weight will be rising at 2ft/s.
Explanation:This is a physics problem involving related rates under the concept of kinematics. When the worker walks, the total length of the rope (80 ft) remains the same, so as the worker's part of the rope increases, the part attached to the weight decreases causing an upward motion. The rates at which the worker walks away and the weight retracts up are directly related.
When the worker has walked 10 feet, the worker's part of the rope has become 50 ft (original 40ft + 10ft walked), thus the weight's part of the rope is 30ft (80ft total - 50ft). Because the worker is walking at a constant rate of 2ft/s, this means that the weight is also rising at that same constant rate of 2ft/s.
Then, when the worker has walked 30 feet, the worker's part of the rope has become 70ft, thus the weight's part of the rope is 10ft. As previously explained, because the worker has a constant rate of walking away, the weight also has a constant rate of 2ft/s in the upward direction. Regardless of the worker's position, it does not impact the rate of the weight's ascent.
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The weight rises at a constant rate of 1 ft/s regardless of whether the worker has walked 10 feet or 30 feet.
Finding the Rate of the Weight Rising
First, let’s set up the problem with the given data:Distance from the connection point to the ceiling: 40 ft
Worker’s walking speed: 2 ft/s
When the worker is directly next to the weight, the total rope length is 80 ft (rope goes up 40 ft to the pulley, and 40 ft down to the worker).As the worker walks away, the rope is extended, and the weight rises. We need to determine how fast the weight is rising after the worker has walked different distances. Here’s how to do it step-by-step:
Step-by-Step Solution:Let x be the distance the worker has walked away from the initial point. Therefore, the total length of the rope now serves both the height the weight has risen (h) and the horizontal distance the worker has walked (x).
Using the Pythagorean Theorem: the new distance of the rope from the worker to the pulley and down to the weight can be written as:80 ft = 2h + x
Differentiate this equation with respect to time (t):0 = 2(dh/dt) + dx/dt
Given that dx/dt = 2 ft/s (rate the worker walks away), we can solve for dh/dt.2(dh/dt) + 2 = 0
2(dh/dt) = -2
dh/dt = -1 ft/s
Now, we'll analyze the specific cases: when the worker has walked 10 feet and 30 feet respectively.a) For 10 feet: Plugging into the length equation:
2h + 10 = 80
2h = 70
⇒ h = 35 ft
b) For 30 feet: Plugging into the length equation:
2h + 30 = 80
2h = 50
∴ h = 25 ft
The weight rises at a rate of 1 ft/s when the worker has walked either 10 feet or 30 feet because the rate change of height (dh/dt) is constant.
ASAP
What is the area of the rectangle?
Question 1 options:
8 Units
12 Units
20 Units
15 Units
Answer:
12 units
Step-by-step explanation:
The quickest way to go about this is;
From the figure, when you count the number of full square boxes inside the rectangle, they add up to 7 full square boxes of 1 unit by 1 unit. And the number of half square boxes inside the rectangle add up to 10 which is equal to 5 full square boxes.
So the total number of full square boxes of 1 unit by 1 unit inside the rectangle add up to 12 full square boxes. The area of each full square box is 1 * 1 = 1 units, therefore the area of the rectangle is equal to 1 * 12 = 12 units.
Sally has just finished her thirty-fifth year with her company and is getting ready to retire. During her thirty-five years, Sallys average annual salary was 45,603 How much can Sally expect to receive from Social Security annually if she were to retire today?
a. $191.53
b. $1,915.33
c. $19,153.26
d. $191,532.60
Answer:
$19153.26
Step-by-step explanation:
Here is the complete question: Sally has just finished her thirty-fifth year with her company and is getting ready to retire. During her thirty-five years, Sallys average annual salary was 45,603 How much can Sally expect to receive from Social Security annually if she were to retire today? (Assume she will receive 42% of her average annual salary.)
Given: Sally´s average salary while working is $45603.
Sally will receive 42% of her average annual salary as social security.
Now, finding annual income of sally after retirement.
Sally´s income from social security after retirement= [tex]\frac{42}{100} \times 45603= \$ 19153.26[/tex]
∴ Sally receive $ 19153.26 annually from social security.
Which of the following illustrates the truth value of the given conjunction?
The number [tex]-\frac{343}{9}[/tex] is an integer, and a rational number.
The conjunction is false because the number -343/9 is not an integer but is a rational number.
The number [tex]-\frac{343}{9} is an integer, and a rational number.
To determine the truth value of this conjunction, we need to understand that an integer is a whole number like -1, 0, or 1, and a rational number is a ratio of integers like 2/1 or 3/4.
Since the number [tex]-\frac{343}{9} is not an integer and also a rational number (since it can be expressed as -343/9), the conjunction is false.
Rachel runs 2km to her bus stop, and then rides 4.5 km to school. On average, the bus is 45 km/h faster than Rachel's average running speed. If the entire trip takes 25 minutes, how fast does Rachel run?
Answer:6.042km/h 6km/h approximately
Step-by-step explanation:
First off we have to know the formula relating speed, distance and time which is
Speed = distance/time
Now we are looking for Rachel's running speed
We are to find Rachel's running speed, so let's label is x
We are given that the distance Rachel runs to her bus stop is 2km
We were not given the time she uses to run to the bus stop
So let's label the time Rachel uses to run to her bus stop as y
So from the formula speed = distance/time
We have x = 2/y
Now we are told that the speed the bus uses to get to school is 45km/h faster than her speed used to run
So speed of bus = 45 + x
And the overall time for the whole journey is 25mins, changing this to hours, because the speed details given is in km/h we divide 25 by 60 which will give 0.417
Now if the total time is 0.417 hours, and we labeled the time for Rachel to run to the bus as y, so the time for the time for the bus to get to school will be 0.417 - y
We are also told the bus rides for 4.5km to school
So adding this together to relate the speed, distance and time of the bus with the formula speed = distance/time
We get 45 + x = 4.5/(0.417 - y)
So we have two equations
x = 2/y (1)
45+x = 4.5/(0.417-y) (2)
So putting (1) in (2) we have
45 + (2/y) = 4.5/(0.417-y)
Expanding further
(45y + 2)/y = 4.5(0.417-y)
Cross multiplying
(45y + 2)(0.417 - y) = 4.5y
Opening the brackets
18.765y - 45y2 + 0.834 - 2y = 4.5y
Collecting like terms
-45y2 + 18.765y -2y - 4.5y + 0.834 = 0
-45y2 + 12.265 + 0.834 = 0
Dividing all sides by -45 to make the coefficient of y2 1
y2 - 0.273y - 0.019 = 0
Now we have gotten a quadratic equation, and since it's with decimal numbers we can use either completing the square method of almighty formula
I'm using almighty formula her
For solving
ax2 + bx + c = 0
x = (-b +-root(b2-4ac)/2a
For our own equation, we are finding y
From our our quadratic equation
a = 1, b=-0.273, c = -0.834
you = (-(-0.273)+-root(-0.273-4(1)(-0.019))/2(1)
y = (273+-root(0.151))/2
y = (0.273+0.389)/2 or (0.273-0.389)/2
y = 0.331 or -0.085
So we use the positive answer which is 0.331, because time can't be negative
Then we put y = 0.331 in (1)
x = 2/y
x = 2/0.331
x = 6.042km/h
x = 6km/h approximately
Rachel's running speed was calculated by forming equations based on the given scenario of her running and riding the bus, solving these equations simultaneously provides the answer.
Explanation:This problem is a classic case of the combined speed-time-distance problem. It involves two segments: Rachel running and then riding the bus. The time taken for these two segments combined is given as 25 minutes. We can denote Rachel's running speed as 'r' and her running time as 't1', and the bus speed as 'r+45' and bus time as 't2'.
From the question, we can formulate the following two equations:
Distance = Speed X Time, thus: 2 = r x t1 And, 4.5 = (r+45) x t2The total time 't1 + t2' is equal to 25/60 hours (converting to the same unit).
Now, we solve these equations together to find the value of 'r', Rachel's running speed.
This shows the importance and application of average speed, time and distance in real-world situations.
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A sample size of n=12 is a simple random sample selected from a normally distributed population. Find the critical value t* corresponding to a 95% confidence level (two-sided).
For a sample size of n=12, the degrees of freedom (df) would be 11, and the critical t value for a two-tailed 95% confidence interval is typically around 2.201, as determined by a t-distribution table or statistical software.
Explanation:To find the critical t* value corresponding to a 95% confidence level for a sample size of n=12, you must take into account that the degrees of freedom (df) are equal to n - 1, which is 11 in this case. You use a t-distribution, not the z-distribution, because the population standard deviation is unknown. The critical t* value can be found using a t-distribution table or statistical software.
With the degrees of freedom at 11 for a 95% confidence interval (two-sided), the critical t value is typically around 2.201. However, one must look up the exact value using statistical software or a t-distribution table, as the value may vary slightly based on different sources or rounding.
Thus, to answer the student's question: For a two-tailed 95 percent confidence interval and 11 degrees of freedom, the corresponding critical value t* will typically be around 2.201.
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The radius of a cylindrical construction pipe is 3.5 ft. If the pipe is 35 ft long, what is its volume?
Use the value 3.14 for a, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
Volume = 1346.275 [tex]ft^{3}[/tex]
Step-by-step explanation:
The radius of the pipe is 3.5 ft and height is 35 ft.
The volume of cylinder is found by the formula,
V = (π)([tex]R^{2})(h)[/tex]
(think about the formula as area of individual circles multiplied by the height of cylinder)
taking value of π as 3.14,
Where, the r = radius and h is height of cylinder.
inserting the above values,
[tex]V = (3.14)(3.5^{2})(35)[/tex]
V = 1346.275 [tex]ft^{3}[/tex]
Madison bought an empty lot for $2,000 and later sold it for a 25% profit. How much did Madison sell the lot for? A) $500 B) $1,500 C) $2,500 D) $3,000
Answer:
C) $2,500
Step-by-step explanation:
Madison's profit is 25% of the $2000 paid, so is ...
0.25 × $2000 = $500
That means the lot was sold for ...
$2000 + 500 = $2500
_____
Profit can also be expressed as a percentage of the selling price. If that were the case here, Madison's initial cost would be 0.75 of the $2666.67 selling price, and the 25% profit would be $666.67. Since that is not among the answer choices, we presume our assumption is correct that Madison's profit is measured as a percentage of cost.
Answer:
c
Step-by-step explanation:
your welcome
Asked what the central limit theorem says, a student replies, As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal.
Is the student right?
A. No. The central limit theorem says nothing about the histogram of the sample values. It deals only with the distribution of the sample means.
B. Yes. This is exactly what the theorem says
Answer:
A. No, the student is not right. The central limit theorem says nothing about the histogram of the sample values. It deals only with the distribution of the sample means.
Step-by-step explanation:
No, the student is not right. The central limit theorem says nothing about the histogram of the sample values. It deals only with the distribution of the sample means. The central limit theorem says that if we take a large sample (i.e., a sample of size n > 30) of any distribution with finite mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], then, the sample average is approximately normally distributed with mean [tex]\mu[/tex] and variance [tex]\sigma^2/n[/tex].
Yes. The student is exactly what the theorem says.
True. According to the central limit theorem, as the sample size increases, the sampling distribution of the sample means becomes more Normal.
An example illustrates how from a population with a uniform distribution, as samples are drawn and the means are calculated, the distribution of these means approximates a normal distribution as the sample size increases.
The central limit theorem ensures that regardless of the population's distribution, with sufficiently large samples, the distribution of sample means tends towards a normal distribution.
Min collects 334 pounds of aluminum cans on Monday and 124 pounds on Tuesday. Jessica collects 414 pounds on Monday and 314 pounds on Tuesday. How many more pounds does Jessica collect than Min? Enter your answer in the box as a mixed number in simplest form.
Answer:
270 more pounds of aluminium cans collected by Jessica than Min
Step-by-step explanation:
334 + 124 = 458 (Total pounds of aluminium cans collected by min)
414 + 314 = 728 (Total pounds of aluminium cans collected by Jessica)
728 - 458 = 270 (More pounds Jessica collected than Min)
Final answer:
Jessica collected 270 pounds more of aluminum cans than Min did over the two days. Min collected 458 pounds in total, and Jessica collected 728 pounds in total.
Explanation:
The student's question is asking us to compare the total amount of aluminum cans collected by two individuals, Min and Jessica, over a two-day period and determine how much more Jessica collected compared to Min. To solve this, we need to add the amounts collected by each individual for both days and then subtract Min's total from Jessica's total.
First, we find Min's total collection by adding her collections from Monday and Tuesday: 334 pounds + 124 pounds = 458 pounds.
Next, we find Jessica's total collection by adding her collections from Monday and Tuesday: 414 pounds + 314 pounds = 728 pounds.
Finally, we calculate how much more Jessica collected than Min by subtracting Min's total from Jessica's total: 728 pounds - 458 pounds = 270 pounds. Since the question asks for the answer as a mixed number in simplest form and 270 is already a whole number, our answer is simply 270 pounds. There is no need to convert to a mixed number.
the circular ripple caused by dropping a stone in a pond is increasing in area at a constant rate of 20 square meters per second. Determine how fast the radius of this circular ripple is increasing when the area of the circular region is 25 pi
Answer:
2/π ≈ 0.637 m/s
Step-by-step explanation:
The rate of change of area with respect to time is ...
A = πr²
dA/dt = 2πr·dr/dt
Filling in given values in the above equations, we can find r and dr/dt.
25π = πr² ⇒ r = 5
20 = 2π·5·dr/dt
dr/dt = 20/(10π) = 2/π . . . . meters per second
The radius is increasing at the rate of 2/π ≈ 0.637 meters per second.
Brian found 12-19 by breaking apart 19 into 12+7 write equations to show how Brian could have found the difference. ?
Answer:
Answer is 12-19 = -7
Step-by-step explanation:
12- 19 you can break 19 into 12 +7
then
it is easy to find 12-12 = 0
Now subtracts 0 - 7 =- 7
then
break 7 into 3 + 4
then
0 - 3 = -3
-3 - 4 = -7
So ,
12 - 19 = -7
raul is 5 years older than twice carlos age. the sum of their ages is 101. how old is carlos?
Answer:32years old
Step-by-step explanation:
R= 2c+5
R+C= 101
2c+5+c=101
3c+5=101
3c=96
c=32
Answer:
32 years
Step-by-step explanation:
Let the age of Carlos be represented by x
Then the age of Raul can be represented as the sum of twice the age of Carlos and 5.
In other words, Raul's age = 2x + 5
Sum of Carlos and Raul's age is 101
That is, \[x + 2x + 5 = 101\]
Or, \[3x + 5 = 101\]
Or, \[3x = 96\]
Or, \[x = 32\]
Hence, the age of Carlos is 32 years.
Age of Raul on the other hand is 2*32 + 5 = 69 years
Sum of their ages is 32 + 69 = 101 years.
PLEASE HELP ME!!!!!!! I AM NOT GOOD AT MATH!
Given the function f(x)= \frac{x^2+7x+10}{x^2+9x+20} Describe where the function has a hole and how you found your answer.
Only hole of function [tex]f(x) = \frac{x^{2}+7x+10 }{x^{2}+9x+20 }[/tex] is at x=(-4)
Step-by-step explanation:
Given the function is [tex]f(x) = \frac{x^{2}+7x+10 }{x^{2}+9x+20 }[/tex]
In order to find holes of any function, you should find when function is becoming undefined or say " infinity"
Given function is polynomial function.
It will become undefined become denominator become zero
[tex]x^{2}+9x+20=0[/tex]
Solving for x value when denominator become zero
[tex]x^{2}+9x+20=0\\x^{2}+5x+4x+20=0\\x(x+5)+4(x+5)=0\\(x+4)(x+5)=0[/tex]
we get possible holes at x=(-4) and x=(-5)
Check whether you can eliminate any holes
Now, Solving for x value when numerator become zero
[tex]x^{2}+7x+10=0\\x^{2}+5x+2x+10=0\\(x+5)(x+2)=0[/tex]
x=(-5) and x=(-2)
x=(-5) is common is both numerator and denominator.
So that, we can eliminate it.
[tex]f(x) = \frac{(x+5)(x+2)}{(x+5)(x+4)}[/tex]
[tex]f(x) = \frac{(x+2)}{(x+4)}[/tex]
Therefore, Only hole of function [tex]f(x) = \frac{x^{2}+7x+10 }{x^{2}+9x+20 }[/tex] is at x=(-4)
Choose the correct product of (5x − 11)^2.
a. 25x^2 − 110x + 121
b. 25x^2 − 121
c. 25x^2 + 121
d. 25x^2 + 110x + 121
Answer:
A. 25x^2 - 110x + 121
Step-by-step explanation:
(5x - 11)² = (5x)² - 2·5x·11 + (11)² = 25x² - 110x + 121
(a - b)² = a² - 2ab + b²
a. 25x² − 110x + 121
A ladder 10 ft long leans against a vertical wall. If the bottom of the ladder slides away from the base of the wall at a speed of 2 ft/s, how fast is the angle between the ladder and the wall changing when the bottom of the ladder is 6 ft from the base of the wall?
Answer:
[tex]\frac{dx}{dt}=\frac{-8}{3}\frac{ft}{s}[/tex]
Step-by-step explanation:
Be [tex]\frac{dy}{dt}=2\frac{ft}{s}[/tex] to find [tex]\frac{dx}{dt}=?, x=6ft[/tex]
[tex]x^{2} +y^{2}=10^{2};6^{2}+y^{2}=100;y^{2}=100-36=64;y=\sqrt{64}=+-8[/tex]→ y=8 for being the positive distance, deriving from t, [tex]x^{2} +y^{2}=100[/tex]→[tex]2x\frac{dx}{dt}+2y\frac{dy}{dt}=0[/tex]→[tex]2x\frac{dx}{dt}=-2y\frac{dy}{dt};\frac{dx}{dt}=-\frac{2y}{2x}\frac{dy}{dt}; \frac{dx}{dt}=-\frac{y}{x}\frac{dy}{dt}[/tex], if x=6 and y=8
[tex]\frac{dx}{dt}=\frac{-8}{6}2[/tex]→[tex]\frac{dx}{dt}=\frac{-8}{3}\frac{ft}{s}[/tex]
we must find the rate of change in radians over seconds, being the speed 8/3 ft / s = 2.66 ft / s the variation in degrees is determined when traveling 6 ft
An art student is trying to determine how many tubes of paint they will need for their mural. If they are using 3 tubes every 4 days, how many tubes would they use in 8 days?
Answer: 6 tubes
Step-by-step explanation:
Create a simple relationship.
4 days = 3 tubes
8 days = ? tubes
Well, if there is twice as many days, twice as many tubes will be used.
4 days x 2 = 8 days
3 tubes x 2 = 6 tubes
An ideal gas is confined within a closed cylinder at a pressure of 2.026 × 105 Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume. What is the final pressure of the gas when its temperature returns to its initial value?
Answer:
The final pressure of the gas when its temperature returns to its initial value [tex]1.8234\times 10^6[/tex] Pa.
Step-by-step explanation:
Given : An ideal gas is confined within a closed cylinder at a pressure of [tex]2.026\times 10^5[/tex] Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume.
To find : What is the final pressure of the gas when its temperature returns to its initial value?
Solution :
Since the temperature is constant .
The relation between P and V is given by,
[tex]P_1\times V_1 = P_2\times V_2[/tex]
[tex]\frac{P_1}{P_2}=\frac{V_2}{V_1}[/tex] ....(1)
The piston moves until the volume of the gas is reduced to one-ninth of the initial volume i.e. [tex]V_2=\frac{V_1}{9}[/tex]
or [tex]\frac{V_2}{V_1}=\frac{1}{9}[/tex]
[tex]P_1=2.026\times 10^5[/tex]
Substitute in equation (1),
[tex]\frac{2.026\times 10^5}{P_2}=\frac{1}{9}[/tex]
[tex]P_2=9\times 2.026\times 10^5[/tex]
[tex]P_2=18.234\times 10^5[/tex]
[tex]P_2=1.8234\times 10^6[/tex]
The final pressure of the gas when its temperature returns to its initial value [tex]1.8234\times 10^6[/tex] Pa.
One boat travelling 15 mph goes 47 miles downstream in the same amount of time that another boat going 20 mph goes 40 miles upstream. How fast is the current in mph? (Round your answer to the nearest tenth of miles per hour and enter only the numerical part
Answer:
3.9 mi/h
Step-by-step explanation:
We assume that the given speeds are the speeds of the boats relative to the water. If c is the speed of the current, we have ...
time = distance/speed
47/(15 +c) = 40/(20 -c)
47(20 -c) = 40(15 +c) . . . . . . multiply by (20-c)(15+c)
940 -600 = 40c +47c . . . . . add 47c-600
340 = 87c . . . . . . . . . . . . . . . simplify; next divide by 87
c = 340/87 ≈ 3.9080 . . . . mi/h
The speed of the current is about 3.9 mi/h.
A manufacturer of a certain product can expect that between 0.3 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units?
(A) Between $15,000 and $25,000
(B) Between $30,000 and $50,000
(C) Between $60,000 and $100,000
(D) Between $150,000 and $250,000
(E) Between $300,000 and $500,000
Answer:
Step-by-step explanation:
We are told the manufacturer expects 0.3% to 0.5% of units to be defected,
So we find 0.3% and 0.5% of the 20,000units
0.3/100 multiplied by 20000 = 60units
0.5/100 multiplied by 20000 = 100units
So we now know from 20000units, between 60units to 100units will be defected
So we find the price of both 60units and 100units knowing that 1unit cost $2,500
60 multiplied by $2,500 equals $150,000
100 multiplied by $2,500 equals $250,000
So the answer is option D, between $150,000 and $250,000
Going against the current, a boat takes 6 hours to make a 120-mile trip. When the boat travels with the current on the return trip, it takes 5 hours. If x = the rate of the boat in still water and y = the rate of the current, which of the following systems could be used to solve the problem? A) 6(x - y) = 120 B) 5(x + y) = 120 C) 6(x + y) = 120 D) 5(x - y) = 120 E) 6x - 5y = 120 F) x + y = 120
Answer:
You can use A and B systems
Step-by-step explanation:
Lets call z the total speed of the boat. If the boat goes against the current, then, the current will drop the boat natural speed, and therefore z is obtained from substracting y from the rate of the boat on still water, x. Thus, z = x-y. If The boat goes in favor of the current, then the current will raise the speed, and we obtain z by adding y to x. If we want to calculate x and y, we know that:
On the first trip, z = x-y, and it took 6 hours to finish the 120 mile trip, therefore 6z = 120, or equivalently, 6(x-y)=120
On the return trip, z = x+y, and it took 5 hours to finish the trip, so we have 5z = 5(x+y) = 120.
Thus, in order so solve the problem, we can use system A and B.
Note that system A is equivalent to the equation x-y = 20, obtained by dididing everything by 6. If we divide by 5 the second equation we obtain that x+y = 24. We have
x-y = 20x+y = 24By summing this equations it follows that 2x = 44, therefore x = 22. Since x-y = 20, we obtain that y = 2.
Answer:
The correct answer is 6(x - y) = 120 and 5(x + y) = 120
Pilar used six reusable shopping bags on a recent purchase she made at a grocery store. Each bag decreased the amount she spent by 5 cents. What was the change to the amount Pilar spent at the grocery store by using the reusable bags?
Pilar will pay 30 cents less from the original amount by using reusable bags.
Step-by-step explanation:
Bags used by Pilar = b = 6
Price decrease per bag = 5 cents
Let x be the total amount paid by Pilar.
Decrease will lessen the amount paid by Pilar, therefore, according to statement;
P(x) = x - 5b
As she used 6 bags, therefore, putting b=6
[tex]P(x)=x-5(6)\\P(x)=x-30[/tex]
Pilar will pay 30 cents less from the original amount by using reusable bags.
Keywords: subtraction, function
Learn more about subtraction at:
brainly.com/question/2154850brainly.com/question/2367554#LearnwithBrainly
The angle measurements in the diagram are represented by the following expressions.
Solve for X then find the measurement of ∠B:
Answer:
x = 6
∠B = 126
Step-by-step explanation:
∠A = ∠B through alternate interior angles
∠A = ∠B
8x + 78 = 2x + 114
8x - 2x = 114 - 78
6x = 36
x = 36 ÷ 6
x = 6
∠B = 2x + 114
2(6) + 114
12 + 114
= 126
d1 || d2 => ∡A = ∡B
8x + 78° = 2x + 114°
8x - 2x = 114° - 78°
6x = 36°
x = 36° : 6
x = 6°
∡B = 2x + 114°
∡B = 2×6° + 114°
∡B = 12° + 114°
∡B = 126°
The equation [tex]2m^{2}-1m-8=0[/tex] has solutions of the form
M= N +or- sqaure root of D/over M
Solve this equation and find the appropriate values of N,M,and D. Do not worry about simplifying the √D portion of the solution.
N= M= D=
Answer:
N = 1M = 4D = 65Step-by-step explanation:
The given equation is of the form ...
ax² +bx +c = 0
where a=2, b=-1, c=-8.
The quadratic formula gives the solution to the above equation as ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
So, for your equation, the solution is ...
[tex]m=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(2)(-8)}}{2(2)}=\dfrac{1\pm\sqrt{65}}{4}[/tex]
Comparing this to the form ...
[tex]m=\dfrac{N\pm\sqrt{D}}{M}[/tex]
we see ...
N = 1M = 4D = 65