The null hypothesis would be that there is no significant difference between the mean examination score for the new freshman applications and the historical mean of 900. The alternative hypothesis would be that there is a significant difference between the two means.
To determine if the mean examination score for new freshman applications has changed. To do this, you'll need to state your null and alternative hypotheses using the historical mean and given terms.
Step 1: State the null hypothesis (H₀)
The null hypothesis assumes that there is no significant change in the mean examination score for new freshman applications. In this case, the null hypothesis is that the mean remains equal to the historical mean of 900.
H₀: μ = 900
Step 2: State the alternative hypothesis (H₁)
The alternative hypothesis represents a significant change in the mean examination score for new freshman applications. In this case, the alternative hypothesis is that the mean is not equal to the historical mean of 900.
H₁: μ ≠ 900
So, your hypotheses are as follows:
- Null hypothesis (H₀): μ = 900
- Alternative hypothesis (H₁): μ ≠ 900
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In Exercises 17-22, determine which sets of vectors are orthonormal. If a set is only orthogonal, normalize the vectors to produce an orthonormal set.22 [ 1/√18] [ 1/√2 ] [ -2/3 ] [ 4/√18] [ 0 ] [ -2/3]1/√18 -1/√2 -2/3
The set of vectors {[1/√18], [1/√2], [-2/3]} and {[4/√18], [0], [-2/3]} is an orthonormal set.
To verify whether a set of vectors is orthonormal, we need to check two conditions: orthogonality and normalization. Orthogonality means that the dot product of any two distinct vectors in the set is zero. Normalization means that the magnitude or length of each vector is 1.
First, we check for orthogonality. The dot product of the first and second vectors is:
[1/√18] * [4/√18] + [1/√2] * [0] + [-2/3] * [-2/3] = 4/18 + 0 + 4/9 = 8/18
The dot product of the first and third vectors is:
[1/√18] * [1/√2] + [1/√2] * [(-2/3)] + [-2/3] * [(-1/√18)] = 1/√36 - 2/3√2 - 2/3√2 = 0
The dot product of the second and third vectors is:
[4/√18] * [1/√2] + [0] * [-2/3] + [-2/3] * [(-1/√18)] = 2/√36 + 2/√36 = 4/√36
Since the dot product of any two distinct vectors is not always zero, the set is not orthogonal. We need to normalize the vectors to produce an orthonormal set.
To normalize a vector, we divide it by its magnitude. The magnitude of a vector [a, b, c] is √(a^2 + b^2 + c^2). Thus, the normalized version of the first vector is:
[1/√18, 1/√2, -2/3] / √[(1/18) + (1/2) + (4/9)] = [1/√2, √(2/9), -2/√9]
The normalized version of the second vector is:
[4/√18, 0, -2/3] / √[(16/18) + 0 + (4/9)] = [2/√9, 0, -2/√9]
The normalized version of the third vector is:
[1/√18, -1/√2, -2/3] / √[(1/18) + (1/2) + (4/9)] = [1/√2, -√(2/9), -2/√9]
We can now check for orthogonality again:
The dot product of the first and second vectors is:
[1/√2] * [2/√9] + [√(2/9)] * [0] + [-2/√9] * [(-2/√9)] = 0
The dot product of the first and third vectors is:
[1/√2] * [1/√2] + [-√(2/9)] * [-2/√9] + [-2/√9] * [-2/√9] = 1/2 + 2/9 + 4/9 = 1
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What is true about sampling in statistics?
A. As the sample size increases, the variability increases
B. Sample parameters vary and are known
C. Sample Values are estimated from known population
Sample Values are estimated from known population is true about sampling in statistics.
In statistics, sampling refers to the process of selecting a subset of individuals or objects from a larger population. The sample is used to estimate or make inferences about the population from which it was drawn. Option A is false because as the sample size increases, the variability generally decreases as the sample better represents the population. Option B is false because sample statistics (such as the sample mean or sample standard deviation) vary from sample to sample and are estimated from the data in the sample. Option C is true because sample values (such as the sample mean or sample proportion) are estimated from the known population values, and this estimation process involves sampling error due to random variability in the sample.
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: For each of the functions below, indicate whether the function is onto, one-to-one, neither or both. If the function is not onto or not one- to-one, give an example showing why. (a) f: R + R. f(x) = x2 (b) g: R → R. g(x) = x3 ((c) h: Z - Z. h(x) = x3 (d) f. 2+2, f(x) = - 4
One-to-one: Since f(2) = f(-2) = -4, the function is not one-to-one.
(a) f: R → R. f(x) = x^2
The function f is neither onto nor one-to-one. To see why, consider the following:
Onto: A function is onto if every element of the co-domain has at least one pre-image in the domain. In this case, f(x) = x^2 can never be negative, so it does not take on every value in the co-domain R (since R includes negative numbers). Therefore, the function is not onto.
One-to-one: A function is one-to-one if each element in the co-domain corresponds to exactly one element in the domain. However, since f(-x) = f(x) for all x, the function is not one-to-one. For example, f(2) = f(-2) = 4.
(b) g: R → R. g(x) = x^3
The function g is both onto and one-to-one. To see why:
Onto: For any y in the co-domain R, we can find x in the domain R such that g(x) = y by taking the cube root of y. Therefore, g is onto.
One-to-one: Suppose g(a) = g(b) for some a, b in the domain R. Then, we have a^3 = b^3, which implies a = b. Therefore, g is one-to-one.
(c) h: Z → Z. h(x) = x^3
The function h is onto but not one-to-one. To see why:
Onto: For any y in the co-domain Z, we can find x in the domain Z such that h(x) = y by taking the cube root of y. Therefore, h is onto.
Not one-to-one: For example, h(-1) = (-1)^3 = -1 and h(1) = 1^3 = 1, so h is not one-to-one.
(d) f. 2+2, f(x) = -4
The function f is neither onto nor one-to-one. To see why:
Onto: The co-domain is not specified, so it is not clear whether the function is onto or not.
Not one-to-one: Since f(2) = f(-2) = -4, the function is not one-to-one.
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Please solve #8
Multiply each rational expression and simplify
The simplified expression is (x + 7)/(5x² + 30x + 45).
What is the simplification of the expressions?The simplification of the expressions is calculated as follows;
(x² - 3x + 9)/(5x² - 20x - 105) x (x² - 49)/(x³ + 27)
Factorize each expression as follows;
5x² - 20x - 105
5(x² - 4x - 21)
5(x² - 7x + 3x - 21)
5(x(x -7) + 3(x - 7))
5(x-7)(x+3)
x² - 49
apply difference of two squares;
= x² - 7²
= (x - 7)(x + 7)
x³ + 27
apply sum of two cubes;
= x³ + 3³
= (x + 3)(x² - 3x + 9)
The faction is simplified as follows;
(x² - 3x + 9)/5(x-7)(x+3) x (x - 7)(x + 7)/(x + 3)(x² - 3x + 9)
= (x + 7)/(5(x + 3)(x + 3))
= (x + 7)/(5(x + 3)²)
= (x + 7)/(5(x² + 6x + 9)
= (x + 7)/(5x² + 30x + 45)
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In a hypothesis test problem, testing if the population proportion is less than 0.75, you are given the following values:n=p-value =9400.0735
28 Which of the following is the correct statement of the hypotheses?
A. a H0:π≥0.75 H0:π>0.75
B. H0:π<0.75 H0:π≤0.75
C. H1:π<0.75 H1:π≤0.75 D. H1:π≥0.75H1:π>0.75
The correct statement of the hypotheses is option B: H0:π≥0.75 and H1:π<0.75.
In a hypothesis test problem, the null hypothesis (H0) represents the status quo or the default assumption, while the alternative hypothesis (H1) represents the claim or the research question that the investigator wants to test.
In this problem, the null hypothesis is that the population proportion (π) is greater than or equal to 0.75 (i.e., H0:π≥0.75). The alternative hypothesis is that the population proportion is less than 0.75 (i.e., H1:π<0.75), which is what we are testing for.
The p-value of 0.0735 represents the probability of obtaining a sample proportion as extreme as the one observed or more extreme, assuming that the null hypothesis is true. Since the p-value is less than the significance level (usually set at 0.05), we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis. Therefore, the correct statement of the hypotheses is option B.
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in july 2008, the united states had a population of approximately 302,000,000 people. how many americans were there in july 2009, if the estimated 2008 growth rate was 0.88%? group of answer choices 567,760,000 304,657,600 2,657,600 304,000,000
There were approximately 304,657,600 Americans in July 2009. The correct answer is 304,657,600. In July 2009, the estimated population of the United States would be 304,657,600 people. To calculate this, we need to take the 2008 population of 302,000,000 and multiply it by the growth rate of 0.88%.
First, we need to find the amount of growth that occurred between 2008 and 2009. We can do this by multiplying the 2008 population by the growth rate:
302,000,000 x 0.88% = 2,657,600
This tells us that the population increased by 2,657,600 people from 2008 to 2009. To find the total population in 2009, we need to add this growth to the 2008 population:
302,000,000 + 2,657,600 = 304,657,600
Therefore, in July 2009, the estimated population of the United States would be 304,657,600 people, based on a growth rate of 0.88%.
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Confidence Intervals Using the T-Distribution LEARNING OBJECTIVE: Calculate a confidence interval using the t-distribution. Morgan sampled 101 students and calculated an average of 6.5 hours of sleep each night with a standard deviation of 2.14. Using a 90% confidence level, she also found that t = 1.660. confidence interval = t* s/n A 90% confidence interval calculates that the average number of hours of sleep for working college students is between _________ hours. Answer choices are rounded to the hundredths place. O a.) 6.15 and 6.85 O b.) 6.46 and 6.85 O c.) 6.08 and 6.92 O d.) 6.46 and 6.54
Rounded to the hundredth place, this gives us answer choice (D), which is the correct answer. So we can say with 90% confidence that the average number of hours of sleep for working college students is between 6.46 and 6.54 hours.
To calculate the confidence interval using the t-distribution, we use the formula:
Confidence interval = sample mean ± (t-score)*(standard error)
where the standard error is calculated as the standard deviation divided by the square root of the sample size, i.e.,
standard error = standard deviation / sqrt(sample size)
In this case, Morgan sampled 101 students and found an average of 6.5 hours of sleep with a standard deviation of 2.14. So the standard error is:
standard error = 2.14 / sqrt(101) = 0.213
The t-score for a 90% confidence level with 100 degrees of freedom (n-1) is 1.660, as given in the problem.
Therefore, the confidence interval is:
Confidence interval = 6.5 ± (1.660)*(0.213) = (6.46, 6.54).
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Raj has 180 sweets and splits them 1:4 with his freind
The total number of sweets after considering the ratio with both Raj and his friend is 180 sweets.
Total number of sweets = 180
The ratio in which sweets are split = 1:4
Calculating Raj's share -
1 part out of 1+4
= 1/5 of the total sweets
1/5 of 180
= (1/5) x 180
= 36
Similarly,
Calculating the friend's share -
4 parts out of 1+4
= 4/5 of the total sweets
4/5 of 180
= (4/5) x 180
= 144
Total sweets with both Raj and his friend:
Raj's share + Friend's share
= 36 + 144
= 180
Complete Question:
Raj has 180 sweets and splits them 1:4 with his friend. What is the total number of sweets with both?
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c . main 2.7.1: sphere volume. given sphereradius, compute the volume of a sphere and assign spherevolume with the result. use (4.0 / 3.0) to perform floating-point division, instead of (4 / 3) which performs integer division. volume of sphere
sphere volume = (4.0 / 3.0) * 3.14159 * sphere radius ** 3
Here's a step-by-step explanation using the terms "radius", "volume", and "division":
1. Given the sphere's radius (sphere radius), we'll use the formula for calculating the volume of a sphere: V = (4.0 / 3.0) * π * r^3, where V is the sphere's volume and r is its radius.
2. Perform floating-point division by using (4.0 / 3.0) instead of (4 / 3). The floating-point division ensures a more accurate result since it retains decimal values.
3. Compute the sphere's volume (sphere volume) using the formula: sphere volume = (4.0 / 3.0) * π * (sphere radius)^3.
4. Assign the calculated value to the sphere volume.
By following these steps and using the given formula, you can calculate the volume of a sphere with the specified radius.
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as a manager, when faced with ethical crises you shouldmultiple choice a. focus on issues most relevant to stockholders only. b. wait for the other party to make the first move. c. take the initiative to address the problem.d. cover up as much as possible.
As a manager, when faced with ethical crises in time, you should:
C. Take the initiative to address the problem.
As a manager, when faced with ethical crises in time, you should take the initiative to address the problem.
It is important to consider the impact on multiple stakeholders, including employees, customers, and the community. Ignoring the issue or attempting to cover it up can lead to further complications and damage to the company's reputation.
It is important to address the issue head-on and take appropriate actions to prevent similar situations from occurring in the future.
This approach ensures that you proactively identify and resolve ethical issues in a timely and responsible manner, rather than focusing only on stockholders, waiting for others to act, or attempting to cover up the situation.
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SOMEONE HELP PLEASE!! giving brainlist to anyone
Answer:
Arianys:
[tex]61000 {e}^{.07125 \times 14} = 165401.17[/tex]
Yusuf:
[tex]61000( {1 + \frac{.07625}{12} )}^{12 \times 14} = 176796.02[/tex]
$176,796.02 - $165,401.17 = $11,394.85
After 14 years, Yusuf's account will have $11,395 more than Arianys's account.
a check of dorm rooms on a large college campus revealed that 38% had refrigerators, 52% had tvs, and 21% had both a tv and a refrigerator. what's the probability that a randomly selected dorm room has either a refrigerator or a tv (or both)? please enter your answer as a decimal, rounded to two places after the decimal point.
The probability that a randomly selected dorm room has either a refrigerator or a TV (or both) is 0.69, or 69% (rounded to two decimal places).
The probability of a aimlessly named dorm room having either a refrigerator or a television( or both) is0.69, as calculated from the given data. This implies that nearly 70 of the dorm apartments have at least one of these amenities. We can also interpret this as saying that having a television or a refrigerator is a fairly common circumstance in the dorm apartments on this particular council lot.
P(R) = 0.38 (38% had refrigerators)
P(T) = 0.52 (52% had TVs)
P(R and T) = 0.21 (21% had both a TV and a refrigerator)
Substituting these values into the equation, we get:
P(R or T) = 0.38 + 0.52 - 0.21
P(R or T) = 0.69
It's worth noting that having both a television and a refrigerator in a dorm room isn't as common, with only 21 of the apartments having both amenities. This could be due to a number of factors, similar as space constraints or particular preference. still, it's still important to fete that having both amenities can give fresh convenience and comfort to the scholars living in these apartments.
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a caterer is competing for a company's business, the caterer selects a simple random sample of entrees, a simple random sample of sides, and a simple random sample of desserts for a tasting. the sample is a sample.
The sample is a three-stage cluster sample
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2
Select the correct answer from each drop-down menu.
The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides.
The heights of the pyramids are the same.
The volume of pyramid A is
volume of pyramid B is
the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new
the volume of pyramid A.
The volume of pyramid A is twice the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is equal to the volume of pyramid A.
How to calculate the volume of a pyramid?In Mathematics and Geometry, the volume of a pyramid can be calculated by using the following formula:
Volume = 1/3 × b × h
Where:
h represent the height of a pyramid.b represent the base area of a pyramid.Volume of pyramid A = (10 × 20 × h)/3 = 200h/3
Volume of pyramid B = (10 × 10 × h)/3 = 100h/3
Since the heights of the two (2) pyramids are equal, we would substitute them as follows;
Volume of pyramid A = (200 × 3 × Volume of pyramid B)/(100 × 3)
Volume of pyramid A = 2 × Volume B
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Complete Question;
The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same.
The volume of pyramid A is ____ the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is ______the volume of pyramid A.
Student groups are given a six-sided die, with each side labeled a number 1 through 6. Each student group rolls the die 75 times and records the number that is rolled. If there are 8 groups of students participating in this activity, which of the following is most likely the total number of times a 4 was rolled?
A: 98
B: 154
C: 75
D: 13
The expected value of rolling a 4 on a six-sided die is 1/6. Therefore, in a single roll, we can expect to see a 4 appear approximately 1/6 of the time. Each group of students rolls the die 75 times, so we can expect each group to roll a 4 approximately (1/6)*75 = 12.5 times.
With 8 groups participating, we can expect a total of approximately 8*12.5 = 100 times that a 4 is rolled.
To find the most likely total number of times a 4 was rolled, follow these steps:
1. Determine the probability of rolling a 4 on a six-sided die: There is 1 favorable outcome (rolling a 4) and 6 possible outcomes (rolling a number 1 through 6). So, the probability of rolling a 4 is 1/6.
2. Calculate the expected number of times a 4 is rolled in a single group: Since each student group rolls the die 75 times, the expected number of times a 4 is rolled in one group is the probability of rolling a 4 multiplied by the number of rolls: (1/6) * 75 = 12.5.
3. Determine the most likely total number of times a 4 was rolled across all 8 groups: Multiply the expected number of times a 4 is rolled in one group by the total number of groups: 12.5 * 8 = 100.
Since 100 is not one of the options provided, choose the closest option, which is:
A: 98
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does the point (-3,3) lie inside, outside, or on the circle? the center of the circle is (-5,1) and the radius is 3. you must prove this ALGEBRAICALLY
yessss because as you can see the answer is what it is
A factory makes 8000 tubs of ice cream, each tub contains 500 millilitres. How many litres of ice cream does the factory make?
Answer:
4,000 L (4 thousand)
Step-by-step explanation:
1 tub = 500 mL
2 tub = 1000 mL = 1 L
8000 tubs = 4,000,000 mL = 4,000 L
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I need help please I'm stuck on this question
Answer:
84.3%
Step-by-step explanation:
Percentage of people completed the task under 40 s is(rounded) 84.3%
Find the zeros and describe the behavior of the graph at each zero. x^4 - 16x^3 + 63x^2
The zeros of the polynomial given are 9, 7, 0.
Given that a polynomial, x⁴-16x³+63x² we need to find its zeros,
The zeros are,
x⁴-16x³+63x² = 0
x²(x²-16x+63) = 0
x²(x²-9x-7x+63) = 0
x²(x-9)(x-7) = 0
Therefore, the zeros are 9, 7, 0
The end behavior of a function f (x) describes the behavior of the function as x approaches + ∞ and as x approaches -∞.
Hence, the zeros of the polynomial given are 9, 7, 0.
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The graph of the function y = 2x2 + bx + 8 is shown. What is the value of b? Enter your answer in the box. In the xy graph, the range of the x axis is minus three to five by increment of one. The range of the y axis is minus ten to six by increment of two. On x axis minus two, two, and four are labeled and on the y axis minus eight, minus four, and four are labeled. The curve is parabola open upwards. The vertex of the parabola is (3, -10), The parabola passes through the points (2, -8) and (4, -8). b =
The value of b in the given function is 4.
How to calculate the valueSince we know that the coefficient of the term is 2, we can plug in the values of a and b into the equation for the axis of symmetry.
We also know that the vertex of the parabola lies on the axis of symmetry, and we can see from the graph that the vertex is at the point.
Since x = -1 and y = 6, this will be;
6 = 2(-1)² + b(-1) + 8
b = 4
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the cost per item at a supermarket follows an exponential distribution. there are many inexpensive items and a few relatively expensive ones. the mean cost per item is $13.5. what is the percentage of items that cost: a. less than $10.5?
The percentage of items that cost less than $10.5 is 44.78%.
To solve this problem, we need to use the properties of the exponential distribution. We know that the mean cost per item is $13.5, which means that the parameter λ (the rate parameter) of the exponential distribution is 1/13.5 = 0.0741.
To find the percentage of items that cost less than $10.5, we need to calculate the cumulative distribution function (CDF) of the exponential distribution at $10.5:
CDF($10.5$) = 1 - e^(-λ*$10.5$) = 1 - e^(-0.0741*$10.5$) = 0.4478
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Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
3052.08
Step-by-step explanation:
v = 4/3[tex]\pi r^{3}[/tex]
v = [tex]\frac{4(3.14)9^{3} }{3}[/tex]
v = [tex]\frac{4(3.14)(729)}{3}[/tex]
v = [tex]\frac{9156.24}{3}[/tex]
v = 3052.08
Helping in the name of Jesus.
Answer:
The answer for Volume is 3052.08in³
Step-by-step explanation:
Volume of sphere=4/3pir³
V=4_3×3.14×9³
V=4/3×9×9×9×3.14
V=4×3×9×9×3.14
V=12×81×3.14
V=3052.08in³
y = 3x + 9; if x = 6
Part of the population of 4,750 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 2 of them are infected. How many elk are likely to be infected?
There are likely to be 190 elk infected with the parasite in the population of 4,750 elk at the wildlife preserve.
Now, To estimate the number of elk that are likely to be infected, we can use the sample proportion of infected elk to the total population of elk.
Hence, The sample proportion of infected elk is,
⇒ 2/50 = 0.04.
We can use this proportion to estimate the proportion of infected elk in the entire population of ;
4,750: 0.04 = x/4750
Solving for x, we get:
x = 0.04 × 4750
x = 190
Therefore, there are likely to be 190 elk infected with the parasite in the population of 4,750 elk at the wildlife preserve.
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Only the answer no explanation
Answer:
The slope for these to points would be -9/7 (rise/run)
in an experiment, the post-test measures: question 10 options: a) the dependent variable b) the independent variable c) the experimental group d) the control group
The post-test measures the dependent variable.
In an experiment, the post-test measures refer to the data collected after the intervention or treatment has been given to the participants. Question 10 options may include choices related to the variables and groups involved in the experiment. Option a) the dependent variable is the variable being measured and is often affected by the independent variable. Option b) the independent variable is the variable being manipulated by the researcher to see its effect on the dependent variable. Option c) the experimental group is the group that receives the treatment or intervention, and option d) the control group is the group that does not receive the treatment or intervention and is used as a comparison to the experimental group. The question 10 options can help researchers determine the effects of the content loaded in an experiment on the variables and groups involved.
In an experiment, the post-test measures:
Question 10 options:
a) the dependent variable
Your answer: The post-test measures the dependent variable. This is because the dependent variable is the outcome that researchers are interested in measuring, and the post-test is conducted after the experiment to assess the effects of the independent variable on the dependent variable.
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a car travels at an average speed of 68 miles per hour. how long does it take to travel 612 miles
It takes 9 hours for the car to travel 612 miles at an average speed of 68 miles per hour.
To find the time it takes for the car to travel 612 miles at an average speed of 68 miles per hour, we can use the formula:
time = distance ÷ speed
Plugging in the given values, we get:
time = 612 miles ÷ 68 miles per hour
Therefore, the time it would take the car to travel 612 miles is: Time = 612 miles / 68 miles per hour Time = 9 hours. So, it would take the car approximately 9 hours to travel a distance of 612 miles if it maintains an average speed of 68 miles per hour.
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slope fields on page 3 of differential equations 7.1 to 7.5
A slope field is a graphical representation of the slopes of the tangent lines to the solutions of a first-order differential equation, dy/dx = f(x, y).
The goal of a slope field is to provide a visual representation of the behavior of the solutions to the differential equation, without necessarily solving the equation analytically.
To create a slope field, follow these steps:
1. Write down the given first-order differential equation, dy/dx = f(x, y).
2. For each point (x, y) in the field, calculate the slope f(x, y) using the differential equation.
3. At each point (x, y), draw a short line segment with the slope calculated in step 2.
4. Repeat steps 2 and 3 for various points on the field to get a complete visual representation.
5. Observe the overall behavior of the slopes in the field, which can help you understand the behavior of the solution curves.
In summary, a slope field is a useful tool to visualize the behavior of solutions to differential equations. By analyzing the slopes of tangent lines at various points, you can gain insights into the characteristics of the solution curves without solving the equation analytically.
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A piece of clothing contains 6% spandex. Write the percent as a decimal
Answer:60%
Step-by-step explanation: To convert a percentage to a decimal, divide by 100. So 25% is 25/100, or 0.25. To convert a decimal to a percentage, multiply by 100 (just move the decimal point 2 places to the right).
En el vestíbulo de entrada hay un mostrador para la venta de entradas, el arquitecto jefe le
plantea a uno de sus ayudantes que determine cuánto mide de ancho con las siguientes
condiciones: su valor en metros es un número tal que su potencia al cuadrado sumado a su
potencia a la cuarta dará 90. El mostrador tiene que medir de ancho:
The width of the counter is 3 meters or 9/3 meters as a fraction considering the condition that its value in meters is a number such that its power squared added to its power to the fourth will give 90.
Let's represent the width of the counter in meters as "x". As per the given condition, we can form the equation:
x² + [tex]x^4[/tex] = 90
Simplifying the equation, we get:
[tex]x^4[/tex] + x² - 90 = 0
Now, we can factor the equation as:
(x² - 9)(x² + 10) = 0
So, the possible values of "x" are:
x² = 9 or x² = -10
Since the width of the counter cannot be negative, we can ignore the second solution. Therefore, we have:
x² = 9
x = ±√9
x = ±3
Since the width of the counter cannot be negative, the only possible solution is:
x = 3
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The question is -
In the entrance hall, there is a counter for the sale of tickets, the chief architect will ask one of your assistants to determine how wide it is with the following conditions: its value in meters is a number such that its power squared added to its power to the fourth will give 90. Does the counter have to measure the width?