Answer:
c
Step-by-step explanation:
cuzz im right
k(t) = 10t - 19
K(-7) =
Answer:k(-7)=-89
Step-by-step explanation:
since k(t)=10t - 19
K(-7)=10(-7)-19
k(-7)=-70-19
k(-7)=-89
The following observations were made on fracture toughness of a base plate of 18% nickel maraging steel (in ksi in. , given in increasing order)]: 65.2 71.9 72.8 73.1 73.1 73.5 75.5 75.7 75.8 76.1 76.2 76.2 77.0 77.9 78.1 79.6 79.7 79.9 80.1 82.2 83.7 93.8 Calculate a 99% CI for the standard deviation of the fracture toughness distribution. (Round your answers to one decimal place.)
Answer:
[tex]\frac{(21)(5.437)^2}{41.402} \leq \sigma^2 \leq \frac{(21)(5.437)^2}{8.034}[/tex]
[tex] 14.996 \leq \sigma^2 \leq 77.278[/tex]
And the confidence interval for the deviation would be obtained taking the square root of the last result and we got:
3.9<σ<8.8
Step-by-step explanation:
Data given:
65.2 71.9 72.8 73.1 73.1 73.5 75.5 75.7 75.8 76.1 76.2 76.2 77.0 77.9 78.1 79.6 79.7 79.9 80.1 82.2 83.7 93.8
The sample mean would be given by:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
We can calculate the sample deviation with this formula:
[tex]s = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]
And we got:
s=5.437 represent the sample standard deviation
[tex]\bar x[/tex] represent the sample mean
n=22 the sample size
Confidence=99% or 0.99
The confidence interval for the population variance is given by:
[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]
The degrees of freedom given by:
[tex]df=n-1=22-1=21[/tex]
The Confidence is 0.99 or 99%, the value of significance is [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and the critical values are:
[tex]\chi^2_{\alpha/2}=41.402[/tex]
[tex]\chi^2_{1- \alpha/2}=8.034[/tex]
And the confidence interval would be:
[tex]\frac{(21)(5.437)^2}{41.402} \leq \sigma^2 \leq \frac{(21)(5.437)^2}{8.034}[/tex]
[tex] 14.996 \leq \sigma^2 \leq 77.278[/tex]
And the confidence interval for the deviation would be obtained taking the square root of the last result and we got:
3.9<σ<8.8
A city has a population of 360,000 people. Suppose that each year the population grows by 6.75%. What will the population be after 12 years.
Answer:
So, if it grows by 6.75%, each year the population is 106.75% of the year before.
After 1 year, 370,000(1.0675). After two years, 370,000(1.0675)(1.0675).
370,000(1.0675)12 = your answer
Step-by-step explanation:
Answer:
asdfgbhnjm
Step-by-step explanation:
zxcvb
A teacher selects students from her class of 37 students to do 4 different jobs in the classroom: pick uphomework, hand out review forms, staple worksheets, and sort the submissions. Each job is performedby exactly one student in the class and no student can get more than one job. How many ways arethere for her to select students and assign them to the jobs?
Answer:
There are 1,585,080 ways for her to select students and assign them to the jobs
Step-by-step explanation:
The order in which the students are selected is important, since different orderings means different jobs for each student selected. So the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem:
4 students selected from a set of 37. So
[tex]P_{(37,4)} = \frac{37!}{(37-4)!} = 1585080[/tex]
There are 1,585,080 ways for her to select students and assign them to the jobs
1. What is the area of the wall?
84 sq. ft.
78 sq. ft.
60 sq. ft.
27 sq. ft.
2. Wallpaper is sold in rolls that are 2 feet wide. What is the minimum length you would need to purchase to cover the wall?
Answer:
Step-by-step explanation:
Im going to assum the wall your talking about is the one at the bottom.
It is divided into two equal trapezoids, so we can find the area of one trapezoid, multiply it by 2 to find the area of the entire wall.
A= (1/2)(b1+b2)(h)
Where b1 and b2 are the two parrellel sides, and h is the height of the trapezoid.
A= .5*(9+6)(8/4) We divide by 8 by 2 because we are finding the area of one trapezoid which is half the height of the wall.
A= 30 ft squared.
2A= area of whole wall
2*30=60
The entire wall is 60 sq. ft.
2. The area you need to cover need to cover is 60 sqft.
Rolls of wallpaper are rectangular.
A = L*W and they told us the width is 2 ft. and we know the area we need to cover is 60 ft so we can subsitute those in to figure out the length.
60= L*2
L= 30 ft
You need at least 30 feet in length to cover the whole wall.
Giving brainliest for CORRECT awnser.
Answer:
D. x + 8
Step-by-step explanation:
factor. Find factors of x² and 48, in which, when combined, will equal 2x:
x² + 2x - 48
x 8
x -6
(x + 8)(x - 6)
D. x + 8 is your answer.
~
Last year, Jina had 30,000 to invest. She invested some of it in an account that paid 9%simple interest per year, and she invested the rest in an account that paid 5% simple interest per year. After one year, she received a total of $1540 in interest. How much did she invest in each account?
first account :
second:
Answer:
Amount invested in first account = $1,000
Amount invested in second account = $29,000
Step-by-step explanation:
Jina had total amount of $30,000 to invest last year.
Let x be the amount that Jina invested in the first account at interest rate of 9%
Mathematically,
0.09x
she invested the remaining amount in the second account at an interest rate of 5%
Mathematically,
0.05(30,000 - x)
Jina received $1540 in interest.
0.09x + 0.05(30,000 - x) = 1540
0.09x + 1500 - 0.05x = 1540
0.04x = 1540 - 1500
0.04x = 40
x = 40/0.04
x = $1,000
Therefore, Jina invested an amount of $1,000 in the first account at interest rate of 9%
The remaining amount that she invested in the second account is
Amount invested in second account = $30,000 - $1,000
Amount invested in second account = $29,000
Therefore, Jina invested an amount of $29,000 in the second account at interest rate of 5%
Verification:
0.09x + 0.05(30,000 - x) = 1540
0.09(1000) + 0.05(30,000 - 1000) = 1540
90 + 1450 = 1540
1540 = 1540 (satisfied)
The weight of National Football League (NFL) players has increased steadily, gaining up to 1.5 lb. per year since 1942. According to ESPN, the average weight of a NFL player is now 252.8 lb. Assume the population standard deviation is 25 lb. If a random sample of 50 players is selected, what is the probability that the sample mean will be more than 262 lb.
Answer:
The probability that the sample mean weight will be more than 262 lb is 0.0047.
Step-by-step explanation:
The random variable X can be defined as the weight of National Football League (NFL) players now.
The mean weight is, μ = 252.8 lb.
The standard deviation of the weights is, σ = 25 lb.
A random sample of n = 50 NFL players are selected.
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The sample of players selected is quite large, i.e. n = 50 > 30, so the central limit theorem can be used to approximate the distribution of sample means.
[tex]\bar X\sim N(\mu_{\bar x}=252.8,\ \sigma_{\bar x}=3.536)[/tex]
Compute the probability that the sample mean weight will be more than 262 lb as follows:
[tex]P(\bar X>262)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{262-252.8}{3.536})\\\\=P(Z>2.60)\\\\=1-P(Z<2.60)\\\\=1-0.99534\\\\=0.00466\\\\\approx 0.0047[/tex]
*Use a z-table for the probability.
Thus, the probability that the sample mean weight will be more than 262 lb is 0.0047.
To find the probability that the sample mean will be more than 262 lb, calculate the z-score using the sample mean, population mean, standard deviation, and sample size. Then, find the corresponding probability using the standard normal distribution table. Subtract the probability from 1 to get the final result, which is approximately 0.2%.
Explanation:To solve this problem, we need to use the z-score formula and the standard normal distribution table. First, calculate the z-score using the formula: z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. In this case, x = 262 lb, μ = 252.8 lb, σ = 25 lb, and n = 50. Plug in these values and calculate the z-score. Next, find the corresponding probability using the standard normal distribution table. Look up the z-score and find the corresponding probability. The probability that the sample mean will be more than 262 lb can be found by subtracting the probability you found from 1.
Calculating the z-score:
z = (262 - 252.8) / (25 / sqrt(50)) = 2.901.
Using the standard normal distribution table, the probability corresponding to a z-score of 2.901 is approximately 0.998. Therefore, the probability that the sample mean will be more than 262 lb is approximately 1 - 0.998 = 0.002, or 0.2%.
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9+x-7 I need help bad
Step-by-step explanation:
9 + x - 7
Solving like terms
x + 2
If we find the value of x
X + 2 = 0
x = - 2
−6(b+2)+8 answer quick
Answer:
b = 16
Step-by-step explanation:
Answer:
-6b-12+8 which simplifies to -6b-4
Step-by-step explanation:use distrubutive property and then combine like terms
Alexia uses two and one-third cups of flour for each batch of cookies she makes. If she makes three-fourths of a batch of cookies, how much flour does she use?
Answer:
She uses 1.7475 cups of flour.
Step-by-step explanation:
This question can be solved using a rule of three.
For each batch of cookies:
Two and one-third cups of flour.
So [tex]2 + \frac{1}{3} = 2.33[/tex] cups.
If she makes three-fourths of a batch of cookies, how much flour does she use?
3/4 = 0.75 batch of cookies. How much flour?
1 batch - 2.33 cups.
0.75 batches - x cups
x = 2.33*0.75
x = 1.7475
She uses 1.7475 cups of flour.
Answer:
1 3/4
Step-by-step explanation:
The business department at a university has 18 faculty members. Of them, 11 are in favor of the proposition that all MBA students should take a course in ethics and 7 are against this proposition. If 5 faculty members are randomly selected from the 18, what is the probability that the number of faculty members in this sample who are in favor of the proposition is exactly two
Answer:
0.225
Step-by-step explanation:
Total outcomes of choosing 5 out of 18 members = 18C5
Outcomes of choosing 2 out 11 favourers, 3 out of 7 members = 11C2 & 7C3
Probability = Favourable outcomes / Total outcomes
= ( 11C2 x 7C3 ) / 18C5
[ { 11 ! / 2! 9! } {7 ! / 3! 4! } ]
[ 18 ! / 5! 13! ]
( 55 x 35 ) / 8568
1925 / 8568
= 0.2246 ≈ 0.225
Crane Company publishes a monthly sports magazine, Fishing Preview. Subscription to the magazine cost $30 per year. During November 2020, Crane sells 25,000 subscriptions beginning with the December issue. Crane prepares financial statements quarterly and recognizes subscription revenue at the end of the quarter. The company uses the accounts Unearned Subscription Revenue and Subscription Revenue. Prepare the entry in November for the receipt of the subscription
Journal entry
Explanation:
Books of (----Limited)
Journal Entry
Date Account Title and Explanation Debit Credit
Cash / Bank A/c Dr. $750,000
To Unearned Subscription A/c $750,000
(Being Unearned Subscription)
Computation:
Amount of Unearned Subscription = 25,000 × $30
Amount of Unearned Subscription = %750,000
Consider the series Summation from n equals 0 to infinityStartFraction (negative 1 )Superscript n Baseline (x plus 1 )Superscript n Over n exclamation mark EndFraction . (a) Find the series' radius and interval of convergence. (b) For what values of x does the series converge absolutely? (c) For what values of x does the series converge conditionally? (a) Find the interval of convergence. nothing ▼ less than less than or equals x ▼ less than or equals less than nothing Find the radius of convergence. Requals nothing (b) For what values of x does the series converge absolutely? nothing ▼ less than less than or equals x ▼ less than less than or equals nothing (c) For what values of x does the series converge conditionally? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series converges conditionally at xequals nothing. (Use a comma to separate answers as needed.) B. The series does not converge conditionally.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Question 3
A rectangular prism has dimensions 3 inches, 4 inches, and 5 inches. Find the dimensions of another
rectangular prism with the same volume but less surface area.
What are the dimensions of the shape? *
What is its surface area?*
Answer:
Step-by-step explanation:
The formula for finding the volume is
Volume = length × width × height
Volume of the given prism is
Volume = 3 × 4 × 5 = 60 inches³
The formula for determining the surface area of a rectangular prism is expressed as
Surface area = Ph + 2B
Where
P represents perimeter of base
h represents height of prism
B represents base area
Perimeter of base = 2(length + width)
P = 2(3 + 4) = 14 inches
B = 3 × 4 = 12 inches
h = 5 inches
Surface area = 14 × 5 + 2 × 12 = 94 inches²
For another prism,
Assuming h = 3, length = 10 and width = 2, then
Volume = 3 × 10 × 2 = 60 inches³
P = 2(10 + 2) = 24 inches
B = 10 × 2 = 20 inches
Surface area = (24 × 3) + (2 × 20) = 112 inches²
If we keep changing the values, the surface area will always be greater than 94 inches².
Therefore, there is no rectangular prism with the same volume but less surface area.
Answer:
its 60 for volume, but for the area i don't know
Step-by-step explanation:
How many decimal places are in 7,790,200
Final answer:
The number 7,790,200 has zero decimal places as it is a whole number with no fractional part and ends in the unit's place.
Explanation:
The student asked how many decimal places are in 7,790,200. This question is related to place value and decimals in mathematics. The number 7,790,200 has no decimal part since it is a whole number and ends in the unit's place. Therefore, it contains zero decimal places. To expand on place value, when expressing numbers in decimal form, the position of a digit represents its value in powers of ten. For instance, the number 1837 can be decomposed as (1 × 10³) + (8 × 10²) + (3 × 10¹) + (7 × 10⁰), which shows the ones, tens, hundreds, and thousands places respectively.
a show company makes blue shoes and black shoes with a ratio of 3:4 ratio. if the company makes 360 black shoes how many blue shoes will they make? plz halp and if u pway roblox my username is zaw1031 :3
In the given scenario, when the shoe company makes 360 black shoes, they will also make 270 blue shoes as the ratio was provided as 3:4.
Explanation:The problem involves the concept of ratio proportion. Given the ratio of blue shoes to black shoes is 3:4, this means for every 3 blue shoes, 4 black shoes are made. If the company makes 360 black shoes, this is like 90 sets of 4 black shoes (360/4). That means 90 sets of 3 blue shoes must also be made. Therefore, the company will make 270 (90*3) blue shoes when 360 black shoes are made.
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si a un numero le sumas su anterior, obtienes 37. ¿ de que numero hablamos?
Answer:
Would you be able to write it in english so i can help you.
Step-by-step explanation:
4x2 + 8x - 7
is classified as a...
Answer:
Quadratic function (assuming 4x2 is 4x^2)
Step-by-step explanation:
Linear functions are ax+b=y
Quadratic is ax^2+b=y
Cubic is ax^3+b=y
The equation 4x² + 8x - 7 is a Quadratic equation.
What is Quadratic equation?
An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The equation is,
⇒ 4x² + 8x - 7
Now,
Clearly, In the equation;
The highest power of a variable is two.
And, we know that;
In the quadratic equation, the highest power of a equation is two.
Thus, The equation 4x² + 8x - 7 is a Quadratic equation.
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A baseball player threw 82 strikes out of 103 pitches. what percentage of pitches were strikes?
We have been given that a baseball player threw 82 strikes out of 103 pitches. We are asked to find the percentage of pitches that were strikes.
To solve our given problem, we need to find strikes are what percent of pitches.
[tex]\text{Percentage of pitches that were strikes}=\frac{82}{103}\times 100\%[/tex]
[tex]\text{Percentage of pitches that were strikes}=0.7961165\times 100\%[/tex]
[tex]\text{Percentage of pitches that were strikes}=79.61165\%[/tex]
[tex]\text{Percentage of pitches that were strikes}\approx 79.6\%[/tex]
Therefore, approximately [tex]79.6\%[/tex] of pitches were strikes.
PLS HELP WILL GIVE BRAINILIST 20 POINTS!
If you have no more than $15 in your bank account, which of the following inequalities correctly represents the amount of money in your bank account?
m ≤ $15
m ≥ $15
m < $15
m > $15
Answer: M≤ $15
Step-by-step explanation:
The answer is [ m ≤ $15 ]
The question states, "If you have no more than $15." This means that you can only have up to $15 and no more.
So, the solutions to the set are all real numbers except the numbers after 15.
Let's say you had $9. If we were to substitute 9 with m in the inequality, we would get; 9 ≤ 15. This satisfies the inequality since the number is less than 15.
Best of Luck!
Can anyone help me with this, I don’t understand what its asking
Answer:
It's asking you to solve the question or find N
Step-by-step explanation:
Mrs. McDonnell is making 25 paper cones to fill
with popcorn for her daughter's birthday party.
4 inches
2
17 inches
Find the volume of one paper cone if the
diameter is 4 inches and the height is 7 inches.
Round your answer to the nearest cubic inch.
29in?
B. 59in3
88in
D. 117in
Answer:
(A)29 cubic inch
Step-by-step explanation:
Diameter of the Cone =4 Inches
Height of the Cone =7 Inches
Volume of a Cone [tex]=\frac{1}{3}\pi r^2h[/tex]
First, we determine the radius, r.
Radius=Diameter/2=4/2=2 Inches
Therefore:
Volume of one paper cone [tex]=\frac{1}{3}\pi *2^2*7[/tex]
=29.32 cubic inch
=29 cubic inch (to the nearest cubic inch.)
The lifetime of certain type of light bulb is normally distributed with a mean of 1000 hours and a standard deviation of 110 hours. A hardware store manager claims that the new light bulb model has a longer average lifetime. A sample of 10 from the new light bulb model is obtained for a test. Consider a rejection region After testing hypotheses, suppose that a further study establishes that, in fact, the average lifetime of the new lightbulb is 1130 hours. Find the probability of a type II error (round off to second decimal place).
Answer:
There is a probability of P=0.02 of making a Type II error if the true mean is μ=1130.
Step-by-step explanation:
This is an hypothesis test for the lifetime of a certain ype of light bulb.
The population distribution is normal, with mean of 1,000 hours and STD of 110 hours.
The sample size for this test is n=10.
The significance level is assumed to be 0.05.
In this case, when the claim is that the new light bulb model has a longer average lifetime, so this is a right-tailed test.
For a significance level, the critical value (zc) that is bound of the rejection region is:
[tex]P(z>z_c)=0.05[/tex]
This value of zc is zc=1.645.
This value, for a sample with size n=10 is:
[tex]z_c=\dfrac{X_c-\mu}{\sigma/\sqrt{n}}\\\\\\X_c=\mu+\dfrac{z_c\cdort\sigma}{\sqrt{n}}=1000+\dfrac{1.645*110}{\sqrt{10}}=1000+57.22=1057.22[/tex]
That means that if the sample mean (of a sample of size n=10) is bigger than 1057.22, the null hypothesis will be rejected.
The Type II error happens when a false null hypothesis failed to be rejected.
We now know that the true mean of the lifetime is 1130, the probability of not rejecting the null hypothesis (H0: μ=1100) is the probability of getting a sample mean smaller than 1057.22.
The probability of getting a sample smaller than 1057.22 when the true mean is 1130 is:
[tex]z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{1057.22-1130}{110/\sqrt{10}}=\dfrac{-72.78}{34.7851}=-2.0923 \\\\\\P(M<1057.22)=P(z<-2.0923)=0.01821[/tex]
Then, there is a probability of P=0.02 of making a Type II error if the true mean is μ=1130.
Using the normal distribution and the central limit theorem, it is found that there is a 0.0001 = 0.01% probability of a type II error.
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 1130 hours, hence [tex]\mu = 1130[/tex]Standard deviation of 110 hours, hence [tex]\sigma = 110[/tex]Sample of 10 bulbs, hence [tex]n = 10, s = \frac{110}{\sqrt{10}}[/tex].We test if the average lifetime is longer, and a Type II error is concluding that it is not longer when in fact it is longer, hence, it is the probability of finding a sample mean below 1000 hours, which is the p-value of Z when X = 1000.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1000 - 1130}{\frac{110}{\sqrt{10}}}[/tex]
[tex]Z = -3.74[/tex]
[tex]Z = -3.74[/tex] has a p-value of 0.0001.
0.0001 = 0.01% probability of a type II error.
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The first sail has one side of length 9 feet and another of length 6 feet. Determine the range of possible lengths of the third side of the sail.
first find the greatest possible length:
9 + 6 > x
15 > x
x < 15
Then find the lowest possible length:
x + 6 > 9
x > 9 - 6
x > 3
3 < x < 15
To determine the range of possible lengths of the third side of a sail, use the triangle inequality theorem. The range is 3 feet to 15 feet.
Explanation:To determine the range of possible lengths of the third side of the sail, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the two given sides are 9 feet and 6 feet. So, the third side must be less than the sum of these two sides and greater than the difference between these two sides.
Therefore, the range of possible lengths of the third side of the sail is 3 feet to 15 feet.
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Determine between which consecutive integers the real zeros of y(x) = x2 - 4x – 2 are located.
Answer:
The zeros are x1=4.45 and x2=-0.45.
x1 is between 4 and 5.
x2 is between -1 and 0.
Step-by-step explanation:
We have the function:
[tex]y(x) = x2 - 4x-2[/tex]
As this is a quadratic function, we can calculate the zeros of the function with the quadratic equation:
[tex]x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4\cdot 1\cdot(-2)}}{2\cdot 1}\\\\\\x=\dfrac{4\pm\sqrt{16+8}}{2}\\\\\\x=\dfrac{4\pm\sqrt{24}}{2}\\\\\\x=\dfrac{4\pm4.9}{2}=2\pm2.45\\\\\\x_1=2+2.45=4.45\\\\x_2=2-2.45=-0.45[/tex]
The zeros are x1=4.45 and x2=-0.45.
x1 is between 4 and 5.
x2 is between -1 and 0.
The two real zeros of the quadratic equation are located between -1 and 4.
Between which consecutive integers the real zeros located?To determine between which consecutive integers the real zeros of the function y(x) = x² - 4x - 2 are located, we can use the quadratic formula.
The quadratic formula is given as:
x = (-b ± √(b² - 4ac)) / (2a)
In the equation y(x) = x² - 4x - 2, we have a = 1, b = -4, and c = -2.
Let's substitute these values into the quadratic formula to find the values of x:
x = (-(-4) ± √((-4)² - 4(1)(-2))) / (2(1))
x = (4 ± √(16 + 8)) / 2
x = (4 ± √24) / 2
x = (4 ± 2√6) / 2
x = 2 ± √6
From the quadratic formula, we find that the real zeros of the function are x = 2 + √6 and x = 2 - √6.
To determine between which consecutive integers these real zeros are located, we can compare the values to the nearest integers.
x = 2 + √6 is approximately 4.45
x = 2 - √6 is approximately -0.45
Therefore, the real zeros of the function are located between the consecutive integers -1 and 4.
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What is the base 10 representation of the number 1203,?
OA) 128
OB) 178
OC) 324
OD) 476
Answer:
178
Step-by-step explanation:
Amelia flies her airplane through calm skies at a velocity v1. The direction of v1 is 15 degrees north of east, and the speed is 180 km/hr.
Eventually, however, she enters a windy part of the atmosphere and finds that her plane now moves at a velocity v2. The direction of v2 is due east, and the speed is 150 km/hr.
What is the speed of the wind?
In what direction is the wind blowing?
(between 0 and 360 degrees)
Answer:
Step-by-step explanation:
Given
Initially Plane is flying at the speed of [tex]180\ km/hr[/tex]
to the [tex]15^{\circ}[/tex] North of east
Now wind started Blowing and plane started moving towards east with speed [tex]150\ km/hr[/tex]
suppose [tex]1v_o[/tex] is the speed of wind
So,
[tex]\vec{v_2}=\vec{v_1}-\vec{v_o}[/tex]
[tex]150\hat{i}=180[\cos 15\hat{i}+\sin 15\hat{j}]-\vec{v_o}[/tex]
[tex]\vec{v_o}=\hat{i}[180\cos 15-150]+\hat{j}[180\sin 15][/tex]
[tex]\vec{v_o}=\hat{i}[173.866-150]+46.58\hat{j}[/tex]
[tex]\vec{v_o}=23.86\hat{i}+46.58\hat{j}[/tex]
So magnitude of wind is
[tex]\mid v_o\mid=\sqrt{23.86^2+46.58^2}[/tex]
[tex]\mid v_o\mid=\sqrt{2738.996}[/tex]
[tex]\mid v_o\mid=52.33\ km/hr[/tex]
direction [tex]\tan \theta=\frac{46.58}{23.86}[/tex]
[tex]\theta =62.87^{\circ}[/tex] North of east
Answer:
The speed of the wind is 52.3 km/h
The direction of the wind is 243 degrees.
this is the right answer
Step-by-step explanation:
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A glass bead has the shape of a rectangular prism with a smaller rectangular prism removed. What is the volume of the glass that forms the bead?
The volume of the glass bead formed by a rectangular prism with a smaller prism removed can be found by subtracting the volume of the smaller prism from the larger prism. As an example, a larger prism of volume 60 cubic cm and smaller prism of volume 8 cubic cm gives a bead of volume 52 cubic cm.
Explanation:The volume of the glass bead formed by a rectangular prism with a smaller rectangular prism removed can be calculated using the formula for the volume of a rectangular prism, which is length × width × height. The volume of the glass bead would then be the volume of the larger prism minus the volume of the smaller prism.
As an example, if the larger prism has a length of 5cm, width of 4cm, and height of 3cm, its volume would be 5cm × 4cm × 3cm = 60 cubic cm. If the smaller prism removed has a length of 2 cm, width of 2 cm, and height of 2 cm, its volume would be 2cm × 2cm × 2cm = 8 cubic cm. Subtracting the volume of the smaller prism from the larger one gives a volume of 60 cubic cm - 8 cubic cm = 52 cubic cm which is the volume of the glass bead.
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The volume of the glass bead is then 200 cm³ - 6 cm³ = 194 cm³.
Calculating the Volume of a Glass Bead
To find the volume of a glass bead with the shape of a rectangular prism with a smaller rectangular prism removed, follow these steps:
Calculate the volume of the larger rectangular prism. Use the formula Volume = length × width × height.Next, calculate the volume of the smaller rectangular prism that is being removed using the same formula.Subtract the volume of the smaller prism from the volume of the larger prism. This will give you the volume of the glass bead.For example, if the dimensions of the larger rectangular prism are 10 cm (length), 5 cm (width), and 4 cm (height), its volume will be 200 cm³. If the smaller removed prism has dimensions of 3 cm (length), 2 cm (width), and 1 cm (height), its volume will be 6 cm³. The volume of the glass bead is then 200 cm³ - 6 cm³ = 194 cm³.
Select the correct answer.
Determine the solutions to the following equation.
(1 – 4)2 = 81
O
x= -13 and 5
x= -5 and 13
x= -4 and 9
x = -9 and 4
Shouldn't the equation read " (x - 4)² = 81 ", instead of "(1 - 4)² = 81" ?
If so, then the solutions are x = -5 and x = 13 .
If it's really "(1 - 4)² = 81", then that's not even an equation, and there's no solution.
The solutions to the given equation are x = -5 and x = 13.
The correct solutions to the given equation are x = -5 and x = 13.
To solve the equation (1 - 4)2 = 81:
Calculate (1 - 4)2 = 81.Then simplify the equation: (-3)2 = 81, which gives 9 = 81.Finally, since 9 is not equal to 81, the solutions are x = -5 and x = 13.