At 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.
What is the quadratic equation?
Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.
Let x (ft) be the distance from the base of the left pole to the anchor point. Since 2 poles has a distance of 45 ft, the distance from the anchor point to the right pole is 45 - x
The wire length from the top of the left pole to the anchor point is
[tex]L^{2} _l = 30^{2} + x^{2}[/tex]
= x² + 900
Similarly for the 2nd part of the wire
[tex]L^{2} _r = 15^{2} + (45-x)^{2}[/tex]
= 256 + 2025 - 45x + x²
= x² + 2281 - 45x
We want to minimize the length of the wires, or [tex]L_l + L_r[/tex]
√x² + 900 + √ x² + 2281 - 45x
we can take the first derivative of this and set it to 0
[tex]\frac{x}{\sqrt{ x^2 + 900} } + \frac{45 - x}{\sqrt{x^2 + 2281 - 45x} } = 0[/tex]
x = 30
Hence, at 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.
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A researcher is interested in whether using your finger to follow the words you are reading changes reading speed. He has students complete a reading speed test, first without using their fingers to follow the words and then again while using their fingers to follow the words. The researcher randomly selects a sample of 56 students who, at the beginning of the study, scored an average of 256 words per minute on the reading speed test. In the trial where they used their fingers while they read, the students scored an average of 6 words per minute higher. The standard deviation of the difference scores was 29. Since the sample size is larger than 30, the researcher can assume that the sampling distribution of MD is normal. He uses a repeated-measures t test to test that the mean difference is zero, and he describes the results as follows: In the trial where they used their fingers while they read, the reading speed among students is not significantly different than when they do not use their fingers while they read, t(55) = 1.55, p = 0.127. If the researcher had used a repeated-measures ANOVA to test that the mean reading speed is the same before and after using their fingers while they read, he would describe the results as follows (fill in all missing values): In the trial where they used their fingers while they read, the reading speed among students is different than when they do not use their fingers while they read, F()=, p = 0.127.
The confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17
On Subtracting 1 from your sample size, we get
150 – 1 = 149.
On Subtracting confidence level from 1, and then divide by two.
(1 – .95) / 2 = 0.025
Now, df = 149 and α = 0.025
from the table at df = 149 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
28 / √(150) = 2.28
Now, 2.262 × 2.28 = 5.17
So, the confidence interval be,
(150 - 5.17 , 150 + 5.17) = (144.83 , 155.17)
Hence, the confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17
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Factor each polynomial
Answer:
(x + 7)(x² - 8)
Step-by-step explanation:
x³ + 7x² - 8x - 56 =
let's put the total multiplier x² out of brackets
x²(x + 7) - 8x - 56 =
let's put the total multiplier -8 out of brackets
x²(x + 7) - 8(x + 7) =
let's put the total multiplier (x + 7) out of brackets
(x + 7)(x² - 8)
a statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. the 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. suppose the distribution of the population of number of pushups that can be done is approximately normal. what is the standard error of the mean?
Using the t-distribution, we have that the 95% confidence interval for the true mean number of pushups that can be done is (9, 21).
Given that,
One day, a teacher of statistics randomly selected 10 pupils' names from a hat and instructed them to complete as many pushups as they could before class began. The 10 students who were chosen at random performed an average of 15 pushups, with a standard deviation of 9. Assume that the population's distribution of the maximum number of pushups is roughly normal.
We have to find what is the standard error of the mean.
We know that,
For this problem, we have the standard deviation for the sample, thus, the t-distribution is used.
The sample mean is of 15 is x=15 .
The sample standard deviation is of 9 is s=9.
The sample size is of 10 is n=10.
First, we find the number of degrees of freedom, which is the one less than the sample size, thus df = 9.
Then, looking at the t-table or using a calculator, we find the critical value for a 95% confidence interval, with 9 df, thus t = 2.2622
The margin of error is of:
M=ts/n
Then:
M=2.2622(9/√10)
M=6
The confidence interval is:
x±M
x-M=15-6=9
x+M=15+6=21
Therefore, Using the t-distribution, we have that the 95% confidence interval for the true mean number of pushups that can be done is (9, 21).
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a bowling team has 6 members. how many ways can the captain of the team arrange the bowlers for a game
The number of ways in which captain of the team arrange the 6 bowlers for a game is 720.
Explain the term arrangement?Generally speaking, an arrangement among objects is just a collection of them. A combination (ordering is disregarded) or permutation is used to determine the number possible "arrangements" of the components (order is significant). An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets were arranged in a linear or sequential order.For the stated question-
Total members in bowling team = 6.
Number of ways to arrange them = 6!
Number of ways = 6 x 5 x 4 x 3 x 2 x 1
Number of ways = 720
Thus, the number of ways in which captain of the team arrange the 6 bowlers for a game is 720.
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Divide.
8 ÷ 1/9
Enter your answer in the box.
Answer:
0.8888888..... repeating
Step-by-step explanation:
Answer:
72/1
Step-by-step explanation:
multiply 8 and 9/1
Çok acil arkadaşlar lütfen
Answer:
Step-by-step explanation:
PLS HELPP Which algebraic expression is equivalent to 3(2x – 7)
Answer:
6x-21
Step-by-step explanation:
6x*3 - 7*3
what
Expand 2 ( c − 2 )
Answer:
[tex]\boxed{\tt 2c-4}[/tex]
Step-by-step explanation:
[tex]\tt 2\left(c-2\right)[/tex]
Apply the distributive property:-
[tex]\tt 2\left(c-2\right)=2c-2\times \:2[/tex]
[tex]\bf 2\times\:2=4[/tex]
[tex]\tt 2c-4[/tex]
___________________
Hope this helps!
Have a great day!
Calculate the social security and Medicare deductions for the following employee assume a tax rate of 6.2% on $128,400 for social security and 1.45% for Medicare. Logan has a cumulative earnings before this pay period was $128,300 , and pay amount this period was$3,000. What is the social security and what was the medicare
The social security and Medicare deductions for the following employee are $7768 and $1816 respectively.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical process, and extraction of roots
Main body:
Cumulative Earnings before this pay period = $128,300
pay amount this period = $3000
tax rate of 6.2% on social security = 6.2%
effective earning = 128300 = 3000
= 125300
social security deduction = 6.2 % of 125300
⇒ 6.2 *125300 /100
⇒$7768
Medicare deductions = 1.45%
⇒ 1.45*125300/100
⇒$1816
Hence , the social security and Medicare deductions for the following employee are $7768 and $1816 respectively.
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Tell whether 20/8 and 28/9 form a proportion.
The two given fractions [tex]\frac{20}{8}[/tex] and [tex]\frac{28}{9}[/tex] do not form a proportion.
How to find fractions that are in the same proportion?
Proportion shows that two fractions are equivalent or equal.
The given fractions are [tex]\frac{20}{8}[/tex] and [tex]\frac{28}{9}[/tex]
Proportions are expressed in the form a:b::c:d
Where a and b represent antecedent and consequent respectively
This implies that a:b::c:d ⇒ [tex]\frac{20}{8}[/tex] : [tex]\frac{28}{9}[/tex]
The values [tex]\frac{20}{8}[/tex] = [tex]\frac{28}{9}[/tex]
Since (20x9) is not equal to (8x28)
Multiplying the two sides to get
180=224. This is a wrong representation.
Therefore the two fractions do not show a proportion
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PLEASE HURRY! I WILL GIVE BRAINLIEST TO THE PERSON WHO GIVES THE RIGHT ANSWER! DO NOT SPAM OR I WILL REPORT!
2300 dollars is placed in an account with an annual interest rate of 5.5%. To the nearest tenth of a year, how long will it take for the account value to reach 4300 dollars?
Answer:
I think 6.2 years
Step-by-step explanation:
I THINK OK
a hand of 13 cards is dealt at random from a bridge deck of 52 cards. find the probability that the hand contains 4 queens. (round your answer to four decimal places.)
The probability of the hand containing 4 queens when picked at random is 0.0026.
We can solve the given question easily using probability, permutations, and combinations.
We can pick any card other than the queen in the following number of ways = ⁴⁸C₉ (i)
The queen card can be picked in the following number of ways
= ⁴C₄= 1 (ii)
The total number of ways to choose 13 cards is = ⁵²C₁₃ (iii)
Using the values of (i), (ii), and (iii), we get -
Probability = (⁴⁸C₉ * 1) / ⁵²C₁₃
= [tex]\frac{48!/9!(48-9)! *1 }{52!/13!(52-13)! }[/tex]
= 1677106640 * 1 / 635013559600
= 0.00264
If this is rounded to four decimal places, we get = 0.0026.
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. A grain merchant sold 600 quintals of rice at a profit of 7%. If a quintal of rice cost him Rs 250 and his total overhead charges for transportation, etc. were Rs 1000 find his total profit and the selling price of 600 quintals of rice.
Answer:
The total profit for the grain merchant selling 600 quintals of rice is Rs 12800. To calculate this, we first need to calculate the profit on one quintal. The profit percentage is 7%, so if a quintal costs Rs 250 the profit is 7% of 250 which is Rs 17.5. Now we multiply this with the number of quintals sold, which is 600, to get Rs 10500 as the profit. We then add in the overhead charges of Rs 1000 to get a total profit of Rs 12800. The selling price of 600 quintals of rice is therefore Rs 12800 plus Rs 250 times 600, which equals Rs 180000.
Parvinder wants to save $500 for a trip. Which inequality shows the least amount she must save each month for 6 months to accomplish this?
Answer: $84 i think
Step-by-step explanation:
Write an equation for the nth term of the arithmetic seqeuence. Then find a10. 12,1,112,2,.
An equation for the nth term of the arithmetic sequence: an = n - 6.
ad 10th term a10 = 4.
Define the term arithmetic sequence?A sequence of a form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence.A common difference of the sequence is d, and the number an is the first term.The formula for the nth term of the
an = a + (n -1)d
In which,
a = initial termd = common differencen = total number of termsThe arithmetic sequence is given as-
−5,−4,−3,−2, ...
Then, the equation will be
d = a2 - a1
d = -4 - (-5) = 1
an = a + (n -1)d
an = -5 + n - 1
Put n = 10 in the equation.
a10 = 10 - 6
a10 = 4
Thus, the 10th term of the sequence is 4.
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The correct question is-
Write an equation for the nth term of the arithmetic sequence. Then find a10.
−5,−4,−3,−2, ...
please help me i need it bad
Using the secant-secant theorem,
[tex]\frac{13x+7-60}{2}=5x-10 \\ \\ 13x-53=10x-20 \\ \\ 3x-53=-20 \\ \\ 3x=33 \\ \\ \boxed{x=11} \\ \\ \\ \\ \angle RDB=5(11)-10=\boxed{45^{\circ}}[/tex]
I am a number with 3 tens and 23 ones. What number am I
Answer:
Is it 53?
Step-by-step explanation:
3 tens means 30, and adding 23 ones would be 53
An arithmetic sequence has a 2nd term of -2 and a 7th term of 18.
1. What is the 10th term in the sequence? 2. Write an explicit formula for the sequence.
3. Write a recursive formula for the sequence.
4. What is the sum of the first 10 terms?
Answer:
Step-by-step explanation:
A company determines an employee's starting salary according to the number of years of experience, as detailed in the table. Years of experience salary 0 $40,000 1 $42,150 2 $44,260 3 $46,785 4 $48,820 5 $51,126 use the equation for the line of best fit to predict the salary for an employee with 7 years of experience? (round your answer to the nearest dollar. ) $52,900 $53,340 $53,914 $55,573.
The wage for a worker with 7 years of experience may be calculated using the equation for the line of best fit as follows: D. $55,573.
A line of best fit is what?A trend line, also known as a line of best fit, is a statistical (analytical) technique that is used with a scatter plot to ascertain whether or not there is any link (correlation) between a set of data.
In this case, the pay would be placed on the y-axis of the scatter plot and the employee's years of experience would be put on the x-axis.
What is the equation of best fit?A line of best fit can be described by the equation y=mx+b, where m denotes the slope and b the y-intercept. To comprehend the idea of how to roughly approximate the equation of a line of best fit and make predictions, we will look at two examples that show a scatter plot with a line of best fit.
We may rationally and logically conclude that the equation for the line of best fit is given by: by carefully examining the scatter plot that models the data in the provided table (see attachment).
y = 2233.3x + 39940
The wage for an employee with seven years of experience would thus be predicted using the equation for the line of best fit as follows:
y = 2233.3(7) + 39940
y = 15,633.1 + 39940
y = 55,573.1 ≈ $55,573.
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a business major needs 3 humanities courses to graduate. they can be selected from 29 courses offered. how many ways can the 3 courses be selected?
The number of ways 3 courses can be selected is 3654.
How to calculate combination?
The sequence of the results is irrelevant when calculating the overall outcomes of an event using combinations. We will use the formula nCr = n! / r! * (n - r)! to calculate combinations, where n denotes the total number of items and r denotes the number of things being chosen at a time.The sum of all positive integers that are greater than zero and less than your number is known as a factorial. An exclamation point is written after the number to represent a factorial.Total no. of courses available = 29
Courses needed to graduate = 3
No of ways these courses can be selected:
= ²⁹C₃
= 29!/ [(29-3)! - 3!]
= 29! / 26! 3!
= 29 * 28 * 27 * 26!/ 26! 3*2
= 29* 14* 9
=3654
So, the number of ways 3 courses can be selected is 3654.
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by what number do we multiply the initial enrollment to get the enrollment one decade later given a 30 % increase
The final enrollment after one decade is obtained by taking the 30% of the initial enrollment.
Describe the term percentage of the number?A value or ratio that might be stated as a fraction over 100 is thought to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its total and then multiply it by 100. The proportion ultimately refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.For the stated question-
Let initial enrollment = 100.
After one decade, the enrollment added 30% of the initial.
Thus,
= 100 + 30% of 100
= 100 + 130
= 130
Thus, the final enrollment after one decade is obtained by taking the 30% of the initial enrollment.
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what is the minimum number of cards you would have to pull from a deck to guarantee that you have 4 of a kind? (answer: 40)
The probability that a deck to guarantee that you have 4 of a kind is 40.
Probability:
In math probability refers the possibility of event.
Given,
Here we need to find the minimum number of cards you would have to pull from a deck to guarantee that you have 4 of a kind.
As we know that the total number of cards in the deck is 52.
So, the number of ways of choosing 4 cards from a pack of 52 playing cards is calculated as,
=> ⁵²C₄ = 52!/4!48!
=> ⁵²C₄ = 270725
Similarly, the number of ways of choosing 4 cards of same suit
=> ¹³C₄ = 13!/4!9!
=> ¹³C₄ = 715
So, the number of ways of choosing 4 cards of different suit is calculated as,
=> 715/17 = 40
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10c - cd + d^3 (if c = -6 and d= 2)
The required simplified solution of the given expression is -40.
Given that,
To determine the simplified solution of the given expression 10c - cd + d³ at c = -6 and d = 2.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
= 10c - cd + d³
Substitute the values,
= -60 + 12 + 8
= -40
Thus, the required simplified solution of the given expression is -40.
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6. a survey shows that 360 out of 500 females and 600 out of 800 males enjoy a game show. based on this evidence, would you argue that the ratio of female and male viewers who enjoy the game show differs? use a 5% level of significance
It is concluded that the ratio of female and male viewers who enjoy the game shows the difference.
Explain the meaning of the term ratio of the number?When two or maybe more numbers are compared, the ratio shows how big one is in relation to the other. The dividend or quantity being divided is referred to as the antecedent, and also the divisor or quantity that also is dividing is referred to as the consequent. A ratio analyzes numbers by division.According to the survey-
360 out of 500 females enjoy the game.
Thus,
Ratio female = number of females who enjoy/ total number of females.
Ratio female = 360/500
Ratio female = 0.72
Now, 600 out of 800 males enjoy a game show.
Ratio male = number of males who enjoy/ total number of males.
Ratio male = 600/800
Ratio male = 0.75
Thus, Ratio female ≠ Ratio male
Therefore, it is concluded that the ratio of female and male viewers who enjoy the game shows the difference.
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consider the following binomial experiment: a survey shows 53% of households in centercity own a dvd player. in a random sample of 22 households in this city, what is the probability that exactly 17 households own a dvd player? a) 0.0121 b) 0.0124 c) 0.0120 d) 0.0123 e) 0.0126 f) none of the above.
The probability that exactly 17 households own a DVD player is b) 0.0124
How to calculate the probability?P = probability of own DVD player = 53% = 0.53
n = sample of households = 22
x = number of households own a DVD player = 17
Since it is binomial experiment, we use binomial probability formula to calculate the probability.
P(X) = [tex]^{n}C_{x}\times P^{x}\times (1-P)^{n-x}[/tex]
With combination formula as below,
[tex]^nC_x[/tex] = [tex]\frac{n!}{x!(n-x)!}[/tex]
P(X) = [tex]^{22}C_{17}\times 0.53^{17}\times (1-0.53)^{22-17}[/tex]
= [tex]\frac{22!}{17!(22-17)!}\times 0.53^{17}\times 0.47^{5}[/tex]
= 26334 × 0.0000205 × 0.0229345
= 0.0123811
= 0.0124
Thus, the probability is 0.0124 for 17 households own DVD player.
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What is the correct way to do 2x+24+x=150
Answer:
Step-by-step explanation:
for this one you need to solve for x and x=42
Answer:
Step-by-step explanation:
Divide both sides by 2. Divide 24 by 2 to get 12.
There are three methods used to solve systems of equations: graphing, substitution, and elimination.
Use the elimination method to get rid of one of the variables.
Find the value of one variable.
Find the value of the remaining variables using substitution.
Clearly state the final answer.
Check your answer by substituting both values into either of the original equations.
3|2z+9|+12=10. Please help quickly
We will see that the given equation is false for all values of z, thus, the equation has no solutions.
How to solve the equation?Here we have the absolute value equation:
3*|2z + 9| + 12 = 10
To solve this we first need to isolate the absolute value part, so let's do that:
3*|2z + 9| + 12 = 10
3*|2z + 9| = 10 - 12 = -2
|2z + 9| = -2/3
Now, remember that the absolute value is always a positive quantity, then the above equation is false, an absolute value never can be equal to a negative number.
Then our equation has no solutions.
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A CBS News/New York Times poll found that 329 out of 763 randomly selected adults said they would travel to outer space in their lifetime, given the chance. Estimate the true proportion of adults who would like to travel to outer space with 88% accuracy. Round your answers to at least three decimal places.
The true proportion of adults is in the interval 0.4026< P< 0.4594.
Here we have to estimate the true population of adults who would like to travel to outer space with 88% accuracy.
Data provided:
selected (x) = 329
Total(n) = 763
Sample proportion (p') = x/n
= 329/ 763
= 0.431
Critical z-value = 1.59
margin of error(E) = z[tex]\sqrt{p'( 1-p')/n}[/tex]
= 1.59 [tex]\sqrt{0.431(1-0.431) / 763}[/tex]
= 1.59 × 0.0179
= 0.0284
88% confidence interval is:
(p' ± E) = ( 0.431 ± 0.0284)
= 0.4594 and 0.4026
Therefore the estimate is 0.4026< P< 0.4594.
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The hypotenuse of a right triangle measures 15 cm and one of its legs measures 1 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
The value of the other leg of the right angled triangle is found as 4√14 cm.
Explain the term Pythagorean theorem?In a right-angled triangle, every square of a hypotenuse side is equal to total sum of the squares of the remaining two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.For the given question, the values for the right angled triangle are-
Hypotenuse (H) - 15 cm
Side (B) = 1 cm
Let the other side be (P).
Then,
H² = P² + B²
P² = H² - B²
Put the values-
P² = 15² - 1²
P² = 225 - 1
P² = 224
P = 4√14
Thus, the value of the other leg of the right angled triangle is found as 4√14 cm.
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The mathematical way to describe an interaction is: O A difference in differences A A caveat O A qualified main effect O A patterned pattern
The mathematical way to describe an interaction is: A difference in differences.
What is an interaction?In statistics, an interaction may appear when analyzing the relationship between three or more variables, and defines a situation in which the effect of one causal variable on an outcome forms on the state of a second causal variable.
Interactions are often considered in the context of regression analyses or factorial experiments. An interaction happens when an independent variable has a different effect on the outcome depending on the values of another independent variable.
To find an interaction, we need a factorial design, in which the two (or more) independent variables are crossed with one another, so there are reflections at every combination of levels of the two independent variables.
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