By using unitary method, it can be calculated that
For acceleration of 0.9 m/[tex]s^2[/tex], force applied is [tex]\frac{10}{0.25}\times 0.9[/tex] N = 36 N
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here, Unitary method will be used
For acceleration of 0.25 m/[tex]s^2[/tex], force applied is 10 N
For acceleration of 1 m/[tex]s^2[/tex], force applied is [tex]\frac{10}{0.25}[/tex] N
For acceleration of 0.9 m/[tex]s^2[/tex], force applied is [tex]\frac{10}{0.25}\times 0.9[/tex] N = 36 N
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2x4=8
I need help with thi algebra, it i my firt time learning it!
Thank much appreciated
Compare the cube root of 50 and 350% using >, <, or =.
350 percent is less than the cube root of 50
350 percent is greater than the cube root of 50
the cube root of 50 is less than 350 percent
the cube root of 50 is equal to 350 percent
The 350 percent is less than the cube root of 50.
How to compare two numbers?In math, comparing numbers is defined as the process or method of determining whether one number is smaller, greater, or equal to another number based on their values.The greater number is the one with more digits. If two numbers have the same number of digits, compare the numbers' left-most digits.Here given two numbers,
∛50 and 350%
To compare the numbers we have to make to to simplest fraction,
∛50
The radical form of the cube root of 50 is ∛50, and the exponent form is (50)⅓ . The prime factorization of 50 is 2 x 5 x 5,
so the cube root of 50 in its simplest radical form is ∛50 .
50 cube root : 3.684031499
350%
The number 350% can be expressed as ,
350 / 100
350/100 = 3.5
So by comparing 3.684031499 and 3.5, 3.684031499 is larger
So ∛50 is larger than 350%
Therefore 350% is < ∛50.
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Answer:
350 percent is less than the cube root of 50
Step-by-step explanation:
Jason uses his car for business. He must keep accurate records so his company will reimburse him for his car expenses. When he started his trip, the odometer read 42,876. 1. When he ended the trip, it read 43,156. 1. Jason's car gets 35 miles per gallon. His tank was full at the beginning of the trip. When he filled the tank, it cost $17. 20. What price did he pay per gallon of gas on this fill-up?.
The price paid by Jason for the gallons of gas he used for the trip is $2.15per gallon of gas.
As given in the question,
Reading of odometer in the starting of trip = 42,876.1
Reading of odometer in the end of trip = 43,156.1
Total distance covered by Jason on his trip = 43,156.1 - 42,876.1
= 280 miles
Average miles per gallon of Jason's car = 35 miles per gallon
Gallons of gas used by Jason on his trip = 280 / 35
= 8 gallons
Amount of money used to fill gas = $17.20
Price of the gas per gallon = 17.20 / 8
= $2.15 per gallon of gas.
Therefore, the price paid by Jason for the per gallon of gas is equal to $2.15 per gallon of gas.
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a cylindrical silo is 70 feet high and its base is a circle of circumference 125.7 feet. what volume, to the nearest 100 cubic feet, of grain can be stored inside of it?
The Volume of the Cylindrical Silo is 88000 cubic feet
What is Volume?
Volume is a measurement of three-dimensional space that is occupied. It is frequently mathematically quantified using SI-derived units or different imperial or US customary units. The concept of length is linked to the definition of volume.
Solution:
Given:
Height of the Container = 70 feet
Circumference of the Base = 125.7 feet
To Find: Volume of the Container
Volume = πr²h
Circumference = 2πr
125.7 = 2 * 3.14 * r
r = 20.01
Volume = 3.14 * 20.01 * 20.01 * 70
Volume = 88007.94 cubic feet
Volume = 88000 cubic feet (approx)
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Name the sides of triangle FYT for
which angle F is the included angle.
Answer:
1. FY and FT
Step-by-step explanation:
1. Which sides form angle F?
Answer: FY and FT
Sides FY and FT form the sides of ΔFYT for which ∠F is the included angle.
What is a triangle?A triangle is a polygon having three vertices and three edges. Sum of the interior angles of a triangle is 180°.
There are three sides and three angles for the triangle.
For ΔFYT given here, FY, YT and FT are the edges or sides of the triangle. ∠F, ∠Y and ∠T are the angles of this triangle formed at vertices F, Y and T respectively.
∠F is formed by the edges FT and FY
∠Y is formed by the edges FY and YT
∠T is formed by the edges YT and FT
Hence, sides of the triangle FYT for which angle F is the included angle are FT and FY.
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i need help please too get a better grade!
The linear function in this problem is defined as follows:
y = -328.275x + 3142.5.
The number of CD's sold by year decreases by about 328 million per year. About 3143 million of CD's were sold in 2010.
The estimate for the year of 2019 is of: 188 million CD's.
How to define the linear function?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients of the function are defined as follows:
m is the slope, representing the rate of change of the output y relative to the input x.b is the y-intercept, representing the value of the output y when the input x assumes a value of y.Two points of the linear function in this problem are given as follows:
(2, 2485.6), (6, 1172.5)
The slope is given by the change in y divided by the change in x, hence:
m = (1172.5 - 2485.6)/4 = -328.275.
Then:
y = -328.275x + b.
When x = 2, y = 2485.6, hence the intercept b is obtained as follows:
2485.6 = -328.275(2) + b.
b = 2485.6 + 328.275(2)
b = 3142.5.
Hence the function is:
y = -328.275x + 3142.5.
2019 is nine years after 2010, hence the estimate is obtained as follows:
y = -328.275(9) + 3142.5 = 188 million CD's.
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The measure of central angle abc is startfraction pi over 2 endfraction radians. What is the area of the shaded sector?.
The area of the shaded sector is 9π unts²
The term "turn" also refers to a 360° rotation. Angles between 0° and 360° are calculated. We require a circle's circumference, which is equal to 2 r r, where r is the circle's radius.
In any circle of radius r, the ratio of the arc length ℓ to the circumference equals the ratio of the angle θ subtended by the arc at the center and the angle in one revolution. Thus, measuring the angles in radians, ℓ2πr=θ2π⟹ ℓ=rθ.
Find the diagram attached
Given the following
Radius = 6
Theta = pi/2 = 90°
Area of the sector = theta/360×πr²
Area if the sector = 90/360 × π(6)²
Area of the Sector = 1/4 × 36π
Area of the sector = 9π unts²
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suppose that every student in this class earns exactly twice as many points on exam 2 as on the exam 1. what would be the value of the correlation coefficient between exam 1 score and exam 2 score?
The value of the correlation coefficient between exam 1 score and exam 2 score is -1.
Given:
suppose that every student in this class earns exactly twice as many points on exam 2 as on the exam 1.
what would be the value of the correlation coefficient between exam 1 score and exam 2 score = ?
1. the coefficient will be exactly one since it measures linear dependence and these are perfectly linear dependent.
2. the coefficient will be exactly one since it measures linear dependence and these are perfectly linear dependent.
3. the coefficient will be exactly one, it doesn't matter which score is higher.
4. the expected value will be 0 since there won't be any correlation between random values.
5. the coefficient will be -1 every high score is matched by a low score on the other test.
Hence we get the required answer.
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How do you calculate travel time in km?
With the help of time -distance formula we can calculate travel time in km for any given problem or situation.
We know the formula we relate to distance and time that which is called time -distance formula is :
t= d/s, where d is the distance and s is the speed of the object.To calculate travel time in km, first, we need to divide the total distance in km by the average speed of travel in terms of km/hour, later multiplying the result by 60 to get the travel time in minutes.
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What is the radius of a circle whose equation is y2 y2 8x 6y 21 0?
The radius of a circle having the equation x² + y² + 8x - 6y + 21 = 0 is 2 units .
In the question ,
it is given that ,
the circle is having the equation ⇒ x² + y² + 8x - 6y + 21 = 0 ,
we know that ,
general equation of circle is written as x² + y² + 2fx + 2gy + c = 0 ;
so , radius of circle is calculated using the below formula ,
radius = √(f² + g² - c)
On comparing, given equation of circle with general equation of circle ,
we get , the values of f = 4 and g = -3 .
So after substituting the values of f , g and c in the radius formula ,
we get ,
radius = √(16 [tex]+[/tex] 9 - 21)
= √(16 [tex]+[/tex] 9 - 21)
= √(25 - 21) = √4 = 2 .
Therefore , the given circle has radius = 2 units .
The given question is incomplete , the complete question is
What is the radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0 ?
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40 horses to 6 cows
Answer:
20:3 ratio
Step-by-step explanation:
Answer:20 horses to 3 cows or 20:3
Step-by-step explanation:
The answer would be 20:3. If you notice that Both 40 and 6 can be divided by 2 so you would divide 40 by 2 and get 20 as your answer. And for the next you would divide 6 by 2 getting 3. So your ratio would be 20 horses to 3 cows or 20:3. I hope you were able to understand and I hope this helps you! I'm so sorry I didn't see your question earlier!
Is 11/81 an irrational number?
Answer:
Yes, 11/81 is an irrational number.
Step-by-step explanation:
Because it is a fraction with a non-terminating, non-repeating decimal expansion.
If = 3/5 find each of the trigonometric values.
a. cos =
b. sin2 =
c. cos2 =
d. tan2 =
e. csc2 =
f. sec2 =
g. cot2 =
Step-by-step explanation:
To find the values of the trigonometric functions, we need to know the angle whose cosine, sine, etc. we are trying to find. In this case, we are given that the cosine of the angle is 3/5, but we are not told the measure of the angle itself. We can find the values of the other trigonometric functions using the given value of the cosine, but we must first express the value in radians.
Since the cosine of an angle is equal to the x-coordinate of the point on the unit circle that is located on the terminal side of the angle, we can find the value of the angle in radians by finding the inverse cosine (cos^-1) of 3/5. In other words, we want to find the angle such that the cosine of the angle is 3/5.
The inverse cosine function is denoted by cos^-1, so we can write:
$\cos^{-1}(3/5) = \theta$
where $\theta$ is the measure of the angle in radians.
To find the value of the other trigonometric functions, we can use the following relationships:
$\cos^2\theta = 1 - \sin^2\theta$
$\tan^2\theta = \frac{\sin^2\theta}{\cos^2\theta} = \frac{1 - \cos^2\theta}{\cos^2\theta}$
$\csc^2\theta = \frac{1}{\sin^2\theta}$
$\sec^2\theta = \frac{1}{\cos^2\theta}$
$\cot^2\theta = \frac{\cos^2\theta}{\sin^2\theta} = \frac{\cos^2\theta}{1 - \cos^2\theta}$
We can now plug in the value of $\theta$ that we found earlier and use these relationships to find the values of the other trigonometric functions:
a. $\cos\theta = \cos(\cos^{-1}(3/5)) = \frac{3}{5}$
b. $\sin^2\theta = 1 - \cos^2\theta = 1 - (\frac{3}{5})^2 = \frac{4}{25}$
c. $\cos^2\theta = (\frac{3}{5})^2 = \frac{9}{25}$
d. $\tan^2\theta = \frac{\sin^2\theta}{\cos^2\theta} = \frac{\frac{4}{25}}{\frac{9}{25}} = \frac{4}{9}$
e. $\csc^2\theta = \frac{1}{\sin^2\theta} = \frac{1}{\frac{4}{25}} = \frac{25}{4}$
f. $\sec^2\theta = \frac{1}{\cos^2\theta} = \frac{1}{\frac{9}{25}} = \frac{25}{9}$
g. $\cot^2\theta = \frac{\cos^2\theta}{\sin^2\theta} = \frac{\frac{9}{25}}{\frac
this type of bias occurs when researchers fail to choose a representative sample of potential respondents.
Sampling bias, also known as sample selection bias, refers to flaws in research studies that arise when researchers do not appropriately select their subjects.
When a sample is collected in such a way that some members of the intended population have a significantly lower or higher sampling risk than others, sampling bias is reduced.
It yields a skewed sample of a population (or non-human variables) in which not all individuals, but rather cases, were picked in the same way. If this is not considered, the outcomes may be incorrectly attributed to the study problem rather than the sample method.
Sampling bias is often classified as a subset of selection bias, also known as sample selection bias, but some believe it to be a separate type of bias.
The difference between sampling bias and selection bias, though not frequently recognized, is that sampling bias reduces a test's external validity, whereas selection bias only addresses the internal validity of differences or similarities detected in the sample at hand.
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 Is it true that 7w + 4 = 5w + 12.
A. Write three more equations that you know are true based on this information.
B. Find the value of 2w.
C. Find the value of w.
The sum of two polynomials has degree 4 and their difference has degree 2. What is
the degree of their product?
The degree of the product of the two polynomial is 6.
What is a polynomial?
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² − 4x + 7 is an illustration of a polynomial with a single indeterminate x.
Given that there are two polynomial.
The sum of two polynomials has degree 4.
Thus the degree of a polynomial is 4.
The degree of the another polynomial is less than or equal to 4.
Also the difference of their degree is 2.
Thus the degree of the another polynomial is (4 - 2) =2.
The degree of the polynomials whose degree are a and b is a+b.
The degree of the product of the given polynomial is (4 + 2) = 6.
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What types of expenses should you make a savings plan for?
Answer:
It's a good idea to make a savings plan for all of your regular expenses, as well as any unexpected expenses that may come up. This can include things like housing costs, groceries, utilities, transportation costs, insurance premiums, and debt payments. It can also be helpful to save for larger expenses that you know are coming up, such as a vacation or a home repair. By making a plan for your savings, you can ensure that you have the funds available to cover all of your expenses, both expected and unexpected.
Mrs. Gilmore is teaching a 5th grade class. She is standing 15 feet in front of Jonah. Brianna is sitting 8 feet to Jonah's right. How far apart are Mrs. Gilmore and Brianna? feet
Mrs. Gilmore and Brianna are 17 feet apart.
Pythagoras theorem is one of the mathematical principles that can be applied to determine the value of the unknown side of a right angled triangle. Where a right angled triangle is one with one of its angles to equal [tex]90^{o}[/tex].
In the given question, sketching the distance apart of each person, it would form a right angled triangle.
Let the distance in feet between Mrs. Gilmore and Brianna be represented by d.
Then;
[tex]/Hyp/^{2}[/tex] = [tex]Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]d^{2}[/tex] = [tex]15^{2}[/tex] + [tex]8^{2}[/tex]
= 225 + 64
= 289
d = 17
Therefore, Mrs. Gilmore and Brianna are 17 feet apart.
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Allen and his two brothers decided to purchase a video game system together. They determine that each person will need to pay $32.30. How much is the cost for the video game system?
Answer:
The cost for the video game system is $96.90.
Step-by-step explanation:
The sum of 2.69 + (3.84 +1.54) = 2 .69 + = 8.07.
Answer:
it is equal to 8.07
Step-by-step explanation:
scatterplot strength and form: which one of the four scatterplots below shows a strong negative linear association between two variables?
A strong negative linear association between two variables is scatter plot 4.
What is standard normal random?
We shall read probabilities out rather than directly working with Z's density function to compute probabilities for Z. The elements in the tables are probabilities of the kind P(Zz), and they are tables of cumulative probabilities. Following are a number of examples that will help to clarify how to use the tables.The standard normal random.
Very dispersed and lacking in association is scatter plot 1.
Positive correlation may be seen in scatter plots 2 and 3.
Scatter figure #4 clearly illustrates a strong inverse relationship between the variables.
Hence the Correct answer is scatter plot 4.
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what are the x-intercepts of the quadratic equation? 7x(2x+5)=0
The quadratic equation 7 · x · (2 ·x + 5) = 0 have the points x₁ = 0 and x₂ = - 5 / 2 as its x-intercepts.
How to find the x-intercepts of a quadratic equation
In this problem we must determine the the x-intecerpts of a quadratic equation, that is, the values of x such that A · x² + B · x + C = 0. This question can be resolved by means of algebra properties. First, write the quadratic equation:
7 · x · (2 ·x + 5) = 0
Second, expand the expression and simplify until standard form is found:
7 · x · (2 ·x + 5) = 0
14 · x² + 35 · x = 0
Third, complete the square:
x² + (35 / 14) · x + 25 / 16 = 25 / 16
(x + 35 / 28)² = 25 / 16
Fourth, clear the variable x:
x + 35 / 28 = ± 5 / 4
x = - 35 / 28 ± 5 / 4
x = - 5 / 4 ± 5 / 4
The points x₁ = 0 and x₂ = - 5 / 2 are the x-intercepts of the quadratic equation 7 · x · (2 ·x + 5) = 0.
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Suppose the mean daily peak power load ( y) for a power plant and the maximum outdoor temperature (x) for a sample of 6 days is as given in the ff. Table x y 95 214 82 152 90 156 81 129 99 254 100 266 find the ff. The peak power load when the max. Temperature is 84.
As per the daily mean, the peak power load when max is possible to calculate with a computer or calculator.
The highest outdoor temperature and the mean daily peak power load for a sample of 6 days are provided in the table. However, it is impossible to estimate the peak power load when the highest temperature is 84 without more details. The presented data only reflects a sample of 6 days, which may not be typical of the full population, and the connection between peak power load and maximum temperature may not be linear. Furthermore, using the provided data to conduct any calculations is impossible without access to a computer or calculator.
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Write the equation of the line passing through(3,5) and (0,2).
Answer: y = 3x + 2
Step-by-step explanation:
Let's start with what we know. To calculate the slope, we do:
(y1 - y2)/(x1 - x2)
So, for this equation we get:
(5 - 2)/(3-0)
We get 3/3, so the slope = 1. So far, we have:
y = 3x + b
Let's use one of our coordinates to plug this in:
2 = 0 + b
So b = 2.
So our final equation is:
y = 3x + 2
Nathalie weighed 7lbs 9oz when she was born. She now weighs 12 times as much. A) How much does she weigh now in lbs and oz? B) By what percent did her weight increase? URGENT!!!
Assuming that Nathalie's weight is still measured in pounds and ounces and that she has not lost or gained any weight since her birth, we can calculate her current weight as follows:
A) Nathalie weighs 7 pounds and 9 ounces at birth, which is equal to 7.5625 pounds. If she now weighs 12 times as much, she weighs 7.5625 * 12 = 90.75 pounds. In ounces, this is equal to 90.75 * 16 = 1452 ounces.
B) To calculate the percentage increase in Nathalie's weight, we need to first calculate the increase in her weight, which is equal to 90.75 - 7.5625 = 83.1875 pounds. We can then divide this increase by her original weight of 7.5625 pounds and multiply by 100% to express the result as a percentage: (83.1875 / 7.5625) * 100% = 1103.9%. This means that Nathalie's weight has increased by more than 1100% since she was born.
Solve the inequality -2<3m-5≤7 and graph the solution set.
The solution for the given inequality is 1 < m ≤ 4. The graph for the obtained solution set is shown below.
What is an inequality equation?Two expressions are related by comparative operations like 'less than or 'greater than or 'less than or equal or 'greater than or equal. Then that equation is said to be an "inequality equation".
For example, a < k ≥ b, etc.
Calculation:The given inequality equation is
-2 < 3m - 5 ≤ 7
On adding 5 to the inequality, we get
-2 + 5 < 3m - 5 + 5 ≤ 7 + 5
⇒ 3 < 3m ≤ 12
On dividing by 3, we get
⇒ 3/3 < 3m/3 ≤ 12/3
⇒ 1 < m ≤ 4
Therefore, the solution set for the given inequality is (1, 4].
The obtained solution set is shown on the number line here.
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five friends were comparing the height of their dogs. the heights at the shoulders were 400mm, 370mm, 470mm, 330mm and 500mm. what is the standard deviation (nearest integer) of the heights of these dogs?: * a) 60mm b) 400mm c) 70mm d) 414mm e) 2070mm
If the heights of five dogs are 400 mm, 370 mm, 470 mm, 330 mm and 500 mm. Then the standard deviation of the heights of the dogs is:
c) 70 mm
Given:
five friends were comparing the height of their dogs.
the heights at the shoulders were 400mm, 370mm, 470mm, 330mm and 500mm.
we are asked to find out the standard deviation of the heights of these dogs = ?
First find mean :
(400+ 370+470 + 330 + 500)/5
Mean = 2070/5
Mean = 414
standard deviation = √∑(xi - mean)²/N-1
= √(400-414)²+(370-414)²+(470-414)²+(330-414)²+(500-414)²/4
= √(14)²+(-44)²+(56)²+(-84)²+(86)²/4
= √196+1936+3136+7056+7396/4
= √19720/4
= √4930
= 70.21
rounding it to the nearest integer.
= 70 mm
Hence we get the required standard deviation as 70 mm.
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Put the following equation of a line into slope-intercept form,
simplifying all fractions.
2x + 4y = 4
Answer:
Step-by-step explanation:
To put in slope intercept form, isolate y.
4y = -2x +4
Further divide by 4 to isolate y. What you do on one side of an equation, you also do on the other side.
4y/4 = -2x/4 +4/4
y = -1/2x +1
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Pls put how you got it pls
In a game, the probability of winning is 33%. If i play 48 times, how many times should I expect to win?
the chance that a certain type of thumbtack lands point up when you toss it in the air is 80%. this makes the standard deviation of the proportion of times it lands point up out of 100 tosses equal to?
The standard deviation of the proportion of times that it lands point up out of 100 tosses be, 16
Given, the chance that a certain type of thumbtack lands point up when you toss it in the air is 80%.
we have to find the standard deviation of the proportion of the given data that it lands point up out of 100 tosses.
Number of trials be, 100
probability of success be, 80/100 = 0.8
On using the formula of Standard deviation, we get
standard deviation = n×p×(1 - p)
standard deviation = 100×0.8×(1 - 0.8)
standard deviation = 100×0.8×0.2
standard deviation = 16
So, the standard deviation of the proportion of times that it lands point up out of 100 tosses be, 16
Hence, the standard deviation of the proportion of times that it lands point up out of 100 tosses be, 16
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