The acceleration acquired by the object of mass 12 Kg and is pushed with a force of 12 N, is given by 5/3 m/s².
We know that from the first law of Newton's Law that,
F = m*a
where 'F' is applied force; 'm' is mass of object and 'a' is acceleration.
Let the acceleration acquired by the object be 'A'.
Mass of the object is (m) = 12 Kg
The force applied (F) = 20 N
So from Newton's First Law of Motion we get,
F = m*a
20 = 12*A
A = 20/12
A = 5/3
Hence the acceleration will be 5/3 m/s².
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The question is in another language. The question is in English will be -
''What is the acceleration acquired by an object that has a mass of 12 Kg and is pushed with a force of 20N?''
How would you describe the amount of money earned over six weekends?
decreasing
can't be determined
staying the same
increasing
The amount of money earned over six weekends is best described as decreasing. The Option A.
What does decreasing income means?Decreasing income refers to a situation in which an individual or household experiences a reduction in the amount of money earned over a certain period of time.
This can be caused by a variety of factors, such as job loss, reduction in work hours, or a decrease in wages. When income decreases, individuals may find it more difficult to meet their financial obligations, such as paying bills, making rent or mortgage payments, and purchasing basic necessities like food and clothing.
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A cylindrical can holds three balls. The balls touch the top, bottom and sides of the can. The radius of one ball is 6 cm. Find the volume of the remaining space inside the cylinder. Use 3.14 for π. please someone help me.
Answer:
16286.01632
Step-by-step explanation:
V=πr2h=π·122·36≈16286.01632
Find the value of x.
Applying the Angles of Intersecting Chords Theorem, the value of x in the circle is: x = 69 degrees.
What is the Angles of Intersecting Chords Theorem?The Angles of Intersecting Chords Theorem if two chords intersect inside a circle, then the size of the angle formed by the intersection is equal to half the sum of the sizes of the intercepted arcs, along with the size of its vertical angle.
Apply the theorem to find the value of x by creating the equation below:
x = 1/2 * (86 + 52)
x = 1/2 * (138)
x = 69 degrees.
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Hypothesis Testing Using a P-Value Signature Assignment #2
Roller Coasters. The heights in feet of 36 randomly selected top-rated roller coasters are listed. Assume the population standard deviation is 71.6 feet. At a = 0.05, is there enough evidence to reject the claim that the mean height of top- rated roller coasters is 160 feet? (Source: POP World Media, LLC)
325 188 306 107 208 167 105 78 140 232 230 170 170 205 305 135 200 200 100 223 135 195 80 90 120 210 82 161 245 88 70 116 121 146 149 124
1. Express the null and alternative hypothesis in words and as mathematical expressions. Identify which one is the claim?
2. Compute the sample mean and test statistic z. Write out the formulas and show your work. Round off to two decimal places. (EQS)
3. Compute the p value and explain how it was found. (Round off two decimal places.)
4. Describe whether to reject or fail to reject the null hypothesis and explain the decision.
5. Interpret the decision in the context of the original claim. (Critical thinking)
6. In three to five sentence explain how and why hypothesis testing is used. Give an example (Communication)
Null hypothesis: The mean height of top-rated roller coasters is 160 feet (H0: u = 160).
Solution to the aforementioned questions1) Null hypothesis: The mean height of top-rated roller coasters is 160 feet (H0: u = 160). Alternative hypothesis: The mean height of top-rated roller coasters is not 160 feet (Ha: u ≠ 160). The claim is the null hypothesis.
2) Sample mean = (325+188+306+107+208+167+105+78+140+232+230+170+170+205+305+135+200+200+100+223+135+195+80+90+120+210+82+161+245+88+70+116+121+146+149+124)/36 = 164.97 feet. The test statistic z = (x - μ) / (σ / √n) = (164.97 - 160) / (71.6 / √36) = 1.21.
3) The p-value is the probability of observing a test statistic as extreme as the one computed from the sample, assuming the null hypothesis is true. Using a standard normal distribution table, the p-value is 0.1131.
4) At α = 0.05, the p-value (0.1131) is greater than a. Therefore, we fail to reject the null hypothesis.
5) Based on the statistical analysis, we do not have sufficient evidence to reject the claim that the mean height of top-rated roller coasters is 160 feet.
6) Hypothesis testing is a statistical method used to make decisions based on the analysis of sample data. It is used to determine whether a claim or hypothesis about a population is supported by the evidence provided by the sample data.
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According to the U. S. Bureau of the Census, in 2000 there were 35. 3 million residents of Hispanic origin living in the United States. By 2010, the number had increased to 50. 5 million. The exponential growth function A = 35. 3ekt describes the U. S. Hispanic population, A, in millions, t years after 2000. A. Find k, correct to three decimals places. B. Use the resulting model to project the Hispanic resident in population in 2015. C. In which year will the Hispanic resident population reach 70 million?
The value of k is approximately 0.034. The projected Hispanic resident population in 2015 is approximately 73.9 million. The Hispanic resident population will reach 70 million in approximately 24.7 years after 2000, which corresponds to the year 2024.
To find k, we can use the fact that A = 35.3 million when t = 0 (i.e., in 2000), and A = 50.5 million when t = 10 (i.e., in 2010). Substituting these values into the exponential growth function, we get
35.3 = 35.3e^0k
50.5 = 35.3e^(10k)
Dividing the second equation by the first equation, we get
50.5/35.3 = e^(10k)
Taking the natural logarithm of both sides, we get
ln(50.5/35.3) = 10k
Solving for k, we get
k ≈ 0.034
Therefore, the exponential growth function is A = 35.3e^(0.034t).
To project the Hispanic resident population in 2015, we need to find A when t = 15 (i.e., 15 years after 2000). Substituting t = 15 into the exponential growth function, we get
A = 35.3e^(0.034*15) ≈ 73.9 million
Therefore, the projected Hispanic resident population in 2015 is approximately 73.9 million.
To find the year in which the Hispanic resident population reaches 70 million, we need to solve the exponential growth function for t when A = 70. Substituting A = 70 into the exponential growth function, we get
70 = 35.3e^(0.034t)
Dividing both sides by 35.3, we get
e^(0.034t) = 70/35.3
Taking the natural logarithm of both sides, we get
0.034t = ln(70/35.3)
Solving for t, we get
t ≈ 24.7
Therefore, the Hispanic resident population will reach 70 million in approximately 24.7 years after 2000, which corresponds to the year 2024.
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how do I do 3 + 2n = 7
In the given equation which is 3 + 2n = 7, the value of n = 2.
For, further explanation to find the value of the variable in the given equation, we can solve the given equation by transferring the non-variable digits to one side either to L.H.S or R.H.S.
Given equation = 2n + 3 =7
In the above equation, the variable is 'n' and the non-variable digits are '3' and '7'. To find the value of 'n', we can transfer the non-variable digits to the R.H.S (Right Hand Side) as shown below:
2n + 3 = 7
2n = 7 - 3
2n = 4
n = [tex]\frac{4}{2}[/tex]
n = 2.
So, from the above solution the value of 'n' is 2.
Given question is incomplete/incorrect, I assume the given question was to "obtain the value of n from the linear equation 3 + 2n = 7"
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Jayla's math certificate is 19 centimeters tall and 29 centimeters wide. Jayla wants to put the certificate in a fancy frame that costs $0.03 per centimeter. How much will it cost to frame Jayla's math certificate?
Answer: It will cost $2.88 to frame Jayla's math certificate with the fancy frame.
Step-by-step explanation: To calculate the cost of framing Jayla's math certificate, we need to determine the perimeter of the certificate, which is the sum of the lengths of all four sides.
Perimeter = 2 × (height + width)
Perimeter = 2 × (19 + 29)
Perimeter = 2 × 48
Perimeter = 96 centimeters
So the perimeter of the certificate is 96 centimeters.
To find the cost of framing, we need to multiply the perimeter by the cost per centimeter of the fancy frame:
Cost = perimeter × cost per centimeter
Cost = 96 × $0.03
Cost = $2.88
Therefore, it will cost $2.88 to frame Jayla's math certificate with the fancy frame.
What is the first step in constructing a circumscribed circle around triangle XYZ? Construct a line parallel to segment YZ. Construct the perpendicular bisector of segment XY. Construct a copy of angle X. Construct the angle bisector of angle Y.
Answer: Construct the perpendicular bisector of segment XY
Step-by-step explanation:
Construct the perpendicular bisector of segment XYI am pretty sure this is the answer. I assume you r taking flvs just like me. this is the answer because to construct a circumscribed circle u will need to draw a perpendicular bisector to the sides of the polygon. Which o think is the first step.
MAKE THE FOLLOWING STATEMENTS ABOUT EXPONENTS TRUE.
--- When multiplying polynomials with the same base,
[Select]
the coefficients.
---
When dividing polynomials with the same base, [Select]
[Select]
[Select]
✓the coefficients.
--- When raising a power to a power, distribute the exponent by [Select]
and applying the exponent to the coefficient.
--- When raising anything to the Zero power, the answer will be [Select]
-- When raising anything to the 1st power, the answer will be [Select]
exponents and
exponents and
exponents
--- When trying to leave a variable without a negative exponent, you should flip the position of the variable
to the reciprocal and [Select]
✓the negative exponent.
Your friend in college decides to purchase textbooks using his credit card, which has an APR
(Annual Percentage Rate) of 12.5% compounded continuously. He charges $500 for the
textbooks. Without making any payments, after how many years will his credit card balance be
$1360? Round your answer to the nearest year.
If your friend in college decides to purchase textbooks using his credit card. The number of year his credit card balance be $1360 is 8 years.
How many years will his credit card balance be?We can use the continuous compounding formula to solve this problem:
A = Pe^(rt)
where A is the ending balance, P is the initial balance, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.
In this case, we want to solve for t when P = 500 and A = 1360. The interest rate is given as 12.5% compounded continuously, which means r = 0.125. Substituting these values into the formula, we get:
1360 = 500e^(0.125t)
Dividing both sides by 500, we get:
e^(0.125t) = 2.72
Taking the natural logarithm of both sides, we get:
0.125t = ln(2.72)
Solving for t, we get:
t = ln(2.72)/0.125 ≈ 8
Rounding to the nearest year, we get that it will take 8 years for the credit card balance to reach $1360 without making any payments.
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of 100 patients selected at random from a clinic, 33 were found to have high blood pressure. construct a 95% confidence interval for the percentage of all patients at this clinic that have high blood pressure.
We can say with 95% certainty that the genuine rate of all patients at this clinic who have high blood pressure is between 24% and 42%.
To develop a 95% certainty interim for the rate of all patients at this clinic that have tall blood weight, we will utilize the equation:
CI = p ± z*(p*(1-p)/n))
where p is the sampling extent, z is the z-score related to the required certainty level (in this case, 1.96 for 95% certainty), and n is the test measure.
We are given that out of a test of 100 patients, 33 have high blood weight. In this manner, the test extent is:
p = 33/100 = 0.33
Utilizing the equation over, we will calculate the edge of the mistake:
Arduino
ME = z*(p*(1-p)/n)) = 1.96*(0.33*(1-0.33)/100)) ≈ 0.09
At that point, we are able to develop the 95% certainty interim:
CI = p ± ME = 0.33 ± 0.09 = (0.24, 0.42)
Hence, able to say with 95% certainty that the genuine rate of all patients at this clinic who have high blood weight is between 24% and 42%.
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Convert the rectangular coordinates (-3√3, 0) into polar form. Express the angle
using radians in terms of over the interval 0 ≤ 0 < 27, with a positive value of r.
The polar form of the rectangular coordinates (-3√3, 0) is r = 3√3 and θ = 0
To convert the rectangular coordinates (-3√3, 0) into polar form, we can use the following equations:
r = √(x² + y²)
θ = tan⁻¹(y/x)
In this case, x = -3√3 and y = 0, so we have:
r = √((-3√3)² + 0²) = 3√3
θ = tan⁻¹(0/(-3√3)) = tan⁻¹(0) = 0
Since the angle is given in radians over the interval 0 ≤ θ < 2π (which is equivalent to 0 ≤ θ < 6.28318), we need to add 2π to θ if it is negative, to ensure that θ is in the specified interval.
However, in this case, θ is already equal to 0, which is within the specified interval.
Therefore, the polar form of the rectangular coordinates (-3√3, 0) is:
r = 3√3
θ = 0 (in radians, over the interval 0 ≤ θ < 2π)
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6)
The value of Tony's investment was $1140 on January 1st. On this date
three years later, his investment was worth $1824. The average rate of
change for this investment was $19 per
(1) day
(2) month
(3) quarter
(4) year
Answer:
Step-by-step explanation:
Average rate of change = (Ending value - Beginning value) / Time elapsed
Using the formula for the average rate of change, we get:
(1824 - 1140) / 1095 = $0.55 per day
(1824 - 1140) / 36 = $19 per month
(1824 - 1140) / 12 = $54 per quarter
(1824 - 1140) / 3 = $228 per year
Therefore, the average rate of change for Tony's investment was $19 per month.
Y'all I really need some help here. 100 points.
Answer:
42 degrees
Step-by-step explanation:
So, first to find <QUT, which is a vertical angle, we have to figure out either QUR or TUS. So:
9x+3=11x-27
solve for x:
x=15
Then, plug it into one of the equations. Let's use 9x+3.
9(15)+3=138
So, we know that QUR is 138 degrees.
That means that TUS is ALSO 138.
138x2=276
Now we know that QUT and RUS have to equal whatever 360-276 is:
360-276=84
QUT and RUS have to equal 84 degrees, so we DIVIDE by 2.
84/2=42
So, QUT=42 degrees
Answer:
42 Degrees
Step-by-step explanation
Becuase (11x-27) and (9x+3) are vertical angles that means they are equal to each other
(11x - 27) = (9x + 3)
First you will add 27 to both sides
11x -27 = 9x +3
+27 +27
Making it to:
11x = 9x + 30
Now you need to subtract 9x from both sides
11x = 9x +30
-9x -9x
Turning it into this
2x= 30
Now Lastly, divide both sides by 2
2x = 30
2x 2x
And the answer is...... X=15
Now that you have the x value, we go back to the 11x-27 and replace the X with 15
11(15) -27 = 138 degress
Now because angle QUT and 138 degrees make a straight line that means together they will be 180 degress so you will subtract 180 by 138
Giving you the final answer of
42 Degrees
Given that event E has a probability of 0.31, the probability of the complement of event E
Explanation: We subtract the given value from 1
1-0.31 = 0.69
The complement of an event is the complete opposite.
Example: heads vs tails
A pitcher contains 3 quarts of iced
tea. John is going to pour the iced tea
into glasses that each hold 1½ cups.
How many glasses will John fill?
John will be able to fill 8 glasses with iced tea.
How many cups are in 3 quarts of iced tea?To convert quarts to cups, we need to multiply the number of quarts by 4, since 1 quart is equal to 4 cups. So, 3 quarts of iced tea is equivalent to 3 x 4 = 12 cups of iced tea.
Since each glass holds 1½ cups of iced tea, John will need to divide the total cups of iced tea by the capacity of each glass: 12 cups / 1.5 cups/glass = 8 glasses.
Therefore, John will fill 8 glasses with iced tea.
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can anyone help to answer this question
Answer:
it's 17.04 as u showed in the answer
Step-by-step explanation:
1st u change the mixed no. to improper fraction
2nd u will multiply it by it's resprocal then u will get 17.04
Last week, Austin's Diner sold 2 milkshakes with whipped cream on top and 23 milkshakes without whipped cream. What percentage of the milkshakes had whipped cream?
Answer:
8%
Step-by-step explanation:
You want to know what percentage of milkshakes had whipped cream if 2 had whipped cream and 23 didn't.
PercentageThe fraction of the total number that had whipped cream is ...
2/(2+23) = 2/25
The percentage is found by multiplying the fraction by 100%:
2/25 × 100% = 8%
8% of the milkshakes had whipped cream.
HELP PLEASE I NEED THIS DONE ASAP
Answer:5
Step-by-step explanation:
it would be 5 because
Im stuck on this question
An image of a right rectangular prism is shown. A rectangular prism with dimensions of 4.5 centimeters by 6 centimeters by 4 centimeters. What is the surface area of the prism? 138 cm2 169 cm2 31 cm2 69 cm2
The prism's surface area is 138 [tex]cm^{2}[/tex]. As a result, option (a) is correct.
What is the meaning of surface area?A three-dimensional object's surface area is the sum of all its faces.
The formula for the surface area of a right rectangular prism is:
surface area = 2lw + 2lh + 2wh
where l, w, and h are the prism's length, breadth, and height, respectively.
When we substitute the provided values, we get:
Surface Area = 2(4.5)(6) + 2(4.5)(4) + 2(6)(4)
Surface Area = 54 + 36 + 48
surface area = 138 [tex]cm^{2}[/tex]
As a result, the prism's surface area is 138 [tex]cm^{2}[/tex]. As a result, option (a) is correct.
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When we add together the NPV and the false omission rate for any test, why is the sum always 100%?
The sum of the NPV and false omission rate for any test will always be 100%.
Explaining why is the sum always 100%?The NPV (Negative Predictive Value) is the proportion of people who test negative for a condition and actually do not have it, while the false omission rate is the proportion of people who have the condition but test negative for it.
When we add together the NPV and the false omission rate for any test, we are essentially considering all the cases where the test result is negative.
The NPV represents the proportion of people who truly do not have the condition and test negative for it, while the false omission rate represents the proportion of people who actually have the condition but test negative for it.
Together, these two values cover all possible cases where the test result is negative, which means that they represent the entirety of the negative results for the test.
Since the sum of all probabilities for an event must always equal 100%, the sum of the NPV and false omission rate must also equal 100%.
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PLEASE HELP MY MOMS GONNA KICK MT BUTT AND I JUST DONT GET THIS!!!Add.
(2h + 8) + (9h² + 2h)
apply the half-angle identities for sine and cosine to rewrite or evaluate the following expression.
[tex]tan(\frac{11\pi}{12} )[/tex]
Answer: We can use the halfangle formula for the tangent to answer this question. Using this formula we get that [tex]$\tan\left(\frac{11\pi}{12}\right) = \sqrt{3} - 2[/tex].
Step by Step Explanation: The half angle formula for tangent is [tex]$\tan\left(\frac{A}{2}\right) = \frac{\sin(A)}{1+\cos(A)}[/tex] . So
[tex]$\tan\left(\frac{11\pi}{12}\right)[/tex]
[tex]$= \frac{\sin(\frac{11\pi}{6})}{1+\cos(\frac{11\pi}{6})}[/tex]
[tex]$= \frac{\sin(2\pi - \frac{\pi}{6})}{1+\cos(2\pi - \frac{\pi}{6})}[/tex]
[tex]$ = \frac{-\sin(\frac{\pi}{6})}{1+\cos(\frac{\pi}{6})}[/tex]
[tex]$= \frac{-1/2}{1 + \sqrt{3}/2}[/tex]
[tex]$= -\frac{1}{2+\sqrt{3}}[/tex]
[tex]$= - \frac{2-\sqrt{3}}{(2+\sqrt{3})(2-\sqrt{3})}[/tex]
[tex]= - \frac{2 -\sqrt{3}}{4-3}}[/tex]
[tex]= \sqrt{3} -2[/tex]
What are the half angle identitiesThese are some of the common halfangle identities:
[tex]\cos(A/2) = \sqrt{\frac{1+\cos(A)}{2}[/tex]
[tex]\sin(A/2) = \sqrt{\frac{1-\cos(A)}{2}[/tex]
[tex]\tan(A/2) = \frac{\sin(A)}{1+\cos(A)} = \frac{1 - \cos(A)}{\sin(A)}[/tex]
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monthly sales are independent normal random variables with mean and standard deviation a. find the probability that exactly of the next months have sales greater than 100. b. find the probability that the total of the sales in the next
Answer: We can use the properties of the normal distribution to solve both parts of this problem.
a) The number of months with sales greater than 100 is a binomial random variable with parameters n = the number of months and p = the probability of a single month having sales greater than 100. Since each month is an independent normal random variable, we can use the standard normal distribution to find this probability. Let X be the number of months with sales greater than 100. Then:
X ~ Binomial(n, p)
where n is the number of months and p is given by:
p = P(X_i > 100) = P(Z > (100 - a) / a)
where Z is a standard normal random variable.
Using the binomial probability formula, the probability of exactly k months having sales greater than 100 is:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
So the probability of exactly 3 months having sales greater than 100 is:
P(X = 3) = (n choose 3) * p^3 * (1 - p)^(n - 3)
= (12 choose 3) * P(Z > (100 - a) / a)^3 * [1 - P(Z > (100 - a) / a)]^(12 - 3)
b) The total sales in the next 12 months is a normal random variable with mean 12a and standard deviation sqrt(12)a. Let Y be the total sales in the next 12 months. Then:
Y ~ Normal(12a, sqrt(12)a)
The probability of the total sales being greater than some value x can be found by standardizing Y and using the standard normal distribution:
P(Y > x) = P((Y - 12a) / (sqrt(12)a) > (x - 12a) / (sqrt(12)a))
= P(Z > (x - 12a) / (sqrt(12)a))
where Z is a standard normal random variable. So the probability of the total sales in the next 12 months being greater than 1500 is:
P(Y > 1500) = P(Z > (1500 - 12a) / (sqrt(12)a))
Step-by-step explanation:
Where will the parabola intersect the line? What equation did you solve to find the intersection? Question content area bottom
Part 1 Use the equation to find the intersection.
The parabola will intersect the line at____enter your response here.
From the graph of the parabola, line, and the given values we found out that the parabola will intersect the line at coordinates ([tex]2\sqrt{14}[/tex],7).
What is a parabola and how do we obtain the equations of the same?A parabola is a type of curve that can be described as a symmetrical U-shape. The generalized equation of a parabola is [tex]y=ax^{2} +bx+c[/tex], where a, b, and c are constant values.This equation represents a vertical parabola with its vertex at the point [tex](-b/2a, c - b^2/4a)[/tex] and an axis of symmetry that is parallel to the y-axis.This equation represents a parabola that opens to the right or left, with its vertex at the point [tex](c - b^2/4a, -b/2a)[/tex] and an axis of symmetry that is parallel to the x-axis. The specific coefficients in the equation depend on the particular characteristics of the parabola, such as its vertex, axis of symmetry, and whether it opens up or down or left or right.As the parabola is originating from the origin and opens at the y-axis, hence:
Equation of parabola = [tex]x^{2} =4ay[/tex] {where a =2} .....................(1)Equation of the line=[tex]y-7=0[/tex].............................................(2)From equation 2 we obtain y=7 and will put this value in 1.After computing the above values in 1 we get: [tex]x^{2} =4*2*7\\x=\sqrt{4*2*7}\\ x=2\sqrt{14}[/tex] and y=7So the coordinates at which the parabola intersects the line is [tex](2\sqrt{14} ,7)[/tex]To know more about the parabola visit:
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A 4-cup bottle of soda costs $6.80. What is the price per pint?
Answer: $0.85
:)
hope this hellps
Answer:
$3.40 per pint
Step-by-step explanation:
4 cups is equal to 2 pints, as there are 4 cups in 2 pints.
So let's set up an equation:
6.80/2
3.40
A circle has a diameter of 28 centimeters.
Estimate the area of the circle. Use
3.14
or
22
7
for
π
.
What is the volume of the rectangular prism?
A rectangular prism has a length of 10.4 millimeters, a width of 5 millimeters, and a height of 8 millimeters.
The area of the given circle is 616 sq.cm.
The volume of rectangular prism is 416 mm³
What is a circle?A circle is a particular type of ellipse when the eccentricity is zero and both foci are present. The locus of points drawn equally apart from the centre is also referred to as a circle. The radius of a circle is the separation between its centre and its periphery. The circle's diameter, which is equal to twice its radius, is the line that splits the circle into two equal pieces.
What is area of circle?Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2, (Pi r-squared) where r is the radius of the circle. The unit of area is the square unit, such as m², cm², etc.
Area of Circle = πr² or πd²/4, square units
where π = 22/7 or 3.14
according to question,
Area = pi times the radius squared
A = pi * r²
A = 22/7 * 14²
A = 22/7 * 196
A = 4,312 / 7
A = 616 sq. cm.
V = l*w*h
To determine the volume, multiply all three dimensions together.
For Connexus users Rectangular prisms and volume quiz part 2:
l * w * h = 8 * 5 * 10.4 = 416
the volume of rectangular prism is 416 mm³
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For a trip of x miles, a taxi company charges f(x)=2. 20+0. 6[4x] dollars A. ) What is the cost of a 2. 7-mile trip?
If a taxi company charges f(x)=2. 20+0. 6[4x] dollars, the cost of a 2.7-mile trip is $8.68.
To find the cost of a 2.7-mile trip using the given function f(x) = 2.20 + 0.6[4x], we substitute x = 2.7 in the function.
f(2.7) = 2.20 + 0.6[4(2.7)]
f(2.7) = 2.20 + 0.6[10.8]
f(2.7) = 2.20 + 6.48
f(2.7) = 8.68
The function f(x) = 2.20 + 0.6[4x] represents the cost of a taxi ride based on the distance traveled. The first term 2.20 represents the base fare, which is added to the cost regardless of the distance.
The second term 0.6[4x] represents the variable cost, which is calculated by multiplying the distance traveled by 4 and then by 0.6. This function helps the customers to calculate their fare in advance and plan their expenses accordingly.
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answer correctly
Spirit
The coordinates of point P are (6.4, 18, -12).
What is the coordinate of point?A coordinate of a point refers to a set of values that specify the position of that point in a particular reference system or coordinate system. Coordinates are used to uniquely identify the location of a point in a geometric space, such as a plane or a three-dimensional space.
According to the given information:
To find the coordinates of point P, we can use the concept of vector comparison. We are given that the ratio of vector AB to vector AP is 6:4.
Let's denote the coordinates of point P as (x, y, z).
Given:
AB vector = (10, 2, -6)
B coordinates = (4, 6, -8)
AB:AP = 6:4
We can calculate the coordinates of point P as follows:
Since AB:AP = 6:4, we can express this as a vector equation:
(10, 2, -6) / (x - 4, y - 6, z + 8) = 6/4
Now we can cross-multiply to get:
10 / (x - 4) = 6/4
2 / (y - 6) = 6/4
-6 / (z + 8) = 6/4
Simplifying further, we have:
10(x - 4) = 6 * 4
2(y - 6) = 6 * 4
-6(z + 8) = 6 * 4
Expanding the equations, we get:
10x - 40 = 24
2y - 12 = 24
-6z - 48 = 24
Solving these equations, we get:
10x = 64
2y = 36
-6z = 72
Dividing by the respective coefficients, we get:
x = 6.4
y = 18
z = -12
So, the coordinates of point P are (6.4, 18, -12).
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please solve and explain
The length of curve DE is equal to 26.25 units.
What is Pythagorean theorem?In Mathematics and Geometry, Pythagorean's theorem is modeled by the following mathematical expression:
x² + y² = z²
Where:
x, y, and z represents the length of sides or side lengths of any right-angled triangle.
In order to determine the length of the hypotenuse in this right-angled triangle, we would have to apply Pythagorean's theorem as follows;
AC² + BC² = AB²
20² + 15² = AB²
AB² = 400 + 225
AB = √625
AB = 25 units.
For the length of curve DE, we have:
DE = 105% of AB
DE = 1.05 × 25
DE = 26.25 units.
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