The measure of the angle through which the minute hand of a standard 12-hour clock rotates from the time Monique looked at the clock at the beginning of class to the time she looked at it again at the end of class is 6t degrees, where t is the time elapsed in minutes.
What is order of rotation ?The number of times the figure rotates around for a central point throughout the course of a full 360-degree rotation is referred to as the order of rotation in mathematics. Since it takes 4 of these revolutions to accomplish a full 360-degree rotation, a figure that swings 90 degrees and then returns to its original location has an order of rotation of 4. The idea of rotational symmetry—the characteristic of an image that remains constant during a rotation of a specific angle—and the order of rotation are closely related. The number of rotations a figure with symmetrical can undergo and yet maintain its original appearance is known as the order of rotation.
In the given question,
A normal 12-hour clock's minute hand completes one full rotation every 60 minutes. This implies it rotates 360 degrees in 60 minutes, or at a rate of 6 degrees per minute.
Now, locate the location of the minute hand at the start of class. When Monique looked at the clock at the start of class, the minute hand would be pointing directly at the number 12. As a result, the minute hand begins at 0 degrees.
Then, at the conclusion of class, find the location of the minute hand. If Monique glanced at the clock again at the conclusion of class, she would notice that the minute hand had moved t minutes from its initial position. As a result, the minute hand would be at:
6 degrees per minute × t minutes = 6t degrees
Now, we can find the angle through which the minute hand rotates by taking the difference between the starting and ending positions of the minute hand:
Ending position - Starting position = 6t degrees - 0 degrees = 6t degrees
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The complete question is: What is the measure of the angle through which the minute hand of a standard 12-hour clock rotates from the time Monique looked at the clock at the beginning of class to the time she looked at it again at the end of class?
Kevin's GPS tracker tells him that he just ran 7 miles. He actually ran 10 miles. What was the percent error? HELP PLEASE!
Answer:42.8571429%
Step-by-step explanation:
His GPS tracker got 7 miles while he actually ran 10. 10 - 7 = 3. Then you divide 3 by 7 which is [tex]\frac{3}{7}[/tex] and that is around 42.8571429%.
If y varies directly as x and y = 32 when x = 4, find the value of y when x = 5.
Answer:
first find constant term
y=kx
32=k(4)
32/4=4k/4
k=8
find value of y when x=5
y=kx
y=8×5
y=40
A house is valued at 210000 correct to 2 significant figures
What is the lowest possible value of the house?
A house with value at 210000 correct to 2 significant figures. The lowest possible value of the house is equals to the £205000.
The second significant figure of a number is the digit after the first significant figure. This is true even in case of the digit is zero. We have a house is valued at £210000 correct to 2 significant figures. So, it is bounded question. Since, two significant figures is correct then there is error in 10000 range in £210000. The rounded up value is £2.10 × 10⁵. Steps to determine these bounds
Let assumes that a certain number x must be rounded by a number y. Divide y by 2, i.e. y/2.Upper bound is addition of specific number and y/2, i.e. upper bound = x + y/2.To calculate the lowest value subtract y/2 from the given number, i.e. lower limit = x - y/2.here x = £210000, y = 10000
Since 2 significant digits are correct,
is about 10,000 of £210,000. The lowest possible number rounded to 2 significant digits in the £210,000 range is £205,000, because anything below that looks like £204....that doesn't round up to £21. Hence required value is £205000.
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Tell whether the angles are adjacent or vertical. Then find the value of x . (4x -25) and 75
The angles are vertical and the value of x from the angles (4x -25) and 75 can be expressed as 25.
How can the value of x be calculated?A pair of angles that are vertically opposed to one another are always equal. Moreover, a vertical angle and the angle to which it is adjacent are supplementary angles, meaning their sum is 180 degrees. When two lines join to form an angle, say X=45°, the opposite angle is also 45°, for instance.
From the fiqure we can see that the angles the vertically opposite angles, base on this condition we can form the equation as;
(4x-25)=75
4x=(75+25)
4x=100
x=100/4
x=25
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A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given. a. Find BC, the distance from Tower 2 to the plane, to the nearest foot. b. Find CD, the height of the plane from the ground, to the nearest foot.
In linear equation, 6499 ft CD, the height of the plane from the ground, to the nearest foot.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Part A) Find BC, the distance from Tower 2 to the plane, to the nearest foot.
in the triangle ACD
sin16=CD/(7600+BD)--------> CD=sin16*(7600+BD)---------> equation 1
in the triangle BCD
sin24=CD/BD-----------> CD=sin24*BD---------------> equation 2
equation 1=equation 2
sin16*(7600+BD)=sin24*BD-----> sin16*7600+sin16*BD=sin24*BD
sin24*BD-sin16*BD=sin16*7600----> BD=[sin16*7600]/[sin24-sin16]
BD=15979 ft
in the triangle BCD
cos24=BD/BC---------> BC=BD/cos24-------> 15979/cos24-------> 17491
BC=17491 ft
= BC is 17491 ft
Part 2) Find CD, the height of the plane from the ground, to the nearest foot.
CD=sin24*BD ( remember equation 2)
BD=15979 ft
CD=sin24*15979 -----------> CD=6499 ft
= CD is 6499 ft
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Can't Seem to be able to solve this help
An angle measurement, m∠BOC = 60° degrees where O is the center of the corcle.
What is an angle?
Since the ΔABC has three similar sides, we know that it is an equilateral triangle, meaning that all three angles are equal and each angle measures 60°.
Since A, B, and C are points on a circle with O as the center, we know that each of the distances OA, OB, and OC is equal to the radius of the circle.
Let's call this radius r.
Since ΔABC is equilateral, we know that each side has length r. We can also draw radii from the center O to points A, B, and C to form three congruent triangles AOB, BOC, and COA, each with two sides of length r and one angle of 60°.
Since the sum of the angles in a triangle is 180° degrees, each of the other two angles in each of these congruent triangles must measure 60° as well.
Thus, we see that ∠BOC is one of the angles in the isosceles ΔBOC, which has two angles of 60° and a third angle x, which we want to find.
We can use the fact that the sum of the angles in a triangle is 180° to find x:
x + 60 + 60 = 180
Simplifying, we get:
x = 60
Therefore, angle BOC measures 60°
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Complete question is: m∠BOC = 60° degrees where O is the center of the corcle.
Hong knit scarves for his friends. Altogether, the scarves had a total length of
436.8 in. If he knit 7 scarves, and each scarf was the same length, how long
was each scarf? Write your answer in feet.
Use the table of conversion facts as necessary, and do not round your answer
Answer:
5.2 feet
Step-by-step explanation:
436.8/7/12 feet
b. John took out a loan from the bank for $221 and was told he would have to pay back
some interest on top of the $221 dollars. John had to pay back 321 dollars, how much.
money did the bank make after John Paid them back?
The bank made $100 in profit from the loan.
What is simple interest?
Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept that is used in many sectors such as banking, finance, automobile, and so on.
If John had to pay back $321 in total and the original loan was $221, then the bank made $100 in interest from John.
Interest = Amount John had to pay - Original Loan
Interest = 321 - 221
Interest = $100
So, the bank made $100 in profit from the loan.
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consider a 20-foot chain that weighs 2 pounds per foot hanging from a winch 20 feet above ground level. find the work done by the winch in running the winch until the bottom of the chain is at the 10-foot level.
The work done by the winch in running the winch until the bottom of the chain is at the 10-foot level is 200 foot-pounds.
Given, The weight of the chain per foot = 2 pounds
Total length of the chain = 20 feet
The chain is hanging from a winch 20 feet above ground level.
The work done by the winch in running the winch until the bottom of the chain is at the 10-foot level is to be determined.
The force required to lift the chain is equal to the weight of the chain. Therefore, the force needed is F = 2 × 20 = 40 pounds. The work done is the product of force and distance.
Therefore, Work done = force × distance= 40 × (20 − 10)= 400 foot-pounds
Thus, the work done by the winch in running the winch until the bottom of the chain is at the 10-foot level is 200 foot-pounds.
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pls help asap The following is a right angle. Find X:
x =
Answer:
x = 11
Step-by-step explanation:
3x + 5x + 2 =90
(3x + 5x) + (2) = 90
8x + 2 = 90
8x + 2 -2 = 90 -2
8x = 88
8x/8 = 88/8
x = 11
Dan and Paul share some money in the ratio 11:5.
Dan decides gives Paul £39 of his share to make the ratio 1:1.
How much did Paul originally have?
D = Dan's share
P = Paul's share
[tex]\stackrel{D}{11}~~ : ~~\stackrel{P}{5}\qquad \implies \qquad \cfrac{D}{P}=\cfrac{11}{5}\implies D=\cfrac{11P}{5}[/tex]
now Dan decides to give Paul £39, so that means that Dan has £39 less whilst Paul has £39 more, so the new shares will be D - 39 and P + 39, and that puts them in a 1 : 1 ratio.
[tex]\stackrel{D-39}{1}~~ : ~~\stackrel{P+39}{1}\qquad \implies \qquad \cfrac{D-39}{P+39}=\cfrac{1}{1}\implies D-39=P+39 \\\\\\ \stackrel{\textit{substituting from the 1st eqution}}{\left(\cfrac{11P}{5} \right)-39~~ = ~~P+39}\implies \cfrac{11P}{5}=P+78\implies 11P=5P+390 \\\\\\ 6P=390\implies P=\cfrac{390}{6}\implies \boxed{P=65}[/tex]
a manager of a sports club keeps information concerning the main sport in which members participate and their ages. to test whether there is a relationship between the age of a member and his or her choice of sport, 651 members of the sports club are randomly selected. conduct a test of independence at the 5% lev
The calculated value is 15.16, and the degrees of freedom are 12, the p-value is less than 0.05.
As a result, we must reject the null hypothesis.
A manager of a sports club maintains data about the main sport in which members participate and their ages.
To verify if there is a connection between the age of a member and their sport preference, a test of independence is performed on 651 sports club members who were randomly selected at a 5% level.200 Words:
Test of independence: Test of independence is a statistical method that helps to determine if there is a connection between two groups, and if there is, what is the magnitude of the relationship.
A test of independence is performed using the chi-square statistic.
The null hypothesis in this test is that there is no relationship between the two group S.
We will use a chi-square test to determine whether there is a connection between the age of the member and the sport in which they participate.
Hypotheses:
Null hypothesis: There is no link between the age of a member and the sport in which they participate.
Alternate hypothesis: There is a relationship between the age of a member and the sport in which they participate.
Level of significance = 5%.
Step 1: Prepare the contingency table for observed values
Age Basketball Football Hockey Soccer Other Under 20 years 25 30 20 10 15 20-29 years 20 50 35 30 25 30-39 years 15 40 40 35 30 40-49 years 10 35 25 25 20 Over 50 years 5 15 10 15 10
Step 2: Calculate the marginal frequencies.
Age Basketball Football Hockey Soccer Other Total Under 20 years 25 30 20 10 15 100 20-29 years 20 50 35 30 25 160 30-39 years 15 40 40 35 30 160 40-49 years 10 35 25 25 20 115 Over 50 years 5 15 10 15 10 55 Total 75 170 130 115 100 651
Step 3: Compute the expected frequencies.
The predicted frequency for each group is (row total) * (column total) / total number of observations.
Age Basketball Football Hockey Soccer Other Under 20 years 11.5 26.1 19.9 17.7 15 20-29 years 30.9 70.1 53.4 47.5 40.1 30-39 years 30.9 70.1 53.4 47.5 40.1 40-49 years 21.3 48.2 36.8 32.7 27.6 Over 50 years 9.4 21.4 16.4 14.6 12.3
Step 4: Calculate the test statistic:
We will use a chi-square test statistic to determine whether the null hypothesis should be accepted or rejected.
Chi-square test formula is:χ2 = Σ (Observed frequency – Expected frequency)2 / Expected frequency.
Degrees of freedom = (Number of rows – 1) * (Number of columns – 1)
χ2 = (25-11.5)2 / 11.5 + (20-30.9)2 / 30.9 + (15-30.9)2 / 30.9 + (10-21.3)2 / 21.3 + (5-9.4)2 / 9.4 + (30-26.1)2 / 26.1 + (50-70.1)2 / 70.1 + (40-70.1)2 / 70.1 + (35-48.2)2 / 48.2 + (15-21.4)2 / 21.4 + (20-19.9)2 / 19.9 + (35-53.4)2 / 53.4 + (40-53.4)2 / 53.4 + (25-36.8)2 / 36.8 + (10-16.4)2 / 16.4 + (15-14.6)2 / 14.6 + (15-32.7)2 / 32.7 + (25-27.6)2 / 27.6 + (10-12.3)2 / 12.3χ2 = 15.16
Degrees of freedom = (5-1) * (4-1) = 12
Step 5: Determine the p-value:
The p-value is determined by looking up the chi-square value and the degrees of freedom in the chi-square table.
The p-value is the probability of obtaining a result as extreme as or more extreme than the calculated value if the null hypothesis is true.
We will use a 5% level of significance.
Since the calculated value is 15.16, and the degrees of freedom are 12, the p-value is less than 0.05.
As a result, we must reject the null hypothesis.
There is evidence to suggest that the age of a member is related to the sport in which they participate.
In other words, the age of a member and their sport preference are not independent.
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The GCF of 15
and 30
Answer:
15
Step-by-step explanation:
The factors of 15 are 1,3,5,15
The factors of 30 are 1,2,3,5,6,10, 15, 30
The largest factor that both of these numbers share is 15
A group of marine biologists tags 45 great white sharks off the coast of Mexico to study migratory patterns. All of the tag numbers are unique. Weeks later, the marine biologists travel to Hawaii. While there, they randomly capture and release 20 great white sharks per day, for three consecutive days. On the first day, 3 of the sharks have the original tags. On the second day, 2 of the sharks have the original tags. On the third day, 4 of the sharks have the original tags. Based on the data, what is the estimated population of great white sharks that have migrated from Mexico to Hawaii?
Therefore, the estimated population of great white sharks that have migrated from Mexico to Hawaii is 2,500.
What is Shark Population Estimation?Shark population estimation is the process of determining the size and trends of shark populations in a given area. It involves collecting and analyzing data on shark abundance, distribution, behavior, and other factors to understand their population dynamics.
There are different methods used to estimate shark populations, including mark-recapture studies, aerial surveys, acoustic tracking, and genetic analysis. These methods allow researchers to estimate the number of sharks in a given area, monitor changes in their population over time, and identify potential threats to their survival.
To estimate the population of great white sharks that have migrated from Mexico to Hawaii, we can use the capture-recapture method, also known as the Lincoln-Petersen index.
Let:
N = the total population sizen1 = the number of sharks tagged in Mexicon2 = the number of sharks captured in Hawaii on the first dayn3 = the number of sharks captured in Hawaii on the second dayn4 = the number of sharks captured in Hawaii on the third daym1 = the number of sharks captured in Hawaii on the first day that were previously taggedm2 = the number of sharks captured in Hawaii on the second day that were previously taggedm3 = the number of sharks captured in Hawaii on the third day that were previously taggedThe Lincoln-Petersen index formula is:
[tex]N = (n_1 * n_2 * n_3) / (m_1 * m_2 * m_3)[/tex]
Plugging in the given values, we get:
[tex]N = (45 * 20 * 20 * 20) / (3 * 2 * 4)[/tex]
[tex]N = 60,000 / 24[/tex]
[tex]N = 2,500[/tex]
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Sue bought a piece of fabric that was 98.96 meters long. Then she cut 3.56 meters of it off to use in a sewing project. How much fabric is left?
HELP ASAP. WILL GIVE BRAINLIEST AND ALL MY POINTS.
Find DB. D DC = 5 B C DB= [?]√ [ ] Give your answer as a simplified radical. Enter
The measure of diagonal DB in the given square is 5√2.
What is triangle?A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides. The sum of the three angles in a triangle is always 180 degrees. Triangles can be classified based on the length of their sides and the size of their angles.
Using Pythagoras theorem of right triangle
DB² = DC² + BC²
Here given that
DC = BC
Then
DB² = DC² + DC²
DB² = 5² + 5²
DB² = 25 + 25
DB² = 50
DB = √50
DB = 5√2
Thus, the measure of diagonal DB in the given square is 5√2
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a lattice point is a point with integer coordinates such as 2, 3. in how many ways can we pick 3 lattice points such that both coordinates of each point are positive integers less than 5, and the three points form a triangle?
The possible triangle whose vertices are given by the lattice points with positive integer coordinates less than 5 is 20.
To solve this, we apply principles of permutation and combination to count the number of possible triangles that can be formed from the given set of lattice points.
Here are the different ways of arranging the lattice points with lattice point coordinates less than 5:
If we want to choose any three lattice points, we can pick the first point from the 20 given in the table above.
Then, we can pick the second point from those lattice points that lie strictly above and strictly to the right of the first point.
For the third point, we can only pick lattice points lying above and to the right of the line segment connecting the first two points.
So, there are 20 possible triangles whose vertices are positive integer coordinates less than five.
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Joe has $2500 in a savings account that earns 9% interest per year. How much amount in dollars will he have in 3 years?
To calculate the amount of money Joe will have in 3 years, we can use the formula:
A = P(1 + r/n)^(nt)
where:
A = the amount of money Joe will have in 3 years
P = the principal amount = $2500
r = the annual interest rate = 9% = 0.09 (expressed as a decimal)
n = the number of times the interest is compounded per year (assuming annual compounding, n = 1)
t = the number of years = 3
Plugging in these values, we get:
A = $2500(1 + 0.09/1)^(1*3)
= $2500(1.09)^3
= $2500(1.29503)
= $3237.58 (rounded to two decimal places)
Therefore, Joe will have $3237.58 in 3 years.
what is the volume of the right circular cylinder with a diameter of 10 meters and a height of 16 meters. leave the answer in terms of pi.
if it has a diameter of 10, that means its radius is half that or 5.
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=16 \end{cases}\implies V=\pi (5)^2(16)\implies V=400\pi[/tex]
Answer: The answer is A, 400π m3
Step-by-step explanation:
12) To make a miniature ice cream truck, you need tires with a diameter between 1.465 cm and 1.472 cm. Will a tire that is 1.4691 cm in diameter work?
Answer: Yes
Step-by-step explanation:
1.4691 is more than 1.465, and less than 1.472
Identify the radius and the center of a circle whose equation is (x â€" 5)² y² = 81. the radius of the circle is units. the center of the circle is at ( , ).
The radius of the circle is 9 units. The center of the circle is at (5, 0).
The given equation is (x – 5)²y² = 81.
To identify the radius and center of this circle, we can rewrite the equation in standard form.
First, let's divide both sides by 81 to get (x – 5)²y²/81 = 1.
Next, we can take the square root of both sides to eliminate the squared terms.
This gives us the equation (x – 5)/9 · y/3 = 1.
The standard form of a circle is (x – h)² + (y – k)² = r², where (h, k) is the center of the circle and r is the radius.
Comparing this form to our equation, we can see that (x – 5)/9 and y/3 correspond to (x – h) and (y – k), respectively.
Therefore, we can solve for h and k by setting (x – 5)/9 = 0 and y/3 = 0, respectively.
This gives us h = 5 and k = 0, so the center of the circle is (5, 0). Finally, we can solve for the radius r by noting that the
distance from the center (5, 0) to the edge of the circle is 3 units in the x-direction and 9 units in the y-direction.
Therefore, the radius of the circle is 9 units, and we can express our final answer as:
The radius of the circle is 9 units. The center of the circle is at (5, 0).
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The sum of two numbers is -10. Negative three times the first number minus the second number equals 2.
Find the numbers.
Answer:
x = 4, y = -14
Step-by-step explanation:
1. x + y = -10 and -3x - y = 2
2. y= -10 - x > plug in for y > -3x - (-10 - x) = 2
3. solve for x > -3x + 10 + x = 2
-2x + 10 = 2 > -2x = -8 > x= 4
4. plug x into original equation > 4 + y = -10 > y = -14
[100 POINTS!!!]
According to the Fundamental Theorem of Algebra, how many zeros does the function f(x) = 5x^6+2x^3−4x + 1
There are____________ Zeros.
Step-by-step explanation:
According to the Fundamental Theorem of Algebra, a polynomial of degree n has exactly n complex zeros (counting multiplicities).
The degree of the polynomial f(x) = 5x^6+2x^3−4x + 1 is 6, which means that it is a sixth-degree polynomial. Therefore, it has exactly 6 complex zeros (counting multiplicities).
Note that the zeros may be real or complex, and they may not all be distinct. To find the exact number of zeros and their values, we would need to use additional methods such as factoring, the rational zeros theorem, or numerical methods.
Answer:
The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root. In the case of the polynomial function f(x) = 5x^6+2x^3−4x + 1, it is a sixth-degree polynomial function, which means it has at most six complex roots. However, the Fundamental Theorem of Algebra does not tell us the exact number of roots, nor does it tell us whether the roots are real or complex.
To determine the number of real roots of the function f(x), we can use the Intermediate Value Theorem or graph the function to find the number of times it crosses the x-axis. However, determining the number of complex roots requires more advanced techniques, such as the use of the Fundamental Theorem of Algebra in combination with the Factor Theorem, Rational Root Theorem, or other methods.
Therefore, based on the Fundamental Theorem of Algebra alone, we can say that the function f(x) = 5x^6+2x^3−4x + 1 has at least one complex root, but we cannot determine the exact number or nature of the roots without additional analysis.
Alexander owes \$3,200$3,200 on his credit card. The bank charges an annual interest rate of 16. 8%, compounded monthly. If Alexander wants to pay off his credit card using equal monthly payments over the next 8 months, what would the monthly payment be, to the nearest dollar?
Alexander would need to make monthly payments of $430 for the next 8 months to pay off his credit card debt.
To calculate the monthly payment that Alexander needs to make, we can use the formula for the present value of an annuity, which is:
[tex]PMT=PV*(r*(1+r)^n)/(1+r)^n-1)[/tex]
Where:
PMT = Monthly payment
PV = Present value of the debt
r = Monthly interest rate
n = Total number of payments
First, we need to calculate the monthly interest rate. The annual interest rate is 16.8%, which means the monthly interest rate is 16.8%/12 = 1.4%.
Next, we can calculate the total number of payments that Alexander needs to make over 8 months.
n = 8
Now, we can plug in the values:
[tex]PMT = 3200*\frac {(0.014*(1+0.014)^8)}{((1+0.014)^8-1)}[/tex]
This works out to approximately $430 per month (rounded to the nearest dollar).
Therefore, Alexander would need to make monthly payments of $430 for the next 8 months to pay off his credit card debt.
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100 POINTS!
A soccer player kicks a ball from the ground with a speed of 16 m/s at an angle of 63°.
a. What is the horizontal component of the velocity?
b. What is the vertical component of the velocity?
c. How long does it take the ball to reach its highest point?
d. What is the maximum height of the ball?
e. What is the total amount of time that the ball is in the air?
f. How far is the ball from the soccer player when it lands? (2 points)
Please show work for all questions
Answer:
a) v.h=v*cos(63)=7.26 m/s
b) v.v=v*sin(63)=14.26 m/s
c) t=v.v/g=14.26/9.8=1.46 s since time the body takes to go upward is defined by the acceleration due to gravity and the vertical component of the speed
d) h=1/2*gt^2=7.15 m
e) T=2t=2.92 s
f) R=v.h*t=7.26*1.46=10.6 m since horizontal displacement is defined by the horizontal component of the speed only.
Step-by-step explanation:
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Write a polynomial function in standard form with zero's -5,-4,and 3
The equation of the polynomial function in standard form is P(x) = x³ + 6x² - 7x - 60
Calculating the polynomial function in standard formGiven that we have the following
zeros = -5,-4,and 3
The polynomial function in standard form is calculated as
P(x) = (x - zeros)
So, we have
P(x) = (x + 5)(x + 4)(x - 3)
Opening the brackets, we have the following equation
P(x) = x³ + 6x² - 7x - 60
Hence, the polynomial is P(x) = x³ + 6x² - 7x - 60
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Where can I get the answers to both of these worksheets?
The probability that more than 7 of the 15 patients have hyperextending joints is 0.015, or about 1.5%.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
This is a binomial distribution problem, where we have n = 15 trials and the probability of success (a patient having hyperextending joints) is p = 0.2.
A. To find the probability that exactly 5 of the 15 patients have hyperextending joints, we can use the formula for the binomial probability mass function:
P(X = 5) = (15 choose 5) * 0.2^5 * 0.8^10
where (15 choose 5) is the number of ways to choose 5 patients out of 15. Using a calculator, we get:
P(X = 5) = 0.188
So the probability that exactly 5 of the 15 patients have hyperextending joints is 0.188, or about 18.8%.
B. To find the probability that no more than 7 of the 15 patients have hyperextending joints, we need to add up the probabilities of having 0, 1, 2, ..., 7 patients with hyperextending joints. We can use the cumulative distribution function (CDF) of the binomial distribution:
P(X ≤ 7) = Σ(P(X = k)) for k = 0 to 7
Again, using a calculator, we get:
P(X ≤ 7) = 0.985
So the probability that no more than 7 of the 15 patients have hyperextending joints is 0.985, or about 98.5%.
C. To find the probability that more than 7 of the 15 patients have hyperextending joints, we can use the complement rule:
P(X > 7) = 1 - P(X ≤ 7)
We already know from part (B) that P(X ≤ 7) = 0.985, so:
P(X > 7) = 1 - 0.985 = 0.015
Therefore, the probability that more than 7 of the 15 patients have hyperextending joints is 0.015, or about 1.5%.
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How do you find the Surface area of a rectangular prism make it simple and correct answer gets brainliest
The rectangular prism's length, width, and height can also be labelled, and the surface area (SA) can be calculated using the formula:
SA = 2lw+2lh+2hw.
Explain about the rectangular prism?A face is just a flat surface in the geometric sense, and edges are formed where surfaces meet. Pyramids and prisms are both examples of polyhedra. A pyramid, however, is not a prism.
A polyhedron having two identical and parallel faces is referred to as a prism.A rectangular prism is one of the more typical shapes for prisms. One definition of a rectangular prism is a prism with rectangle-shaped bases. An other faces also were rectangles because the bases are rectangles.Method to find surface area:
A three-dimensional shape's surface area is the total area on its surface. Add these areas of each of the six rectangular sides of a cuboid to determine its surface area.Thus, the rectangular prism's length, width, and height can also be labelled, and the surface area (SA) can be calculated using the formula:
SA = 2lw+2lh+2hw.
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Surface Area = (width×length + height×length + height×width) × 2
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Please remember to revise this and make it in your own words if you want! I tried making this as simple as possible! I hope this helps you. -Doodle
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I need helppppppppp please help me
The measures of angles in a rhombus are m∠2=130, m∠3=50 and m∠4=50.
What is angle measure?Angle measure is a term used in geometry to describe the size of an angle. It is usually expressed in degrees, which is a unit of measurement for angles. A degree is defined as 1/360th of a complete revolution around a circle.
According to question:In the rhombus, m∠1 =130
In a rhombus, opposite angles are congruent.
The angle opposite to angle 1 is angle 2.
so m∠1 =m∠2
m∠2= 130 degrees
Other pair of opposite angles are also congruent.
so m∠3=m ∠4
We know that the sum of 4 angles = 360
m∠1+m∠2+m∠3+m∠4=360
130+130+m∠3+m∠4=360
260+m∠3+m∠4=360
m∠3+m∠4=360-260
m∠3+m∠3=100
2m∠3=100
m∠3=50
Now, m∠3=50
m∠4=50
Therefore, m∠2=130, m∠3=50 and m∠4=50
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I WILL GIVE SOMEONE BRAINLIEST IF YALL ANSWER THIS!!!!
Answer:
v<-4/35. If you want interval notation it is (-infinity, -4/35)
Step-by-step explanation: