The closest answer to the p-value for this result is 0.0124.The p-value for this result, we need to first calculate the test statistic. Since we are testing a proportion, we will use the z-test.
The formula for the z-test is:
z = (p - P) / sqrt(P * (1 - P) / n)
where p is the sample proportion, P is the hypothesized population proportion, n is the sample size, and sqrt is the square root function. In this case, our sample size is n = 120, and our hypothesized population proportion is P = 0.85. Our sample proportion is p = 94/120 = 0.783.
Plugging in these values, we get:
z = (0.783 - 0.85) / sqrt(0.85 * 0.15 / 120) = -2.24
The p-value, we need to look up the area to the left of this value on the standard normal distribution. Using a table or calculator, we can find that this area is approximately 0.0124.
Toknow more aboutstatistic visit:-
https://brainly.com/question/28486320
#SPJ11
After heating up in a teapot, a cup of hot water is poured at a temperature of
20
3
∘
203
∘
F. The cup sits to cool in a room at a temperature of
6
9
∘
69
∘
F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below:
�
=
�
�
+
(
�
0
−
�
�
)
�
−
�
�
T=T
a
+(T
0
−T
a
)e
−kt
�
�
=
T
a
= the temperature surrounding the object
�
0
=
T
0
= the initial temperature of the object
�
=
t= the time in minutes
�
=
T= the temperature of the object after
�
t minutes
�
=
k= decay constant
The cup of water reaches the temperature of
18
5
∘
185
∘
F after 1.5 minutes. Using this information, find the value of
�
k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes.
Enter only the final temperature into the input box.
The cup of water reaches a temperature of 173 F after 4.5 minutes.
What is temperature?Temperature is a measure of the average kinetic energy of particles in a system. It is an important physical quantity used to describe the state of a system and is widely used in science, engineering, and everyday life. Temperature is a thermodynamic property of a system that shows how much energy is available to do work. In everyday terms, temperature is a measure of how hot or cold something is.
k = -0.2416
The equation for the cooling rate of the cup of water is:
T(t) = 203- 0.2416t
After 4.5 minutes, the temperature of the cup of water can be found by substituting t = 4.5 into the equation:
T(5) = 203- 0.2416(4.5 ) = 173.08 F
Therefore, the cup of water reaches a temperature of 173 F after 4.5 minutes.
To learn more about temperature
brainly.com/question/25677592
#SPJ1
Which of the following inequalities has a solution set represented by the following graph?
There are two ways you could approach this.
The first is to solve each inequality separately and see which one ends up equal to x ≥ -1.
Another and faster option is to test 0 in each inequality, because 0 is in the solution set and 0 is easy to work with. (You could do this for any value in the solution set.)
A: Is 4(0) + 3 > 7 true? No. 3 > 7 is false. This eliminates A.
B. Is 0/3 - 2 ≥ 2 true? No. -2 ≥ 2 is false. This eliminates B.
C. Is -2(0) - 3 ≤ -1 true? Yes. -3 ≤ -1 is false. We cannot eliminate C.
D. Is 0 + 5 < 4 true? No. 5 < 4 is false. This eliminates D.
So based on using x=0, the only possible solution is C.
You can double check this by solving 2x - 3 ≤ -1 for x:
-2x - 3 ≤ -1
-2x ≤ 2 (by adding 3 to both sides)
Now when you divide by -2 to solve for x, remember to flip the inequality.
-2x ≤ 2
x ≥ -1
So this confirms that C is correc.
what are the properties of a diamond plane shape
Step-by-step explanation:
A diamond is a two-dimensional flat quadrilateral with four closed straight sides. A diamond is also called a rhombus because it's sides are of equal measure and because the inside opposite angles are equal. Diamonds are also considered to be parallelograms because their opposite sides are parallel to each other
The points (7,-5) and (r,5) lie on a line with slope . Find the missing coordinate .
The missing coordinate is equal to 15.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
5/4 = (5 + 5)/(r - 7)
5/4 = 10/(r - 7)
5(r - 7) = 40
5r - 35 = 40
5r = 75
r = 75/5
r = 15.
Based on the information provided, the slope is the change in y-axis with respect to the x-axis and it is equal to 5/4.
Read more on slope here: brainly.com/question/3493733
#SPJ1
Complete Question:
The points (7,-5) and (r,5) lie on a line with slope 5/4. Find the missing coordinate
A 2-pint bottle of salad dressing costs $13.76. What is the price per cup?
Submit
The price per cup of salad dressing in a 2-pint bottle that costs $13.76 is $0.86.
To calculate the price per cup of salad dressing, we need to know that there are 2 cups in a pint. Therefore, there are 4 cups in a 2-pint bottle of salad dressing.
To find the price per cup, we divide the total cost of the bottle by the number of cups in the bottle.
$13.76 ÷ 4 cups = $3.44 per cup
Therefore, the price per cup of salad dressing is $0.86, which is obtained by dividing $3.44 by 4.
It is important to know the price per unit, whether it is per ounce, per pound, per liter, or per cup, to be able to compare the cost of different products accurately.
For more information regarding divide, click below:
https://brainly.com/question/1627825#
Which composite figure is made up of a cylinder and a half sphere?
PQR is a tangent to circle QABCD. AB || QD. CB=CD. Let 2, -30° and D₂ =70°. P A 1.1 Calculate Q₁. 1.2 Prove that C=110 A 1.3 Calculate B1
kimberly sent gifts to her friends. for each gift she used either a rectangular gift box or a cylindrical gift box. each box contains exactly one gift: either a fragrant soap or a pack of spicy roasted almonds. if half of the boxes she sent were cylindrical, and a third of the rectangular boxes contained soap, then how many cylindrical boxes contained soap?
Kimberly sent approximately 34 cylindrical boxes that contained soap
Let's assume Kimberly sent a total of 100 gift boxes. Since half of the boxes were cylindrical, that means she sent 50 cylindrical boxes.
If a third of the rectangular boxes contained soap, then 1/3 * (100 - 50) = 1/3 * 50 = 50/3 ≈ 16.7 rectangular boxes contained soap. Since we cannot have a fraction of a box, let's round it down to 16 rectangular boxes containing soap.
Now, since each box contains exactly one gift, the remaining cylindrical boxes must contain the pack of spicy roasted almonds. Therefore, out of the 50 cylindrical boxes, 50 - 16 = 34 cylindrical boxes contain soap.
Know more about cylindrical here:
https://brainly.com/question/30627634
#SPJ11
.
The terminal side of theta in standard position contains the point (-2, -6). Find the exact value of sin theta.
The exact value of sin theta as required to be determined in the task content is; sin theta = -3 / 2√10.
What is the exact value of sin theta as required?It follows from the task content that the exact value of sin theta is required to be determined from the given information.
Since the given terminal side of theta is; (-2, -6) it follows that the length of the hypothenuse in the arrangement is;
= √((-2)² + (-6)²)
= √(4 + 36)
= √40
= 4√10.
Therefore, since sin theta = opposite / adjacent;
Sin theta = -6 / 4√10
sin theta = -3 / 2√10.
Read more on terminal side of angles;
https://brainly.com/question/31029994
#SPJ1
Will make brainiest if two people answer ૮ ˶ᵔ ᵕ ᵔ˶ ა
The length of side LJ as shown in the similar shapes is 12.92.
What is similar shapes?Similar shapes are enlargements of each other using a scale factor.
To calculate the length of side LJ, we use the formula below
Formula:
XZ/XY = KJ/KL....................... Equation 1From the diagram,
Given:
/XZ/ = 8.2/XY/ = 8.7/KJ/ = 12.18Substitute these values into equation 1 and solve for KL
8.2/8.7 = 12.18/KLKL = 8.7×12.18/8.2KL = 12.92Hence, the right option is 12.92.
Learn more about similar shapes here: https://brainly.com/question/29782860
#SPJ1
a simple random sample of 50 adults was surveyed, and it was found that the mean amount of time that they spend surfing the internet per day is 54.2 minutes, with a standard deviation of 14.0 minutes. what is the 99% confidence interval (z-score
The 99% confidence interval for the population mean time spent on the internet, in minutes, is given as follows:
(48.9, 59.5).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 50 - 1 = 49 df, is t = 2.68.
The parameter values are given as follows:
[tex]\overline{x} = 54.2, s = 14, n = 50[/tex]
Then the lower bound of the interval is given as follows:
[tex]54.2 - 2.68\frac{14}{\sqrt{50}} = 48.9[/tex]
The upper bound of the interval is given as follows:
[tex]54.2 + 2.68\frac{14}{\sqrt{50}} = 59.5[/tex]
More can be learned about the t-distribution at https://brainly.com/question/17469144
#SPJ1
1. If we had a large 16 inch pizza for $14, what is the price per square inch?
$0.07
$0.09
$0.14
$0.25
2. If we had a medium 14 inch pizza for $12, what is the price per square inch?
$0.07
$0.09
$0.14
$0.25
Answer: $0.07 and $0.08
Step-by-step explanation: 1. To find the price per square inch of a 16 inch pizza for $14, we need to first calculate the area of the pizza.
The formula for the area of a circle is A = πr^2, where r is the radius of the circle. In this case, the radius is half of the diameter, which is 8 inches.
So, the area of the pizza is A = π(8)^2 = 64π square inches.
The price per square inch is the total price divided by the area of the pizza:
Price per square inch = Total price / Area
Price per square inch = $14 / (64π) square inches
Price per square inch ≈ $0.07
Therefore, the price per square inch of a 16 inch pizza for $14 is approximately $0.07.
Answer: $0.07
2. Following the same method as above, for a 14 inch pizza for $12, the radius is 7 inches and the area is A = π(7)^2 = 49π square inches.
The price per square inch is:
Price per square inch = Total price / Area
Price per square inch = $12 / (49π) square inches
Price per square inch ≈ $0.08
Therefore, the price per square inch of a 14 inch pizza for $12 is approximately $0.08.
Answer: $0.08
How many horizontal asymptotes can the graph of y = f(x) have? (Select all that apply.)
A. 0
B. 1
C. 2
D. 3
E. 4
The number of horizontal asymptotes that graph of y = f(x) can have is (c) 2.
As x approaches negative infinity, the function f(x) approaches the horizontal-asymptote y = 0 because the term 1/x becomes negligible compared to other terms. This occurs in the portion of the function defined as 1/x when x < 0.
As x approaches positive infinity, the function f(x) approaches the horizontal-asymptote y = 2 because the term 2x becomes dominant compared to other terms. This occurs in the portion of the function defined as 2x - 1 when x ≥ 0.
Therefore, the graph of y = f(x) has two horizontal asymptotes: y = 0 as x approaches negative infinity and y = 2 as x approaches positive infinity. The correct answer is (c) 2.
Learn more about Asymptote here
https://brainly.com/question/29337557
#SPJ4
The given question is incomplete, the complete question is
How many horizontal asymptotes can the graph of y = f(x) have? (Select all that apply.)
f(x) = {1/x , if x<0,
= {2x - 1 , if x≥0.
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4
Polar Coordinates
4. Name two different representations of the
point on the interval of [-2π, 2π].
Given P = (2,π /4).
Please help me, I got it wrong.
Please refer to picture.
The polar coordinates are solved the point is P ( 2 , π/4 )
Given data ,
Given the point P = (2, π/4) on the interval [-2π, 2π], here are two different representations of this point:
Cartesian Coordinates: (2, π/4)
In the Cartesian coordinate system, the point P is represented by its x and y coordinates. The x-coordinate is 2, and the y-coordinate is π/4.
Polar Coordinates: (2, 45°)
In polar coordinates, the point P is represented by its radius (distance from the origin) and angle. The radius is 2, and the angle is π/4, which is equivalent to 45 degrees.
To learn more about polar coordinates click :
https://brainly.com/question/26193139
#SPJ1
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A system of linear equations is given by the tables. One of the tables is represented by the equation y = - + 7.
The Equation for Table I is y= 1/3x + 5.
The solution of the Equation is (3, 6).
Equation for Table II
y= -1/3 x +7
Table I:
Slope = (6-5)/ (3-0)
slope = 1/3
and, using slope intercept form
y - 5 = 1/3 (x - 0)
y-5 = 1/3x
y = 1/3x + 5
Now, solving the equation for both table we get
x= 3 and y= 6
Learn more about Slope here:
https://brainly.com/question/3605446
#SPJ1
Directions: Find the volume of each figure. Round to the nearest hundredth.
2.
1.
3.
5.
8 m.
7.
34 m
3 km
** This is a 2-page
EXER
11 cm
P
4.
end 1601 02
6.
11 yd
Tw
10.8 ft
Directions: Find the surface area of each figure. Round to the nearest hundredth.
8.
0-
29 in
8.6 ft
boil Co
II in
3.
13.4 mm
5.
98
7.
1956
The calculated volumes of the figures are 2145.52 cubic meters, 697.19 cubic yards, 20587.81 cubic meters, 2639.40 cubic feet, 56.57 cubic km and 6387.60 cubic inches
How to find the volume of the figuresThe sphere 1
The volume is calculated as
V = 4/3πr³
Where
r = Radius = 8 meters
So, we have
V = 4/3 * 22/7 * 8³
Evaluate
Volume = 2145.52 cubic meters
The sphere 2
The volume is calculated as
V = 4/3πr³
Where
r = Radius = (11/2) yards
So, we have
V = 4/3 * 22/7 * (11/2)³
Evaluate
Volume = 697.19 cubic yards
The sphere 3
The volume is calculated as
V = 4/3πr³
Where
r = Radius = (34/2) meters
So, we have
V = 4/3 * 22/7 * (34/2)³
Evaluate
Volume = 20587.81 cubic meters
The hemisphere 4
The volume is calculated as
V = 2/3πr³
Where
r = Radius = 10.8 feet
So, we have
V = 2/3 * 22/7 * 10.8³
Evaluate
Volume = 2639.40 cubic feet
The hemisphere 5
The volume is calculated as
V = 2/3πr³
Where
r = Radius = 3 km
So, we have
V = 2/3 * 22/7 * 3³
Evaluate
Volume = 56.57 cubic km
The hemisphere 6
The volume is calculated as
V = 2/3πr³
Where
r = Radius = 29/2 in
So, we have
V = 2/3 * 22/7 * (29/2)³
Evaluate
Volume = 6387.60 cubic inches
Read more about volumes at
brainly.com/question/463363
#SPJ9
Solve 2x(3x+5)+3(3x+5)=ax 2 +bx+c
Answer:
6x² + 19x + 15
Step-by-step explanation:
2x(3x+5)+3(3x+5)
= (3x + 5) (2x + 3)
= 6x² + 9x + 10x + 15
= 6x² + 19x + 15
So, the answer is 6x² + 19x + 15
We can start by simplifying the left side of the equation using the distributive property:
2x(3x+5)+3(3x+5) = (2x)(3x) + (2x)(5) + (3)(3x) + (3)(5)
= 6x^2 + 10x + 9x + 15
= 6x^2 + 19x + 15
Now we can compare this expression with the right side of the equation, which is a polynomial in x with unknown coefficients a, b, and c:
ax^2 + bx + c
Since the two sides are equal, their corresponding coefficients must be equal as well. This gives us a system of three equations in three unknowns:
a = 6 (the coefficient of x^2)
b = 19 (the coefficient of x)
c = 15 (the constant term)
Therefore, the solution to the equation 2x(3x+5)+3(3x+5)=ax^2+bx+c is:
2x(3x+5)+3(3x+5) = 6x^2 + 19x + 15
Tommy opens a bank account with an initial amount of $650. The account has an annual
interest rate of 3.5%. What will the account balance (principle+interest) be after 8 years if
the account is compounded:
a) annually?
b) quarterly?
c) weekly?
d) daily?
e) continuously?
Annually: $822.49
Quarterly: $842.67
Weekly: $849.01
Daily: $850.98
Continuously: $853.39
The slope of the line tangent to the graph of y = \ln \left( {1 - x} \right) at x=-1 is
(A) -1
(B) - \frac{1}{2}
(C) \frac{1}{2}
(D) \ln \left( 2 \right)
(E) 1
To find the slope of the line tangent to the graph of y = ln(1 - x) at x = -1, we can use the derivative of the function.
The derivative of y with respect to x can be found using the chain rule:
dy/dx = d/dx[ln(1 - x)] = 1 / (1 - x) * (-1) = -1 / (1 - x)
Substituting x = -1 into the derivative, we have:
dy/dx = -1 / (1 - (-1)) = -1 / 2
Therefore, the slope of the line tangent to the graph at x = -1 is -1/2.
The correct answer is (B) -1/2.
To learn more about slope : brainly.com/question/3605446
#SPJ11
The number of times 100 groups took a
selfie is as follows.
Takes
1 2 3
4
Frequency 27 29 18 14
5
12
Find the probability a group will take their
selfie exactly 3 times.
P(3) = [?]
The probability a group will take their selfie exactly 3 times is 0.18.
We have,
The total groups = 100
The number of groups that took selfies 3 times = 18
Now,
The probability a group will take their selfie exactly 3 times.
= 18/100
= 0.18
Thus,
The probability a group will take their selfie exactly 3 times is 0.18.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ1
measuring the concentration of a certain pollutant in a lake results in the determination that observations are normally distributed with mean (expectation) 210 units, and that there is a probability of 0.05 that a given measurement will exceed 250 units. 1. what is the standard deviation? 2. assuming that the standard deviati
The standard deviation is approximately 24.28 units.
1. The standard deviation can be calculated using the formula for the normal distribution:
P(X > 250) = 0.05
Using a standard normal distribution table, we can find the corresponding z-score for a probability of 0.05, which is approximately 1.645.
z = (250 - 210) / σ
Solving for σ, we get:
σ = (250 - 210) / z = (250 - 210) / 1.645 = 24.28 units
Therefore, the standard deviation is approximately 24.28 units.
To determine the standard deviation of a normally distributed pollutant concentration in a lake, we first use the probability of exceeding 250 units (0.05) and a standard normal distribution table to find the corresponding z-score (1.645). Using this z-score and the given mean (210 units), we can solve for the standard deviation using the formula for the normal distribution. The resulting standard deviation is approximately 24.28 units.
The standard deviation is an important measure of variability in a dataset and can be calculated using the formula for the normal distribution. In this case, the standard deviation of a normally distributed pollutant concentration in a lake was calculated using the mean and probability of exceeding a certain value.
To know more about standard deviation visit:
brainly.com/question/13498201
#SPJ11
Factorize a2 - b2
[tex]a {?}^{2} - b {?}^{2} \\ \\ [/tex]
The factorization of the given expression, a² - b², is (a + b)(a - b)
Factorizing an expressionFrom the question, we are to factorize the given expression.
From the given information, the given expression is
a² - b²
This is a special case in the factorization of polynomials. This is called difference of two squares.
Given the expression
x² - y²
The above expression can be written in the factorized form as
(x + y)(x - y)
Check:
Check by expanding the above factored form
(x + y)(x - y)
Applying the distributive property
x(x - y) + y(x - y)
x² - xy + xy - y²
Simplify further
x² - y²
Thus,
x² - y² = (x + y)(x - y)
In the same manner,
a² - b² = (a + b)(a - b)
Hence, the factorization of a² - b² is (a + b)(a - b)
Learn more on Factorizing an expression here: https://brainly.com/question/24673551
#SPJ1
[tex]\frac{2x-1}{3} -\frac{3x}{4} =\frac{5}{6}[/tex]
The value of the variable is -14
What are fractions?Fractions are simple defined as the part of a whole number or variable.
From the information given, we have that;
2x - 1/3 - 3x/4 = 5/6
Find the LCM, we have;
4(2x - 1) - 3(3x) /12 = 5/6
expand the bracket, we get;
8x - 4 - 9x/12 = 5/6
collect the like terms
-x - 4/12 = 5/6
cross multiply the values
-6x - 24 = 60
collect like terms
-6x = 84
make 'x' the subject
x = -14
Learn about fractions at: https://brainly.com/question/11562149
#SPJ1
how many units is -1+(-4) from -1
The expression -1 + (-4) is 4 units away from -1.
How to find the unitsThis can be solved using the concept of number line.
A number line is a visual representation of all real numbers placed on a straight line with an arbitrary point as the origin the origin is usually represented as zero and the numbers increase from left to right or from right to left
Another way is to find how many units -1 + (-4) is from -1, we need to subtract -1 from -1 + (-4) this is done below
= -1 + (-4) - (-1)
= -1 - 4 + 1
= -4
we can say that, -1 + (-4 ) is 4 units away from -1.
Learn more about number line at
https://brainly.com/question/24644930
#SPJ1
Help with my math please
Answer:
Step-by-step explanation:
x+y=5; x-y=3Adding both equations, we get:
2x = 8
x = 4Substituting the value of x in any of the equations:
x+y=5
4+y=5
y=1So the solution to this system of equations is: x=4, y=1.3x+y=11; y=x+3Substituting y=x+3 in the first equation:
3x+x+3=11
4x=8
x=2Substituting x=2 in the second equation:
y=x+3
y=2+3
y=5So the solution to this system of equations is: x=2, y=5.x+3y=0; 2x-y=-7Multiplying the second equation by 3 to eliminate y:
6x-3y=-21Adding both equations, we get:
7x=-21
x=-3Substituting x=-3 in the first equation:
x+3y=0
-3+3y=0
y=1So the solution to this system of equations is: x=-3, y=1.y=-3x-2; 6x+2y=-4Substituting y=-3x-2 in the second equation:
6x+2(-3x-2)=-4
6x-6x-4=-4
-4=-4This means that the two equations are equivalent and represent the same line. Therefore, there are infinitely many solutions to this system of equations.-4x+5y=27; x-6y=-2Multiplying the second equation by 5 to eliminate y:
5x-30y=-10Adding both equations, we get:
x-4x+5y-30y=-2+27
-x-25y=25
25y=-x-25
y=-(1/25)x-1Substituting y=-(1/25)x-1 in the first equation:
-4x+5(-(1/25)x-1)=27
-4x-5/5x-5=27
-9x=32
x=-32/9Substituting x=-32/9 in the expression for y:
y=-(1/25)(-32/9)-1
y=83/225So the solution to this system of equations is: x=-32/9, y=83/225.
What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
The range of the given function is {y|y>9}. Therefore, option B is the correct answer.
The given function is f(x)=3x+9.
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Substitute x=0, 1, 2, 3, 4,....in y=3x+9, We get
When x=0
y=9
When x=1
y=12
When x=2
y=15
When x=3
y=18
So, the range is {9, 12, 15, 18,.....}
Therefore, option B is the correct answer.
To learn more about the range of the function visit:
brainly.com/question/17440903.
#SPJ1
3.a coin is tossed, and a die is rolled. what is the probability that the outcome is a head or an even number?
According to the statement the probability of getting either a head or an even number on the die is 3/4.
To calculate the probability of getting a head or an even number, we can use the formula for the probability of the union of two events:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
In this case, A represents getting a head, and B represents getting an even number on the die.
P(A) = Probability of getting a head = 1/2 (since there are two sides of the coin: heads and tails)
P(B) = Probability of getting an even number on the die = 3/6 (since there are three even numbers out of six possible outcomes: 2, 4, and 6)
P(A ∩ B) = Probability of getting both a head and an even number. Since these two events are independent, we can find this probability by multiplying the individual probabilities: P(A) * P(B) = (1/2) * (3/6) = 1/4
Now, we can find the probability of the union:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = (1/2) + (3/6) - (1/4) = 1/2 + 1/2 - 1/4 = 3/4
So, the probability of getting either a head or an even number on the die is 3/4.
To know more about probability visit :
https://brainly.com/question/30177872
#SPJ11
An athlete throws a shot put with an initial vertical velocity of 40 feet per second. He releases the shot put at a height of 5.69 feet.
Use an equation that models the height h (in feet) of the shot put as a function of the time t (in seconds) after it is thrown to find the time that the shot put is in the air.
Round your answers to the nearest whole numbers.
The shot put is in the air for approximately 3 seconds.
The height h (in feet) of the shot put as a function of the time t (in seconds) after it is thrown can be modeled by the equation:
h(t) = h + vt - (1/2)gt²
where v is the initial vertical velocity in feet per second, and s is the initial height in feet.
Here, the initial vertical velocity is 40 feet per second, and the initial height is 5.69 feet. Therefore, we can plug in these values to get:
h = -16t² + 40t + 5.69
To find the time that the shot put is in the air, we need to find the value of t when h = 0, since the shot put will hit the ground when its height is 0.
Therefore, we can set the equation equal to 0 and solve for t:
0 = -16t² + 40t + 5.69
Using the quadratic formula, we get:
t = (-b ± √(b² - 4ac)) / 2a
where a = -16, b = 40, and c = 5.69.
Plugging in these values, we get:
t = (-40 ± √(40² - 4(-16)(5.69))) / 2(-16)
Simplifying, we get:
t ≈ 3 or t ≈ 0.2
Since the shot put cannot be in the air for negative time, the only possible answer is t ≈ 3.
Therefore, the shot put is in the air for approximately 3 seconds.
Learn more about quadratic function here:
brainly.com/question/14083225
#SPJ1
a rectangular lot is 135 yards long and 100 yards wide, give the length and width of another rectangular lot that has the same perimeter but a larger area.
Evaluate the following expression.
25
1/25
-25
-1/25
The expression is evaluated to 1/25. Option B
What are index forms?Index forms are simply described as distinct mathematical forms that are used in the representation of variables or numbers that are too large or too small in more convenient forms.
These index forms are also referred to as scientific notations or standard forms.
Some rules of index forms are;
Add the exponent value of variables or number that have the same bases and are being multipliedSubtract the exponent value of variables or number that have the same bases and are being dividedThe value of a number with negative power is its inverseFrom the information given, we have that;
1/5⁻²
Take the inverse power
1/25
Learn more about index forms at: https://brainly.com/question/15361818
#SPJ1
