Given the quadratic function : f(x)=x^24x-12
Find the vertex.
Can you show the steps?!?
A number cube is rolled 120 times. The number 4 comes up 47 times. What is the experimental probability of rolling a 4? What is the theoretical probability of rolling a 4?
A. 47/120; 1/30
B. 47/120; 1/6 ******
C. 4/47; 1/6
D. 1/6; 47/120
Am I Correct?
A number cube is rolled 120 times. The number 4 comes up 47 times.
We have to determine the experimental probability of rolling a 4.
The formula to evaluate probability of an event is given by:
Probability = [tex] \frac{Favourable outcomes}{Total outcomes} [/tex]
So, Probability of rolling a 4 = [tex] \frac{ Total number of times when 4 appears}{Total number of times number cube rolled} [/tex]
= [tex] \frac{47}{120} [/tex]
Now, we have to find the theoretical probability of rolling a 4.
Total number of outcomes of number cube = {1,2,3,4,5,6}
Probability of rolling a 4 = [tex] \frac{1}{6} [/tex]
So, Option B is the correct answer.
Today, 32 customers at Tasha's Juice Emporium bought a total of 512 ounces of juice. How much juice did each customer buy on average?
The amount of juice did each customer buy on average is,
⇒ 16 ounces
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Today, 32 customers at Tasha's Juice Emporium bought a total of 512 ounces of juice.
Hence, The amount of juice did each customer buy on average is,
⇒ 512 / 32
⇒ 16 ounces
Thus, The amount of juice did each customer buy on average is,
⇒ 16 ounces
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Caleb and Emily are standing 100 yards from each other. Caleb looks up at a 45° angle to see a hot air balloon. Emily looks up at a 60° angle to see the same hot air balloon. Approximately how far is the hot air balloon off the ground?
Answer:
63.39 yards.
Step-by-step explanation:
Refer the attached figure
We are given that Caleb and Emily are standing 100 yards from each other i.e. BC = 100
Let BD = x
So, DC = 100-x
We are given that Caleb looks up at a 45° angle to see a hot air balloon i.e. ∠ABD = 45° and Emily looks up at a 60° angle to see the same hot air balloon i.e. ∠ACD = 60°
Let AD be the height of the balloon denoted by h.
In ΔABD
Using trigonometric ratio
[tex]tan \theta = \frac{Perpendicular}{Base}[/tex]
[tex]tan 45^{\circ} = \frac{AD}{BD}[/tex]
[tex]1= \frac{h}{x}[/tex]
[tex]x=h[/tex] ---1
In ΔACD
Using trigonometric ratio
[tex]tan \theta = \frac{Perpendicular}{Base}[/tex]
[tex]tan 60^{\circ} = \frac{AD}{DC}[/tex]
[tex]\sqrt{3}= \frac{h}{100-x}[/tex]
[tex]\sqrt{3}(100-x)=h[/tex] ---2
So, equating 1 and 2
[tex]\sqrt{3}(100-x)=x[/tex]
[tex]100\sqrt{3}-\sqrt{3}x=x[/tex]
[tex]100\sqrt{3}=x+\sqrt{3}x[/tex]
[tex]100\sqrt{3}=x(1+\sqrt{3})[/tex]
[tex]\frac{100\sqrt{3}}{1+\sqrt{3}}=x[/tex]
[tex]63.39=x[/tex]
Thus the height of the balloon is 63.39 yards.
Answer:
B
Step-by-step explanation:
Find the 86th term of the arithmetic sequence 21, 15, 9, ...21,15,9,...
The 86th term of the arithmetic sequence is [tex]\(-489\).[/tex]
To find the 86th term of the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:
[tex]\[ a_n = a_1 + (n - 1) \cdot d \][/tex]
where:
- [tex]\( a_n \)[/tex] is the nth term,
- [tex]\( a_1 \)[/tex] is the first term,
- ( n ) is the term number,
- ( d ) is the common difference.
In this sequence:
- [tex]\( a_1 = 21 \),[/tex]
- [tex]\( d = 15 - 21 = -6 \).[/tex]
Now, we can plug these values into the formula to find the 86th term:
[tex]\[ a_{86} = 21 + (86 - 1) \cdot (-6) \][/tex]
[tex]\[ a_{86} = 21 + 85 \cdot (-6) \][/tex]
[tex]\[ a_{86} = 21 - 510 \][/tex]
[tex]\[ a_{86} = -489 \][/tex]
So, the 86th term of the arithmetic sequence is [tex]\(-489\).[/tex]
Which pair of numbers are not opposites? Select one: a. |7| and -7 b. 72 and -72 c. 27 and |-27| d. 27 and -27
Keisha can jog 2 miles in 24 minutes. At the same rate , how many miles can she jog in 60 minute
Which graph shows a plot of the complex number i - 2
Find the exact values ofcos (3pi/4radians) and sin (3pi/4 Radians)
Solve x2 + 10x + 12 = 36 for x. x = â12 or x = 2 x = â11 or x = 1 x = â2 or x = 12 x = â1 or x = 11
The Menswear Department of Nancy‘s Department Store had sales of $191,000, cost of goods sold of $134,000, indirect expenses of $13,550, and direct expenses of $27,800 for the current period. What is the Menswear Department's contribution to overhead as a percent of sales?
To calculate the overhead contribution, divide the indirect expenses by the total sales, and multiply by 100. The Menswear Department's contribution to overhead as a percent of sales for this period is approximately 7.09%.
Explanation:The student is asking about calculating the overhead contribution rate. Overhead contribution can be calculated by dividing indirect expenses by total sales and multiplying by 100. In this case, total sales for the Menswear Department are $191,000 and indirect expenses are $13,550.
Therefore, the rate is calculated as follows: ($13,550 / $191,000) * 100 = 7.09%. Thus, the Menswear Department's contribution to overhead as a percent of sales is 7.09%.
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!!!!WILL MARK BRAINLIEST IF CORRECT AND IF YOU ANSWER ALL PARTS OF QUESTION! SHOW WORK PLEASE!!!!!
2. A cube-shaped aquarium has edges that are 3 ft long. The aquarium is filled with water that has a density of 62 lb/ft^3
(a) Should the aquarium be placed on a table that can support a maximum weight of 200 lb? Explain why or why not.
(b) Would the density of the water change if the aquarium was only half full? Explain.
The dot product of u with itself is 24. what is the magnitude of u?
Answer - u = 4.8989
u ^ 2 = 24
u = sqrt (24)
u = 4.8989
Answer:
[tex]2\sqrt6[/tex]
Step-by-step explanation:
We have been given that the dot product if u with itself is 24.
Now, we know that the dot product of vector a and b is given by
[tex]a\cdot b=|a||b|\cos\theta[/tex]
Here, [tex]\theta[/tex] is the angle between the vectors a and b.
We have to find the dot product of u with itself. Hence,
a = u
b = u
[tex]\theta=0[/tex]
Thus, dot product is given by
[tex]u\cdot u=|u||u|\cos0\\\\24=|u||u|\cdot1\\\\|u|^2=24\\\\|u|=2\sqrt6[/tex]
Thus, the magnitude of u is [tex]2\sqrt6[/tex]
What is true about side AB and side AD?
1) The slopes are the same.
2)The slopes are the opposite reciprocal.
If x varies directly as y, and x = 48 when y = 16, find x when y = 5.
A) 5/3
B) 153.6
C) 15
A classroom of children has 16 boys and 19 girls in which five students are chosen to do presentations. what is the probability that at least four boys are chosen?
The probability of at least four boys from five selected students depends on the ratio of the favorable outcomes (either four boys and one girl, or all five are boys) to the total combinations of five students from 35, calculated using Combinatorics.
Explanation:The subject of your question is Probability, which falls under Mathematics. The question can be approached through Combinatorics, a branch of Mathematics that deals with combinations of objects belonging to a finite set following certain constraints.
To address your question, we first need to find the total number of ways that five students can be selected from the total 35 (16 boys and 19 girls). This can be calculated using combinations, denoted as C(n, r), where n is the total number of elements and r is the number of elements to choose from the total. In this case, the total combinations would be C(35, 5).
Next, we need to find the combinations where at least four boys are chosen. This could mean either four boys and one girl are chosen, or all five chosen are boys.
For the situation where four boys and one girl are chosen, the possible combinations would be C(16, 4) * C(19, 1). For the situation where all chosen are boys, the possible combinations would be C(16, 5).
So, the total desired combinations would be C(16, 4)*C(19, 1) + C(16, 5).
The probability of choosing at least four boys would be the ratio of desired combinations to the total combinations. Thus, Probability = [C(16, 4)*C(19, 1) + C(16, 5)] / C(35, 5).
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A basketball is theown upwards. The height F(t), The height in feet, in time, t, in seconds is goven by the following. f(t)= -16t(2) +44+ 12. Which of the following is a reasonable domain of the graphof the function when the basketball falls from ots maximum height to the ground?
Which expression is another way to show 9/2
The expression 9/2 can be equivalently expressed as the mixed number 4 1/2, or by multiplying the numerator and denominator by the same number, such as 18/4.
Explanation:The question asks for an expression that is equivalent to 9/2. One way to express this fraction differently is by converting it into a mixed number. Since 9 divided by 2 is 4 with a remainder of 1, we can express 9/2 as 4 1/2 (four and a half). Another method is to multiply both the numerator and the denominator by the same number, which does not change the value of the fraction.
For example, multiplying both by 2 gives us 18/4, which is equivalent to 9/2. Multiplying or dividing both the numerator and denominator by the same non-zero number is a skill that can provide equivalent fractions.
57(1.31)^t interpret the meaning of the expression
A. The initial number of bacteria is 57 and the growth rate is 3.1% per hour
B. The initial number of bacteria is 57 and the growth rate is 31% per hour
C.the initial number of bacteria is 131 and the growth rate is 5.7% per hour
D.the initial number of bacteria is 131 and the growth rate is 57% per hour
B. The initial number of bacteria is 57 and the growth rate is 31% per hour
57 is the initial all by itself and 31 is the growth rate. Don't really know why and how to explain the Percentage application but I got the answer correct on my test so.................................
Is this function one-to-one? Explain how you determine your answer
A movie theater is 3 blocks due north of a supermarket and a beauty parlor is 4 blocks due east of the movie theater. how many blocks long is the nearest street that runs directly from the supermarket to the beauty parlor?
What is the value of y?
I think the hypotenuse is 8 and if it is, am I supposed to do
C^2 - B^2 = A^2?
"25 students, and has a distribution of grades with a mean of 70 and standard deviation of 15, what is the standard error of the mean?"
Find the area of the entire slice of pizza. Since the slice of pizza is part of a whole pie, let’s think of the pizza as a sector of a circle. Calculate the area. Be sure to show all of you work.
Answer:
The area of the entire slice of pizza = 14.13 square inches
Step-by-step explanation:
From the given figure of pizza.
The radius of the pizza is 6 in.
Central angle = 45°
The pizza is in the shape of the circle. We need to find the entire slice of pizza.
Here we have to use the formula to find the area of sector of a circle.
Area of a sector of a circle = [tex]\frac{Central angle}{360} *\pi *r^2[/tex]
Now plug in central angle = 45, r = 6 in the above formula to find the area of the slice of the pizza.
The area of the entire slice of pizza = [tex]\frac{45}{360} *3.14*6^2[/tex]
The value of π = 3.14
= [tex]\frac{45}{360} *3.14*36[/tex]
Simplifying, we get
= [tex]\frac{45}{10} *3.14[/tex]
= 141.3/10
The area of the entire slice of pizza = 14.13 square inches
A total of 705 tickets were sold for the school play. they were either adult tickets or student tickets. there were 55 more student tickets sold than adult tickets. how many adult tickets were sold?
There were 380 student tickets and 325 adult tickets were sold for the school play.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let the number of student tickets would be x and the number of adult tickets would be y
As per the given question, the following system of equations:
x - y = 55 ....(i)
x + y = 705 ....(ii)
Add both equations,
x - y + x + y = 55 + 705
2x = 760
x = 760 / 2
x = 380
Substitute the value of x = 380 in equation (ii),
x + y = 705
380 + y = 705
y = 705 - 380
y = 325
Hence, there were 380 student tickets and 325 adult tickets were sold for the school play.
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The position of an object at time t is given by s(t) = -9 - 5t. Find the instantaneous velocity at t = 4 by finding the derivative.
Answer:
Instantaneous Velocity is [tex]-5[/tex]
Step-by-step explanation:
Velocity refers to the speed along with direction or we can say velocity refers to rate of change of position of an object with respect to time.
Let [tex]s\left ( t \right )[/tex] be the position of object . Then the instantaneous velocity is given by [tex]v\left ( t \right )=s'\left ( t \right )[/tex] . At time [tex]t=t_0[/tex] , velocity is given by [tex]v\left ( t_0 \right )=s'\left ( t_0 \right )[/tex]
Given: [tex]s\left ( t \right )=-9-5t[/tex]
On differentiating with respect to time t , we get :
[tex]v\left ( t \right )=s'\left ( t \right )=-5[/tex]
At [tex]t=t_0=4[/tex] ,
[tex]v\left ( 4 \right )=s'\left ( 4 \right )=-5[/tex]
If you work 52 weeks/year and 40 hours/week, how many hours would you work in one year?
Write the sum using summation notation, assuming the suggested pattern continues.
-8 - 3 + 2 + 7 + ... + 67
Remark: L = a + (n - 1)d is your starting point. In order to find the sum, you must know the value of n.
Givens: a = - 8; d=5; L = 67
Substitute and solve
67 = - 8 + (n - 1)*5 Add 8 to both sides.
67 + 8 = -8 + 8 + (n - 1)*5
75 = (n - 1)*5 Divide by 5 on both sides.
15 = n - 1 Add one to get the answer.
16 = n
Part Two: Use The summation notation to find the sum. Unfortunately, I don't know how to do this in latex.
Sum (n = 1 to 16) -8 + 5*(n - 1)
The number of plastic straws produced by a machine varies directly as the amount of time the machine is operating. If the machine produces 20,000 straws in 8 hours, how many straws can it produce in 50 hours?
Given is the direct relationship between number of produced straws and the hours of operating machine.
Given that 20,000 straws are produced in 8 hours of machine's operation.
Let's assume that 'x' straws are produced in 50 hours of machine's operation.
Using the concept of proportions, x straws in 50 hours would be proportional to 2000 straws in 8 hours.
[tex] \frac{X \;straws}{50 \;hours} =\frac{20,000 \;straws}{8 \;hours} \\\\\frac{X \;straws}{20,000 \;straws} =\frac{50 \;hours}{8 \;hours} \\\\\frac{X}{20,000} =\frac{50}{8} \\\\Cross \;multiplying \\\\8*X = 50*20000 \\\\8X = 1,000,000 \\\\\frac{8X}{8} =\frac{1,000,000}{8} \\\\X=125,000 \;straws [/tex]
Hence, total 125,000 straws would be produced in 50 hours.
Say it with symbols a pool has lenght of 3s and a width of 2s. square tiles that are 1 ft. by 1ft. will be placed around the pool as the a border. write an expression that can be used to determine to create the border for pool size.