Answer:
The maximum height that the object will reach is of 9 feet.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]
In this question:
[tex]f(t) = -16t^{2} + 16t + 5[/tex]
So
[tex]a = -16, b = 16[/tex]
The instant of the maximum height is:
[tex]t_{v} = -\frac{16}{2*(-16)} = 0.5[/tex]
The maximum height is:
[tex]f(0.5) = -16*(0.5)^2 + 16*0.5 + 5 = 9[/tex]
The maximum height that the object will reach is of 9 feet.
Answer:
24
Step-by-step explanation:
Please answer this correctly
Answer:
75%
Step-by-step explanation:
There are 6 numbers that fit the rule, 1, 2, 3, 4, 6, 8. Since there are a total of 8 numbers, there is a 6/8 chance picking one or 75% chance.
Answer:
50%
Step-by-step explanation:
so the original fraction is 4/8 or 1/2 so it is 50%.
Suppose we know that a confidence interval for a population proportion is (0.572,0.662), with a sample proportion of p′=0.617. What is the margin of error?
Explanation:
The sample proportion 0.617 is at the exact midpoint of the interval from 0.572 to 0.662
We can confirm this by applying the midpoint formula.
The distance from the center (0.617) to either endpoint will be the margin of error. In other words, it is half the width of the confidence interval
L = lower boundary of confidence interval = 0.572
C = center of confidence interval = 0.617
U = upper boundary of confidence interval = 0.662
We have three methods to find the confidence interval
margin of error = U - C = 0.662-0.617 = 0.045margin of error = C - L = 0.617 - 0.572 = 0.045margin of error = (width)/2 = (U-L)/2 = (0.662-0.572)/2 = 0.045Each yielding the same result of 0.045
With the third method, you don't need to know the center of the confidence interval.
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.y=-6x+6 y=-3x-3
Hey there! :)
Answer:
Has one solution.
(Graphed below)
Step-by-step explanation:
***The equations are graphed below, but this can also be solved algebraically.***
Set each equation equal to each other:
-6x + 6 = -3x - 3
Add 6x to both sides:
6 = 3x - 3
Add 3 to both sides:
9 = 3x
x = 3.
Plug in the value of x into an equation to solve for y:
y = -6(3) + 6
y = -18 + 6
y = -12.
The system of equations only has ONE solution at (3, -12).
On the graph, as well, the point of intersection is at (3, -12). This is the solution.
Solve 6 + 5 √ 2 4 9 − 2 x = 7
[tex]
6+5\sqrt{249}-2x=7 \\
-2x=7-6-5\sqrt{249} \\
-2x\approx-77.9 \\
x\approx\frac{-77.9}{2}\approx38.95
[/tex]
Hope this helps.
Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. Andrew asked seven of his friends how many cousins they had. The results are listed below. Find the mean number of cousins. 15 12 5 14 4 4 6
Answer:
8.57Step-by-step explanation:
Mean is defined as the ratio of the total sum of all the given datas to the total number of data present. It is expressed mathematically as;
[tex]\overline x = \frac{ \sum Xi}{N}[/tex] where;
[tex]\overline x = mean\\Xi= individual \ data\\N = total\ amount\ of \ data[/tex]
Given N = 7
[tex]\overline x = \frac{15+12+5+14+4+4+6}{7}[/tex]
[tex]\overline x= \frac{60}{7} \\\overline x = 8.57[/tex]
The mean number of cousins is 8.57
A toy falls from a window 80 feet above the ground. How long does it take the toy to hit the ground?
Answer:
2.24 s
Step-by-step explanation:
Given:
Δy = 80 ft
v₀ = 0 ft/s
a = 32 ft/s²
Find: t
Δy = v₀ t + ½ at²
80 ft = (0 ft/s) t + ½ (32 ft/s²) t²
t = 2.24 s
(+3
+(+2)
help me with directed numbers pls
Answer:
5
Step-by-step explanation:
(+3 + (+2))
Remove the brackets.
3 + (+2)
3 + 2
Add the numbers.
= 5
Answer:
+5 or 5
Step-by-step explanation:
(+3)+(+2)
=> According to the rule, ( + )( + ) = ( + )
So,
=> +3+2
=> +5
You want to install a 1 1 yd wide walk around a circular swimming pool. The diameter of the pool is 23 yd. What is the area of the walk? Use 3.14 for pi π.
Complete Question:
You want to install a 1 yd wide walk around a circular swimming pool. The diameter of the pool is 23 yd. What is the area of the walk? Use 3.14 for pi π.
Answer:
75.36 square yard
Step-by-step explanation:
From the question,
The diameter of this circular pool inside is 23 yd.
This means that the radius = Diameter/2 = 23yd/2 = 11.5 yd.
The formula for the area of a circle =
A = πr²
A = π(11.5)²
A =3.14 × 11.5²
A = 415.265 yd²
This is the Area of the inner circle.
We were told in the question also that he wants to install a walk of 1 yard
Hence, the radius of outer circle =
radius of inner circle +length of the walk
11.5yard + 1 yard
= 12.5 yard
A = πr²
A = 3.14 × (12.5)²
A = 490.625yd²
Area of the walk = Area of the Outer circle - Area of the inner circle
= (490.625 - 415.265)yd = 75.36 yd²
Therefore, the area of the walk is 75.36 square yards.
a solution to the inequality n ÷ 4 – 125 > 300
Answer:
n > 1700
Step-by-step explanation:
n ÷ 4 – 125 > 300
Add 125 to both sides.
n ÷ 4 > 425
Multiply both sides by 4.
n > 1700
Answer:
n > 1700
Step-by-step explanation:
n ÷ 4 - 125 > 300
Add 125 to both parts.
n ÷ 4 > 300 + 125
n ÷ 4 > 425
Multiply both sides with 4.
n > 425 × 4
n > 1700
What is the height of the triangle?
Triangle MNO is an equilateral triangle with sides
measuring 16V3 units.
O 12 units
N
0 24 units
VX
0 36 units
16/3
16/3
O 72 units
M
O
R
16/3
->
Answer:
(B)24 Units
Step-by-step explanation:
Triangle MNO is an equilateral triangle with sides measuring [tex]16\sqrt{3}[/tex] units.
The height divides the base into two equal parts of lengths [tex]8\sqrt{3}[/tex] units.
As seen in the diagram, we have a right triangle where the:
Hypotenuse = [tex]16\sqrt{3}[/tex] units.Base = [tex]8\sqrt{3}[/tex] units.Using Pythagoras Theorem
[tex](16\sqrt{3})^2=(8\sqrt{3})^2+h^2\\16^2*3-8^2*3=h^2\\h^2=576\\h=\sqrt{576}\\ h=24$ units[/tex]
The height of the triangle is 24 Units.
The height of the given equilateral triangle is gotten as;
B: 24 units
Equilateral Triangles
The height of an equilateral triangle starts from the mid - point of the base to the ap ex.
Now, if the sides of the equilateral triangle are 16√3 units, then it means we can use pythagorean theorem to find the height h.
Half of the base will be; ¹/₂ * 16√3 = 8√3
Thus, the height h can be calculated from;
h²= ((16√3)² - (8√3)²)
h² = 3(256 - 64)
h² = 576
h = √576
h = 24 units
Read more about equilateral triangles at; https://brainly.com/question/4293152
A LINE PASSES THROUGH THE POINTS. what is the EQUATION OF THE LINE? (2,-4) and (6,10)?
Hey there! :)
Answer:
y = 7/2x - 11
Step-by-step explanation:
Use the slope formula to calculate the slope:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the coordinates:
[tex]m = \frac{10-(-4)}{6-2}[/tex]
Simplify:
[tex]m= \frac{14}{4}[/tex]
[tex]m = \frac{7}{2}[/tex]
Slope-intercept form is y = mx + b. Plug in the slope, as well as the coordinates of a point given to solve for b:
10 = 7/2(6) + b
10 = 42/2 + b
10 = 21 + b
10 - 21 = b
b = -11.
Write the equation:
y = 7/2x - 11
11. If AD = 8 centimeters, what is BD?
A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm
find the greatest number that divides 36 and 60 without leaving a remainder
Answer:
12
Step-by-step explanation:
36= 2 × 2 × 3 × 3
60= 2 × 2 × 3 × 5
HCF(36, 60)= 2 × 2 × 3 = 12
12 is the greatest number that divides 36 and 60 without leaving a remainder
look at the figure below:
Answer: A) ΔABD ≡ ΔECD
Step-by-step explanation:
Match up the letters of the congruent sides.
AD = ED and BD = CD
A D B D → ABD
E D C D → ECD
This can be written in any order as long as the letters are matched properly. A & E, D & D, B & C
ADB or BDA or ...
EDC CDE
The only correct option provided is option A.
Answer:
Answer is option 1)
Answer is given below with explanations.
Step-by-step explanation:
[tex]triangle \: ABD \: and \: triangle \:ECD \: are \: congruent \\ length \: of \: BD \: = \: length \: of \: CD \\ \: and \: also \\ length \: of \: AD = length \: of \: ED \\ angle \: BDA \: = \: angle \: CDE \\ by \: \: side \: - angle - side \: postulate \\ triangle \: ABD \: and \: triangle \:ECD \: are \: congruent.[/tex]
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
PLEASE HELP Kelly wants to join an aerobics class. The initial membership fee is $25.00, and each clas costs $10.00. She pays a total of $115.00 to register for a certain number of classes. Create an equation to find the number of classes Kelly registered for.
Answer:
$25.00 + $10x = $115.00
Step-by-step explanation:
We know that the initial charge of joining is $25. Each class costs $10 each. She spent a total of $115. What we don't know is how many classes she took. With this equation, we can easily find out how many classes she took.
10.
AA'B'C' is a dilation image of AABC. Which is the correct description of the dilation?
12
of a
А)
6
B' =B
С
Answer:
Option (2)
Step-by-step explanation:
In the figure attached,
ΔA'B'C' is a dilation image of ΔABC or both the triangle are similar.
Therefore, by the property of similarity of two similar triangles, corresponding sides these similar triangles will be proportional.
Scale factor = [tex]\frac{\text{Side of image triangle}}{\text{Side of the pre-image}}[/tex]
= [tex]\frac{\text{B'A'}}{\text{B'A}}[/tex]
= [tex]\frac{\text{(B'A+AA')}}{\text{B'A}}[/tex]
= [tex]\frac{(6+12)}{6}[/tex]
= 3
Therefore, scale factor is 3 when center of dilation is B.
Option (2) will be the answer.
A restaurant offers a special pizza with any 4 toppings. If the restaurant has 15 topping from which to choose, how many different special pizzas
are possible.
Answer: 1,365 possible special pizzas
Step-by-step explanation:
For the first topping, there are 15 possibilities, for the second topping, there are 14 possibilities, for the third topping, there are 13 possibilities, and for the fourth topping, there are 12 possibilities. This is how you find the number of possible ways.
15 * 14 * 13 * 12 = 32,760
Now, you need to divide that by the number of toppings you are allowed to add each time you add a topping.
4 * 3 * 2 * 1 = 24
32,760 / 24 = 1,365
There are 1,365 possible special pizzas
Using the combination principle, the number of special pizzas from which to choose from is 1365
Total number of toppings to choose from = 15 Number of topping on a special pizza = 4Using Combination :
nCr = [(n! ÷ (n - r)! r!)]
15C4 = [(15! ÷ (15 - 4)! 4!)]
15C4 = [(15! ÷ 11!4!)]
15C4 = (15 × 14 × 13 × 12) ÷ (4 × 3 × 2 × 1)
15C4 = 32760 / 24
15C4 = 1365
Therefore, 1365 different special pizzas can be made.
Learn more : https://brainly.com/question/19120549
There is 278 calories for 100g of kiri cheese, each portion of kiri cheese has 46 calories. how many kiri portions do I need to equal 50g?
Answer:
Two Portions!!!
Step-by-step explanation:
If 1 card is drawn at random from a standard 52-card deck, what is the probability that the card drawn is a king?
Answer:
1/13 chance or roughly 7.7% chance.
Step-by-step explanation:
There are 4 Kings in a standard 52-card deck. If one King was to be pulled out, you'd get a probability of 4/52 chance of pulling a king. Simplified, 4/52 is 1/13 chance.
A regression equation is determined that describes the relationship between average January temperature (degrees Fahrenheit) and geographic latitude, based on a random sample of cities in the United States. The equation is: Temperature = 110 ‑ 2(Latitude). How does the estimated temperature change when latitude is increased by one?
Answer:
Decreases by 2 degrees
Step-by-step explanation:
The expression that describes temperature as a function of latitude is:
[tex]T=110-2(Latitude)[/tex]
This equation represents a linear relationship between latitude and temperature in a way that an increase in latitude causes a decrease in temperature. The magnitude of this decrease is quantified by the slope of the linear equation, which is -2. Therefore, the estimated temperature decreases by 2 degrees when latitude is increased by one.
Find the area of the figure to the nearest square unit.
Answer:
357 mi²
Step-by-step explanation:
The shape is made of a triangle and a half-square
we will calculate the area of each one
The half square:let A1 be the area of the half-circle:
A1= (10²*π)/2 = 50π mi²
The rectangle:Let A2 be the area of the triangle:
A2= 10*20=200 mi²
The whole shape:let At be the total area:
At =A1+A2= 200+50π =357.07≈ 357 mi²
What angle is included by AB and BC ?
B
A
O A. ZB
OB. ZA
O c. Zc
Answer:
[tex] \angle B[/tex]
Step-by-step explanation:
[tex] \angle B[/tex] is included by AB and BC, because B is the common vertex in AB and BC,
Buchtal, a manufacturer of ceramic tiles, reports on average 2.3 job-related accidents per year. Accident categories include trip, fall, struck by equipment, transportation, and handling. The number of accidents is approximately Poisson. Please upload your work for all of the parts at the end. a) What is the probability that more than one accident occurs per year? Include at least 3 decimal places in your answer. Submit Answer Tries 0/5 b) Suppose that 5 years are randomly selected. What is the expected number of accidents in this time period? Submit Answer Tries 0/5 c) What is the standard deviation of the number of accidents in 5 years? Submit Answer Tries 0/5 d) What is the probability that exactly 8 accidents occur in 5 years? Include at least 3 decimal places in your answer. If you get an error on your calculator, please use an online source like Wolfram Alpha to calculate the number. Submit Answer Tries 0/5
Answereippcb.jrc.ec.europa.eu
Step-by-step explanation:
this I the wed go on it and you will get your answer
HELP PLS!!! ITS DUE ASAP AND I NEED HELP ITS THE LAST QUESTION
Answer:
See below.
Step-by-step explanation:
Recall the volume of a sphere: [tex]V=\frac{4}{3}\pi r^3[/tex]
We know that the diameter is 14, so the radius is 7.
Plug it into the equation:
[tex]V=\frac{4}{3}(3.14)(7^3)\approx 1436.03cm^3[/tex]
A division problem is shown below. 4 and one-third divided by 5 and StartFraction 1 over 6 EndFraction The reciprocal of a fraction must be found to solve the problem. What is the reciprocal fraction that is required?
Answer:
6/5
Step-by-step explanation:
you have to flip the numerator and denominator. If it is 5/6 then it would be 6/5.
The reciprocal fraction that is required will be 31/26.
What is a fraction?A fraction is a numerical number that is represented in the numerator and denominator form.
We have Two mixed fractions, the First fraction = 4(1/3) and the Second fraction = 5(1/6).
Now,First, convert mixed fractions into simple fractions,i.e.First fraction = 4(1/3) = 13/3And,Second fraction = 5(1/6) = 31/6
Now, According to the question,
Divide First fraction by Second fraction;i.e.= (13/3) / (31/6)Now simplify,= ( 13 × 6) / (31 × 3)
Now, We get,= 26/31
So, the reciprocal fraction = 31/26.
Hence we can say that the reciprocal fraction that is required will be 31/26.
To learn more about fractions click here,https://brainly.com/question/10354322
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Use the 4 step process to find the f'(x) of the function f(x)=x^2-3/2
Answer:
see below
Step-by-step explanation:
Modified problem
(x)^2-3/x
Step 1: Find f(x+h)
(x+h)^2-3/(x+h)
x^2 +2hx + h^2 -3/(x+h)
Step 2: Find f(x + h) − f(x)
x^2 +2hx + h^2 -3/(x+h) - ( x^2-3/x)
Distribute the minus sign
x^2 +2hx + h^2 -3/(x+h) - x^2+3/x
Combine like terms and get a common denominator
2hx + h^2 -3x/(x(x+h)) +3(x+h)/(x(x+h)
2hx + h^2 +3h/(x(x+h))
Step 3: Find (f(x + h) − f(x))/h
(2hx + h^2+3h/(x(x+h)) )/h
2hx/h + h^2/h+3h/(x(x+h)) /h
2x +h +3/(x(x+h))
Step 4: Find lim h→0 (f(x + h) − f(x))/h
2x+0 +3/(x(x+0))
2x +3/x^2
what is the Expected value of the probability distribution also called?
Answer:
The expected value is also known as the expectation, mathematical expectation, mean, average, or first moment.
Shopping at discount clothing stores can save you a lot of money. Felicia recently bought a jacket
at a discount store for $20 that would normally cost $60 at a retail store. What percent discount
off the retail price did Felicia get the jacket for?
Answer:
33.33%
Step-by-step explanation:
use a proportion
20/60 =10/30=1/3=33.333%
hope this helped!
For what values of x is the expression below defined?
Look at the picture(15 points)
Answer:
D. -5 <= x < 1
Step-by-step explanation:
the values under the square-root radical must not be negative, AND
the value of the denominator must not be 0 or negative
x+5 >=0 or x >= -5
and 1-x > 0 or x < 1
So the answer is -5 <= x < 1
What is the volume of this aquarium?
Answer:
2,973 in^3
Step-by-step explanation:
3000- large section
27- smaller center cut-out
Answer:
2973 in³
Step-by-step explanation:
volume of cuboid - volume of cube
20*15*10 - 3³
3000 - 27
= 2973
The volume of the aquarium is 2973 in³.