The diver will be in the air for approximately 0.78 seconds to the nearest hundredth of a second.
The equation that represents the height of the diver above the surface of the pool is given by:
h(t) = -16t² + 6t + 33
where t is the time in seconds and h(t) is the height of the diver above the surface of the pool in feet.
The diver will be in the air until he reaches the surface of the pool, which means that his height will be 0. Therefore, we can set h(t) equal to 0 and solve for t:
-16t² + 6t + 33 = 0
We can use the quadratic formula to solve for t:
t = (-b ± sqrt(b² - 4ac)) / 2a
where a = -16, b = 6, and c = 33.
Plugging in these values, we get:
t = (-6 ± sqrt(6² - 4(-16)(33))) / 2(-16)
t = (-6 ± sqrt(36 + 2112)) / (-32)
t = (-6 ± sqrt(2148)) / (-32)
Simplifying:
t = (-6 ± 46.34) / (-32)
So we have two solutions:
t = (-6 + 46.34) / (-32) ≈ 0.78 seconds
t = (-6 - 46.34) / (-32) ≈ 2.64 seconds
Since the diver cannot be in the air for a negative amount of time, we reject the second solution.
To learn more about the quadratic equation;
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When you fill your coffee at a gas station, you're supposed to get 8 ounces of coffee with a standard deviation of .7 ounces. A random sample of 50 "8 ounce" coffees is collected and measured and the mean was found to be 7.8 ounces.
Answer:
The answer is below
Step-by-step explanation:
When you fill your coffee at a gas station, you're supposed to get 8 ounces of coffee with a standard deviation of .7 ounces. A random sample of 50 "8 ounce" coffees is collected and measured and the mean was found to be 7.8 ounces. a) Find a 90% confidence interval. b) Interpret the confidence interval in the context.
Solution:
The confidence = 90% = 0.9, mean (μ) = 7.8 ounces, standard deviation (σ) = 0.7 ounces, sample size (n) = 50
α = 1 - C = 1 - 0.9 = 0.1
α/2 = 0.1 / 2 = 0.05
The z score of α/2 is the same as the z score of 0.45 (0.5 - 0.05) which is equal to 1.65
The margin of error (E) is given by:
[tex]E = z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } \\\\E=1.65*\frac{0.7}{\sqrt{50} } =0.16[/tex]
The confidence interval = μ ± E = 7.8 ± 0.16 = (7.64, 7.96)
b) This means that we are 90% confident that any selected coffee has a weight between 7.64 ounce to 7,96 ounce
A triangle has sides with lengths of 72 inches, 78 inches, and 30 inches. Is it a right triangle?
Answer:
yes
Step-by-step explanation:
Using the converse of Pythagoras' identity.
If the square of the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right.
longest side = 78 and 78² = 6084
72² + 30² = 5184 + 900 = 6084
Then the triangle is right
Pls help ASAP!!!
Buffy attends a night school, and the ages of the people in his study group are: 42, 55, 36, 41, 38, 33, and 46. What is the best estimate of the population mean for ages of night school attendees? Enter your answers rounded to the nearest tenth.
Answer:41.6
Step-by-step explanation:
Isaac and his wife received an award of $ 9,000 each for their work as researchers.
Isaac invests his money and earns 9% annual simple interest while his wife invests it at 9% compound interest per year. How much more money did Isaac's wife make than Isaac after 10 years?
F $5,500.00
G $3,455.50
H $4,206.30
J $4,998.50
Answer:
H
Step-by-step explanation:
I don't know if I did it wrong because I got 4,206.27 but I probably did
NEED HELP will give BRAINLY
Answer:
y=1x+8
Step-by-step explanation:
The best way to remember the formula is y=mx+b aka (your mom's ex bf)Just by looking at the slope you can automatically tell it's moving by one so in your formula, 'm' is the slope.Add 1x to replace 'm' or you can leave x alone because x is already one, your choice.b is the indication on where your slope started in the y-axis. In this case, by looking at the y-axis on the graph, the slope starts at 8 so that will be your b.Therefore, your answer is y=1x+8Nancy received a birthday gift of $35. She decided to
use this money to start a savings account and then
deposited $5 into the account every week.
Which equation represents the relationship between
w, the number of weeks she has saved, and s, the
total amount saved?
s = 35W - 5
s= 5W - 35
S = 35W + 5
s = 5W + 35
Answer:
Everybody's laughing in my mind
Rumors spreading 'bout this other guy
Do you do what you did when you did with me
Does he love you the way I can
Did you forget all the plans that you made with me?
'Cause baby I didn't
That should be me, holding your hand
That should be me, making you laugh
That should be me, this is so sad
That should be me
That should be me
That should be me, feeling your kiss
That should be me, buying you gifts
This is so wrong
I can't go on
Till you believe
That should be me
That should be me
A wire is bent into semicircles. How long is the wire to the neared hundredth? The diameter is 32 cm
Answer:
200.96
Step-by-step explanation:
2πr is the perimeter or circumference of a circle
.
diameter is 32cm so radius=16cm
2*3.14*16=100.48cm is long
what is 4.13 to the nearest tenth
Answer:
4.1
Step-by-step explanation:
Find the measures of the exterior angles of the polygon.
Answer:
D : 125°,125°,55°,55°
Step-by-step explanation:
Finding the interior angles makes the question easier.
The two base angles for b1 are both 125°, and the two base angles for b2 are both 55°.
Because a straight line is 180°, we can find the exterior angles by subtracting the interior angles from 180°.
180°-55° = 125°
180°-125° = 55°
Pythagorean Theorem Digital Escape Puzzle 5,Need Answer Immediately!!!
Answer: a = 6.53
Step-by-step explanation:
Answer: its HCFD i just did it
Step-by-step explanation:
base, 6 millimeters;
height, 4 millimeters
Answer:
You would multiply them which would be 24 brainliest?
Step-by-step explanation:
Given AE ≈ EC, for what value of x is quadrilateral ABCD a parallelogram?
Answer:
X = 1/3 (to make it short) plz brainliest
Step-by-step explanation:
The students in Ms. Gonzales' fifth grade math class earned the following grades on their first test: 46, 56, 64, 64, 72, 76, 77, 82, 94, 96,99 What was the mean of the grades? (round to the nearest whole number) A. 826 OB. 75 O c. 76 OD. 64 O E 83
Answer:
75
Step-by-step explanation:
mean = average so add up all your numbers, then divide by the amount of numbers so
46 + 56 + 64 + 64 + 72 + 76 + 77 + 82 + 94 + 96 + 99 = 826
826 ÷ 11 = 75.09 (about)
simplify 3+4(y-7)+5y
Answer:
9y-25
Step-by-step explanation:
Answer:
9y-25
Step-by-step explanation:
Math
Is the point on the line ?
Answer:
i think the answer is no i used tge desmo graphing calculator and tht point wasnt on it
Mhanifa please help this is late and I don’t get it
Answer:
Sin k jajs
Step-by-step explanation:
pleaseee help mee!
..
Answer:
Step-by-step explanation:
f(x)=x2. what is g(x)?
Answer:
A
Step-by-step explanation:
Hi again. In this case, the graph enlarges. Coefficient of x is <1. Try to substitute x = 3 to (1/3x)^2 and (1/9x^2)
(1/3 * (3))^2=1
a) (-6)* = -6° b) (-3) = -3$ c) 82 = (-8)
[tex]( 5 + 4 {)}^{2} = {5}^{2} + {4}^{2} [/tex]
Answer:
pues yo pienso que es 8 es que no se muy bien
In the rectangle below, SU= 4x-2, RT = 5x-10, and m ZSVT= 84º.
Find RV and m ZVUR.
R
S
U
T
Answer:
RV = 15, ∠ VUR = 48°
Step-by-step explanation:
The diagonals of a rectangle are congruent , so
RT = SU , that is
5x - 10 = 4x - 2 ( subtract 4x from both sides )
x - 10 = - 2 ( add 10 to both sides )
x = 8
Then
RT = 5x - 10 = 5(8) - 10 = 40 - 10 = 30
The diagonals bisect each other , then
RV = 0.5 × 30 = 15
---------------------------------------------------------------
∠ RVU = ∠ svt = 84° ( vertical angles )
RV = UV ( diagonals are congruent and bisect each other )
Then Δ RVU is isosceles with base angles congruent , then
∠ VUR = [tex]\frac{180-84}{2}[/tex] = [tex]\frac{96}{2}[/tex] = 48°
(05.06 LC)
Which graph best represents a decreasing function?
A graph shows a non linear curve that joins the ordered pairs 0, 0, and 3, 1.5, and 5, 5.
A graph shows a straight line that joins the ordered pairs 5, 0 and 5, 5.
A graph shows a non linear curve that joins the ordered pairs 0, 5, and 1, 2, and 5, 0.
A graph shows a straight line that joins the ordered pairs 0, 3 and 5, 3.
What is the value of -2(x+5) Please I'm in need of help
Answer:
-2x - 10
Step-by-step explanation:
-2 x X = -2x
-2 x 5 = -10
Put them together to get:
-2x - 10
Answer:
-2(x) or (-2×x)
then you get = -2x
then you take
-2×+5 or (-2×5) you'll get = -10
last but not least you join the equation
and the answer will be
= -2x-10
What is the maximum height of of Anna's golf ball? The equation is y=x−0.04x2.
Given:
The height of a golf ball is represented by the equation:
[tex]y=x-0.04x^2[/tex]
To find:
The maximum height of of Anna's golf ball.
Solution:
We have,
[tex]y=x-0.04x^2[/tex]
Differentiate with respect to x.
[tex]y'=1-0.04(2x)[/tex]
[tex]y'=1-0.08x[/tex]
For critical values, [tex]y'=0[/tex].
[tex]1-0.08x=0[/tex]
[tex]-0.08x=-1[/tex]
[tex]x=\dfrac{-1}{-0.08}[/tex]
[tex]x=12.5[/tex]
Differentiate y' with respect to x.
[tex]y''=(0)-0.08(1)[/tex]
[tex]y''=-0.08[/tex]
Since double derivative is negative, the function is maximum at [tex]x=12.5[/tex].
Substitute [tex]x=12.5[/tex] in the given equation to get the maximum height.
[tex]y=(12.5)-0.04(12.5)^2[/tex]
[tex]y=12.5-0.04(156.25)[/tex]
[tex]y=12.5-6.25[/tex]
[tex]y=6.25[/tex]
Therefore, the maximum height of of Anna's golf ball is 6.25 units.
115
11.5
Find the area of the shaded region
Answer:
227 units²
Step-by-step explanation:
Area of rectangle
a = (2 * 11.5) * (4 * 11.5)
a = 1,058
Area of circles
a = 2(π * 11.5²)
a = 830.9512568745
Shaded area
a = 1,058 - 830.9512568745
a = 227.0487431255
a ≈ 227
What is 1/6-1/30 equal to (simplified form)
Answer:
I'm pretty sure it is 2/15
help please please please
Answer:
A
Step-by-step explanation:
because every 3 bats he hit 1
the volume of the cylinder above is 2,119.5^m3 what is the radius of the cylinder
Answer:
7.5
Step-by-step explanation:
Pi * r^2 * 12 = 2119.5
r^2 = 56.25
r = sqrt(56.25) = 7.5
C
3 m
4 m
What is the length of the hypotenuse?
Answer:
5 meters
Step-by-step explanation:
The values given, 3 and 4, are the legs a and b. The hypotenuse is the third and longest side, c.
To find the length of the hypotenuse, use the formula a² + b² = c².
Substitute our values for a and b and solve.
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²
√25 = √c²
5 = c
The hypotenuse is 5 meters long.
I hope this helps <3
The product ( the result of a multiplication problem ) of 2 rational expressions is x+22x−3 with the restrictions x≠– 3, x≠32, x≠4 and x≠ 5. Find an expression that meets the criteria. You may leave your answer in factored form.
Answer:
x + 22x - 3 = 4 (5x) + 3 (x-1)
Step-by-step explanation:
x + 22x - 3
23x - 3
20x + 3x - 3
5x + 15x + 3x - 3
5x (1 + 3) + 3 ( x - 1)
4 (5x) + 3 (x-1)
-2/5 + 1 1/3 find the sum
Answer: =14/15
Step-by-step explanation: Hope this help :D, Can I have a Brainliest I really needed it please!