Answer:
a) The initial height of the rock is of 48 feet.
b) It takes 1 seconds for the rock to reach maximum height.
c) The rock's maximum height is 50 feet.
d) It takes 6 seconds for the rock to land on the ground.
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]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
The height of the ball after t seconds, in feet, is given by:
[tex]h(t) = -2t^2 + 4t + 48[/tex]
Which is a quadratic equation with [tex]a = -2, b = 4, c = 48[/tex]
a) What is the initial height?
This is [tex]h(0) = 48[/tex]. So the initial height of the rock is of 48 feet.
b) How many seconds does it take to reach the maximum height?
This is the value of t at the vertex. So
[tex]t_{v} = -\frac{b}{2a} = -\frac{4}{2(-2)} = 1[/tex]
It takes 1 seconds for the rock to reach maximum height.
c) What is the rock's maximum height?
This is the height of the ball after 1 second. So
[tex]h(1) = -2(1)^2 + 4(1) + 48 = 50[/tex]
The rock's maximum height is 50 feet.
d) How many seconds does it take to for the rock to land on the ground?
This is t for which [tex]h(t) = 0[/tex], so we solve the quadratic equation.
[tex]\bigtriangleup = (4)^2-4(-2)(48) = 400[/tex]
[tex]t_{1} = \frac{-4 + \sqrt{400}}{2*(-2)} = -4[/tex]
[tex]t_{2} = \frac{-4 - \sqrt{400}}{2*(-2)} = 6[/tex]
Time is a positive measures, so it takes 6 seconds for the rock to land on the ground.
Kayla works as a hairdresser. She earned $228.50 in tips in five days. If she earned the same amount each day, about how much did
Kayla earn per day? Explain your answer.
Answer: $45.70 per day
Step-by-step explanation:
$228.50/5=$45.70 per day
Evaluate the expression. (38 + 10) ÷ 12 + 52
Answer:
56
Step-by-step explanation:
(Use PEMDAS for the order of operations)
First, solve everything in parentheses. You get this:
48 ÷ 12 + 52
Next, divide. You get this:
4 + 52
Lastly, add for the answer:
56
ILL GIVE 50 POINTS AND BRAINLIEST!!!
A business assistant must leave more than $50 in the supply account. There is $175 in the account. The assistant needs to order x boxes of pens that cost $6.50 each.
What is the maximum number of boxes of pens the business assistant can buy? Please show your math work and justify your answer.
Classify the numbers. Some numbers may belong in more
than one box.
Answer:
there's no attachment? can you re list
In the rectangle below what is X
Answer:
X = 114
Step-by-step explanation:
if one corner is 33 degrees. and the opposite corner is the same then you know that makes 66 degrees.
you take that minus 180. so 66 - 180 which leaves 114.
so X is 114
Please help me!!!!!!!!
Answer:
They have the same domain and range (0,∞)
Step-by-step explanation:
solve the following system of equations using the substitution method
x=2y
2x+5y=9
Answer:
y=1
x=2
(2,1)
Step-by-step explanation:
x=2y
2x+5y=9
2(2y)+5y=9
4y+5y=9
9y=9
y=1
x=2(1)
x=2
(2,1)
Can someone help me with this? I literally cant think today. ;-; Thanks if you answer it correctly. ಥ‿ಥ
Answer:
The slope is 300
Step-by-step explanation:
Rise over run we see two points how many times do we rise and run to get there?
(Slope= rise/run)
So you rise 300 times (Since half of 600 is 300) then you run 1 time which is 300/1 which is 300
Answer please!!!!
Award Brainliest!!!
Answer:
53
Step-by-step explanation:
60 + 67 = 127
180 - 127 = 53
Your answer will be 53
Factcheck:
60 + 67 + 53 = 180
In a survey of a community, it was found that 55%
like summer season, 20% like winter season, 40%
don't like both seasons and 750 like both seasons. By
using Venn diagram, find the number of people who
like winter season.
Answer:
The number of people who like winter season is 1000.
Step-by-step explanation:
Event event correspond to a set in the Venn diagram, and we use it to find the percentages.
I am going to say that:
Event A: Like summer season
Event B: Like winter season.
55% like summer season
This means that [tex]P(A) = 0.55[/tex]
20% like winter season
This means that [tex]P(B) = 0.2[/tex]
40% don't like both seasons
This means that 100% - 40% = 60% like at least one, which means that [tex]P(A \cup B) = 0.6[/tex]
Proportion who like both:
This is [tex]P(A \cap B)[/tex]. The measures are related by the following equation:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]
Using what we have
[tex]P(A \cap B) = 0.55 + 0.2 - 0.6 = 0.15[/tex]
750 like both seasons.
This is 15% of the sample. So the total number of people is t, for which:
[tex]0.15t = 750[/tex]
[tex]t = \frac{750}{0.15}[/tex]
[tex]t = 5000[/tex]
20% like winter season
Out of 5000. So
0.2*5000 = 1000
The number of people who like winter season is 1000.
Each day after school, Chelsey runs 2.8 miles farther than Kyle.
Part A. Write an equation that represents the number of miles Chelsey runs, c, compared with Kyle, k.
plzz help
Part B. If Kyle runs 4 miles, how many miles does Chelsey run?
Answer:
6.8 miles
Step-by-step explanation:
First, create the equation representing Chelsey's miles compared to Kyle's:
c = k + 2.8
Next, find how many miles Chelsey runs if Kyle runs 4 miles.
Plug in 4 as k into the equation:
c = k + 2.8
c = 4 + 2.8
c = 6.8
So, Chelsey runs 6.8 miles
Answer:
Question :-Each day after school, Chelsey runs 2.8 miles farther than Kyle.
Part A. Write an equation that represents the number of miles Chelsey runs, c, compared with Kyle, k.
plzz help
Part B. If Kyle runs 4 miles, how many miles does Chelsey run?
Solution :-Let the miles walk by Chelesy be x
Now,
x = 4 + 2.8
x = 6.8 miles
Therefore,
x = Kyle's mile walked + 2.86.8 miles[tex] \\ [/tex]
A fair 10 sided dice numbered 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is rolled once. What is the PERCENTAGE probability that it lands on a number that is prime? *
Answer:
40% probability that it lands on a number that is prime.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
10 sided dice
So 10 total outcomes.
Prime numbers:
Of those, 2, 3, 5 and 7 are prime, so 4 of the outcomes.
4*100/10 = 40%
40% probability that it lands on a number that is prime.
Find the area of a triangle where the base is 3 3/4 in and the height is 4 inches.
Of all ladies over the age of 50, 72% report that they color their hair to hide their gray. What is the probability
that under 70% color their hair in a group of 85 older women?
Answer:
0.3409 = 34.09% probability that under 70% color their hair in a group of 85 older women.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the Central Limit Theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex].
72% report that they color their hair to hide their gray.
This means that [tex]\mu = p = 0.72[/tex]
What is the probability that under 70% color their hair in a group of 85 older women?
For a sample of 85, we have that [tex]s = \sqrt{\frac{0.72*0.28}{85}} = 0.0487[/tex]
This probability is the pvalue of Z when X = 0.7. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.7 - 0.72}{0.0487}[/tex]
[tex]Z = -0.41[/tex]
[tex]Z = -0.41[/tex] has a pvalue of 0.3409
0.3409 = 34.09% probability that under 70% color their hair in a group of 85 older women.
The standard form of an equation of a circle with center at
(h, k)
and radius r is _____.
(y − h)2 + (x − k)2 = r2
(x − h)2 − (y − k)2 = r2
(y + h)2 − (x + k)2 = r2
(x − h)2 + (y − k)2 = r2
(x + h)2 − (y + k)2 = r2
Answer:
The standard form of an equation of a circle with center at (h, k) and radius r is
(x - h)² + (y - k)² = r²
which of these show equivalent fractions? A. 1/4=4/8 B. 1/2=2/4 C. 3/5 = 5/10 D. 2/3 = 3/6
1. Isosceles Triangle The two equal sides of an isosceles triangle are each 42
centimeters. If the base measures 30 centimeters, find the height and the
measure of the two equal angles. Round your answer to the nearest tenth.
Answer:
1. H = 29 cm
2. θ = 44°
Step-by-step explanation:
1. We can find the height of the triangle by considering the isosceles triangle as two right triangles. The height can be found by using Pitagoras:
[tex] L^{2} = H^{2} + B^{2} [/tex]
Where:
L: is the sides of the isosceles triangle = 42 cm
B: is the base = 30 cm
H: is the height =?
Then, the height is:
[tex] H = \sqrt{L^{2} - B^{2}} = \sqrt{(42 cm)^{2} - (30 cm)^{2}} = 29.4 cm = 29 cm [/tex]
2. The two equal angles (θ) can be found using the following trigonometric identity:
[tex] cos(\theta) = \frac{B}{L} [/tex]
[tex] \theta = cos^{-1}(\frac{30 cm}{42 cm}) = 44.4^{\circ} = 44^{\circ} [/tex]
Hence, the two equal angles are 44°.
I hope it helps you!
notacion cientifica 123000000
Answer:
puro puto✌✌✌✌
Answer:
1.23× 10 ^8
Step-by-step explanation:
mark brainliest
What does 60/8 x 13?
My calculator says 97.5
Answer:
195/2
Step-by-step explanation:
60/8=15/2
15/2*13=195/2
The ordered pairs show amounts y (in inches) of rainfall equivalent to x inches of snow.(16, 1.5), (12, 1.3), (18, 1.8), (15, 1.5), (20, 2.1),(23, 2.4) About how many inches of rainfall are equivalent to 6 inches of snow? Round your answer to the nearest hundredth, if necessary.
Answer:
0.57 inches of rainfall is equivalent to 6 inches of snow
Step-by-step explanation:
The given data are presented here as follows;
[tex]\begin{array}{cc}x&y\\16&1.5\\12&1.3\\18&1.8\\15&1.5\\20&2.1\\23&2.4\\\end{array}[/tex]
The data points are approximately linear
From the the trend line of the plotted points of the graph, created with Microsoft Excel, with Forecasting, when there is 6 inches of snow the rainfall is 0.575 inches
By linear regression, we have;
Y = a + b·X
Where;
[tex]b = \dfrac{n \cdot \sum XY - \left (\sum X \right ) \cdot \left (\sum Y \right )}{n \cdot \sum X^{2} - \left (\sum X \right )^{2}}[/tex]
[tex]a = \dfrac{\sum Y - b \cdot \sum X}{n}[/tex]
∑x = 104
∑y = 10.6
∑(x·y) = 191.7
(∑x)·(∑y) = 1102.4
(∑x)² = 10816
n = 6
SigX^2 = 1878
Plugging in the values, gives;
[tex]b = \dfrac{6 \times191.7 - 1102.4}{6 \times 1878 - 10816} \approx 0.10575[/tex]
[tex]a = \dfrac{10.6 - 0.10575 \times 104}{6} \approx -0.06637[/tex]
Therefore;
Y = 0.10575·x - 0.06637
When x = 6 inches, we have;
Y = 0.10575 × 6 - 0.06637 = 0.56813
Y = 0.56813 inches ≈ 0.57 inches of rainfall
Therefore;
0.57 inches of rainfall is equivalent to 6 inches of snow
Six out of the 12 members of the school choir boys. In the simplest form, what fraction of the choir is boys? Pls help out with this question
25/35 and 10/14 simplified
Answer:
(25/5)/(35/5)
=> 5/7
(10/2)/(14/2)
=> 5/7
Hence both of the numbers simplify to 5/7
Hope it helps
Write 3.08 × 10-5 as an ordinary number.
Answer:
0.0000308
Step-by-step explanation:
there are 5 places that it has moved from.
A square garden has a diagonal of 12m. What is the perimeter of the garden? Express in simplest radical form.
Answer:
24√2
Step-by-step explanation:
Let the side of the square be x
If the diagonal is 12m (hypotenuse), then;
x^2 + x^2 = 12^2
2x^2 = 144
x^2 = 144/2
x^2 = 72
x = √72
x = √36*2
x = 6√2
Perimeter of the square garden = 4x
Perimeter of the square garden = 4(6√2)
Perimeter of the square garden = 24√2
Please help!
//Thank you!
Answer:
x=9
Step-by-step explanation:
It’s 9 trust me I know it’s 9 ok it’s 9 I’m sure it’s 9 ok the answer is 9 got it 9 byee
Factor the polynomial completely.
9g^2 - 30gh + 25h^2
Answer:
Step-by-step explanation:
It's a perfect square.
It factors into (3g - 5h)^2
or (3g - 5h)(3g - 5h)
Make sure it is correctly factored.
3g*3g = 9g^2
3g * - 5h = - 15gh
-5h*3g = - 15gh
5h*5h = 25h^2
These four terms add to 9g^2 - 15gh - 15gh + 25h^2 = 9g^2 - 30gh + 25h^2 which is exactly what you started with.
A typist type 1800 words in 1 hour. find the number of words she can type per minute.
Answer:
1800/60=30
Step-by-step explanation:
Answer:
the first answer is correct
Nabil Francisco's tips from working at the hair salon were $4.50, $2.00, $3.50, $5,$8.00, and $4.50. What was his average tip?
Answer:
$4.58
Step-by-step explanation:
Add all of your numbers up.
$27.50
Divide by 6
4.58 is the average.
i hope this helps, good luck :)
What is the answer of 1/3 x 1/4
Answer:
1/12
Step-by-step explanation:
Multiply across
Hope this helps
You are charged $9.2 in total for a meal. Assuming that the local sales tax is 7.7%, what was the menu price of this item?
Answer:
9.91
Step-by-step explanation: