Check the picture below, so it reaches the maximum height at the vertex, let's check where that is
[tex]h(t)=64t-16t^2+0 \\\\[-0.35em] ~\dotfill\\\\ \textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+64}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 64}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (64)^2}{4(-16)}\right)\implies \stackrel{maximum~height}{(2~~,~~\stackrel{\downarrow }{64})}[/tex]
find the value of 85²-15² using the difference of two squares method
Answer:
[tex]7000[/tex]
Step-by-step explanation:
Recall the form of the difference of squares.
[tex]x^2 - y^2 = (x+y)(x-y)\\\\\\[/tex]
Now let's apply it to your numbers:
[tex]85^2 - 15^2 = (85 + 15)(85 - 15)[/tex]
Simplify:
[tex](100)(70) = 7000[/tex]
Ryan buys some jumpers to sell on a stall.
He spends £130 buying 40 jumpers.
He sells 80% of the jumpers for £12 each.
He then puts the rest of the jumpers on a Buy one get one half price offer.
He manages to sell half the remaining jumpers using this offer.
How much profit does Ryan make?
What is the value of x in this figure?
Step-by-step explanation:
Tan = Opposite/ Adjacent
Tan 50 = 100/Adj
Adj = 100/tan50
Similarly, Tan30 = Opposite/ Adjacent
Opposite = 100tan30
therefore X= 100/tan 50 - 100 tan30
In a small private school, 16 students are randomly selected from eighteen available students. What is the probability that they are the four youngest students?
Answer:
1/72
Step-by-step explanation:
16 * 18 = 288
4/288 = 1/72
9. A quilt pattern will use the block shown in the graph with regular hexagon
ABCDEF that has points A(4,0) and D(-4, 0). What is the area of the hexagon
to the nearest tenth? Show all work. [5 points]
From the given coordinates of point A(4, 0), and D (-4, 0), the area of the hexagon is 33.94 units square.
How can the area of the hexagon be found?The given parameters are;
Shape of the quilt pattern = A regular hexagon
Coordinates of point A = A(4, 0)
Coordinates of point D = D(-4, 0)
Required;
The area of the hexagon
Solution;
The coordinates of the center of the hexagon, P = (0, 0)
A regular hexagon consist of six equilateral triangles.
The length of a side of the triangle = PA
Length of PA = 4 - 0 = 4
Therefore;
Length of a side of the triangle = 4
Height of the triangle = PA × sin(60)
Which gives;
Height of the triangle = 4 × (√3)/2 = 2•√3
Area of one triangle = (4 ÷ 2) × 2•√3 = 4•√2
Area of the 6 triangles is therefore;
A = 6 × 4•√2 = 24•√2
Area of the 6 triangles = Area of the hexagon
Therefore;
Area of the hexagon = 24•√2 = 33.94 square units.Learn more about the area of regular shapes here;
https://brainly.com/question/10572314
Find the value of each variable in the parallelogram.
Answer:
b=10
C=99
D=140
Step-by-step explanation:
because it’s a parallelogram
A manager drew this box-and-whisker plot to represent the ages of the company’s 240 employees. How many employees are younger than 42?
24
48
60
75
Answer:
its 60, need proof?
Step-by-step explanation:
Answer: 60
Step-by-step explanation: I took the test and got it right. Goodluck with the rest!
Which point is on the graph of the inverse function g–1(x)?
(–3, 0)
(0, –3)
(2, 3)
(3, 4)
Answer:
A
Step-by-step explanation:
The answer is (-3,0) which is A.
Answer:
A
Step-by-step explanation:
Math I need help I with it if you can help me out
Answer: 49.44807
Round that however you need to. Unfortunately the rounding instructions on the screenshot are cut off, so I cannot see what that part says.
=======================================================
Work Shown:
sin(angle) = opposite/hypotenuse
sin(22) = h/132
h = 132*sin(22)
h = 49.44807
Quadrilateral A B C D is shown. Sides A D and B C are parallel. Sides A B and C D are congruent. Angle A is 115 degrees.
What is the measure of ADC in quadrilateral ABCD?
45°
65°
115°
135°
Since no diagram attached there are two possible options.
Option 1
The quadrilateral is parallelogram.
In this case ∠A and ∠D sum up to 180°, therefore:
∠ADC = 180° - 115° = 65°Option 2
The quadrilateral is isosceles trapezoid.
In this case ∠A is congruent with ∠D, therefore:
∠ADC = ∠A = 115°Answer:
115
Step-by-step explanation:
(Please show work and No links) If you bought 28 shares of stock at $30/sh and sold them at $25/sh. And How much did you net after selling the shares? Was it a profit or a loss?
Let C be the total cost;
[tex]c = 28 \times 30 = 840[/tex]
Let R be the total revenue;
[tex]r = 28 \times 25 = 700[/tex]
Let P be the net profit;
[tex]p = r - c[/tex]
[tex]p = 700 - 840 = - 140[/tex]
There was a 140$ net loss.
After eating a meal at a restaurant, we decided to tip 25%, building a grand total of $87.50. What was the price before the tip?
Answer:
65.62
Step-by-step explanation:
Given:
After eating a meal at a restaurant, we decided to tip 25%, building a grand total of $87.50.
To find:
Price before tip
Solution:
87.50 × 25% = 21.875
~Round~: 21.875 to 21.88
87.50 - 21 .88 = 65.62
Thus the price before the tip is 65.62
Check Answer:
Formula: Higher number - Lower number ÷ original number × 100
Solve:
87.50 - 65.62 = 21.88
21.88 ÷ 87.50=0.25005714285
0.25005714285 × 100 = 25.0057142857
Round - 25%
~lenvy~
A bag of chocolates is labeled to contain 0.384 pounds of chocolates. The actual weight of the chocolates is 0.3798 pounds. Are the chocolates heavier or lighter than the weight stated on the label?
Based on the information given the chocolates stated on the label is 0.0042-ounce lighter.
Weight:
Using this formula
Chocolate weight=Current weight-Actual weight
Where:
Current weight=0.384
Actual weight=0.3798
Let plug in the formula
Chocolate weight=0.384-0.3798
Chocolate weight=0.0042 ounce
In conclusion, the chocolates stated on the label are 0.0042-ounce lighter.
The Shah family basement floor is shaped like a tropezoidal. The basement has sides of 36 feet and 24 feet and two sides of 21 feet. They are going to carpet the basement. The carpeting will cost $35 per square yard. What is the area, in square feet, of the basement floor?
The area in square feet of the the basement floor that is trapezoidal is 603.6 feet square.
Area of a trapezium
area = 1 / 2 (a + b)h
where
a and b are the base of the trapeziumh = height of the trapezium.Therefore,
a = 24 ft
b = 36 ft
h² = 21² - 6²
h² = √405
h = 20.1246117975
h = 20.12 ft
Therefore,
area = 1 / 2 (24 + 36)20.12
area = 603.6 ft² = 67.066667 yard²
Therefore,
1 yard² = $35
67.1 yard² = ?
cost of carpeting = 35 × 67.1 = $2348.5
learn more on trapezium here: https://brainly.com/question/8591668
Out of 100 people sampled, 36 had kids. Based on this, construct a 95% confidence interval for the true
population proportion of people with kids.
Give your answers as decimals, to four places
This is the same as saying 0.2659 < p < 0.4541
=========================================================
Work Shown:
At 95% confidence, the z critical value is about z = 1.96 which is determined through a table or calculator.
x = number of people who had kids = 36
n = sample size = 100
phat = sample proportion of those who had kids
phat = x/n
phat = 36/100
phat = 0.36
E = margin of error
E = z*sqrt(phat*(1-phat)/n)
E = 1.96*sqrt(0.36*(1-0.36)/100)
E = 0.09408
This value of E is approximate because z = 1.96 is approximate.
-------------
L = lower bound
L = phat - E
L = 0.36 - 0.09408
L = 0.26592
L = 0.2659
U = upper bound
U = phat + E
U = 0.36 + 0.09408
U = 0.45408
U = 0.4541
The values of L and U are approximate since E is approximate.
-------------
The confidence interval in the format (L, U) is (0.2659, 0.4541)
This is equivalent to writing 0.2659 < p < 0.4541
which is the format L < p < U
We're 95% confident that the true population proportion (p) is somewhere between 0.2659 and 0.4541; i.e. we're 95% confident the true percentage of people who had kids is somewhere between 26.59% and 45.41%
Need help with this question.Find the value of x
Answer:
x=14
Step-by-step explanation:
According to Thales' theorem, the triangle inside 6,7,8 is similar to the triangle 12,x,16:
[tex]\frac{12}{6}= \frac{16}{8} =\frac{x}{7} =2[/tex]
[tex]x=7(2)=14[/tex]
Hope this helps
Ms Lim bought x pencils and two more pens than pencils. (b) Each pencil costs 60 cents and each pen costs $2. Write down, in terms of x, the total cost in dollars of the pencils and pens which Ms Lim bought
Answer:
0.60x + ((x+2)(2)) = total cost
Step-by-step explanation:
The pencils = 60 cents
0.60x = (0.60, the money, multiplied by x number of pencils)
The pens = 2 dollars
2(x+2) = (2, the money, multiplied by x number of pencils + 2 more pens)
Answer:
($2.60x + $4 = TC(x)
Step-by-step explanation:'
The number of pens bought would be x + 2, where x is the number of pencils bought. Then:
Total cost = ($0.60/pencil)x + ($2/pen)(x + 2) = ($2.60x + $4 = TC(x)
What is five sixths divided by nine thirds?
Answer:
0.270.27777777777
Step-by-step explanation:
You draw a diagram and color each side in for both of them
What is the factorization of the expression below?
16x^2 - 49
A. (4x + 7)(4x - 7)
B. (4x - 7)(4x - 7)
C. (8x - 7)(2x - 7)
D. (8x + 7)(2x - 7)
Answer:
[tex](4x+7)(4x-7)[/tex]
Step by step explanation:
[tex]16x^2 -49\\\\=(4x)^2-7^2\\\\=(4x+7)(4x-7)~~~~~~~~~~;[a^2-b^2 =(a+b)(a-b)][/tex]
Karen, Lamar, and John sent a total of 160 text messages over their cell phones during the weekend. John sent 4 times as many messages as Lamar. Lamar sent 10 fewer messages than Karen. How many messages did they each send?
Answer:
Karen= 35 messages
Lamar= 25 messages
John= 100 messages
Step-by-step explanation:
[tex]\textcolor{steelblue}{\text{\textcircled{1} Define the variables}}[/tex]
Let the number of messages Karen, Lamar and John send be K, L and J messages respectively.
[tex]\textcolor{steelblue}{\text{\textcircled{2} Form equations with given information}}[/tex]
K +L +J= 160 -----(1)
J= 4L -----(2)
L= K -10 -----(3)
[tex]\textcolor{steelblue}{\text{\textcircled{3} Solve by substitution}}[/tex]
Substitute (3) into (2):
J= 4(K -10)
J= 4K -40 -----(4)
Substitute (3) and (4) into (1):
K +(K -10) +(4K -40)= 160
Simplify:
6K -50= 160
6K= 160 +50
6K= 210
Divide both sides by 6:
K= 210 ÷6
K= 35
Substitute K= 35 into (3):
L= 35 -10
L= 25
Substitute L= 25 into (2):
J= 4(25)
J= 100
[tex]\textcolor{steelblue}{\text{\textcircled{4} Concluding statement}}[/tex]
Thus Karen, Lamar and John sent 35, 25 and 100 messages respectively.
Find the value of each variable in the parallelogram.
Answer:
x = 9 and y = 15
Step-by-step explanation:
this is the answer because each side is equivalent to the parallel line so y would be whatever is across from it
Answer:
y=15
x=9
Step-by-step explanation:
they are parallel and equal to the opposite sides
Explain how to find the length of one side of a regular polygon if you are given its perimeter.
I
Answer:
If you are only given the perimter, then you can only find the side lengths of a square
Step-by-step explanation:
e.g. say perimeter = 16
16 / 4 = 4 so each length is 4.
Question
Write an equation of a line that passes through the point (4,3) and is perpendicular to the graph of the equation y=−1/3+4
Answer:
Step-by-step explanation:
Hello:
an equation for the line is : y =mx +b (m: is a slope )
perpendicular to the line described by : y = -1/3 x +4
So : product for two slopes = -1 means : m×-1/3=-1
m = 3
now : y = 3 x+b
but this line :
through the point (4,3) : 3 =3(4)+b....... b=-9
conclusion :
the equation is : y =3x -9
Find the value of x.
Answer:
6 .x = 121°
Sum of all interior angles of a 7 sided polygon is 900°.
if the log↓b(a)=0, what is the value of a?
explain why log↓0 (3) and log↓1 (3) do not exist.
Answer:
1. a = 1
2. See explanation below.
Step-by-step explanation:
First Question
Given:
[tex]\displaystyle \large{\log_b a = 0}[/tex]
Convert to exponential:
[tex]\displaystyle \large{\log_b a = c \to b^c = a}[/tex]
Thus [tex]\displaystyle \large{\log_b a = 0 \to b^0 = a}[/tex]
Evaluate:
[tex]\displaystyle \large{b^0 = a}[/tex]
We know that for every values to power of 0 will always result in 1, excluding 0 to power of 0 itself.
Solution:
[tex]\displaystyle \large{a = 1}[/tex]
__________________________________________________________
Second Question
Given:
[tex]\displaystyle \large{log_0 3}[/tex] and [tex]\displaystyle \large{\log_1 3}[/tex]
Let’s convert to an equation:
[tex]\displaystyle \large{\log_0 3 = x}[/tex] and [tex]\displaystyle \large{\log_1 3 = y}[/tex]
The variables represent unknown values of logarithm.
Convert to exponential:
[tex]\displaystyle \large{0^x = 3}[/tex] and [tex]\displaystyle \large{1^y = 3}[/tex]
Notice that none of x-values and y-values will satisfy the equations. No matter what real numbers you put in, these equations will always be false.
Hence, no solutions for x and y.
SOLVE ASAP PLEASE Point theif = ban
Answer:
Given dimensions of room:
length = 12 ftwidth = 14 ftheight = 8 ftGiven cost of materials:
floor tiles = $4 per ft²wall & ceiling paint = $16 per 146 ft²Total square feet of floor = length × width
= 12 × 14
= 168 ft²
Total cost of flooring = $4 × 168
= $672.00
Total square feet to be painted = area of walls + area of ceiling
= 2(12 × 8) + 2(14 × 8) + (12 × 14)
= 584 ft²
Total cost of paint = (584 ÷ 146) × $16
= $64.00
Total cost to tile and paint the room = $672 + $64
= $736.00
What is the product of 3/4 and -6/7?
Answer:
-9/14
Step-by-step explanation:
Hey there!
Guide:
• Difference means subtract/subtraction
• Product means multiply/multiplication
• Sum means add/addition
• Quotient means divide/division
• Now that we know what “product” means… we can make the question/equation easier to solve.
3/4 × -6/7
= 3(-6) / 4(7)
= -18 / 28
= -18 ÷ 2 / 28 ÷ 2
= -9 / 14
Therefore, your answer is: -9/14
Good luck on assignment & enjoy your day!
~Amphitrite1040:)
Need help with calculus asap with steps
Answer:
p=7/2
Step-by-step explanation:
Rember that a p series can be represented by
[tex] \frac{1}{k {}^{p} } [/tex]
Here, notice that
[tex] \frac{1}{8 \sqrt{2} } = \frac{1}{2 {}^{3} \sqrt{2} } = \frac{1}{2 {}^{3} \times 2 {}^{ \frac{1}{2} } } = \frac{1}{2 {}^{ \frac{7}{2} } } [/tex]
This is true for all parts of the series because
[tex]27 \sqrt{3} = 3 {}^{ \frac{7}{2} } [/tex]
So p=7/2
The area labeled B is 9 times the area labeled A. Express b in terms of a.
b=_____?
Hi there!
For the graph on the left, we know that the area A is equal to:
[tex]A = \int\limits^a_0 {e^x} \, dx[/tex]
Area 'B' is 9 times this area, so:
[tex]B = 9 \cdot \int\limits^a_0 {e^x} \, dx[/tex]
We can evaluate the integral:
[tex]B = 9 \cdot \int\limits^a_0 {e^x} \, dx \\\\B = 9 \cdot e^x \left \| a}} \atop {0}} \right. \\\\B = 9 (e^a - 1)[/tex]
We also know that:
[tex]B = \int\limits^b_0 {e^x} \, dx[/tex]
Evaluate:
[tex]B = e^x \left \| b}} \atop {0}} \right. = e^b - 1[/tex]
Set the two equations for 'B' equal:
[tex]e^b - 1 = 9(e^a - 1)\\\\e^b - 1 = 9e^a - 9 \\\\e^b = 9e^a - 8[/tex]
Take the natural log of both sides:
[tex]ln(e^b) = ln(9e^a - 8)\\\\\boxed{b = ln(9e^a - 8)}[/tex]
find x correct to 2 decimal places
Answer:
Step-by-step explanation: