Answer:
(a)Height of the platform=40 feet
(b)Initial Velocity=54 ft/sec
(c)4 seconds
Step-by-step explanation:
The equation [tex]h(t) = -16t\² + 54t + 40[/tex] gives the height of the baton, in feet, t seconds after it is thrown from the platform.
(a)Height of the platform
The Height of the platform is the height at which t=0
[tex]h(0) = -16(0)\² + 54(0) + 40[/tex]
Height of the platform=40 feet
(b)To determine the speed at which the baton was thrown, we find the velocity, v(t).
[tex]v(t)=\frac{dh}{dt} =\frac{d}{dt} (-16t\² + 54t + 40)=-32t+54\\$At t=0\\v(0)=-32(0)+54=54 feet/sec[/tex]
(c)The baton will hit the ground when its height, h(t)=0
[tex]-16t\² + 54t + 40=0\\\text{Solving the quadratic formular}\\t = \frac{-54\pm \sqrt{(-54)^2 - 4*40*(-16)} }{2*-16}\\= \frac{-54\pm \sqrt{5476 }}{-32}\\= \frac{-54\pm 74}{-32}\\t=\frac{-54+ 74}{-32},\frac{-54- 74}{-32}\\t=-0.625\:or \:t=4[/tex]
Since -0.625 is not valid, the baton will hit the ground 4 seconds after it is thrown.
What is the area of this circle?
Answer:
100 pi (314.16)
Step-by-step explanation:
Because the diameter is 20 in, that makes the radius = 20/2 inches = 10 inches.
10^2 * pi = area
100 pi = area
314.16 is approx. area.
Answer:
It should be 1,256.6 in square inches
Step-by-step explanation:
Question 1 (1 point)
A recent shipment of 2,500 iPhones at the local Best Buy store needed to be checked for manufacturing defects. The
manager chose 25 at random and found 4 to be defective.
How many iPhones can he expect to be defective?
b
400
7
625
250
Answer: 400
Step-by-step explanation:
25÷4=6.25
2500÷6.25=400
Based on the random sample of 25 iPhones in which 4 were found to be defective, it is projected that approximately 400 iPhones in the total shipment of 2,500 would be defective.
Explanation:The question is essentially asking for a projection based on a statistical sample. In this case, the sample is 25 iPhones, out of which 4 were found to be defective. This implies that, out of every 25 iPhones, we can expect approximately 4 to be defective.
To project this onto the entire shipment of 2,500 iPhones, we can use the proportion found in the sample. Divide the total number of iPhones by the sample size to find the number of 'samples' in the shipment: 2500 ÷ 25 = 100. Then multiply this by the number of defective iPhones found in the sample: 100 x 4 = 400.
So based on the sample, the manager can expect approximately 400 iPhones in the shipment to be defective.
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At Sports Shoe Warehouse, the cost of 11 pairs of soccer shoes is $1100 plus $66 for each additional pair. From Winning Team Shoes, the cost of 11 pairs of soccer shoes is $825 plus an additional 6% for each additional pair. For how many total pairs of soccer shoes does each vendor cost about the same? Write the equations
Final answer:
Both vendors cost about the same for 20 pairs of soccer shoes.
Explanation:
For Sports Shoe Warehouse, the cost for 11 pairs is $1100, and each additional pair costs $66. So, the total cost for x additional pairs would be $1100 + $66x.
For Winning Team Shoes, the cost for 11 pairs is $825, and each additional pair costs 6% more than the previous pair. So, the total cost for x additional pairs would be $825 + 0.06(825)x.
To find when both vendors cost the same, we set their expressions equal: $1100 + $66x = $825 + 0.06(825)x. Solving for x gives x = 20. Therefore, both vendors cost about the same for 20 pairs of soccer shoes.
bring the help!!!!!!!!!!!!!!!!!
What is the answer?
9514 1404 393
Answer:
1278 × 4
Step-by-step explanation:
Apparently, a 4-digit number is being multiplied by a 1-digit number. We expect that the partial products are the result of multiplying single digit numbers with different place values.
So, 4000 = 1000 × 4 or 500 × 8
800 = 200 × 4 or 100 × 8
We don't think 8 is the multiplier, because 500 and 100 have digits with the same place value multiplier (100).
Continuing, ...
280 = 70 × 4
32 = 8 × 4
The numbers being multiplied seem to be 1278 × 4.
how do i solve this using imaginary numbers? PLEASE HELP
Answer:
14 -2i
Step-by-step explanation:
9 + sqrt(-4) - ( -5 + sqrt(-16))
We know the sqrt of a negative number is i * sqrt(number)
9 + isqrt(4) - ( -5 + isqrt(16))
9 + 2i - (-5 + 4i)
Distribute the negative sign
9+2i +5 -4i
Combine like terms
14 -2i
Find log 47.2 to four decimal places.
Step-by-step explanation:
log 47.2 in four decimal places
= 1.6739
Final answer:
To find log 47.2 to four decimal places, use the logarithmic function. The result is approximately 1.6739
Explanation:
To find log 47.2 to four decimal places, we need to use the logarithmic function. The logarithm function is the inverse of exponentiation. In this case, we are looking for the logarithm of 47.2.
Using a scientific calculator or logarithmic tables, we can find that log 47.2 ≈ 1.6739 to four decimal places.
The four decimal places are determined by the precision of the logarithm function and the number of significant figures in the input value (47.2 has four significant figures).
What is the sum of 2 2/4 and 8 3/4
Answer:
11 1/4 or 11.25.
Step-by-step explanation:
You are researching different phone companies. Company one is going to charge you $10 per
line plus a $40 data charge. Company 2 does not have a data charge and will charge you $20 per
line. How many lines would result in the two companies costing the same?
Answer:
4 lines
Step-by-step explanation:
40 + 10x = 20x
40 = 10x
4=x
Which number best represents the situation. "A plane descends 1, 500ft?
1,500
15
-1,500
-15
Answer:
-1500
Step-by-step explanation:
"descends," means to go down (ascend means to go up), so the number would be negative. The number given is 1500, so we use that, and get -1500.
Answer:
-1500
Step-by-step explanation: Descending means "going down" negative numbers are below normal. They had descended from the normal numbers.
If the circumference of the circle is 37.68 units, what is the area? (Use 3.14 for pi .)
Answer:
Area of the circle = [tex]113.04\;units^2[/tex]
Step-by-step explanation:
Circumference = [tex]37.68\;units[/tex]
Circumference of the circle = [tex]2\times \pi \times r[/tex]
As,
[tex]\pi =\dfrac{22}{7}=3.14[/tex]
[tex]37.68=2\times \pi \times r\\\\37.68=2\times 3.14 \times r\\\\37.68=6.28\times r\\\\r=\dfrac{37.68}{6.28} \\\\r=6\;units[/tex]
Area of a circle = [tex]\pi \times r^2[/tex]
[tex]=3.14\times (6\times 6)\\\\=3.14\times 36\\\\=113.04\;units^2[/tex]
Answer:
113.04 units²
Step-by-step explanation:
A = πr2 = π(d2)2 A = C24π π = 3.1415 A = area C = circumference or perimeter r = radius, d = diameter
Hope this helps
Express in lowest terms.
Answer:
3x^3
Step-by-step explanation:
57/19=3
x^5 - x^2 = x^3
Answer:
3x^3
Step-by-step explanation:
You have to divide 15 over nineteen, which is 3x with the exponent of 5 over x with the exponent of 2. Then you have to apply the exponent rule and subtract the exponents:5-2, which would give you 3x with the exponent of 3
Find the length of a pendulum that makes one swing in 3 s. The equation for the time of one swing of a pendulum is T= 2pi sqrt(L/32) , where T is the time in seconds and L is the length in feet. Round to the nearest hundredth.
Answer:
7.30
Step-by-step explanation:
T = 2π √(L/32)
3 = 2π √(L/32)
3/(2π) = √(L/32)
(3/(2π))² = L/32
L = 32 (3/(2π))²
L ≈ 7.30
The length of the pendulum in feet nearest to hundredth is 7.29 feet.
What is an equation?
Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given that the equation for the time of one swing of a pendulum is
T = 2π √(L/32).
And pendulum makes one swing in 3 seconds.
Now T is 3 second.
So , substituting the value of T in given expression;
3 = 2π √(L / 32)
3 / (2π) = √(L / 32)
Taking square on both sides,
{ (3/(2π) }² = L / 32
L = 32 × { 3 / (2π) }²
L = 7.295
L ≈ 7.29
Therefore, the length of the pendulum in feet nearest to hundredth is 7.29 feet.
To learn more about the equation;
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1. Evaluate 4x
if x = 3.
Answer:
[tex]12[/tex]
Step-by-step explanation:
Step 1: Set x to 3 and solve
[tex]4x[/tex]
[tex]4(3)[/tex]
[tex]4 * 3[/tex]
[tex]12[/tex]
Answer: [tex]12[/tex]
The table shows three unique, discrete functions. Which statements can be used to accurately compare the functions? Select two options. g(x) has the lowest minimum. f(x) has the greatest maximum. All three functions have a y-intercept. All three functions have an x-intercept. The domain of all three functions is the same.
The answer to your question would be:
B- f(x) has the greatest maximum.
C- All three functions have a y-intercept.
(I know this question is old but I hope it helps someone else.)
:)
What are interest rates? Please explain.
Answer:
An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited or borrowed. The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited or borrowed.
Given the m<8=45, find the other angle measures. Be able to say how you found each angle measure. PLEASE help!
Answer:
m<1 = 135°, m<2 = 45°, m<3 = 135°, m<4 = 45°, m<5 = 135°, m<6 = 45°, m<7 = 135°
Step-by-step explanation:
We know that a straight line always gives us a measure of 180° total. This would mean 180° = m<8 + m<7. So, if we plug in the real value of m<8, we get 180 = 45 + m<7. From there, we can subtract 180 by 45, and we get 135° = m<7.
We know that vertical angles are congruent - so m<5 is the same as m<7 - making m<5 = 135° as well. This could also apply to m<8 and m<6, so m<6= 45°.
From there, we can also say that alternate interior angles are congruent to each other - meaning m<5 = m<3, and m<6 = m<4. So, m<3 = 135° and m<4 = 45°.
Alternate exterior angles are congruent too, which means m<8 = m<2, and m<7 = m<1. So, m<2 = 45° and m<1 = 135°.
In summary,
m<7 = 135° because angle subtraction.
m<5 = 135° and m<6= 45° because vertical angles are congruent.
m<3 = 135° and m<4 = 45° because alternate interior angles are congruent.
m<1 = 135° and m<2 = 45° because alternate exterior angles are congruent!
Hope this makes sense! Not sure if I explained it well.
The following sector has a radius of 10 inches and a central angle of 30 . Which of the following is its arc length, in inches?
Answer:
option 1
Step-by-step explanation:
step 1
Find the arc length of the complete circle
The circumference of the circle ios given by
[tex]C=2\pi r[/tex]
we have
[tex]r=10\ in[/tex]
substitute
[tex]C=2\pi (10)[/tex]
[tex]C=20\pi\ in[/tex]
step 2
Find the arc length for a sector with a cenytral angle of 30 degrees
we know that
The complete circle subtends a central angle of 360 degrees
so
using proportion
[tex]\frac{20\pi}{360^0}=\frac{x}{30^o}\\\\x=20\pi(30)/360\\\\x=\frac{5}{3} \pi\ in[/tex]
Te dog’s nap started at 7:14am and ended
at 7:57am. How long was the dog’s nap?
Answer:
The answer is 43 minutes I'm pretty sure.
Answer:
43 mins
Step-by-step explanation: All you have to do is subtract 57 from 14 then you will get your amount of time. And that is all you have to do
Please can anyone help me answer this question I'm really struggling with it
Answer:
[tex]v = {210cm}^{3} [/tex]
Step-by-step explanation:
Formula for finding the volume of a triangular prism is given as:
[tex]v = \frac{1}{2} \times b \times h \times l[/tex]
where,
b = breadth = 7cm
h = height = 6cm
l = length = 10cm
Thus,
[tex]v = \frac{1}{2} \times 7cm \times 6cm \times 10cm[/tex]
[tex]v = \frac{1}{2} \times 420 {cm}^{3} [/tex]
[tex]v = \frac{ {420cm}^{3} }{2} [/tex]
[tex]v = {210cm}^{3} [/tex]
A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. Find Peo, the score which separates the lower 60% from the top 40%.
Round to one decimal place.
O A. 212.7
OB. 207.8
OC. 211.3
OD. 187.5
Answer:
A. 212.7
Step-by-step explanation:
To find the score that separate the lower 60% from the top 40% , we need to know the z value that satisfy:
P(Z<z) = 0.6
So, using the standard normal table, we know that the z value is equal to 0.2533
Then, the score x that is equivalent to the z value 0.25 can be calculate as:
[tex]z=\frac{x-m}{s}\\x=(z*s)+m[/tex]
Where m is the mean and s is the standard deviation. Therefore, replacing z by 0.25, m by 200 and s by 50, we get:
[tex]x=(0.2533*50)+200\\x=212.7[/tex]
Use a half-angle identity to find the exact value
Given:
[tex]\cos 15^{\circ}[/tex]
To find:
The exact value of cos 15°.
Solution:
[tex]$\cos 15^{\circ}=\cos\frac{ 30^{\circ}}{2}[/tex]
Using half-angle identity:
[tex]$\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos (x)}{2}}[/tex]
[tex]$\cos \frac{30^{\circ}}{2}=\sqrt{\frac{1+\cos \left(30^{\circ}\right)}{2}}[/tex]
Using the trigonometric identity: [tex]\cos \left(30^{\circ}\right)=\frac{\sqrt{3}}{2}[/tex]
[tex]$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}[/tex]
Let us first solve the fraction in the numerator.
[tex]$=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}[/tex]
Using fraction rule: [tex]\frac{\frac{a}{b} }{c}=\frac{a}{b \cdot c}[/tex]
[tex]$=\sqrt{\frac {2+\sqrt{3}}{4}}[/tex]
Apply radical rule: [tex]\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}[/tex]
[tex]$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}[/tex]
Using [tex]\sqrt{4} =2[/tex]:
[tex]$=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]
[tex]$\cos 15^\circ=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]
I need help pleeeeeeeeeeeeeease
Answer:
Tj hit 85% of the balls pitched to him
Step-by-step explanation:
Can someone actually answer this question pls its my 3rd time posting it and ill ive gotten was wrong or answers that make no sence. Pls explain your work!!!!! THANKS
Answer:
(-2+-5) equals -7.
Because the signs are the same, we dont change it.
(3+5) equals 8. Same like the other equation, the signs are the same so we do not change it.
Now we do (-7+8) The answer will be 1. Lets use a little graph since its hard to explain.
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Mark -7 anyway you want. (Circle it, draw a line under it, what ever you want.)
Now Move the line 8 times.
When you do that your line will stop at 1.
And thats how you do it.
Step-by-step explanation:
Answer:
All you have to do is Subtract the first number of both equation so 2-3= 1.
Step-by-step explanation:
PLZ answer fast 100 points
Consider a function y = f(x). Choose all options in which the effect on the graph of f is correctly described.
y = f(x + 3)
Shifts 3 units right.
y = f(x − 2) + 4
Shifts 2 units right, 4 units up.
y = −f(x − 3)
Shifts 3 units right, reflects in x-axis.
y = 2f(x) + 3
Shifts 2 units right, 3 units up.
y = f(x + 5)
Shifts 5 units left.
Answer:
Can i have brainliest
The second one
The third one
and the last ones
Step-by-step explanation:
The x values are opposite
and the y stay the same
Answer:
y = f(x − 2) + 4
Shifts 2 units right, 4 units up.
y = −f(x − 3)
Shifts 3 units right, reflects in x-axis.
y = f(x + 5)
Shifts 5 units left
Step-by-step explanation:
Let the initial function be y = f(x)
Then,
y = f(x − 2) + 4 is obtained by translating the function 2 units towards right and 4 units up
y = -f(x - 3) is obtained by translating the graph 3 units towards right and then reflection along the x-axis
y = f(x + 2) is obtained by translating the graph 2 units towards left
The Fibonacci sequence is the sequence 1, 1, 2, 3, 5, ... where the first and second terms are 1 and each term after that is the sum of the previous two terms. What is the remainder when the 100th term of the sequence is divided by 8?
The remainder when the 100th term of the Fibonacci sequence is divided by 8 is 3.
Explanation:The Fibonacci sequence is a sequence where each term is the sum of the previous two terms. The sequence starts with 1, 1, and then continues with 2, 3, 5, and so on. To find the remainder when the 100th term of the sequence is divided by 8, we can calculate the terms of the sequence modulo 8 until we reach the 100th term.
First term: 1 mod 8 = 1Second term: 1 mod 8 = 1Third term: (1 + 1) mod 8 = 2Fourth term: (1 + 2) mod 8 = 3Fifth term: (2 + 3) mod 8 = 5Sixth term: (3 + 5) mod 8 = 0Seventh term: (5 + 0) mod 8 = 5Eighth term: (0 + 5) mod 8 = 5Ninth term: (5 + 5) mod 8 = 2Tenth term: (5 + 2) mod 8 = 7We can see from the pattern that the terms modulo 8 repeat every 6 terms. Therefore, to find the remainder when the 100th term is divided by 8, we can calculate the remainder when 100 is divided by 6. 100 mod 6 = 4. So, the remainder when the 100th term of the Fibonacci sequence is divided by 8 is the same as the remainder when the 4th term is divided by 8, which is 3.
Which one of the following is NOT true about the expression shown
9x^2-8x-3
A) The expression is trinomial
B) The degree is 2
C) the leading coefficient is 9
D) The constant term is 3
Answer:
A) The expression is a trinomial.
Step-by-step explanation:
If the degree is 2, the expression would be a binomial, not a trinomial. If this answer is correct, please make me Brainliest!
In the 7th grade class, 25 students have dogs, and 1/4 of the students do not have dogs. What is the total number of students in the class who do not have dogs?
Answer:
6.25? is that even possible?
Step-by-step explanation:
New help can anybody help
Answer:
we need the question
Step-by-step explanation:
A playing card has an area of 50 square centimeters and a perimeter of 30 centimeters. What are the dimensions of the playing card?
The dimensions of playing card is L = 10 centimeter and W=5 centimeter, If the playing card has an area of 50 square centimeter and a perimeter of 30 centimeters.
Step-by-step explanation:
The given is,
Playing card has an area of 50 square centimeters
A perimeter of 30 centimeters
Step:1
A playing card is in the shape of rectangle,
Formula for perimeter of rectangle is,
[tex]Perimeter, P = 2(l+w)[/tex] .........................(1)
Formula for area of rectangle is,
[tex]Area, A= lw[/tex]......................................(2)
Where, l - Length of rectangle
w - Width of rectangle
Step:2
From the given values equation (1) becomes,
[tex]30 = 2(l+w)[/tex]
[tex]\frac{30}{2}=(l+w)[/tex]
[tex]15 =(l+w)[/tex]
[tex]w=15-l[/tex] .............................(3)
Width value in terms of length is calculated.
Step:2
Equation (2) becomes,
[tex]50 = (15-l)(l)[/tex]
[tex]50= 15l -l^{2}[/tex]
[tex]l^{2}-15l+50=0[/tex]
Solving the above equation,
[tex]=10[/tex]
[tex]l=10 cm[/tex]
Step:3
Equation (3) becomes,
[tex]w=15-l[/tex]
[tex]=15-10[/tex]
[tex]=5[/tex]
w = 5 cm
Result:
The dimensions of playing card is L = 10 centimeter and W = 5 centimeter, If the playing card has an area of 50 square centimeter and a perimeter of 30 centimeters.
Final answer:
By creating an equation system using the area and perimeter formulas for a rectangle, the dimensions of the playing card are found to be either 5 cm by 10 cm or 10 cm by 5 cm.
Explanation:
To determine the dimensions of a playing card given its area and perimeter, we need to set up an equation system based on the properties of a rectangle. Let's call the length L and the width W. The area (A) of a rectangle is A = L × W, which in this case is 50 sq cm. The perimeter (P) is P = 2(L + W) and is given as 30 cm.
From the perimeter, we can rearrange this to find L in terms of W:
30 cm = 2(L + W)
15 cm = L + W
L = 15 cm - W
Now, substituting L in the area equation gives us:
50 cm² = (15 cm - W) × W
This can be rearranged to form a quadratic equation:
0 = W² - 15W + 50
Factoring, we find:
0 = (W - 5)(W - 10)
So we have two solutions, W = 5 cm or W = 10 cm.
If we take W as the width, then L (the length) would be the other dimension, which would be 15 cm - W. So, we have two possible dimension pairs based on the standard card size: (5 cm by 10 cm) or (10 cm by 5 cm).