Answer:
5/ 2 x
Step-by-step explanation:
If you earn one penny every 10 seconds of your life ,how many dollars would you have after 65 years?
There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year. You are assuming that 65 years is the length. We will find the number of seconds in 65 years.
60 x 60 x 24 x 365 x 65 = 2,049,840,000 seconds.
We should note that every 4 years there is an extra day, so if we find 65 % 4 or the modulus of 65 then we can add this. The modulus of this is 16.
60 x 60 x 24 x 16 x 65 = 89,856,000 seconds
2,139,696,000 seconds (when you add the two calculations together).
You are finding it "every 10 seconds" so divide this value by 10. Then divide by another 100 because you are only counting dollars and 100 pennies is equal to 1 dollar.
The answer is : $2,139,696
Jamie has a deck of 60 sports cards, of which some are baseball cards and some are football cards. jamie pulls out a card randomly from the deck, records its type, and replaces it in the deck. jamie has already recorded three baseball cards and nine football cards. based on these data, what is, most likely, the number of baseball cards in the deck?
12
15
24
30
3 baseball + 9 football 9+3 = 12
3 out of 12 were base ball
3/12=0.25
60*0.25 = 15
so there would be 15 baseball cards
Answer:
The answer is 15
Step-by-step explanation:
i took the test
A football is thrown with an initial upward velocity of 25 feet per second from a height of 5 feet above the ground. The equation h = −16t^2 +25t + 5 models the height in feet t seconds after it is thrown. After the ball passes its maximum height, it comes down and hits the ground. About how long after it was thrown does it hit the ground?
Answer:
1.74 second long after it was thrown does it hit the ground.
Step-by-step explanation:
Given : A football is thrown with an initial upward velocity of 25 feet per second from a height of 5 feet above the ground. The equation [tex]h =-16t^2+25t+5[/tex] models the height in feet t seconds after it is thrown.
To find : How long after it was thrown does it hit the ground?
Solution :
The equation model is [tex]h(t)=-16t^2+25t+5[/tex]
After the ball passes its maximum height, it comes down and hits the ground.
i.e. h=0
So, [tex]-16t^2+25t+5=0[/tex]
Solve by quadratic formula of equation [tex]ax^2+bx+c=0[/tex] is [tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
Here, a=-16 , b=25 and c=5
[tex]t=\frac{-25 \pm \sqrt{(25)^2-4(-16)(5)}}{2(-16)}[/tex]
[tex]t=\frac{-25 \pm \sqrt{625+320}}{-32}[/tex]
[tex]t=\frac{-25 \pm \sqrt{945}}{-32}[/tex]
[tex]t=\frac{-25+\sqrt{945}}{-32},\frac{-25-\sqrt{945}}{-32}[/tex]
[tex]t=-0.179,1.741[/tex]
We reject t=-0.179.
Therefore, 1.74 second long after it was thrown does it hit the ground.
When a certain type of thumbtack is flipped, the probability of its landing tip up (U) is 0.54 0.54 and the probability of its landing tip down (D) is 0.46 0.46. Suppose you flip two such thumbtacks, one at a time. The probability distribution for the possible outcomes of these flips is shown below. a. Find the probability of getting 0 ups, 1 up, or 2 ups when flipping two thumbtacks. b. Make a probability distribution graph of this.
600 is 1/10 of6000 true or false
Benjamin has $6000 invested in two accounts. One earns 8% interest per year, and the other pays 7.5% interest per year. If his total interest for the year is $472.50, how much is invested at 8%?
Answer:
Benjamin invested $4,500 at 8%.
Step-by-step explanation:
We know that Benjamin has invested $6,000 in two different accounts.
Let account 1 earn 8% interest per year be defined as [tex]x[/tex] and account 2 earn 7.5% interest per year as [tex]y[/tex].
The sum of both accounts must be $6,000:
[tex]x+y=6,000[/tex]
We also know that at the end of the year Benjamin earned $472.50, which is the sum of the interest he earned of the amount he invested in account 1 and in account 2, with their different interest rates (in this case, it is useful for us to transform the expression of the interest rate by dividing it by 100, so that it can be simplified):
[tex](0.08x)+(0.075y)=472.5[/tex]
We need to express the [tex]y[/tex] in terms of [tex]x[/tex].
From our first expression, we know that:
[tex]y=6,000-x[/tex]
So we substitute this value in our second equation and solve it:
[tex](0.08x)+(0.075(6,000-x))=472.5[/tex]
[tex](0.08x)+((0.075*6,000)-0.075x)=472.5[/tex]
[tex](0.08x)+((0.075*6,000)-0.075x)=472.5[/tex]
[tex]0.08x+450-0.075x=472.5[/tex]
[tex]0.08x-0.075x=472.5-450[/tex]
[tex]0.005x=22.5[/tex]
[tex]x=\frac{22.5}{0.005}[/tex]
[tex]x=4,500[/tex]
This way, we know that the amount that Benjamin invested in the account that earns 8% interest per year is $4,500.
Factor and simplify the algebraic expression.
3x^-4/3 +6x^1/3
Thanks in advance if you can help me!
The numbers of seats in the first 12 rows of a high-school auditorium form an arithmetic sequence. The first row has 9 seats. The second row has 11 seats. a) Write a recursive formula to represent the sequence. b) Write an explicit formula to represent the sequence. c) How many seats are in the 12th row?
The recursive formula for the sequence is an = an-1 + 2. The explicit formula is an = 9 + (n-1)(2). There are 31 seats in the 12th row.
Explanation:a) Recursive formula: The difference between the numbers of seats in consecutive rows is always 2. So, the recursive formula can be written as: an = an-1 + 2. Here, an represents the number of seats in the nth row, and an-1 represents the number of seats in the (n-1)th row.
b) Explicit formula: The first term of the arithmetic sequence is 9, and the common difference is 2. The explicit formula can be written as: an = a1 + (n-1)d. Substituting the values, we get an = 9 + (n-1)(2).
c) Seats in the 12th row: Using the explicit formula, we can calculate the number of seats in the 12th row: a12 = 9 + (12-1)(2) = 9 + 22 = 31. So, there are 31 seats in the 12th row.
Consider an assembly line with 20 stations. Each station has a 0.5% probability of making a defect. At the end of the line, an inspection step singles out the defective units. The inspection step catches 80% of all defects. From inspection, units that are deemed to be non-defective are moved to the shipping department. If a defect is found at inspection, it is sent to the rework department. Rework fixes about 95% of the defective units. Units are directly shipped from the rework department with no further inspection taking place. What is the probability that a unit ends up in rework (in decimal form)?
To find the probability of a unit ending up in rework in an assembly line process, you calculate the probabilities at each step of the process, including station defects, inspection, and rework.
To find the probability that a unit ends up in rework, we need to consider the probability at each step:
The probability of a defective unit at any station is 0.5% or 0.005.
The inspection catches 80% of defects, so the probability of defect detection at inspection is 0.8.
For the units that are sent to rework, the rework department fixes about 95% of the defects, making the probability of a defective unit passing rework 0.05.
Calculating the probability that a unit ends up in rework:
Multiplying the probabilities at each step: 0.005 (station) * 0.2 (not caught at inspection) * 0.95 (not fixed at rework) = 0.00095. Therefore, the probability that a unit ends up in rework is 0.00095 or 0.095% in decimal form.
two similar triangles have areas of 18 and 32 find the ratio of their perimeters
STVU is an isosceles trapezoid. If SV= 3x - 11 and TU = x + 13, find the value of x.
Evaluate the expression for s = 11 and v = 8.
(s – v)2
A. 113
B. 6
C. 9
D. 57
Answer:
C. 9
Step-by-step explanation:
s=11
v=8
(11-8)²
(3)²
9
0.02 is 10 times 0.2
How much would $500 invested at 6% interest compounded monthly be worth after 4 years? Round your answer to the nearest cent
The total amount accrued, principal plus interest, with compound interest on a principal of $500.00 is $635.24.
Compound InterestGiven Data
Principal p = $500Rate r = 6%Time t = 4 yearsA = P + I where
P (principal) = $500.00
I (interest) = $135.24
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 6/100
r = 0.06 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 500.00(1 + 0.06/12)(12)(4)
A = 500.00(1 + 0.005)(48)
A = $635.24
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Find dy/dx and d2y/dx2, and find the slope and concavity (if possible) at the given value of the parameter. (if an answer does not exist, enter dne.) parametric equations point x = 6 cos θ, y = 6 sin θ θ = π 4
We are given the parametric equations:
x = 6 cos θ
y = 6 sin θ
We know that the derivative of cos a = - sin a and the derivative of sin a = cos a, therefore taking the 1st and 2nd derivates of x and y:
d x = 6 (-sin θ) = - 6 sin θ
d^2 x = -6 (cos θ) = - 6 cos θ
d y = 6 (cos θ) = 6 cos θ
d^2 y = 6 (-sin θ) = - 6 sin θ
Therefore the values we are asked to find are:
dy / dx = 6 cos θ / - 6 sin θ = - cos θ / sin θ = - cot θ
d^2 y / d^2 x = - 6 sin θ / - 6 cos θ = sin θ / tan θ = tan θ
We can find the value of the slope at θ = π/4 by using the dy/dx:
dy/dx = slope = - cot θ
dy/dx = - cot (π/4) = - 1 / tan (π/4)
dy/dx = -1 = slope
We can find the concavity at θ = π/4 by using the d^2 y/d^2 x:
d^2 y / d^2 x = tan θ
d^2 y / d^2 x = tan (π/4)
d^2 y / d^2 x = 1
Since the value of the 2nd derivative is positive, hence the concavity is going up or the function is concaved upward.
Summary of Answers:
dy/dx = - cot θ
d^2 y/d^2 x = tan θ
slope = -1
concaved upward
Reduce the following fraction: -36x^4y^4z^5/-12x^6y^3z
A. -3x^2yz^4
B. 3yz^4/1x^2
C. -9yz^5/-3x^2
D. 36yz^5/12x^2
Find the value of a and z: x5⋅x4=axz a = , z = Find the values of a and z: 6x20+5x20=axz a = , z = Find the value of a and z: (x5)4=axz a = , z = Find the value: x25−x25 = Find the values of a, b and z: 8x−9=abxz a = , b = , z =
To find the values of a and z, we need to solve the given equations. Without specific numerical values, we cannot determine the exact values of a and z.
Explanation:To find the values of a and z, we need to solve the given equations. Let's go through each question:
1. For the equation x^5 * x^4 = axz, we can simplify it as x^9 = axz. Since there is no specific numerical value given, we cannot find the exact values of a and z.
2. Similarly, for the equation 6x^20 + 5x^20 = axz, we can simplify it as 11x^20 = axz. Again, without a specific value for x, we cannot determine the values of a and z.
3. In the equation (x^5)^4 = axz, we can simplify it as x^20 = axz. Without numerical values, we cannot find the exact values of a and z.
4. The equation x^25 - x^25 simplifies to 0. There are no variables to solve for.
5. Lastly, for 8x - 9 = abxz, we cannot determine the values of a, b, and z without additional information.
When a jug is half- filled with marbles, it weighs 2.6 kg. The jug weighs 4 kg when it is full. Find the weight of the empty jug.
the difference between a full jug and a jug that is half full will give us the weight of the marbles only in a half full jug:
4 - 2.6 = 1.4 kg
In a half full jug that weighs 2.6 kg, the weight of the marbles is 1.4 kg
the weight of the jug = 2.6 - 1.4 = 1.2 kg
Answer:
The jug weights empty 1.2 kg.
Step-by-step explanation:
In this case we can define two equations based on the description to find the weight of the empty jug, this is:
Eq. 1: [tex]Jug+\frac{1}{2} Marbles=2.6[/tex]
Eq. 2: [tex]Jug+Marbles=4[/tex]
Now putting the Eq. 2 in the Eq. 1 we have:
[tex]Jug+\frac{1}{2} (4-Jug)=2.6[/tex]
Clearing Jug:
[tex]\frac{1}{2}Jug=2.6-2[/tex]
[tex]Jug=0.6*2[/tex]
[tex]Jug=1.2[/tex]
The jug weights empty 1.2 kg.
Pat writes all the 7-digit numbers in which all the digits are different and each digit is greater than the one to its right (so the tens digit is greater than the units, the hundreds greater than the tens, and so on). For example, 9,865,320 is one of the numbers that Pat writes down.
One of Pat's numbers is chosen at random. What is the probability that the middle (thousands) digit is a 5?
A container holds 10 quarts of water. How much is this in gallons? Write your answer as a whole number or a mixed number in simplest form
what is the sum of -7/10 + 1/4
a tree casts a 9 ft shadow at the same time that a person 6 ft tall casts a 4 ft shawdow. what is the height of the tree?
What is the simplified form of the rational expression below? 5x^2-5 over 3x^2+3x
The equation y = 30x + 40 represents the line of best fit showing Ted’s earnings in terms of the number of hours he works as a plumber. If x is the number of hours he works and y is Ted’s earnings, which statement describes this situation correctly? Ted’s initial charge is $30, and his hourly charge is $40. Ted’s initial charge is $40, and his hourly charge is $30. Ted does not charge an initial amount, and his hourly charge is $40. Ted does not charge an initial amount, and his hourly charge is $70.
Answer: Ted’s initial charge is $40, and his hourly charge is $30.
Step-by-step explanation:
We know that the general equation of a line in intercept form is given by :-
[tex]y=mx+c[/tex], where m is the slope of the line and c represents the y-intercept of the function.
The given function :-The equation [tex]y = 30x + 40[/tex] represents the line of best fit showing Ted’s earnings in terms of the number of hours he works as a plumber.
Here, Slope =30
The y-intercept = 40
If x is the number of hours he works and y is Ted’s earnings.
Then by comparing the general equation of line in intercept form, the initial amount charged by Ted =y-intercept = $ 40
His hourly charge = Slope = $ 30
Which equation represents the average of the x-intercepts for 4x^2-24x+20
Suppose a triangle has sides a, b, and c with side c the longest side, and that a^2 + b^2 > c^2. Let theta be the measure of the angle opposite the side of length c. Which of the following must be true? Check all that apply.
the triangle in question is a right triangle
cos(theta) <0
the triangle is not a right triangle
theta is an acute angle
The inequality [tex]a^2 + b^2 > c^2[/tex] indicates that the triangle is not a right triangle and the angle theta is acute. The cosine of an acute angle theta will be positive, not negative.
When it is given that a triangle has sides a, b, and c, with c being the longest side, and the inequality [tex]a^2 + b^2 > c^2[/tex] holds, we can deduce certain characteristics of the triangle and angle theta, which is opposite to side c. This inequality indicates that the triangle is not a right triangle, because for a right triangle, according to the Pythagorean theorem, the relationship between the sides is [tex]a^2 + b^2 = c^2.[/tex]
Since [tex]a^2 + b^2 > c^2[/tex], we can infer that the angle opposite the longest side, theta, must be acute because the sum of the angles in any triangle equals two right angles. Therefore, if theta were obtuse, the sum of the angles would be greater than two right angles, which contradicts the basic properties of triangles.
The correct statements are that the triangle is not a right triangle and that theta is an acute angle. cos(theta) is not necessarily < 0; for an acute angle, the cosine value will be positive. The first statement that the triangle is a right triangle is incorrect because it contradicts our given information and the Pythagorean theorem.
EASY 5 POINTS!!! Shaundra wants to triple the volume of a square pyramid. What should she do?
Answer: Triple the height of the pyramid
Step-by-step explanation:
To triple the volume of a square pyramid, triple the height of the pyramid. Therefore, the option C is the correct answer.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
The volume of a square pyramid refers to the space enclosed between its five faces. The volume of a square pyramid is one-third of the product of the area of the base and the height of the pyramid. Thus, volume = (1/3) × (Base Area) × (Height).
To triple the volume of a square pyramid, triple the height of the pyramid.
Therefore, the option C is the correct answer.
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In a school, the probability that a student takes environmental science and geography is 0.72.The probability that a student takes technology is 0.25. What is probability that a student takes geography given that the student is taking environmental science?
32x - 4 = 4x2 + 60 For the equation shown, choose the description of the solutions.
Final answer:
The quadratic equation 32x - 4 = 4x2 + 60 has real and equal solutions after rearranging to 4x2 - 32x + 64 = 0 and recognizing it as a perfect square.
Explanation:
To solve the equation 32x - 4 = 4x2 + 60, we first rearrange it into standard quadratic form ax2 + bx + c = 0.
We move all terms to one side: 4x2 - 32x + 64 = 0. Once in this form, we can use the quadratic formula, x = (-b ± √(b2 - 4ac)) / (2a), or factor if it is factorable, to find the solutions for x. After rearranging, we note that the quadratic is a perfect square, giving us (2x - 8)2 = 0, which means that the solution for x is 4, with multiplicity of two since it is a repeated root.
The description of the solutions would be that they are real and equal, since we have a repeated solution.
As part of Kayla's exercise program, she either runs 6 miles/day or rides her bike 10 miles/day. Her new goal is to cover a minimum distance of 200 miles, with at least 15 of the days running. She would like to determine the number of days it would take to accomplish this.
Answer:
Kayla will be able to cover the distance of 200 miles by riding bike for 11 days and by running for 15 days.
Step-by-step explanation:
Numbers of days Kayla's has to run be x
Numbers of days Kayla's has to ride bike be y
Speed while running = 6 miles/day
Distance covered by running in x days = 6miles/day × x
Speed while riding a bike = 10 mile/day
Distance covered by riding bike in y days = 10 miles/day × y
Distance desired by Kayla to cover = 200 miles
[tex]200miles=6 miles/day\times x+10 miles/day \times y[/tex]
At least 15 of the days running.Put x = 15 days in above equation:
[tex]200miles=6 miles/day\times 15 days+10 miles/day \times y[/tex]
[tex]200 miles - 90 miles=10 miles/day \times y[/tex]
[tex]\frac{110 miles}{10 miles/day}=y[/tex]
y= 11 days
Kayla will be able to cover the distance of 200 miles by riding bike for 11 days and by running for 15 days.