"4. Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x= 12. y = -10 when x = 2 "

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

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.

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.

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.

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.

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.

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.

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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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.

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.

Answer:

C. 9

Step-by-step explanation:

s=11

v=8

(11-8)²

(3)²

9

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.

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.

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

The total amount accrued, principal plus interest, with compound interest on a principal of $500.00  is $635.24.

Given Data

A = 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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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

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.

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

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.