A man wants to make up 100 one-pound jars of nuts to sell for 66 cents a jar. He plans to use 40 pounds of nuts worth 75 cents a pound. What should be the price of the other type of nuts he uses? Answer:

Susan and Joseph can fix 17 broken cars together in 12 hours.

To calculate the time it takes for Susan and Joseph to fix 17 broken cars together, we can calculate their individual rates of work.

Susan takes 3 hours to fix 2 cars, so her rate is 2/3 cars per hour.

Joseph takes 4 hours to fix 3 cars, so his rate is 3/4 cars per hour.

When they work together, their rates are additive. So their combined rate is (2/3 + 3/4) cars per hour. This is equal to (8/12 + 9/12) cars per hour, which simplifies to 17/12 cars per hour.

To find the time it takes to fix 17 cars, we can divide the number of cars by the combined rate: 17 cars / (17/12 cars per hour) = 12 hours.

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a)[tex]\[ h(t) = 13 - 6\cos\left(\frac{2\pi}{15} t\right) \][/tex]

This formula gives the distance \( h \) from you to the ground after \( t \) seconds of riding.

b) you are 10 meters above the ground at [tex]\( t = \frac{5}{2} \)[/tex] seconds, which is \( 2.5 \) seconds after starting at the lowest point.

Let's break down this problem step by step:

a. To find a formula for the distance ( h ) (in meters) from you to the ground after ( t ) seconds of riding, we can use trigonometry and the properties of circular motion.

1. The Ferris wheel has a radius of 6 meters and is centered 7 meters above the ground. This means that at the lowest point, you are ( 7 + 6 = 13 ) meters above the ground, and at the highest point, you are ( 7 - 6 = 1 ) meter above the ground.

2. The angular speed of the Ferris wheel is given as 24 degrees per second. Since the Ferris wheel completes one full rotation (360 degrees) in[tex]\( \frac{360^\circ}{24^\circ/\text{sec}} = 15 \)[/tex] seconds, its angular velocity is[tex]\( \omega = \frac{2\pi}{15} \)[/tex]radians per second.

3. Let [tex]\( \theta \)[/tex] be the angle in radians that the Ferris wheel has rotated through at time ( t ) seconds. The height ( h ) above the ground can be expressed as:

[tex]\[ h = 13 - 6\cos(\theta) \][/tex]

To relate[tex]\( \theta \) to time \( t \)[/tex], we use the formula for angular displacement in circular motion:

[tex]\[ \theta = \omega t \][/tex]

Substitute [tex]\( \omega = \frac{2\pi}{15} \)[/tex] into the equation above to get:

[tex]\[ \theta = \frac{2\pi}{15} t \][/tex]

Now, substitute [tex]\( \theta \)[/tex]back into the equation for height \( h \):

[tex]\[ h(t) = 13 - 6\cos\left(\frac{2\pi}{15} t\right) \][/tex]

This formula gives the distance \( h \) from you to the ground after \( t \) seconds of riding.

b. To find the times when you are 10 meters above the ground, we set \( h(t) = 10 \) and solve for \( t \):

[tex]\[ 10 = 13 - 6\cos\left(\frac{2\pi}{15} t\right) \][/tex]

First, subtract 10 from both sides:

[tex]\[ -3 = -6\cos\left(\frac{2\pi}{15} t\right) \][/tex]

Divide both sides by -6:

[tex]\[ \frac{1}{2} = \cos\left(\frac{2\pi}{15} t\right) \][/tex]

Now, take the inverse cosine (arccos) of both sides:

[tex]\[ \frac{2\pi}{15} t = \cos^{-1}\left(\frac{1}{2}\right) \][/tex]

Solve for \( t \) by dividing both sides by [tex]\( \frac{2\pi}{15} \)[/tex]:

[tex]\[ t = \frac{15}{2\pi} \cos^{-1}\left(\frac{1}{2}\right) \][/tex]

Using the fact that [tex]\( \cos^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{3} \)[/tex], substitute this value into the equation:

[tex]\[ t = \frac{15}{2\pi} \times \frac{\pi}{3} \]\[ t = \frac{5}{2} \][/tex]

So, you are 10 meters above the ground at [tex]\( t = \frac{5}{2} \)[/tex] seconds, which is \( 2.5 \) seconds after starting at the lowest point.

To find the number of seven-digit phone numbers beginning with 336 that have the given property, we need to determine the number of possible combinations for the middle three digits. The number of different seven-digit phone numbers that satisfy the given property is 7.

To find the number of seven-digit phone numbers beginning with 336 that have the given property, we need to determine the number of possible combinations for the middle three digits.

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Answer:

Convection

Step-by-step explanation:

A is the correct answer.

Question

Answer

EF = 32

The amount that goes into the principal when friend pays you $200.00 at the end of the first month is $296.56.

The first interest will be:

= 1137.45 × (0.036/12)

= 3.41

The amount owed at the month end will be:

= 1137.45 + 3.41

= 1140.86

The new balance after 200 payment will be:

= 1140.86 - 200

= 940.86

Therefore, the reduction in principal will be:

= 1137.45 - 940.86

= 196.59

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Final Answer:

In the isosceles triangle, the base angles are congruent, and the given angle at the top is [tex]\(70^\circ\)[/tex]. Using the sum of angles in a triangle, we find that the value of (x) is [tex]\(40^\circ\)[/tex]. Therefore, the final answer is [tex]\(x = 40^\circ\)[/tex].

Step-by-step explanation:

The base angles of the isosceles triangle as (A) and (B), and the vertex angle as (x). Since we know that the angles opposite the congruent sides are congruent, we have:

[ A = B ]

Now, let's consider the sum of angles in a triangle. The sum of all angles in a triangle is always [tex]\(180^\circ\)[/tex]. Therefore:

[tex]\[ A + B + x = 180^\circ \][/tex]

But since (A = B), we can rewrite this as:

[tex]\[ 2A + x = 180^\circ \][/tex]

Now, substitute (A) with [tex]\(70^\circ\)[/tex] (as given in the problem):

[tex]\[ 2(70^\circ) + x = 180^\circ \][/tex]

Simplify the equation:

[tex]\[ 140^\circ + x = 180^\circ \][/tex]

Now, isolate (x) by subtracting [tex]\(140^\circ\)[/tex] from both sides of the equation:

[tex]\[ x = 180^\circ - 140^\circ \][/tex]

[tex]\[ x = 40^\circ \][/tex]

So, the value of (x) in the given isosceles triangle is [tex]\(40^\circ\)[/tex].

Final answer:

The value of x in the isosceles triangle is 40 degrees, which is found by using the property that the angles opposite the congruent sides are congruent and the sum of the angles in any triangle is always 180 degrees.

Explanation:

To find the value of x in an isosceles triangle where one of the angles at the base is 70 degrees, we employ the property that the angles opposite the congruent sides of an isosceles triangle are also congruent. This means that the other angle at the base is also 70 degrees. Since the sum of the angles in any triangle is always 180 degrees, we can set up an equation to solve for x:

70° (angle at the left base) + 70° (angle at the right base) + x (angle at the top) = 180°

Adding the base angles together gives us:

70° + 70° = 140°

To find x, we simply subtract the sum of the base angles from 180 degrees:

180° - 140° = 40°

Therefore, the value of x, the angle at the top of the isosceles triangle, is 40 degrees.

Answer:  The correct options are :

(4). (A) [tex](5b+3y)(a+1).[/tex]

(5). (C) [tex] (x+7)(4x^2+7).[/tex]

(6). (D) [tex] (3x+5)(7x^2+3).[/tex]

(7). (C) [tex] (10x+3)(y+2a).[/tex]

Step-by-step explanation:  We are given to completely factor the following expressions :

Expression 4 :

The given expression is

[tex]E_1=5ab+3ay+5b+3y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

The factorization of expression (i) is as follows :

[tex]E_1\\\\=5ab+3ay+5b+3y\\\\=a(5b+3y)+1(5b+3y)\\\\=(5b+3y)(a+1).[/tex]

So, option (A) is CORRECT.

Expression 5 :

The given expression is

[tex]E_2=4x^3+28x^2+7x+49~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

The factorization of expression (ii) is as follows :

[tex]E_2\\\\=4x^3+28x^2+7x+49\\\\=4x^2(x+7)+7(x+7)\\\\=(x+7)(4x^2+7).[/tex]

So, option (C) is CORRECT.

Expression 6 :

The given expression is

[tex]E_3=21x^3+35x^2+9x+15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]

The factorization of expression (iii) is as follows :

[tex]E_3\\\\=21x^3+35x^2+9x+15\\\\=7x^2(3x+5)+3(3x+5)\\\\=(3x+5)(7x^2+3).[/tex]

So, option (D) is CORRECT.

Expression 7 :

The given expression is

[tex]E_4=10xy+3y+20ax+6a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)[/tex]

The factorization of expression (iv) is as follows :

[tex]E_4\\\\=10xy+3y+20ax+6a\\\\=y(10x+3)+2a(10x+3)\\\\=(10x+3)(y+2a).[/tex]

So, option (C) is CORRECT.

Answer:

A. [tex]y=2x[/tex]

Step-by-step explanation:

We are asked to find the equation that represents a direct variation.

We know that a direct variation is in form [tex]y=kx[/tex], where y is directly proportional to x and k is constant of variation.

Upon looking at our given choices, we can see that equation [tex]y=2x[/tex] represents direct variation, where [tex]k=2[/tex].

Therefore, option A is the correct choice.

To solve this question we will have to make use of one of the properties of the inscribed quadrilateral. That property is: "Opposite angles in any quadrilateral inscribed in a circle are supplements of each other".

Thus, as we can see from the diagram given, [tex] \angle B+\angle D=180^{\circ} [/tex]

[tex] (2x+3)+(4x+3)=180^{\circ} [/tex]

[tex] \therefore 6x+6=180^{\circ} [/tex]

[tex] 6x=174^{\circ} [/tex]

[tex] \therefore x=\frac{174^{\circ}}{6} =28^{\circ} [/tex]

Thus, now that we know the value of x, we can easily find the value of the [tex] \angle C [/tex] because we know that:

[tex] \angle C=2x+1 [/tex]

[tex] \therefore \angle C=2(29^{\circ})+1=59^{\circ} [/tex]

Thus, [tex] \boldsymbol{59^{\circ}} [/tex] is the correct answer.

Answer:

D) 5.45 hours

Step-by-step explanation:

I got it correct on USATP.

Hope this helps!

From: Aug1e