Lola has a collection of 432 trading cards, and Joel has a collection of 505
trading cards.
At the end of each month, Lola buys a box of 40 trading cards and Joel
buys a box of 32 trading cards.
After how many months will Lola have more trading cards than Joel?

Answer:

1

Step-by-step explanation:

The equation to represent this would be (1 - (1 / 3)) / 2

1 - (1 / 3) = 2 / 3

2 / 3 / 2 = 1 / 3

Answer:

Step-by-step explanation:

B.

Answer:

11

Step-by-step explanation:

Answer:

Step-by-step explanation:

11.

Thus, in ΔCDE the m/∠D = 130⁰, which can be calculated using angle sum property of triangle.

Triangle is derived from the Latin word triangulus, which means "three-cornered" or "having three angles," and is composed of the roots tri-, "three," and angulus, "angle or corner." Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.

Given that: In ΔCDE

m/∠C = (x-4)°

m/∠D = (9x + 4)°

m/∠E = (2x + 12)°

Now, to find m/∠D

So, We know that sum of internal angles of a triangle is equal to 180⁰ .Here, we are given a ΔCDE and all its three internal angles.

Putting the sum of all three equal to 180⁰:

∠C + ∠D + ∠E = 180⁰(x-4)°+ (9x + 4)°+ (2x + 12)°

= 180⁰12x +12

= 180⁰x +1 = 15⁰

x = 14⁰

Thus, Putting value of x in m/∠D = (9x + 4)°.

m/∠D = (9 × 14 +4)⁰

m/∠D = 130⁰

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The complete question is as follows:

In ΔCDE, m ∠ C = ( x − 4 ) ∘ m∠C=(x−4) ∘ , m ∠ D = ( 9 x + 4 ) ∘ m∠D=(9x+4) ∘ , and m ∠ E = ( 2 x + 12 ) ∘ m∠E=(2x+12) ∘ . Find m ∠ D.

The volume of foam needed for the 45 cones is

v = 16,956 cm³

We know that the volume of a cone of diameter F and height H is:

V = pi*(D/2)²*H/3

Where pi = 3.14

Here we know that:

D = 12cm

H = 10cm

And we want to find the volume of 45 of these cones, so the total volume of foam needed is:

v = 45*V = 45*(3.14*(12cm/2)²*10cm/3

v = 16,956 cm³

That is the volume of foam needed.

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when the charged rod is brought closer to the sphere negative charges get induced on the sphere by gathering some electrons from the ground and the negative  remain on the sphere even after disconnecting it.

here the ground acts as a reservoir of electrons.a conducting sphere of radius r is connected to ground through a battery with a voltage vo as shown. a. assuming ground is at infinity, find the net charge on the sphere. the sphere is disconnected from the battery, and a thick shell of a neutral, polarizable material is placed around the sphere.

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5 radical 8 to the power of 3

Step-by-step explanation:

The equation of the line that passes through (3, 4) and (-1, -4) will be y = 2x - 2. Then the correct option is C.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The points are (3, 4) and (-1, -4). Then the equation of the line is given as,

(y + 4) = [(4 + 4) / (3 + 1)](x + 1)

y + 4 = 2(x + 1)

y = 2x + 2 - 2

y = 2x - 2

The equation of the line that passes through (3, 4) and (-1, -4) will be y = 2x - 2. Then the correct option is C.

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a regression equation for this formula, where x represents the number of years enrolled and y represents the tuition.

y = 34000 - 2300x

Regression is a statistical technique that connects one or more independent (explanatory) variables to a dependent variable. If there is a relationship between changes in one or more of the explanatory factors and changes in the dependent variable, it can be shown using a regression model.

The regression equation for this formula would be:

Y = 34,000 - 2,300x

where Y is the tuition cost and x is the number of years in school.

The equation states that the tuition cost for any year in school (x) is equal to the freshman year tuition cost (34,000) minus 2,300 multiplied by the number of years in school (x).For example, if x = 4 (4 years in school), then the tuition cost for that year would be 34,000 - 2,300(4) = 25,400.

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Check the picture below.

The margin of error for a sampling distribution is found as 3.34.

Margin of error = z × σ/√n

Thus, put the values;

z-score for 93% confidence level = 1.67

Margin of error = 1.67 ×12/√36

Margin of error = 3.34

Thus, the margin of error for a sampling distribution is found as 3.34.

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The system of equation that is used to determine the number of cans of soup purchased and the number of frozen dinners purchased is 300x+450(x+5)=6000mg.

A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation. The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.

Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.

Sodium contains in a can of soup is 300mg

Sodium contains in a can of frozen dinners is 450mg

Let the number of cans of soup purchased be x

Then, the number of frozen dinners purchased=x+5

Total sodium purchased=6000mg

So, 300x+450(x+5)=6000mg

Therefore, the system is 300x+450(x+5)=6000mg

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Part (d) is correct.

i.e. The variance of the random variable associated with this given experiment is 2.4510.

What is Binomial experiment?

It is an experiment with a set number of independent trials, each having the same chance of success and the two outcomes of success or failure. A binominal distribution can be used to describe the likelihood of a certain number of successes.

Given that,

No. of independent trials ( n ) = 10

Probability of success in each trail ( p ) = 0.43

∴ probability of failure in each trial ( q ) = 0.57

we can find the variance of a binomial experiment by using the formula i.e. npq.

∴ Variance = npq

                  = 10 × 0.43 × 0.57

                  = 2.4510.

Hence, part (d) matches with the answer.

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After solving, the value of Test statistic z is 1.449.

In the given question,

A sample of 1700 computer chips revealed that 36% of the chips fail in the first 1000 hours of their use.

The company's promotional literature states that 39% of the chips fail in the first 1000 hours of their use.

Then we have to find the value of z statistic.

Hypothesized proportion (p) = 36%=0.36

Sample proportion (p') = 39% = 0.39

Sample size (n) = 1700

Hence,

Test statistic z

z= (0.76-0.78)/√(0.78* 0.22/900)

z= (-0.02)/√(0.78* 0.000244)

z= -0.02/√0.00019032

z= -0.02/0.0138

z = -1.449

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The measure of an inscribed angle is half the measure of the intercepted arc:

Angles a and b sum to a right angle since inscribed between the tangent and diameter.

Then we have:

Answer: 5^2

Step-by-step explanation:

5 x 5 = 25

and (x-7)^2 = 25

The height of tree in meter is 11.5 meter after the conversion from 37.95 feet to meter.

A conversion factor is measurement value in numbers that is used in converting one unit to another unit by arithmetic operations.  

Given that a tree is 37.95 feet tall and 1 meter is 3.3 feet.

So to find 37.95 feet tree in meter we have to divide 37.95 by 3.3  

= 37.95 / 3.3

= 11.5 meter

1 meter is 3.3 feet, then 11.5 meter is 37.95 feet.

Therefore, the height of tree in meter is 11.5 meter.

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The value of n when the function g(n) assumes a value of 3 is of:

n = 10.

In the case of an inverse proportional relationship, as is the case in this problem, the output variable y is obtained as the division of the constant of proportionality k by the input variable x, as follows:

y = k/x.

Considering the variables in this problem, the equation is given as follows:

g(n) = k/n.

g(n)= 10 when n=3, hence the constant is obtained as follows:

10 = k/3

k = 3 x 10

k = 30.

Hence the equation is:

g(n) = 30/n.

When the input variable n when g(n) = 3 is obtained as follows:

3 = 30/n

3n = 30

n = 30/3

n = 10.

(we replaced the output variable g(n) by it's value and solved for the input variable)

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Answer:

Step-by-step explanation:

B because that is the letter of my first name!

The wire should be anchored to the ground to minimize the amount of wire needed 20 ft from the left pole.

What is the quadratic equation?

ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Let x (ft) be the distance from the base of the left pole to the anchor point. Since 2 poles has a distance of 30 ft, the distance from the anchor point to the right pole is 30 - x.

The wire length from the top of the left pole to the anchor point is

[tex]L^{2} _{l} = 20^{2} + x^{2} = x^{2} + 400[/tex]

Similarly for the 2nd part of the wire

[tex]L^{2} _{t} = 10^{2} + (30 - x^{2})[/tex]

= 100 + 900 - 60x + x²

= x²+ 1000 - 60x

We want to minimize the length of the wires, or [tex]L^{2} _{l} + L^{2} _{r}[/tex]

[tex]\frac{x}{\sqrt{{x}^2 + 400} } + \frac{x - 30}{\sqrt{{x}^2 + 400}} = 0[/tex]

we can take the first derivative of this and set it to 0

x = 20

Hence, the wire should be anchored to the ground to minimize the amount of wire needed  20ft.

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After using the test statistic z, P(3.6<X<53.5) = 0.967.

In the given question, suppose X is a normal random variable with mean 35 and sdev 10.

We have to find P(3.6<X<53.5).

Fro the given question,

Mean x = 35

sdev s = 10

Z = X - mu / sd

P(3.6<X<53.5) = P ( 3.6-35/10 < Z < 53.5-35/10 )

P(3.6<X<53.5) = P ( -31.4/10 < Z < 18.5/10 )

P(3.6<X<53.5) = P ( -3.14 < Z < 1.85 )

P(3.6<X<53.5) = P ( Z < 1.85) - P ( Z < -3.14)

left tail of both

P(3.6<X<53.5) = 0.9678 - 0.0008

P(3.6<X<53.5) = 0.967

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The right answer is:

Suppose X is a normal random variable with mean 35 and sdev 10. Find P(3.6<X<53.5)

Answer:

answer is c!

because it's domain is -7!!

The measure of each angle are mentioned below

What is angle ?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

The measure of each angle is

∠a = 90°

∠b = 45°

∠c = 45°

∠d = 90°

∠e = 45°

∠f = 45° {coordinate judgment angle }

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[tex] \Large{\boxed{\sf d = \sqrt{40} }} [/tex]

[tex] \\ [/tex]

The distance between two points is given by the following formula:

[tex] \Large{\sf d = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2}} [/tex]

Where:

[tex] \\ [/tex]

First, let's identify our values:

[tex] \sf (\underbrace{\sf -3}_{\sf x_A} \: , \: \overbrace{\sf 2}^{\sf y_A}) \: \: and \: \: (\underbrace{\sf 3}_{\sf x_B} \: , \: \overbrace{\sf 0}^{\sf y_B}) [/tex]

[tex] \\ [/tex]

Now, substitute these values into our formula:

[tex] \sf d = \sqrt{\sf (3 - (-3))^2 + (0 - 2)^2} \\ \\ \sf d = \sqrt{\sf 6^2 + (-2)^2} \\ \\ \sf d = \sqrt{\sf 36 + 4 } \\ \\ \boxed{\boxed{\sf d = \sqrt{40} }} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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The probability that the sum of the faces is 7 = 15/216

The value of m = 15 and the value of n = 216

In this question, we have been given three regular dice are rolled simultaneously.

We need to find the probability that the sum of the faces is 7.

When three dice are rolled simultaneously, the total number of outcomes

n(S) = 6 * 6 * 6

n(S) = 216

Let event A: sum of the faces is 7

A = {(1, 2, 4), (1, 4, 2), (4, 1, 2), (4, 2, 1), (2, 1, 4), (2, 4, 1), (1, 3, 3), (3, 3, 1), (3, 1, 3), (2, 2, 3), (2, 3, 2), (3, 2, 2), (1, 5, 1), (5, 1, 1), (1, 1, 5)}

n(A) = 15

So, the probability that the sum of the faces is 7 = 15/216

Hence, if the probability that the sum of the faces is 7 can be represented by m/n in simplest form then m = 15 and n = 216

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The rounded upper level of the 68% confidence interval estimate is

164.5 ± 3.260.

Given:

a cheese merchant looks a again at the data set about total cheese of sales, in which the sample mean is 164.5 and the sample of standard deviation is 103.

μ = x =164.5

σ = s = 103

n = 987

z score at 68 % :

= 0.9945

Confidence interval CI = x + z * s/[tex]\sqrt{n}[/tex]

= 164.5 + 0.9945 * 103 / √987

= 164.5 ± 3.260

Therefore The rounded upper level of the 68% confidence interval estimate is  164.5 ± 3.260.

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Answer:

Below

Step-by-step explanation:

You didn't include the picture......

each cube has a volume of  1/4 * 1/4 * 1/4 = 1/64 cm^3

     count the total number of cubes and multiply by  1/64

                                         to get volume in cm^3

4.84 HP is the amount of work energy used.

Given info,

A helicopter is lifting an 800-pound unit at a rate of 200 feet per minute.

1 horsepower = 550 foot-pounds per second

⇒ 800 x 200 = 160,000 foot-pounds per minute

                      = 160,000/60 foot pounds per second.

Horsepower = 160,000/60 * 550 = 428/33

                                                       = 4.848 HP

Therefore, the horsepower of work energy used is 4.84 HP

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The converse of the following conditional True which is If a polygon is a triangle, then it has exactly three sides."

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

A polygon has precisely three sides if it is a triangle. The opposite is also accurate.

Contrarily, a polygon is a triangle if it has precisely three sides. Both of the statements can be joined to create a biconditional because they are both true.

Thus, the converse of the following conditional True which is If a polygon is a triangle, then it has exactly three sides."

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