use substitution to solve the system 3x+8y = -56 2x-y = 7

Answer:

8/18

Step-by-step explanation:

the probability of the marble being red is 5/9 and it being blue is 4/9

so the probability of it being a blue marble two times is

4/9 + 4/9

=

8/18

Vertically compressing the exponential parent function f(x) = 2^x by a factor of 3 means multiplying every function value by 1/3, resulting in a steeper and narrower curve closer to the x-axis.

If we vertically compress the exponential parent function f(x) = 2^x by a factor of 3, it means that every point on the graph of the function will be compressed closer to the x-axis. In other words, the function values will be multiplied by 1/3.

Let's consider a point on the original exponential function, (x, f(x)). After the vertical compression, this point will have the coordinates (x, (1/3)f(x)). For example, if f(x) = 8 for some x, after compression, the corresponding point will be (x, (1/3)(8)) = (x, 8/3).

This vertical compression affects all points on the graph uniformly, resulting in a steeper and narrower curve compared to the original exponential function.

The y-values of the compressed function will be one-third of the y-values of the original function for each x-value. Therefore, the graph will be squeezed vertically, with the y-values closer to the x-axis.

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The mean should be set to 12.07 ounces, so that 1% of the cups will overfill.

12 + (0.07 * 2) = 12.14; 12.14 - (12.14 * 0.01) = 12.07

The mean amount of coffee to be dispensed should be set to 12.07 ounces in order to allow 1% of the cups to overfill. This is calculated by taking the normal value of 12 ounces, and adding the standard deviation of 0.07 ounce, resulting in 12.14 ounces. Then, 1% of that value is subtracted, giving 12.07 ounces. This amount will ensure that 1% of the cups will overfill, while the other 99% will be filled to the normal value of 12 ounces. This is beneficial for the customer, as it guarantees that no cup will be underfilled. It also ensures that the vending machine will not waste any coffee by overfilling the cups too much. Setting the mean to 12.07 ounces is the best solution for both the customer and the vending machine.

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The solution for the given expression is given below:

a. vertical asymptote. b. the graph of f will pass through the point (0, 15). c. to keep f(x) within 0.01 units of 7, we need to keep x between 2.9986 and 3.0014.

What is expression?

In general, an expression is a combination of symbols, numbers, and/or operators that can be evaluated to produce a value. In programming, an expression typically refers to a sequence of one or more operands and operators that can be evaluated to produce a single value.

a. When x = 3, the denominator of f(x) becomes zero, and therefore f(3) is undefined (or does not exist). This is called a vertical asymptote.

b. To plot the graph of f, we can factor the numerator as follows:

f(x) = (4x-3)(x-5)/(x-3)

The graph of f will have a vertical asymptote at x = 3, and the function will be undefined at that point. The factor (4x-3)(x-5) has zeros at x = 3/4 and x = 5, so the graph will cross the x-axis at those points. We can also find the y-intercept by setting x = 0:

f(0) = (4(0)-3)(0-5)/(0-3) = 15

Therefore, the graph of f will pass through the point (0, 15).

c. The limit of f(x) as x approaches 3 is given by:

lim[x→3] f(x) = lim[x→3] (4\(x^2\)-17x+15)/(x-3) = 7

To find how close to 3 we need to keep x in order for f(x) to be within 0.01 units of 7, we can use the definition of a limit:

|f(x) - 7| < 0.01

This inequality can be rewritten as:

-0.01 < f(x) - 7 < 0.01

\(-0.01 < (4x^2-17x+15)/(x-3) - 7 < 0.01\)

Solving for x using this inequality is difficult, but we can use a graphing calculator or a numerical method to find the values of x that satisfy it. For example, using a graphing calculator, we can graph the function (4x^2-17x+15)/(x-3) and the horizontal lines y = 7.01 and y = 6.99, and find the values of x where the graph intersects those lines. We get:

x ≈ 3.0014 and x ≈ 2.9986

Therefore, to keep f(x) within 0.01 units of 7, we need to keep x between 2.9986 and 3.0014.

Similarly, to find how close to 3 we need to keep x in order for f(x) to be within 0.0001 units of 7, we can use the inequality:

|f(x) - 7| < 0.0001

This inequality can be rewritten as:

-0.0001 < f(x) - 7 < 0.0001

\(-0.0001 < (4x^2-17x+15)/(x-3) - 7 < 0.0001\)

Using a similar method as before, we can find that we need to keep x between approximately 2.99994 and 3.00006 to keep f(x) within 0.0001 units of 7.

To keep f(x) arbitrarily close to 7 just by keeping x close to 3 but not equal to 3, we can use the fact that the function approaches 7 as x approaches 3 from both sides. This means that we can make f(x) as close to 7 as we want by choosing a small enough positive or negative deviation from 3.

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Answer:

2 * ( x+2.9) = 97.4

2x + 5.8 = 97.4

2x = 97.4 - 5.8

2x = 88.9

x = 88.9 / 2

x = 44.45

Answer:

10 multiply 40, 10 multiply 3, 7 multiply 40, and 7 multiply 3.

Step-by-step explanation:

hope it helps!

Answer:

If eight students pay $50 each, then the total cost is 8 x $50 = $400. If three students back out, then the remaining five students will have to pay a higher amount to cover the cost. The new cost per student is $400/5 = $80.

As per the set theory, the number of student who take math course is 800

Set:

In math, set means an organized collection of objects and can be represented in set-builder form or roster form.

Given,

Here we know that suppose that all of the 1000 first-year students at a certain college are enrolled in a math or an English course. suppose 400 are taking both math and English and 600 are taking English.

Now, we need to find the number of students who take math course.

While looking into the given question we have identified that,

Total Number of students = 1000

Number of students in both course = 400

Number of students taking English = 600

Then the number of students who take math course is calculated as

=> 1000 - 600 + 400

=> 800

Therefore, the resulting number of students is 800.

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Given:

Drawing a vowel from letter tiles that spell out MATHEMATICS.

Chances = \(\dfrac{?}{?}\)

To find:

The correct values for the blanks.

Solution:

Vowels are a, e, i, o, u.

In MATHEMATICS, the vowels are A, E, A, I.

Number of vowels = 4

We know that,

\(Probability=\dfrac{\text{Number of selected vowels}}{\text{Total number of vowels}}\)

\(Probability=\dfrac{1}{4}\)

So, the chance of drawing a vowel from letter tiles that spell out MATHEMATICS is \(\dfrac{1}{4}\).

Blank 1: 1

Blank 2: 4

Therefore, the value for blank 1 is 1 and the value for blank 2 is 4.

30

Given the expression for the instantaneous voltage expressed as:

Given the following parameter:

θ = 30⁰

Substitute the given parameter into the formula to have:

Therefore the instantaneous voltage when θ = 30⁰ is 30.

Answer:

88 dollars

Step-by-step explanation:

8 x 6 = 48 dollars (hours)

600 x .05 = 40 (commissions)

48 + 40 = 88 total dollar

Answer:

End of Unit Project: Mathdonalds, Chez Mathématiques, and Was 7×3, Is 10 + 11, Always Will Be 30 – 9.

Step-by-step explanation:

Therefore, after 10 payments, Jeff owes $1160.

Since $1160 is less than $2200, we can conclude that Jeff's furniture costs less than Ella's.

A mathematical equation, such as 6 x 4 = 12 x 2, can be used to compare two amounts or values. a significant noun. An equation is employed when it's required to integrate two or more elements in order to understand or fully explain a situation.

To determine whose furniture costs more, we need to compare the amounts owed by Jeff and Ella for the same number of payments.

Jeff's equation is y = -108x + 2240, which gives the amount owed after x payments.

Ella's graph does not have an equation provided, but we can see that after 10 payments, she owes approximately $2200.

To compare the amounts owed after 10 payments, we can substitute x = 10 into Jeff's equation:

y = -108(10) + 2240

y = -1080 + 2240

y = 1160

Therefore, after 10 payments, Jeff owes $1160.

Since $1160 is less than $2200, we can conclude that Jeff's furniture costs less than Ella's.

Answer: Ella's furniture costs more than Jeff's.

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Area of region A is equal to the sum of area of region B and area of region C when a right-angled triangle is formed by the diameters of three semi-circular regions A, B, and C.

Let the diameters of semicircle A, B and C be a, b and c respectively.

We know area of a semi-circular region of diameter d is

A = (1/2)(πd²/4)

A = πd²/8

Thus,

area of region A is πa²/8

area of region B is πb²/8

area of region C is πc²/8

The triangle formed is a right angled triangle, with hypotenuse a and legs b and c. By Pythagoras theorem

a² = b² + c²

Multiplying both sides by π/8

(π/8)a² = (π/8)(b² + c²)

πa²/8 = πb²/8 + πc²/8

Area of region A = Area of region B + Area of region C

Hence proved.

--The question is incomplete, answering to the question below--

"A right-angled triangle is formed by the diameters of three semi-circular regions A, B, and C as shown in the diagram. Show that area of region A = area of region B + area of region C."

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True. It's because the capacitance between two plates depends on the electric field between them, which is naturally geometry-dependent; if you have charges in different places, you get a different electric field.

A capacitor's capacitance is affected by the area of the plates, the distance between the plates, and the dielectric's ability to support electrostatic forces.
The capacitance of a parallel plate capacitor (depending on its geometry) is given by the formula C=Ad C = A d, where C is the capacitance value, A is the area of each plate, d is the distance between the plates, and is the permittivity of the material between the parallel capacitor's plates.
The curvature of the plates indicates whether the plates are spherical or cylindrical. As a result, the only factor that has no effect on the capacitance of the capacitor is the type of material used to make the plates.

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Answer:

232.74

Step-by-step explanation:

We can do $215 times 1.0825 to find the cost. This gets us 232.74 rounded up.

Answer:

how do I get started here

Answer:

a juice bo has 20% more juice than the original package. the original package holds 12 ounces.

first find what 100% of 12 is. 12 obvi. then divide 12 by 10 to get what 10% is. 10% of 12 is 1.2 so multiply 1.2 by 2 which is 2.4, and thats 20% of 12.

now add 2.4 to 12, and you get 14.4, how much the new juice box holds

The following hyperbolas have horizontal openings:

(A) (x+2)^2/3^2-(2y-10)^2/8^2=1

(B) (x-1)^2/6^2-(2y+6)^2/5^2=1

A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.

A hyperbola is made up of two mirror images of one another that resemble two infinite bows.

These two sections are known as connected components or branches.

The collection of points in a plane known as a hyperbola has constant distances from two fixed points known as its foci.

So, a hyperbola with the following equation opens horizontally:

(x-h)^2/a^2-(y-k)^2/b^2)=1

The following are hyperbolas that open horizontally:

(x+2)^2/3^2-(2y-10)^2/8^2=1

(x-1)^2/6^2-(2y+6)^2/5^2=1

Therefore, the following hyperbolas have horizontal openings:

(A) (x+2)^2/3^2-(2y-10)^2/8^2=1

(B) (x-1)^2/6^2-(2y+6)^2/5^2=1

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As range doesn't reveal anything about the distributive property of the data, it is the least helpful measure of variability because it is the most generic.

1. Sort the data either ascendingly or descendingly.

2. Determine how many items are in the data set.

3. The median is the number in the middle of the list if the number of items is odd.

4. The median is the average of the two middle numbers in the list if the number of items is even.

To figure out the range:

1. Sort the data either ascendingly or descendingly.

2. To determine the range, deduct the smallest number from the largest.

As range does not reveal anything about the distribution of the data, it is the least useful measure of variability because it is the most generic. Range does not indicate where the values fall within the range; rather, it measures the difference between the highest and lowest values in a data collection.

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Answer:

31 is the missing angle

Step-by-step explanation:

Right Angle = 90 degrees

90 - 59 = 31 degress

25% discount means we pay 100% - 25% = 75% of the original price.

Relationship between sale price and regular price?

SalePrice = (1 - 25/100) × RegularPrice

Sale price is 75% of regular price.

The soccer ball reaches a maximum height of approximately 34.8 feet.

The parametric equations for the motion of the soccer ball are:

x(t) = 39*cos(44°)t ≈ 26.9t

y(t) = \(39\sin(44)*t - 16t^2\) ≈ \(22.7t - 16t^2\)

where t is the time elapsed since the ball was kicked.

To find the maximum height of the ball, we need to find the vertex of the parabolic trajectory given by y(t).

The maximum height occurs at the vertex, which is at the time t = -b/2a, where a = -16 and b = 39*sin(44°).

So, t = -b/2a ≈ 1.1 seconds.

Substituting this value of t into the equation for y(t), we get the maximum height:

y(max) = \(39*\sin(44)1.1 - 16(1.1)^2 = 34.8 feet.\)

Therefore, the soccer ball reaches a maximum height of approximately 34.8 feet.

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1. We notice that the claim stating "if p is a prime number, then p^2 is composite" is false. We provided a counterexample, which was the prime number 2, showing that its square (2^2) is not composite but rather a perfect square. 2. The square of a prime number does not necessarily correspond to the golden ratio.

The golden ratio, often denoted by the Greek letter φ (phi), is approximately equal to 1.6180339887. It is a mathematical constant that has various geometric and mathematical properties. The golden ratio is typically derived from the quadratic equation x^2 = x + 1, where the positive solution is φ.

In the case of the claim we discussed, there is no direct relationship between the square of a prime number and the golden ratio. The golden ratio arises from a specific quadratic equation and is unrelated to the properties of prime numbers and their squares.

The claim about the square of a prime number being composite does not have any direct correspondence to the golden ratio. The golden ratio is derived from a distinct mathematical equation, and its properties are not influenced by the nature of prime numbers or their squares. Therefore, there is no connection between the claim discussed earlier and the golden ratio.

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Answer:

x=120 I believe

Step-by-step explanation:

use corresponding angles to make this equation:

20+40+x=180

60+x=180

x=120

Answer i dont know the amount of the items

Step-by-step explanation:

give us the amount of them please

The four criteria that can be used to prove triangles are congruent and can be used to prove the triangles are congruent.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. These triangles can be moved around, rotated, flipped, and turned to have a same appearance. They match up with one another when moved.

The four criteria that can be used to prove triangles are congruent are SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SSS (Side-Side-Side). Additionally, CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can be used to prove the triangles are congruent.

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Answer: Since this is the right triangle so

\(Sin B = \frac{AC}{AB} =\frac{AC}{6} \\=> AC = sin(20) * 6 = 5.478 = 5.48\)

Apply Pythagorean theorem:

\(AC^{2} +CB^{2} =AB^{2} \\5.48^{2} +CB^{2} =6^{2}\)

\(CB = \sqrt{6^{2} -5.48^{2} } = 2.44\)