What is the probability of guessing all of the correct answers?
P(correct) = _______

The thief stole 22 oranges using algebraic equations.

To solve this problem, we need to use algebra. Let x be the number of oranges the thief stole.

According to the problem, the thief gave the guard half of the stolen oranges and two more. This means that he gave away (1/2)x + 2 oranges.

We also know that the thief was left with only 9 oranges. So we can set up the equation:

x - [(1/2)x + 2] = 9

Simplifying this equation:

(1/2)x - 2 = 9
(1/2)x = 11
x = 22

Therefore, the thief stole 22 oranges.

The problem presents us with a scenario where a thief entered an orange garden and stole some oranges. However, he was caught by the guard. In order to get rid of the guard, the thief decided to give him half of the stolen oranges and two more. As a result, the thief was left with only 9 oranges.

To solve this problem, we used algebraic equations. We let x be the number of oranges the thief stole. We also knew that the thief gave away (1/2)x + 2 oranges to the guard. Using this information, we were able to set up an equation where x - [(1/2)x + 2] = 9. Simplifying the equation, we were left with (1/2)x - 2 = 9. Solving for x, we found that the thief had stolen 22 oranges.

In conclusion, algebraic equations are a useful tool in solving mathematical problems. By setting up an equation and simplifying it, we were able to determine the number of oranges that the thief had stolen.

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To find the end behavior of the function:

We look at the graph of it:

And look at what happens when the x is to small and to big.

• When x goes to infinity the function goes to infinity.

• When x goes to minus infinity the function goes to infinity.

The other way to find this is taking the limits to infinity in each end:

Answer:

125

Step-by-step explanation:

125x5=625

125x8=1000

In a shipment of 3500 tomatoes can be expected to weight from 0.32 lb to 0.92 lb is 3340. When A vegetable distributor knows that during the month of august, the weights of its tomatoes are normally distributed with a mean Of 0.62 lb and a standard deviation of 0.15.

A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean. The standard deviation measures the degree of dispersion of a set of data. Each data point is compared to the average of all the data points, and standard deviation gives a determined value that indicates whether the data points are clustered together or dispersed. The standard deviation of a normal distribution indicates how far values deviate from the mean.

Given,

A vegetable distributor knows that during the month of august, the weights of its tomatoes are normally distributed with a mean Of 0.62 lb and a standard deviation of 0.15.

Normal variable of x = 0.32

Z = X - mean/ standard deviation

Z = 0.32 - 0.62/0.15

Z = -2

Now, normal variable of x = 0.92

Z1 = X - mean/ Standard deviation

Z1 = 0.92 - 0.62/ 0.15

Z1 = 2

Required area,

P(-2 ≤ z ≤ 2)

2P(0 ≤ z ≤2 )

2 × 0.4772

0.9542

Weight of 3500 tomatoes

3500 × 0.9542

3340

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The sum of 488 in scientific notations is 4.88 × 10^1.

We are given that;

The number = 488

Now,

488 in scientific notation

Step 1: Move the decimal point so that there is only one non-zero digit to the left of it.

488.0

The decimal point is moved one place to the left.

4.88

Step 2: Write the number as a product of the decimal and a power of 10.

The decimal point was moved one place to the left, so the exponent is 1.

4.88 × 10^1

Therefore, by the algebra the answer will be 4.88 × 10^1.

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Answer:

354 m

Step-by-step explanation:

to find the height substitute t = 3.5 into the height polynomial

height = - 16(3.5)² + 550 = - 16(12.25) + 550 = - 196 + 550 = 354

Answer:

4

Step-by-step explanation:

10 =  one time

6 = two times

4 = three times

1 = one time

mode means most, which number is there the most of

There was 110%  percent increase in the number of visitors.

Percent:

Basically, percentage refers the number or ratio that can be expressed as a fraction of 100.

Given,

p x 3,700=4,070

There was a % percent increase in the number of visitors.

Here we need to find the increase in the percentage.

While we looking into the given question we have identified that,

The Old population = 3700

And the new population  = 4070

So, the value of P is calculated as,

=> p = 4070/3700

=> p = 1.1

When we convert this into percent then we get 110% as increase.

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Answer:

neither ordered pair is a solution

Step-by-step explanation:

to determine if the pairs are a solution, substitute the x- coordinate into the left side of the equation and if equal to the right side then they are a solution.

(- 9, 3 ) with x = - 9

6(- 9) = - 54 ≠ 14 ← not a solution

(2, - 4 ) with x = 2

6(2) = 12 ≠ 14 ← not a solution

Answer:

b) y = f(x) = -3x+4

Step-by-step explanation:

Explanation

Given that the equation   9x+3y =12

Let 'x' be an independent variable and 'y' be the dependent variable then the function is of the form

        y = f(x)

      3 y = 12 - 9x

        \(y = \frac{-9x+12}{3}\)

      y = -3x+4

The function represented by  y = -3x+4

Answer: B & D

Step-by-step explanation:

In this scenario we want to come out with a situation where both sides are in an even playing field, as the equation solves to zero.

If a diver is 35 feet below water (-35) and he comes up to breathe, he goes up 35ft (35) meaning he is at the surface (0).

If Manuel is in debt for 35$ (-35) and then he pays off the 35$ (+35) then he is even (at 0).

Answer:

A diver is 35 feet below the surface of the water and then comes up to the surface.

Answer: y = |x - 4| − 10

Step-by-step explanation: Reflection over the y-axis switched the first sign and -2 was added to -8 due to the translation 2 units down.

Hope this helps!

Answer:

perimeter=16root(5) mm

area=80 mm^2

Step-by-step explanation:

perimeter of a square is =4a=4*4root(5) mm

                                               =16root(5) mm

area of a square is=a^2=(4root(5))^2=80 mm^2

Answer:

(-2y-6)(-3y-8)

= 6y²+16y+18y+48

= 6y²+ 34 y +48

Hope this helps

if u have question let me know in comments ^_^

Answer:

Here is your answer!!!

Step-by-step explanation:

-2y(-3y-8)-6(-3y-8)

6y^2+16y+18y+48

6y^2+34y+48

Answer:

5. x=80°, y= 80°

Step-by-step explanation:

5.x=80 (Vertically opposite angle V.O.A)

y=80 (alternate angle)

We can write the system of equations:

x = y + 15

x + y = 105

Solving the system, we will see that Robin has 45 apples and Linda 60 apples.

Here we can only solve the first part, as the second is incomplete.

Let's define the variables:

x = apples that Linda has.

y = apples that Robin has.

We know that Linda has 15 more apples than Robin, and that between the two there are 105 apples, so we can write the system of equations:

x = y + 15

x + y = 105

To solve this, we can replace the first equation into the second one, so we get:

(y + 15) + y = 105

2y + 15 = 105

2y = 105 - 15 = 90

y = 90/2 = 45

So Robin has 45 apples, and Linda has 15 more, so she has:

x = 45 + 15 = 60

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Answer:

.6239 as a fraction is 6239/10000.

Answer:

first term: degree=4, coefficient= -2

second term: degree=3, coefficient=1

third term: degree=1, coefficient= -8

fourth term: degree= 1, no coefficient

fifth term: degree=2, coefficient=5

Step-by-step explanation:

Answer:

Hey there!

First term, degree 4, coefficient -2.

Second term, degree 3, coefficient 1

Third term, degree 1, coefficient -8

Fourth term, degree 1, coefficient none

Fifth term, degree 2, coefficient 5

Hope this helps :)

Answer:

His average daily pay was $90.

Step-by-step explanation:

78+94+115+108+67+78=540

540/6= 90.

The value of ML = 3, using the mid-point theorem of triangles.

According to the midpoint theorem, "the line segment of a triangle crossing the midpoints of two sides of the triangle is said to be parallel to its third side and also half the length of the third side."

In the question, we are given that triangle ABC is an equilateral triangle, and L, M, and N are the midpoints of BC, AB, and CA respectively.

Thus, by the midpoint theorem, we can say that:

Assuming AB = BC = AC = x units, we get:

Thus, the triangle LMN is an equilateral triangle.

Thus, MN = ML = NL.

Given MN = 3, we can write the value of ML = 3.

Thus, the value of ML = 3, using the mid-point theorem of triangles.

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The given question is in Spanish. The question in English is:

"Triangle ABC is equilateral and L, M, and N are the midpoints of BC, AB, and CA respectively. If MN = 3, what is the value of ML?"

The determinant of the matrix is (g(b) - g(a))^2 - 4δ(g(b) - g(a))(δ(b - a)).If (g(b) - g(a))^2 - 4δ(g(b) - g(a))(δ(b - a)) = 0, then the non-trivial solution exists. Otherwise, only the trivial solution exists.

The given functions are cos(24), 1₂(x) - 1₁g(x) + CO²(x). We are to solve for C₁, C₂, and C₃ so that b) 0 on the interval (a, b). If a nontrivial solution exists, state it. If only the trivial solution exists, state that as well.Step-by-step solution:

Given functions: cos(24), 1₂(x) - 1₁g(x) + CO²(x)Let A(x) = cos(24)B(x) = 1₂(x) - 1₁g(x) + CO²(x)Consider the following conditions:

At x = a, A(a) = cos(24)At x = b, A(b) = cos(24)B(a) = 1₂(a) - 1₁g(a) + CO²(a)B(b) = 1₂(b) - 1₁g(b) + CO²(b)Condition: b) 0 on the interval (a, b)A(a) = cos(24)A(b) = cos(24)B(a) = 1₂(a) - 1₁g(a) + CO²(a)B(b) = 1₂(b) - 1₁g(b) + CO²(b)On applying integration on the given functions, we get:∫A(x)dx = cos(24)(x - x) = 0 At x = a, ∫B(x)dx = C₁(x - a) + C₂(x - a)g(a) + C₃(x - a)Owing to the conditions, we have∫B(x)dx = 0 On substituting the values of a and b, we have C₁(b - a) + C₂(g(b) - g(a)) + C₃(δ(b - a) = 0 If the determinant of the matrix is zero, then there exist non-trivial solutions for C₁, C₂, and C₃.δ is the Kronecker delta function given as:δ(t) = 1 if t = 0 and δ(t) = 0 if t ≠ 0

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Vector z can be expressed as a linear combination of vectors in S, while vectors v and w cannot be expressed in terms of S.

(a) To express vector z = (11, -8, 20) as a linear combination of the vectors in S = {(2, -1, 3), (5, 0, 4)}, we need to find scalars x and y such that z = x(2, -1, 3) + y(5, 0, 4). By solving the system of equations, we find that x = 3 and y = 1. Therefore, z = 3(2, -1, 3) + (5, 0, 4) = (11, -8, 20), so it is possible.

(b) To express vector v = (23, ?, 75, 4) as a linear combination of the vectors in S = {(2, -1, 3), (5, 0, 4)}, we add the two vectors in S together: (2, -1, 3) + (5, 0, 4) = (7, -1, 7). However, since the given vector v has a missing component denoted by "?", we cannot determine the linear combination of v using the vectors in S. Therefore, it is not possible to express v as a linear combination of the vectors in S.

(c) To express vector w = (1, -8, 12) as a linear combination of the vectors in S = {(2, -1, 3), (5, 0, 4)}, we need to find scalars x and y such that w = x(2, -1, 3) + y(5, 0, 4). However, upon solving the system of equations, we find that there are no values of x and y that satisfy the equation. Therefore, it is impossible to express w as a linear combination of the vectors in S.

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Answer:

x = 1

Step-by-step explanation:

\(\frac{2}{3}\) (9x - 6) = \(\frac{1}{4}\) (12 - 4x) ← distribute parenthesis on both sides

6x - 4 = 3 - x ( add x to both sides )

7x - 4 = 3 ( add 4 to both sides )

7x = 7 ( divide both sides by 7 )

x = 1

Answer:

\(\displaystyle y=-\frac{1}{2}(x+4)(x-2)\)

Step-by-step explanation:

We want to find a quadratic that passes through the points:

\((-4, 0), \, (2, 0), \text{ and } (6, -20)\)

In intercept form.

First, note that the first two given points are the x-intercepts of our quadratic. Intercept or factored form is given by:

\(y=a(x-p)(x-q)\)

Where p and q are the x-intercepts, and a is the leading coefficient.

So, we will substitute -4 and 2 for p and q:

\(y=a(x-(-4))(x-(2))\)

Simplify:

\(y=a(x+4)(x-2)\)

Next, the third point (6, -20) tells us that y = -20 when x = 6. So:

\((-20)=a(6+4)(6-2)\)

Solve for a:

\(-20=10(4)a\Rightarrow 40a=-20\)

Thus:

\(\displaystyle a=\frac{-20}{40}=-\frac{1}{2}\)

Hence, our equation in intercept from is:

\(\displaystyle y=-\frac{1}{2}(x+4)(x-2)\)

The values of x which are solutions to the given quadratic equation as required to be determined are; x = (1 ± i√11) / 2.

It follows from the task content that the given quadratic equation is to be solved for variable, x.

3x² + 4x - 5 = 5x² + 2x + 1;

By collect like terms and evaluating; we have that;

2x² - 2x + 6 = 0

By solving the equation by means of the formula method; we find that;

x = (1 ± i√11) / 2

Ultimately, the values of x which holds True are; x = (1 ± i√11) / 2.

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Answer:

Function 1 is negative with a slope of -5 and Function 2 is positive with a slope of 3.

Step-by-step explanation:

Slope Formula: (y2 - y1)/(x2 - x1)

Function 1: m = -2 - (-12) / 1 - 3

m = 10 / -2

m = 5 / -1

m = -5

Function 2: m = 3/1

m = 3

The ratio strength of the final product is 1:0.4.

One technique to indicate concentration is through ratio strength, which uses a ratio to characterize drug concentration. In this context, concentration is defined as the quantity of a solute that makes up one unit in the whole volume of a solution or combination. You should be an expert in ratio strength calculations as a pharmacy student. Ratio strength uses a ratio to describe the medication concentration. So, what it implies is, you have one unit of solute contained in the complete amount of preparation and so generally your ratio strength is expressed as one is to something. In the case of a weight-in-weight, volume-in-volume, or weight-in-volume situation, you would interpret a ratio of 1:2,000 differently.

Drug strength = 800mg

whole volume =2ltrs

The ratio of the solution in 1 ltr is = 400 mg

The ratio strength of the solutions is = 1:0.4

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