Two pencils and a ruler cost 98 cents in total. One pencil and 2 rulers cost $1.24 in total. Find the cost of each item.

Answer:

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To find P(A | B),  first we use the formula P(A | B) = P(A ∩ B) / P(B).To find P(B | A), we use the formula P(B | A) = P(A ∩ B) / P(A).  To determine if A and B are independent, we need to compare P(A ∩ B) with P(A)P(B). If P(A ∩ B) = P(A)P(B), then A and B are independent. If P(A ∩ B) ≠ P(A)P(B), then A and B are dependent.

a. Plugging in the given values, we have:
P(A | B) = 0.20 / 0.50 = 0.40
So, P(A | B) = 0.4000 (to 4 decimals).

b. Plugging in the given values, we have:
P(B | A) = 0.20 / 0.50 = 0.40
So, P(B | A) = 0.4000 (to 4 decimals).

c. Given values are:
P(A) = 0.50
P(B) = 0.50
P(A ∩ B) = 0.20
Calculating P(A) * P(B):
0.50 * 0.50 = 0.25

Since P(A ∩ B) ≠ P(A) * P(B), events A and B are not independent. The occurrence of one event affects the probability of the other event occurring.

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The polynomials are multiplied to give the expression x³ + 3x² - 22x - 24

We need to know that algebraic expressions are described as expressions that are composed of terms, variables, their coefficients, factors and constants.

Also, these expressions are made up of mathematical operations. They are listed as;

From the information given, we have the expression;

(x+6)(x2−3x−4)

expand the bracket, we get;

x³ - 3x² - 4x + 6x² - 18x - 24

add the like terms, we get;

x³ + 3x² - 22x - 24

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The area of the region bounded by the two lines is 19 square units.

The two lines intersect at the point where they have the same

y-coordinate, so we can set y=3x-6 equal to y=-2x+8 and solve for x:

3x - 6 = -2x + 8

5x = 14

x = 2.8

Therefore the two lines intersect at x=2.8, and the corresponding y-coordinate is y = 3(2.8) - 6 = 6.4.

We can find the coordinates of the two other corners of the region by setting x=0 and x=5:

x=0: y = 3(0) - 6 = -6

x=5: y = 3(5) - 6 = 13

So the other two points are (0, -6) and (5, 13).

We will use the Shoelace Theorem to find the area:

A = 1/2 * |(0 * 6.4) + (2.8 * 13) + (5 * -6) - (6.4 * 5) - (13 * 2.8) - (-6 * 0)|

A = 1/2 * |(0 * 6.4) + (37.4) + (30) - (32) - (36.4) - 0|

A = 1/2 * |37.4 + 30 - 32 - 36.4|

A = 1/2 * |38| = 19

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Answer:

Step-by-step explanation:

Answer:

$36

Step-by-step explanation:

Use the simple interest formula, I = prt

Plug in the interest rate, original amount of money, and number of years:

I = prt

I = (150)(0.08)(3)

I = 36

So, $36 in interest would be made

Answer:

-4

Step-by-step explanation:

9-8=1

1x-2=-2

-2x2=-4

well, let's noticed, the original amount is $271 and 12 years later it turned to $417, so

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$417\\ P=\textit{initial amount}\dotfill &271\\ r=rate\to r\%\to \frac{r}{100}\dotfill &0\\ t=years\dotfill &12\\ \end{cases}\)

\(417=271(1 + \frac{r}{100})^{12}\implies \cfrac{417}{271}=\left( \cfrac{100+r}{100} \right)^{12} \implies \sqrt[12]{\cfrac{417}{271}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[12]{\cfrac{417}{271}}=100+r\implies 100\sqrt[12]{\cfrac{417}{271}}-100=r\implies {\Large \begin{array}{llll} \stackrel{\%}{3.657\approx r} \end{array}}\)

Answer:

b= 16√15 or 23

Step-by-step explanation:

Input your values into the Pythagorean theorem.

c^2=a^2+b^2

576=36+b^2

b=√540

b=16√15 or 23

Answer:

\(\displaystyle y = x + 6\)

Step-by-step explanation:

The line diagonally intersects the y-intercept of \(\displaystyle [0, 6],\)and through every endpoint in its way, therefore the b-value is 6 and the rate of change is 1.

I am joyous to assist you at any time.

A function assigns the value of each element of one set to the other specific element of another set. The value of the function f(-2) when the value of x is -2 is -8.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

First, we'll try to form the function based on the given statements

F(x) = {Part 1 : \(x^{3}\) x< -3 , Part 2 : 2\(x^{2}\) - 9 -3\(\leq\)x<4 , Part 3 : 5x+4 x\(\geq\)4 }

As the value of the function is needed to be found when the value of f(x) when x is -2, therefore, we can write the function as,

So from the piecewise function we'll use the Part 1 function to find the value of f(-2)

f(x) = \(x^{3}\)

f(-2) = \((-2)^{3}\)

f(-2) = -8

Hence, the value of the function f(-2) when the value of x is -2 is -8.

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Answer:

its -1

Step-by-step explanation:

I got it right on the test

Answer:

Step-by-step explanation:

Answer:

(B)

Step-by-step explanation:

4 cans - $0.98

1. $0.98/4 = $0.245 will cost 1 can

2. $0.245 × 5 = $1.225 will cost 5 cans

so $1.225 = $1.23

so the answer is B

Answer:

if you need help with some subjects you can come here in brainly it helps me a lot i just started grad 6 so yeah

like if you have a math question just go to ask question you and someone will help

Answer:

Step-by-step explanation:

The expected value of one six-sided dice is (1 + 2 + 3 + 4 + 5 + 6)/6 = 3.5.

So, the expected value of the sum of 222 dice is 3.5 * 222 = 777.

This means that the expected value of playing this game is 0, since the expected outcome is to break even.

Thus, Carlos's expected value of playing this game is 0, rounded to the nearest cent.

Answer:

Step-by-step explanation:

The expected value of Carlos playing this dice game is

$0.42

Answer: A

Step-by-step explanation: I has a negative slope, which means that its line is shaped like a backslash. This graph is shaped like a forward slash, so it cannot be that one. III is a quadratic equation in factored form. The graph for a quadratic equation is shaped like a U or an upside down U, so it cannot be that one either. Using process of elimination, the only one that it can be is A, II and III.

I also used Desmos graphing calculator to double check and I was right. Here it is:

The appropriate test to compare one sample to another sample to see if one is greater than another in some way is called a "two-sample hypothesis test."

In a two-sample hypothesis test, the null hypothesis states that there is no significant difference between the means of the two samples, while the alternative hypothesis states that there is a significant difference between the means.

The specific type of test used depends on several factors, including the type of data being compared, the sample sizes, and the level of significance desired. Commonly used tests include the t-test, z-test, and ANOVA.

It is important to choose the appropriate test for the data being analyzed to ensure accurate results and conclusions.

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Each point in a scatter plot represents a single observation of the two numerical variables being plotted.

The x-coordinate of the point represents the value of one variable, and the y-coordinate represents the value of the other variable. The position of the point on the plot provides information about the relationship between the two variables for that particular observation.

A scatter plot is a useful tool for visualizing the relationship between two numerical variables because it allows us to easily see patterns in the data. The position of each point on the plot represents the values of the two variables for a single observation, which makes it easy to spot trends or clusters in the data. By plotting multiple points on the same graph, a scatter plot allows us to see patterns that might be difficult to discern from a list of raw data. Additionally, it can help identifying outliers, correlation, and distribution of the data.

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The required C is the independent variable and X is the dependent variable.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given function,
F = 9/5C + 32

Where C > -273.15
Since the value of C in the function is justified while the value of F is not, So F will be the dependent variable and C will be the independent variable.

Thus, the required C is the independent variable and X is the dependent variable.

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According to the question The probability that a New York teenager owns a skateboard or a bicycle is 0.82.

Let's denote the event of owning a skateboard as \(\(A\)\) and the event of owning a bicycle as \(\(B\).\)

We are given:

\(\(P(A) = 0.37\)\) (probability of owning a skateboard)

\(\(P(B) = 0.81\)\) (probability of owning a bicycle)

\(\(P(A \cap B) = 0.36\)\)  (probability of owning both skateboard and bicycle)

To find the probability that the teenager owns a skateboard or a bicycle    \((\(A \cup B\))\) , we can use the formula:

\(\[P(A \cup B) = P(A) + P(B) - P(A \cap B)\]\)

Substituting the given values:

\(\[P(A \cup B) = 0.37 + 0.81 - 0.36\]\)

Calculating:

\(\[P(A \cup B) = 0.82\]\)

Therefore, the probability that a New York teenager owns a skateboard or a bicycle is 0.82.

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Using the formula °F = 1.8°C +32°, The temperature in Degrees Celsius of an oven that is 500°F is 260°C.

For everyday purposes, Fahrenheit is used in the United States, its territories, and related states (all of which are covered by the U.S. National Weather Service), as well as in Liberia, the Cayman Islands, and other places. For instance, temperatures for freezing, cooking, and other conditions are typically given in degrees Fahrenheit in the United States.

On the Celsius scale, one of the two temperature scales used in the International System of Units along with the Kelvin scale, the unit of temperature is the degree Celsius. The term "degree Celsius" can be used to describe either a specific temperature on the Celsius scale or a measurement of the difference between two temperatures.

Here,

°F=1.8°C+32°

500°F=1.8°C+32°

1.8°C=468°F

°C=468/1.8

°C=260°C

The temperature in Degrees Celsius of an oven that is 500°F is 260°C by using the formula °F = 1.8°C +32°.

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Answer:Answer:The equation that could be used to determine the length of each of the four pieces of wood he cut is 3.5 = 0.6 + 4x and the solution is x = 0.725

Part A: Write an equation that could be used to determine the length of each of the four pieces of wood he cut.

Represent the length of the four pieces with x

So, the given parameters are:

Initial length = 3.5 feet

Remaining length = 0.6 feet

Number of pieces = 4

The equation that could be used to determine the length of each of the four pieces of wood he cut is represented as:

Initial length = Remaining length + Number of pieces * x

This gives

3.5 = 0.6 + 4x

Hence, the equation that could be used to determine the length of each of the four pieces of wood he cut is 3.5 = 0.6 + 4x

Part B: Explain how you know the equation from Part A is correct.

The equation in part (A) is correct because it can be used to determine the length of each of the four pieces of wood he cut

Part C: Solve the equation from Part A.

In part A, we have:

3.5 = 0.6 + 4x

Subtract 0.6 from both sides

2.9 = 4x

Divide both sides by 4

x = 0.725

Hence, the solution is x = 0.725

Step-by-step explanation:

Hope I helped ;)

The equation of the quadratic function that passes through these points is:

\(y = -3x^2 - 12x - 8.\)

What is quadratic equation?

A quadratic equation is a polynomial equation of the second degree, which means it contains one variable with an exponent of 2. The general form of a quadratic equation is:

\(ax^2 + bx + c = 0\)

Using polynomial interpolation with these 5 points, we can find a quadratic polynomial that passes through all the points. Let the equation of the polynomial be \(y = ax^2 + bx + c\).

Using the point (0, -8), we get:

\(-8 = a(0)^2 + b(0) + c\)

c = -8

Using the point (-1, 1), we get:

\(1 = a(-1)^2 + b(-1) - 8\)

a - b = 9

Using the point (-3, 1), we get:

\(1 = a(-3)^2 + b(-3) - 8\)

9a - 3b = 27

Using the point (-4, -8), we get:

\(-8 = a(-4)^2 + b(-4) - 8\)

16a - 4b = 0

Using the point (-2, 4), we get:

\(4 = a(-2)^2 + b(-2) - 8\)

4a - 2b = 12

Solving this system of equations, we get:

a = -3

b = -12

c = -8

Therefore, the equation of the quadratic function that passes through these points is:

\(y = -3x^2 - 12x - 8.\)

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56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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Answer: Melinda’s loan will be equal to the value of the car after 10 months.

Step-by-step explanation:

Hi, to answer this question we have to equal both equations:

Melinda’s loan will be equal to the value of the car

y = y

10,000 – 250x = 8,000 – 50x

Solving for x:

10,000-8,000 = -50x+250x

2,000 = 200x

2,000/200 =x

10 = x

Melinda’s loan will be equal to the value of the car after 10 months.

Feel free to ask for more if needed or if you did not understand something.

Answer:

IJ = 68.6 feet

Step-by-step explanation:

In ΔHIJ, the measure of ∠J=90°, the measure of ∠H=84°, and HI = 69 feet. Find the length of IJ to the nearest tenth of a foot.

We solve the above question using the Trigonometric function of Sine

sin x = Opposite/Hypotenuse

x = ∠H=84°

Opposite = IJ

Hypotenuse = HI = 69 feet.

Hence

sin 84 = IJ/69

Cross Multiply

IJ = sin 84 × 69

IJ = 68.62201078 feet

Approximately = 68.6 feet

Answer:

yeeet

Step-by-step explanation:

Given that we have to find the probability of each of the following when we roll a pair of fair dice:

Probability of getting a sum of 1 = 0

Probability of getting a sum of 5= {4}/{36}=0.1111

Probability of getting a sum of 12= {1}/{36}= 0.0278

Explanation: When we roll a pair of dice, there are 36 possible outcomes or events. When we roll the dice, the number on the dice will be an integer from 1 to 6.

The following table represents the possible outcome when we roll a pair of dice.

There is only one way to obtain the sum of 1, i.e., when both dice show 1. As there is only one way, the probability is 0.

There are 4 possible ways to obtain the sum of 5. They are (1,4),(2,3),(3,2),(4,1). The probability is 4/36.

There is only one way to obtain the sum of 12, i.e., when both dice show 6. As there is only one way, the probability is 1/36.

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Answer:

61

Step-by-step explanation:

By the triangle midsegment theorem, 2(SP)=RQ.

So, 2(x-16)=x+29, meaning x=61.

The area of triangle FGH to the nearest square centimeter is 73787 cm².

Using the trigonometric triangle's surface area formula, A = \(\frac{1}{2}\) × base × height, we first need to find the length of the base by applying the law of cosines:

g² = f² + h² - 2fhcos(G)

920² = f² + 950² - 2f950cos(110°)

f² - 1900f × cos(110°) + (920² - 950²) = 0

Solving for f using the quadratic formula, ax² + bx + c = 0, the solutions for x are given by:

f² - 1900f × cos(110°) + (920² - 950²) = 0

x = (-b + \(\sqrt{}\)(b² - 4ac)) ÷ 2a

In this case, a = 1, b = -1900 × cos(110°) and c = 920² - 950².

f = (-(-1900 × cos(110°)) + \(\sqrt{}\)((-1900 × cos(110°))² - 4(1)(920² - 950²))) ÷ 2(1)

f ≈ 1683.34 cm

Thus, the area of the triangle:

A = \(\frac{1}{2}\) × f × h × sin(F)

A ≈ 73786.71 cm²

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The complete question is:

In triangle FGH, g = 920 cm, h = 950 cm and angle F=110°. Find the area of the triangle FGH, to the nearest square centimeter.