solve these simultaneous equations
4a+3b=-9
2a+5b=-1

Jorge has a ticket has a probability of 0.3 of winning a prize. after seven days, probability that jorge has won at least one prize is 0.9176

Let the probability of Jorge winning be 0.3 so ,

Probability of not winning be (1-0.3)⁷

(0.7)⁷

= 0.0823

Therefore, Jorge not winning is 0.0823.

If he wins at least one prize is,

1 - P(win nothing)

1 - 0.0823

= 0.9176

Therefore, the probability that the Jorge wins at least one prize is 0.9176.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

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If the probability of Dan winning is 'p', then the probability that he does not win is ' 1-p' .

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. The probability of a event happening and the same event not happening is 1 or 100%.

Let Dan winning in a raffle is Event A.

Let Dan not winning in a raffle is Event B.

Probability of Dan winning + Probability of not winning = 1

   p + P(B) = 1

P(B) = 1 - p

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Median of the probability distribution is 1.

Correct option is B.

The median of a set of data is the middlemost number or center value in the set. The median is also the number that is halfway into the set.

The median for a random variable X is m such that P(X≤m)≥1/2 and P(X≥m)≥1/2.

Given,

The probability distribution for the number of events in which a student competes is provided.

X is number of events,

P(X) is probability

Here,

For median value, P(x) ≥ 1/2

P(x) = 4/8 = 1/2

Value of X for P(x) = 1/2 is 1.

Median = 1

Hence, 1 is the median of probability distribution.

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Answer:The function rule for Thalia's height (h) in years (t) is h(t) = 104 + 2.2t.

The linear function's parameters are: h0 = 104 (initial height), and k = 2.2 (the rate of growth in cm per year).

The function rule for the population of manatees (P) in years (t) is P(t) = 5,067 * (1.011)^(-t), where t is the number of years passed since 2011.

The exponential function's parameters are: P0 = 5,067 (the initial population), t (the number of years passed since 2011), and k = 0.011 (the decay rate).

Problem 3 describes decay. The population of manatees is decreasing by a certain percentage each year, indicating a decrease in the number of animals over time.

The decay rate in problem 3 is 1.1% (or 0.011 in decimal form).

Step-by-step explanation:

1.) The function rule (equation) for Thalia's height over time can be modeled as h(t) = 104 + 2.2t, where h(t) is her height in cm at time t in years.

2.) In the equation for Thalia's height, 104 is the y-intercept and 2.2 is the slope.

3.) The function rule for the manatee population in Florida can be modeled as P(t) = P0 * 0.989^t, where P(t) is the population at time t in years and P0 is the initial population (5,067).

4.) In the equation for the manatee population, P0 is the initial population and 0.989 is the decay rate. The independent variable is t (time in years) and the dependent variable is P (population).

5.) Problem 3 describes decay. This is because the population of manatees in Florida is decreasing at a constant rate of 1.1% per year.

6.) The growth or decay rate in problem 3 is -1.1%.

Step-by-step explanation:

hope you appreciate it.

This inequality can be expanded to x - 214 ≤ -23, which means that any value of x that is less than or equal to -23 satisfies the inequality.

1. x + 191 ≥ 214

2. x - 214 ≤ -23

1. To solve this inequality, we add 23 to both sides of the equation: x - 23 = 191.

x + 191 ≥ 214

2. To solve this inequality, we subtract 191 from both sides of the equation: x - 23 = 191.

x - 214 ≤ -23

1. x + 191 ≥ 214

This inequality can be expanded to x + 191 ≥ 214, which means that any value of x that is greater than or equal to 214 satisfies the inequality.

2. x - 214 ≤ -23

This inequality can be expanded to x - 214 ≤ -23, which means that any value of x that is less than or equal to -23 satisfies the inequality.

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The sum in degrees of Angle A and Angle B is 28 degrees

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

3x + 2 = x + 10

This means that

2x = 8

Divide by 2

x = 4

S, we have

Sum = 3x + 2 + x+ 10

Evaluate

Sum = 3 * 4 + 2 + 4 + 10

Sum = 28

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The expression for x² in standard form is x² = (yˣ×10)²= y²×10².

Expression  is a mathematics combination of symbol such as number and operators which produce the mathematical result and expression can involve a single trauma multiple term and usually consist of a combination of constant variables operators function.

This means that if x is given in the form of x = y×10, then x² can be expressed as y² × 10². This form is advantageous because it allows for easier manipulation of the numbers. For example, if x = 5 ×10², then x²can be expressed as (5×10²)²= 5²× 10²×²= 25 × 10⁴. This expression is much easier to understand than the expanded form of x² = 5²× 10² × 10² = 25 ×10².

In addition, this expression for x²allows for efficient calculation of larger powers of x. For example, if x = 5 ×10², then x²can be expressed as (5×10² = 5³ × 10²×³= 125 × 10⁶. This is much faster to calculate than the expanded form of x³= 5³ ×10² ×10²× 10² = 125 ×10⁶.

Therefore, the expression for x² in standard form is an effective way to manipulate and calculate larger powers of x.

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Answer:

x = 2

Step-by-step explanation:

Product = muliplication

Let x represent the number

14x = 28

x = 2

Answer: -12

Step-by-step explanation: -6*-2 = 12 and then 12*-1 = -12.

Answer: -12

Step-by-step explanation:

-6 x -2 x-1

12 x -1

-12

Answer:

The length of the hypotenuse is 6.4 yards.

Step-by-step explanation:

We can use the Pythagorean Theorem to evaluate the hypotenuse.

The formula for the Pythagorean Theorem is

[tex]a^2+b^2=c^2[/tex]

Where [tex]a[/tex] and [tex]b[/tex] are the legs of the triangle; and [tex]c[/tex] is the hypotenuse.

We are given the values of both legs.

[tex]a=4\\b=5[/tex]

Inserting these values into the equation gives us

[tex]4^2+5^2=c^2[/tex]

Lets solve for [tex]c[/tex].

Evaluate [tex]4^2[/tex].

[tex]16+5^2=c^2[/tex]

Evaluate [tex]5^2[/tex].

[tex]16+25=c^2[/tex]

Add [tex]16[/tex] and [tex]25[/tex].

[tex]41=c^2[/tex]

Take the square root of both sides to eliminate the exponent.

[tex]\sqrt{41} =c[/tex]

[tex]\sqrt{41}=6.40312[/tex]

Rounding to the nearest tenth leaves us with

[tex]c=6.4[/tex]

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The percent error would be : {c - 78}/{c} x 100

Given is that the team ends up selling 78 cookies at next year's opening game.

Let the estimated value be {c} cookies. Now, we know -

%error = {a - x}/{x} x 100

%error = {c - 78}/{c} x 100

Therefore, the percent error would be : {c - 78}/{c} x 100.

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The solution of the expression (9t³n³)(−2t n²) will be -18t⁴n⁵.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is (9t³n³)(−2t n²). The given expression will be solved as:-

E =  (9t³n³)(−2t n²)

E = 9 x -2 x t³ x t x n³ x n²

E = -18 x t³⁺¹ x n³⁺²

E = -18t⁴n⁵

Therefore, the solution of the expression is E = -18t⁴n⁵.

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According to the data, the highway is 84 miles, the length of Valley Road is 60 miles, and the shortest mile is 24 miles less than the longest.

To calculate the length of the Highway route we must perform the following mathematical procedure:

To calculate the length of the Valley Road Route we must perform the following mathematical procedure:

To calculate the length that is saved by taking the shortest route we must carry out the following mathematical procedure:

Note: This question is incomplete due to missing information. Here is the missing information.

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Answer: 78

Step-by-step explanation:

(3) + 3 = 6

6(3) - 5 = 13

13 x 6 = 78

:)

Answer:

54.9

Step-by-step explanation:

Substitute the provided values of x and y into the provided expression:

           8.3(3) + 7.5(4)

           = 24.9 + 30.0

           = 54.9

The image here given an example of perpendicular line.

Correct option is: yes, the lines are intersect at right angle.

Two lines are perpendicular if they cross at a point where they provide a pair of linear angles that are congruent. If a transversal in a plane is parallel to one of two parallel lines, it is also parallel to the other line. Lines that cross at a straight angle (90°) are said to be perpendicular. Perpendicular lines are those that cross at a right angle when two non-vertical lines in the same plane. Vertical and horizontal lines, or the axes of the coordinate plane, are perpendicular to one another. Two parallel lines' slopes have negative reciprocal slopes.

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The translated function is g(x) = ∛(x + 4) + 3, so the correct option is C.

We can see that function g(x) is a translation of f(x), which is the parent cubic root function:

f(x) = ∛x

We can see that g(x) is a translation of 3 units up, and 4 units to the left.

Then the function will be written as:

g(x) = f(x + 4) + 3

Replacing f(x) we will get:

g(x) = ∛(x + 4) + 3

Then the correct option is C.

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Answer:

Step-by-step explanation:

It would be 4+g

Since we are trying to find how many lbs in total we would add the total we already know which is 4 and then add the g pounds of green apples

To calculate the total amount of apples Alan has bought, we simply apply the concept of Algebraic Expressions and add the pounds of red apples (which is 4) to the pounds of green apples (which is represented by g). This can be represented in a mathematical expression as 4 + g.

Alan bought 4 pounds of red apples and g pounds of green apples. To find out how many pounds of apples he bought in total, we need to add the quantities together. So, the expression that shows that is 4 + g. This means that Alan bought 4 pounds of red apples and g pounds of green apples, adding those two quantities together gives the total pounds of apples he bought.

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No, it is not possible to have a connected graph with six vertices of degrees 1, 1, 2, 2, 2, and 3.

As we know that the sum of the degrees of the vertices in a connected graph must be equal to twice the number of edges.

So, in this case, the sum of the degrees must be equal to 2 * K, where K is the number of edges in the graph.

Since the degrees of the vertices are 1, 1, 2, 2, 2, and 3,

the sum of the degrees is 1 + 1 + 2 + 2 + 2 + 3 = 11.

The number of edges must be K = 11 / 2 = 5.5,

which is not possible as the number of edges must be a positive integer.

Therefore, it is not possible to have a connected graph with six vertices of degrees 1, 1, 2, 2, 2, and 3.

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Answer:

y = - 8x + 20

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 8x - 5 ← is in slope- intercept form

with slope m = - 8

• Parallel lines have equal slopes , then

y = - 8x + c ← is the partial equation of the parallel line

to find c substitute (3, - 4 ) into the partial equation

- 4 = - 8(3) + c = - 24 + c ( add 24 to both sides )

20 = c

y = - 8x + 20 ← equation of parallel line

The 3 couples can be seated in 20 ways.

The answer I provided uses the concept of permutations. In permutation, we calculate the number of arrangements or ways in which a set of elements can be arranged.

In this case, the question is asking for the number of ways in which 6 individuals (3 married couples) can be seated in a row. To find the number of arrangements, we can use the formula for permutations of multiples:

P(n, k) = n! / (n-k)!

Where n is the number of items to arrange and k is the number of identical items. In this case, n = 6 (number of individuals) and k = 3 (number of married couples).

However, we need to also account for the fact that within each married couple, the two individuals can be seated in either order. Hence, we need to divide the result by 2! for each couple, giving us the formula:

P(6, 3) / (2! * 2! * 2!) = 6! / (3! * 3!) = 20

So there are 20 different ways in which the 3 married couples can be seated in a row.

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By applying the transformation formula (x,y) -> (x-6,y+8) to the location (-4, 1), the pre-image would be (-4+6, 1-8) = (2,-7).

So the appropriate response is: (-2, -7).

Shifts and scaling are two common transformations used in geometry to create new shapes from figures in a plane. Images are the new (modified) shapes, and preimages are the original, unmodified shapes.

The preimage is the body of the object as it was originally, and the transformed shape of the object is termed the image.

The word "preimage" is plural (mathematics) The collection of all domain elements mapped onto a specific subset of the function's arguments.

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The line perpendicular to the line with an equation y = 6x have a slope of -1/6

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept.

Two lines are perpendicular if the product of their slopes is -1.

Line M goes through the points (0, 0) and (1, 6). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-0=\frac{6-0}{1-0} (x-0)\\\\y=6x[/tex]

The slope of the line y = 6x is 6.

The line perpendicular to y = 6x have a slope of -1/6

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The number of possible outcomes will be 524160.

When an order or sequence of arrangement is required, permutations are used. Combinations are used when there are only a limited number of possible groups to find and there is no requirement for the order or sequence of arrangements. For different kinds of things, permutations are used. Combinations are employed for similar items.

Given that a lottery exists where balls numbered 1 to 16 are placed in an urn. To​ win, you must match the balls chosen in the correct order.

The arrangement can be calculated as:-

¹⁶C₅ = 16 x 15 x 14 x 13 x 12

¹⁶C₅ = 524160

Therefore, the number of possible outcomes will be 524160.

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Answer:

Step-by-step explanation:

We know that the bag has dark chocolates and milk chocolates, and the probability of randomly choosing a dark chocolate is g. And, we know that there are 18 dark chocolates in the bag and each is equally likely to be chosen.

Now, let's use this information to find the number of milk chocolates. If there are n total chocolates in the bag, then the probability of choosing a dark chocolate is g, and the probability of choosing a milk chocolate is 1-g. We can write these probabilities as:

g = 18/n

1-g = (n-18)/n

So, if we equate the two expressions, we get:

18/n = (n-18)/n

That means:

18 = n - 18

And finally:

n = 36

So, there must be 36 chocolates in the bag, and 18 of them are dark chocolates, which means there must be 18 milk chocolates!

Answer:

10.4

Step-by-step explanation:

m² =10²+3² = 109

so m =√109 = 10.4

Answer:

9p, because 9x4=36

Step-by-step explanation:

The total cost for a meal of $110 plus a service charge of 18% is $129.8.

Given that, the meal costs $110 plus a service charge of 18%.

The total cost of the meal will be the addition of cost of meal and the service charge.

Total cost = cost of meal + service charge

Total cost = $110 + ( 18% × $110 )

Note that 18% is the same as 18/100

Total cost = $110 + ( 18/100 × $110 )

Total cost = $110 + ( 0.18 × $110 )

Total cost = $110 + ( $19.8 )

Add $110 and $19.8

Total cost = $129.8

Therefore, the total cost of the meal is $129.8.

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Answer:

2a^2b^3−a^2b^4