Can you use matrix multiplication with a matrix with three rows and a matrix with two columns

the graph is showing for every 1 hour the boat is 50 miles further away

 so the speed of the boat is 50 miles per hour

The speed of the boat is 50 miles per hour.

We have given that,

The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours

A graph titled Distance Vs Time is shown with Time in hours labeled on the x-axis and Distance from Island in miles labeled on the y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y-axis shows the numbers 0, 25, 50, 75, 100, 125, 150, 175, 200, 225. The graph shows a straight line joining the ordered pairs 0, 25, and 1, 75, and 2, 125, and 3, 175, and 4,225.

We have to determine the speed of the motorboat.

The speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time it is thus a scalar quantity.

The graph is showing for every 1 hour the boat is 50 miles further away

1hour=50 miles   from the graph

So the speed of the boat is 50 miles per hour.

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Knowing if trigonometry knowledge we can say that the distance will be 305.4 ft.

So knowing how sine and tangent work we can write the equals as:

[tex]sin (32) = CD / 960\\CD = 508.72[/tex]

[tex]tan (32) = 508.72 / AD\\AD = 814.13[/tex]

To calculate the distance, we will decrease the two values ​​found, like this:

[tex]814.13 - 508.72 = 305.4 ft[/tex]

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Based on the mean score and the confidence interval, the sample size required to estimate the mean score is 77.

This can be found as:

= (Z score for 99% interval² x Sample size²) / Points off the true mean ²

Solving gives:

= (2.576² x 17²) / 5²

= 76.7

= 77

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The required solution of the expression is x = -3.

Given that,
To determine the solution of the equation  3x-15/2=4x.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Functions are 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,
Simplification of 3x-15/2=4x.
3x  - 15 = 8x
5x = -15
x = -3

Thus, the required solution of the expression is x = -3.

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Final answer:

A square, rectangle, and certain cases of rhombuses and trapezoids can have two consecutive right angles, while typically a parallelogram and kite do not unless they are special cases of the rectangle or square respectively.

Explanation:

In the context of quadrilaterals with two consecutive right angles, it's important to recognize that certain quadrilaterals have this property by definition. A square and a rectangle both have four right angles, which means they certainly have at least two consecutive right angles.

A parallelogram typically does not have right angles, but a rectangle is a special type of parallelogram with right angles, so it fits this description. A kite generally does not have right angles unless specifically constructed to do so, which is not typical.

A rhombus can have right angles, making it a square, so it fits the criteria too. A trapezoid can also have a pair of consecutive right angles when it is a right trapezoid.

Therefore, the list of quadrilaterals that might have two consecutive right angles is not only the square and the rectangle but extends to include the rhombus and trapezoid as well.

Given these definitions, the correct answer to the question would be:

D. i, ii, iii, v, vi

Final answer:

The quadrilaterals that can have two consecutive angles measuring 90° each are squares, rectangles, and certain parallelograms (when they are squares or rectangles). Therefore, the correct answer to the question is B. This includes a square (i), a rectangle (ii), and some parallelograms (iii).

Explanation:

If a quadrilateral has two consecutive angles measuring 90° each, it could be any of the shapes that inherently contain right angles by definition. These shapes are a square, a rectangle, and certain types of parallelograms, specifically rectangles and squares. Both a square and a rectangle always have four right angles, which makes them valid answers. A rhombus or a general parallelogram may also have right angles, but only in specific cases, such as when a rhombus is also a square. Thus, kites and trapezoids do not necessarily fit this criterion as they do not always have consecutive right angles. Therefore, the correct answer is B, which includes a square, a rectangle, and some parallelograms.

The problem involves setting up an equation based on the given situation to solve for the number of baseball cards Neil and Larry have. By solving the equation, you find that Larry has 400 cards and Neil has 320 cards. So, they have 720 baseball cards together.

This is a problem of percentages and of algebra. First, you know that the number of cards Neil has is 80% of what Larry has. This can be set up as an algebraic equation, where N represents Neil’s cards and L represents Larry’s cards: N = 0.8L. You also know that Neil has 80 fewer cards than Larry, which provides a second equation: N = L - 80.

Because both expressions equal N, you can set them equal to each other to solve for L. This leads to 0.8L = L - 80. Solve this equation for L, and you get L = 400. Substituting this into the equation N = 0.8L, you find that N = 320. Therefore, Neil and Larry have 720 baseball cards altogether.

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Option first is the answer.

Step-by-step explanation:

For finding the are of a right angle triangle, we use the base and the height of the triangle. The height is the right angle leg of the triangle. Hypotenuse is not considered here.

In the given diagram, the base or 'b' is = 10 units

And the height or 'h' is = 24 units

Area of a right triangle is given as :

[tex]A=\frac{bh}{2}[/tex]

So, in the given options the correct option is : Option first.

[tex]A= \frac{10*24}{2 }[/tex] or [tex]\frac{1}{2}(10*24)[/tex]

Answer:

The correct answer is B. Show that the solution to the system of equations 8x − 5y = 11 and 7x − 8y = 6 is the same as the solution to the given system of equations"

Step-by-step explanation:

13/24 = 0.5416666

 since 6 keeps repeating that would be the number that has the line over it.

The value of the motorcycle after 9 years, with a depreciation rate of 3% per year, will be approximately $9,800. This answer has been calculated using the formula for percent decrease applied to the initial value of the motorcycle.

This question revolves around the concept of percent decrease, a fundamental topic in mathematics. To estimate the value of the motorcycle after nine years, we need to apply the percent decrease continuously for these years.

The formula is: Final Value = Initial Value * (1 - rate of decrease)number of years

So in this case, the final value will be: $14,000 * (1 - 0.03)^9.

Calculating that gives us approximately $9,855, so the closest answer would be option C, $9,800.

Therefore after 9 years, the motorcycle will have depreciated to around $9,800 in value given a yearly depreciation rate of 3%.

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Answer:

The statement which best compares the function F(x) and G(x) is that the graph of G(x) is the graph of F(x) stretched vertically.

Step-by-step explanation:

Since the difference between the two functions is in the coefficent which multiplies the square function, 1 and 2/3 respectively in F(x) and G(x). So, as the coefficient are positive and is minor for G(x) than for F(x), the values for G(x) will be smaller and thus the graph of G(x) would be below the graph of F(x). Therefore the graph for G(x) is it compressed vertically respect to F(x). The explanation here is ore understandable by looking at the illustration attached.

Answer:

A. 2 < x < 3

Step-by-step explanation:

The values of x which A ⋃ B = Ø is:

This refers to the grouping of data which can be graphically represented on a Venn diagram.

With this in mind, we have a set of data which makes use of a general set that contains:

Therefore, the values of x to which A ⋃ B = Ø is:

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Answer:

Step-by-step explanation:

$228

Answer:

my brain has exceeded the limit of cofusion

Step-by-step explanation:

The expression is d) [tex]9 \sqrt{6}[/tex]

To simplify the given expressions involving square roots, follow these steps:

a. Square root 6

Since 6 is not a perfect square and has no perfect square factors, [tex]\sqrt{6} i[/tex]s already in its simplest form.

b. Square root 12

Break down 12 into its prime factors: 12 = [tex]2 \times 2 \times 3[/tex]. Therefore,[tex]\sqrt{12}[/tex]can be simplified as follows:

[tex]\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}[/tex]

c. 9 square root 12

We already know that [tex]\sqrt{12} = 2\sqrt{3},[/tex] so we substitute it into the expression:

[tex]9 \sqrt{12} = 9 \times 2\sqrt{3} = 18\sqrt{3}[/tex]

d. 9 square root 6

Since [tex]\sqrt{6[/tex]} is already in its simplest form, the expression remains:

[tex]9 \sqrt{6}[/tex]

The long-distance runner will take 3 hours to run 27 miles.

In simple terms, the unitary method is used to find the price of a single unit from a given multiple.

Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

You divide 27 miles by 9 miles per hour, getting 27/9 (miles/(miles))hour.

The units cancel out to make hours

This runner takes 1 hr to run 9 miles.

So, to run 27 miles the runner will take

= 27/9

= 3 hours.

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Area = 1039.23 square units

 Round answer as needed. See picture for equation

Final answer:

The probability that at least one of four randomly distributed letters ends up in its correct envelope is 62.5%. This calculation uses the complementary approach, subtracting the probability of no matches (9/24) from 1.

Explanation:

The question asks about the probability that at least one letter ends up in its accompanying envelope when four letters are randomly put into four envelopes.

To solve this, we employ the principle of complementary probability, which suggests that the probability of at least one match is 1 minus the probability of no letters matching their envelopes.

Calculating the probability of no matches directly can be complex due to numerous possible permutations, so using the complementary approach is more efficient.

We can calculate the total permutations of the four letters being distributed into four envelopes as 4!, which equals 24.

To find the probability of no letters matching their envelopes (a derangement of 4 items), we use a specific formula or recognition of known patterns, resulting in 9 derangements. Thus, the probability of no matches is 9/24.

The probability of at least one letter matching its corresponding envelope is then 1 - (9/24), which simplifies to 15/24 or 5/8. Therefore, the probability is 0.625 or 62.5%.

Final answer:

After using the Pythagorean theorem to calculate the length of the bike path as approximately 2287 feet, and multiplying by the cost of $2.20 per foot, the total comes to $5031.40. This total cost fits within the city planning budget of $5050.

Explanation:

The city planning committee needs to determine if their $5050 budget is sufficient for the bike path extension, with construction costs at $2.20 per foot. To calculate the cost of the bike path, we first must find the length of the path, which will be the hypotenuse in a right triangle formed by the height (880 ft) and the base (2112 ft). Applying the Pythagorean theorem (a² + b² = c²), where a is the height and b is the base, the length of the path (c) can be calculated as follows:

c = √(880² + 2112²) = √(774400 + 4456444) = √5230844 ≈ 2287 ft.

Now, we can determine the total cost by multiplying the length of the path by the cost per foot:

Total Cost = 2287 ft × $2.20/ft = $5031.40

Thus, the total cost for constructing the path would be $5031.40, which is within the city planning budget of $5050.

Answer:  The required probability is 0.10.

Step-by-step explanation:  Given that Marla is looking for a new car. She has test-driven two cars A and B but can only purchase one.

We are to find the probability  that she will not purchase either car A or car B.

Let, 'C' denotes the event that Marla will purchase car A and 'D' denotes the event that Marla will purchase car 'B'.

Then, according to the given information, we have

[tex]P(A)=0.52,~~~P(B)=0.38.[/tex]

Since Marla cannot purchase both the cars, so the events A and B are disjoint.

That is,

[tex]A\cap B=\phi~~~~~\Rightarrow P(A\cap B)=0.[/tex]

Therefore, the probability that Marla will purchase either car A or car B is given by

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.52+0.38-0=0.90.[/tex]

Hence, the probability that she will not purchase either car A or car B will be

[tex]P^\prime(A\cup B)=1-P(A\cup B)=0-0.90=0.10.[/tex]

Thus, the required probability is 0.10.