Matrices P and Q are defined by P=\(\left[\begin{array}{ccc}x&2\\-5&-1\\\end{array}\right]\) and Q=\(\left[\begin{array}{ccc}2&-3\\4&y\\\end{array}\right]\). Where x,y∈R

(a) Given the determinant of P is 2, obtain:

(i) The value of x.

(ii) \(P^{-1}\)

(iii) \(P^{-1}Q'^{-1}\), where Q' is the transpose of Q.

(b) The matrix R is defined by R=\(\left[\begin{array}{ccc}5&-2\\z&-6\\\end{array}\right]\), where z∈R.

Determine the value of z such that R is singular.

Answer:

P(red or blue) = \(\frac{7}{16}\).

Step-by-step explanation:

We have to find P(A or B), if A and B are independent events for one action, such as spinning a four-color spinner once.

Firstly, as we know that the formula for finding P(A or B) is given by;

P(A or B) = P(A) + P(B) - P(A and B)

Since it is stated that event A and B are independent, this means that there is no dependence of any one event on another event, so;

P(A and B) = P(A) \(\times\) P(B)

Now, we can find P(A or B) = P(A) + P(B) - P(A) \(\times\) P(B); is we know that the probabilities of happening of both events.

Similarly, P(red or blue) = P(red) + P(blue) - P(red) \(\times\) P(blue).

Since the event is spinning a four-color spinner once and assuming there are four different colors, so the probability of wheel stopping on each color is (\(\frac{1}{4}\)).

So, P(red or blue) = \(\frac{1}{4} +\frac{1}{4} -(\frac{1}{4} \times \frac{1}{4} )\)

                             = \(\frac{2}{4} -\frac{1}{16}\)  = \(\frac{7}{16}\).

The correct first step to solving the system of equations in the most efficient manner is x = -4y +19.

The given system of equations is;

\(\rm 3 x + 2 y = 17\\\\x + 4 y = 19\)

The first step would be to rearrange the variables in the second equation so we have a defined expression for x.

We would want to do this so we could then plug in the defined expression for x into the other equation and solve for the other variable.

x + 4y = 19

Rearrange this by getting the 4y to the other side.

We can get 4y on the other side by subtracting 4y from both sides

x + 4y - 4y = 19 - 4y

x = -4y + 19

Hence, the correct first step to solving the system of equations in the most efficient manner is x = -4y +19.

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Answer:

(A)x = negative 4 y + 19

Step-by-step explanation:

i did the test on edge good luck

The total students who are going on the field trip are 320 students out of 400 students which has been obtained by using the concept of fractions.

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).

If 4 out of 5 students are going on the field trip, then the fraction of students going on the field trip is 4/5.

To find out how many students are going on the field trip, we can multiply this fraction by the total number of students:

Number of students going on the field trip = (4/5) x 400

Number of students going on the field trip = 320

Therefore, 320 students are going on the field trip.

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The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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The error in the veterinarian's scale is 0.75 pounds.

To determine the error in the veterinarian's scale when weighing Oliver's new puppy, Boaz, we follow these steps:

Step 1: Identify the measured weight and the actual weight.

Measured weight on the scale: 13.25 pounds

Actual weight: 12.5 pounds

Step 2: Calculate the error by subtracting the actual weight from the measured weight.

Error = 13.25 pounds - 12.5 pounds = 0.75 pounds

Step 3: Analyze the error.

The veterinarian's scale overestimated Boaz's weight by 0.75 pounds.

This indicates that the scale provided a reading that was 0.75 pounds higher than the actual weight of Boaz.

It suggests a positive bias or inaccuracy in the scale's measurement.

The error in the veterinarian's scale when weighing Boaz is 0.75 pounds. It's important to consider this error when using the scale to ensure accurate weight measurements for Boaz and other animals. If precise measurements are needed, it may be necessary to use a different, more accurate scale.

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Step-by-step explanation:

in the form

y = mx + c

m is the gradient (or slope) of the line, and c is the y-intercept (the y-value when x = 0).

y = 4x + c

we get c by using the given point coordinates :

-2 = 4×-3 + c = -12 + c

10 = c

so the full equation is

y = 4x + 10

There will be a vertical stretch with a factor of 3.

This two are characteristics of frequency tables

1. They can be used for quantitative data.

2. They can be used for qualitative data.

Frequency tables have the following characteristics:
1. They can be used for quantitative data:

Frequency tables display the number of occurrences of each value in a dataset, which is particularly useful when dealing with numerical or quantitative data.
2. They can be used for qualitative data:

Frequency tables can also be used for non-numerical or qualitative data, such as categories or groups, by counting the number of occurrences for each category.
4. No observation can fit into more than one class:

In a frequency table, each observation or data point is assigned to only one class or category, ensuring that there is no overlap between classes.

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Answer:

A y = 40x + 75

B 1 hour = 115

2 hour = 155

3 hour = 195

4 hour = 235

5 hour = 275

6 hour = 315

C, D, E look at pic below

plz mark brainliest

Answer:

area of rect = 8/9

Step-by-step explanation:

Area of rect.= (L*W)

Area = (4/9) (2)

Area = (4/9) (2/1)

Area = 8/9

Answer:

8/9 feet

Step-by-step explanation:

Area=l*w

4/9ft*2ft

4/9*2/1=8/9ft

Step-by-step explanation:

If the whole thing is in a square root, then the  answer is sqrt21.

If only sqrt26 is in the square root, then the answer is -5+sqrt26.

(esto es en español) (This is in spanish transalation)

Si todo está en una raíz cuadrada, entonces la respuesta es la raíz cuadrada 21.

Si solo la raíz cuadrada 26 está en la raíz cuadrada, entonces la respuesta es -5 + raíz cuadrada 26.

Answer is x= -2/3

I hope this helps u

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Answer:

638.33

Step-by-step explanation:

\(450(1+.06)^6\)

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The theoretical probability of rolling a sum of 7 on two dice is 1/6, or 16.67%.

The theoretical probability of rolling a sum of 9 is 1/36, or 2.78%. Again, the experimental probability of rolling a sum of 9 is determined by actually rolling two dice and recording the results. This can be done numerous times to determine the likelihood of rolling a sum of 9. To calculate the theoretical probability of rolling a sum of 7 or 9, we can add the two probabilities together. The theoretical probability of rolling a sum of 7 or 9 will be 1/6 + 1/36 = 17/36, or 47.22%. To calculate the experimental probability of rolling a sum of 7 or 9, we can add the results of the two dice rolls together. We can then record the number of times that the sum of the two dice is 7 or 9. The experimental probability of rolling a sum of 7 or 9 will be the number of times a sum of 7 or 9 was rolled, divided by the total number of rolls.

Therefore, the theoretical probability of rolling a sum of 7 or 9 is 47.22%, while the experimental probability of rolling a sum of 7 or 9 will vary depending on the number of rolls taken.

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The three computations covered by the reliability factor table are sample size, index of reliability, and index of precision. Sample size deals with the size of the sample being used in order to achieve a desirable level of reliability.

Index of reliability is used to measure the consistency of results achieved over multiple trials. It does this by calculating the total number of items that contribute significantly to the final result. Finally, the index of precision measures the effect size of the sample, which is determined by comparing the results from the sample with the expected results.

The sample size computation gives the researcher an idea of the number of items that should be included in a sample in order to get the most reliable results. This is done by taking into account a number of factors including the variability of the population, the type of measurements used, and the desired level of accuracy.

The index of reliability is commonly calculated by finding the ratio of the number of items contributing significantly to the total result to the total number of items in the sample. This ratio is then multiplied by 100 in order to get a final score.

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Answer:

1. 78/5

2. 12

3. 25/8

4. 48/35

5. 21/2

Answer:

120in. ezy

Step-by-step explanation:

(a) The first six terms of the sequence are: 1, 2, 2, 4, 8, 32.

(b) The first six terms of the sequence are: 1, 5, 13, 29, 61, 125.

(c) The first six terms of the sequence are: 2, 1, 5, 21, 110, 681.

(d) The first six terms of the sequence are: 4, 5, -1, -6, -47, -312.

(e) The first six terms of the sequence are: 1, 3, -8, -85, -242, -491.

(f) The first six terms of the sequence are: 0, 2, -3, -8, -22, -57.

Here is a brief explanation of each sequence:

(a) In this sequence, each term is the product of the two preceding terms. It starts with 1 and 2 as the first and second terms, respectively. The third term is the product of 1 and 2, which is 2. The fourth term is the product of 2 and 2, which is 4. This pattern continues, where each term is the product of the two preceding terms.

(b) This sequence is defined recursively, where each term is obtained by multiplying the previous term by 2 and adding 3 times the term before that. It starts with 1 as the first term and 5 as the second term. The third term is obtained by applying the recursive formula, and this pattern continues for the remaining terms.

(c) In this sequence, the first two terms are given, and the remaining terms are obtained using the formula On = . The pattern starts with 2 and 1 as the first and second terms, respectively. To find subsequent terms, the formula is applied using the corresponding indices.

(d) This sequence is defined recursively, where each term is obtained by subtracting the term before it from the term two positions earlier. The first two terms are given, and the remaining terms are calculated using the recursive formula.

(e) Similarly to sequence (d), this sequence is defined recursively, where each term is obtained by subtracting 7 times the term before it from the term two positions earlier. The first two terms are given, and the recursive formula is used to find the remaining terms.

(f) In this sequence, each term is obtained by subtracting the sum of the two preceding terms from 5. The first two terms are given, and the pattern continues by applying the formula recursively.

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In a large population, 64 % of the people have been vaccinated. If 5 people are randomly selected, then the probability that AT LEAST ONE of them has been vaccinated is 99.78% or 0.9978.

The probability that at least one person is vaccinated among a sample of five people selected randomly from a population in which 64% have been vaccinated is the complement of the probability that none of the five selected have been vaccinated. The probability of at least one vaccinated person is:

Probability of at least one vaccinated person = 1 - Probability that none of the selected have been vaccinated.

To find this probability, you first need to find the probability that none of the five selected have been vaccinated.

Probability of selecting one person who is not vaccinated = 1 - 0.64 = 0.36

Probability of selecting five persons who are not vaccinated = 0.36 × 0.36 × 0.36 × 0.36 × 0.36= 0.0022

So, the probability of at least one vaccinated person in the sample of five is:

Probability of at least one vaccinated person = 1 - Probability that none of the selected have been vaccinated

                                                                           = 1 - 0.0022

                                                                           = 0.9978

Therefore, the probability that at least one person is vaccinated among a sample of five people selected randomly from a population in which 64% have been vaccinated is 0.9978.

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Answer: Sammy has 5  pies and needs 20 people to eat the pies if you add 5 and 20 how much pies will be eaten?

Step-by-step explanation: i did not fully understand your question but i hope this helps!

Answer: 164 sq. meters

Step-by-step explanation:

first two columns are both 5 by 8 m so 5 * 8 = 40.

To find the top part, you do 15 - 8 to find the remaining portion on top. Multiply that with 12 to get 84.

Answer:

164 sq. meters.

Step-by-step explanation:

area of big square minus area of small square

Answer:

143 Gallons

Step-by-step explanation:

miles/gallon per 26 miles= amount of gallons.

3718/26= 143 gallons of gas.

Answer:

x < - 4

Step-by-step explanation:

Given

2x - 2 > 4x + 6 ( subtract 2x from both sides )

- 2 > 2x + 6 ( subtract 6 from both sides )

- 8 > 2x ( divide both sides by 2 )

- 4 > x , thus

x < - 4

Two non-vertical lines in the same plane are said to be parallel if they have the same slope. No two parallel lines will ever cross. A set of non-vertical lines within the same plane are considered to be perpendicular if they meet at a right angle.

Perpendicular lines and parallel lines both meet at 90 degrees, although parallel lines never do. Lines are perpendicular if the slope of one line is equal to the reciprocal of the second line's negative slope.

Lines that have the same slope are therefore said to be parallel, and if the slope of one line is equal to the negative reciprocal of the slope of the other, the two lines are said to be perpendicular; otherwise, they are just intersecting lines.

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Answer:

leading co-efficent is 4

Answer:

If we have 8 * x + y + y:

We have to first substitute in x and y where they should be:

=> 8 * 9 + 10 + 10

According to the order of operations(PEMDAS(parenthesis, exponents, multiplication, division, addition, subtraction, multiplication and division is you go from left to right order, and same with addition and subtraction.)), we do the multiplication first(8*9):

=> 72 + 10 + 10

Now we just add them up:

=> 92

The polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity is                   x⁴ - 4x³ + 5x²- 4x + 4 = 0. This can be obtained by finding factors and multiplying them.  

Given that zeroes, 2 of multiplicity 2, and i of single multiplicity, that is,       (x - 2), (x - i) and (x + i) are the factors of the polynomial.

Thus the polynomial can be written as  

(x - 2)²(x - i)(x + i) = 0 ((x - 2) is squared as multiplicity is 2)

(x² - 4x + 4)(x²-i²) = 0

(x² - 4x + 4)(x²+1) = 0

x⁴ - 4x³ + 4x² + x² - 4x + 4 = 0

⇒ x⁴ - 4x³ + 5x²- 4x + 4 = 0

Hence the polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity is                   x⁴ - 4x³ + 5x²- 4x + 4 = 0.

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Charlotte's car used \frac{1}{90}​ of a gallon to travel \frac{1}{2} ​ of a mile. How many miles can the car go on one gallon of gas?

Answer:

The car go 45 miles on one gallon of gas

Step-by-step explanation:

From the above question

1/90 gallons of gas = 1/2 mile

1 gallon of gas = x mile

Cross Multiply

1/90 × x = 1/2 × 1

x = 1/2 / 1/90

x = 1/2 × 90/1

x = 45 miles

Hence:

The car can go 45 miles on 1 gallon of gas.