A submarine descends to 1/6 of its maximum depth. Then it descends another 2/3 of its maximum depth. If it is now at 650 feet below sea level, what is its maximum depth.

For the given Augmented Matrix ,the correct option is :

A) The solution set has exactly one element.

The exact solution is x = -25 , y = 2 and z = 2.

Augmented Matrix:

An augmented matrix is ​​a means of solving simple linear equations. Coefficients and constant values ​​of linear equations are represented as matrices called augmented matrices. Simply put, an augmented matrix is ​​a combination of two simple matrices along columns. If the first matrix has m columns and the second matrix has n columns, then the augmented matrix has m + n columns.

Now, as given the Augmented matrix:

[1 7 3 -5]

[0 0 0 3]

[0 0 1 2]

[0 1 -1 4]

From this system we get:

y - z = 4       --------------------------- (1)

    z = 2

and, z = 3

and, x + 7y + 3z =-5   ---------------- (2)

Now, Solving the equation with z = 2,

    y - 2 = 4

⇒ y = 6

and, putting y = 6 and z = 2

   x + 7× 6 + 3×2 = -5

⇒ x + 42 + 6 = -5

⇒ x +48 = -5

⇒ x = -53

Therefore, x = -53, y=6 and z =2

Now, for z = 3 in equation (1)

   y - 3= 4

⇒ y = 7

Putting y =7  and z =3, we get:

   x + 7 × 7 + 3×3 = -5

⇒ x + 49 + 9 =-5

⇒ x + 58 = -5

⇒ x = -63

Therefore, x = -63, y =7 and z =3

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Given :

ATQ,

the volume of the model is thrice the height of the model

so,

the volume of the statue would be thrice it's height

hence,the height of the statue would be 13,500 cm

Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

Here,

Given: Total number of freshman =500

mean =75 and standard deviation =7

a) the percentage of scores that fell between 68 and 82

340 is the number of freshman whose  scores that fell between 68 and 82

thus,

percentage = 340 /500 * 100

=> percentage = 68%

b)the percentage of scores that fell between 61 and 75

237 is the number of freshman whose  scores that fell between 61 and 75

thus,

percentage = 237/500 * 100

=> percentage = 47.4%

Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

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Answer:

length = 20 feet

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

let width be w , then length is 4w

given A = 100 , then

4w × w = 100

4w² = 100 ( divide both sides by 4 )

w² = 25 ( take square root of both sides )

\(\sqrt{w^2}\) = \(\sqrt{25}\)

w = 5

width = 5 feet and length = 4 × 5 = 20 feet

The equation that visualizes the full linear model of the data in a randomized block design with each treatment replicated once per block is: RESPONSE = CONSTANT + BLOCK + TREATMENT

In a randomized block design, the goal is to control the variability associated with the blocks while examining the effect of different treatments.

The equation RESPONSE = CONSTANT + BLOCK + TREATMENT represents the full linear model, where RESPONSE is the dependent variable, CONSTANT is the intercept term, BLOCK is the categorical variable representing the blocks, and TREATMENT is the categorical variable representing the treatments.

Including the BLOCK term in the model allows us to account for the variation associated with different blocks, while the TREATMENT term represents the effect of the treatments.

The model assumes that the effect of the treatments is the same across all blocks.

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Answer:

\(\huge\boxed{\sf 44\ units}\)

Step-by-step explanation:

Solution:

So,

= 3 + 8 + 3 + 6 + 5 + 6 (again) + 4 + 5 + 4

\(\rule[225]{225}{2}\)

Answer:

8-4=4

therefore 6+4=10

then perimeter =2(5)+10+6+2(3)+8+4=44units

Answer:

6:5:4

Step-by-step explanation:

6 + 5 + 4 = 15

3000/15 = 200

200 x 6 = 1200 = eldest

200 x 5 = 1000 = 2nd eldest

1200 + 1000 = 2200

3000 - 2200 = 800

200 x 4 = 800 = youngest

Answer 6 : 5 : 4

Step-by-step explanation:

Its simply because

1200 ÷ 6 is 200 which is a whole number... If you divide for example 1200 by 7 it wont give you a whole... And also the first number of the ratio should be the greatest since the first child got the most money and the last the least which means the least should be the smallest number.

Answer:

y=3

Step-by-step explanation:

good luck

The scale factor of the dilation is 4.472.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

Area of Circle = 10 π

This is dilated so that its image has an area of 25pi cm square.

For Original Circle

πr² = 10 π

r² = 10

r= √10

and, For dilated circle

πR² = 25 π

R² = 25

R = √25

R= 5

So, the scale factor is

R/ r = 5/ √10

R/r = 4.472

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The H0: μ = 70 H1: μ > 70 These are the null and alternative hypotheses in symbolic form for the given scenario.

express the null hypothesis (H0) and alternative hypothesis (H1) for the given situation involving the Carter Motor Company and their claim about the Libra's average city mileage.

The null hypothesis (H0) is the default assumption that there is no difference or relationship between the tested parameters. In this case, it would be that the true average mileage (μ) of the Libra is equal to 70 miles per gallon in the city:
H0: μ = 70

The alternative hypothesis (H1) is the claim that we want to test, which is that the true average mileage (μ) of the Libra is better than (greater than) 70 miles per gallon in the city:
H1: μ > 70

These are the null and alternative hypotheses in symbolic form for the given scenario.

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Answer:

  86%

Step-by-step explanation:

You want the girls' average if the 20 boys in the 30-student class had an average of 62%, and the class average was 70%.

The class average is the weighted average of the boys' score and the girls' score. The weights are the fraction of students of each gender.

  class average = (1/3)(girls' average) +(2/3)(boys' average)

Solving this equation for the girls' average, we get ...

  (1/3)(girls' average) = (class average) -(2/3)(boys' average)

  girls' average = 3(class average) -2(boys' average)

  girls' average = 3(70%) -2(62%) = 210% -124%

  girls' average = 86%

__

Alternate solution

The sum of differences from the class average must be zero. The boys' average is 8 points below the class average, and there are 2 times as many boys as girls. Thus, compared to the girls, the boys contribute a total of 2·8 = 16 points below the class average. The girls must counter by having an average 16 points above the class average: 70+16 = 86.

Answer:

Its B !!!

Step-by-step explanation:

Have a great day

Answer:

1.9 1.9 1.9 1.9 1.9 1.9 1?9 1.9 1.9 1.9

Answer:

x>-8 dooooneeeeeeeeeeeeeee

Answer:

Step-by-step explanation:

Ray can be defined as a part of a line that has a fixed starting point but no end point.

The starting point is B and on its way to infinity, it passes through point A.

Correct sign is

\(\huge\boxed{\overrightarrow{BA}}\)

Answer:

c =

Step-by-step explanation

-2ccc -73 + 73 = -89 + 73

-2ccc = -16

-ccc = -8

ccc = 8

c = √√8 = 2

Answer:

Step-by-step explanation:

\(\sf -2c-73=-89\)

Add 73 to both sides:-

\(\sf -2c-73+73=-89+73\)

\(\sf -2c=-16\)

Divide both sides by -2:-

\(\sf \cfrac{-2c}{-2}=\cfrac{-16}{-2}\)

\(\sf c=8\)

*✧･ﾟ: *✧･ﾟ:

Hope this helps!

Add 3 to each number until there are 21 numbers in the sequence. You should get 58

The 21st term of arithmetic sequence will be equal to 58 .

It is given that the sequence is -2 , 1 , 4 , 7 , ----

We have to find out the value of 21st term of the sequence.

What do you mean by sequences ?

Sequences are a list of numbers which are arranged in a special manner i.e., 2 , 4 , 6 , 8  numbers of this sequence gets increased by 2 every time.

As per the question ;

The common difference ; d = 3

The first term ; a = -2

The no. of terms ; n = 21

We know that ;

The sequence is given by ;

\(a_{n}\) = a + (n-1) d

\(a_{n}\)  = -2 + (21-1) 3

\(a_{n}\) = -2 + 20 × 3

\(a_{n}\)  = -2 + 60

\(a_{n}\)  = 58

Thus , the 21st term of arithmetic sequence will be equal to 58 .

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2/26  that is the answer ok now peace

The terms minimum and infimum are both related to the concept of lower bounds in mathematics. A minimum is the smallest value in a set of numbers, whereas an infimum is the greatest lower bound of a set.

A minimum is a value that is less than or equal to all other values in the set, while an infimum is a value that is less than or equal to all other values in the set, but not necessarily the smallest value.

For example, if we consider the set {2, 4, 6}, the minimum is 2 and the infimum is also 2. However, if we consider the set {2, 4, 6, 8}, the minimum is 2 and the infimum is 4. In the latter set, 4 is the greatest lower bound, meaning that all other values in the set are greater than or equal to 4.

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The table (D) values would produce the same graph as shown.

Mathematical structures known as graphs are used to describe pairwise relationships between things. Graph theory is the study of these mathematical structures. Vertices (also known as nodes or points) and edges are what make up a graph in this sense (also called links or lines). It is possible to distinguish between directed and undirected graphs, where edges connect two vertices asymmetrically and symmetrically, respectively. One of the primary topics in discrete mathematics is graphs.

From the graph, find the intercepts,

At x = 0, the value of y is -1.

At, y = 0, the value of x is 4

So, from the given options, we can see that the values are given in table (D).

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The least appropriate measure of central tendency for a data set that contains outliers is the mean. This is because the mean is calculated by taking the sum of all the values in the data set and dividing it by the number of values. This means that the mean is heavily influenced by outliers, as they are included in the calculation.

The median, 2nd quartile, and 50th percentile are all more appropriate measures of central tendency for a data set that contains outliers, as they are not affected by the presence of outliers. The median is calculated by taking the middle value of the data set, the 2nd quartile is calculated by taking the median of the upper half of the data set, and the 50th percentile is calculated by taking the value at the 50th percentile of the data set.

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The car consumes 3 gallons and 8.2 gallons of fuel respectively.

Milage:

Divide the distance traveled by the amount of gas used. For example, driving 100 miles with a full tank and 5 gallons of gas is 10mpg. When it comes to fuel economy, it's important to know how much your car is costing you each time we drive it.

According to the Question:

The gas mileage is the number of miles that can be covered by a car for a particular amount of fuel.

We are given that the gas mileage of the car is 30 miles per gallon, that means that the car consumes 1 gallon of fuel for each 30 miles covered.

The amount of fuel needed to cover the following distance is:

a) For 90 miles, let x represent the number of gallon of fuel. Hence:

Distance covered / amount of fuel = 30 miles per gallon

  90/x = 30

⇒ x = 90/30

⇒ x = 3 gallons

b) For 246 miles, let x represent the number of gallon of fuel. Hence:

Distance covered / amount of fuel = 30 miles per gallon

⇒ 246/x = 30

⇒ x = 246/30

⇒ x = 8.2 gallons

Therefore, the car consumes 3 gallons of fuel for 90 miles and 8.2 gallons for 246 miles.

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The solution is that the three-digit number is 584.

What are three digit numbers ?

Three-digit numbers are numbers that have three digits, with each digit representing a value in a specific place value position. The first digit represents the hundreds place, the second digit represents the tens place, and the third digit represents the ones place.

For example, the number 357 is a three-digit number. The digit 3 represents 3 hundreds, the digit 5 represents 5 tens, and the digit 7 represents 7 ones. Therefore, the number 357 represents the value of 3 x 100 + 5 x 10 + 7 x 1 = 300 + 50 + 7 = 357.

Three-digit numbers range from 100 to 999, inclusive. There are 900 three-digit numbers in total.

According to the question:
Let the three-digit number be represented by the digits ABC, where A, B, and C are digits (with A representing the hundreds place, B representing the tens place, and C representing the ones place). Since we know that the number is a multiple of 8, we can assume that C = 0, 8, or 6 (since these are the only digits that make the entire number divisible by 8).

Let's start by assuming that C = 0. In this case, the three-digit number is represented by AB0. Adding a quarter of this number gives:

AB0 + 0.25(AB0) = AB0 + 0.25AB = 1.25AB0

Since we know that this amount is less than 740 but greater than 720, we can set up an inequality:

720 < 1.25AB0 < 740

Dividing each term by 1.25, we get:

576 < AB0 < 592

Since we know that AB0 is a multiple of 8, we can test the values of AB0 that satisfy this inequality and are multiples of 8. The only such value is 584, so AB0 = 584.

Therefore, the three-digit number is 584, and adding a quarter of this number gives:

584 + 0.25(584) = 730

which is between 720 and 740 as required.

Therefore, the solution is that the three-digit number is 584.

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Answer:

x^2 +3x-5

Step-by-step explanation:

f(x) = 3x + 1 and g(x) = x^2 - 6

(f+g)(x) = 3x+1+x^2 -6

Combine like terms

           =x^2 +3x-5

50

Step-by-step solution:

    0.3x-42=0.1x-32

    -0.1x

    0.2x-42=-32

                   +42

      0.2x=10

               0.2                

        x=50

(C) Regression analysis is the statistical method commonly used to estimate the level and trend in a time series by modeling the relationship between the data and independent variables.

Regression analysis is the statistical method used to estimate the level and trend in a time series. Time series data represents observations taken at different points in time and is commonly used to analyze trends and patterns over time.

Regression analysis allows us to model the relationship between a dependent variable (in this case, the time series data) and one or more independent variables (such as time or other relevant factors). By using regression analysis, we can identify the underlying trend in the time series and estimate its level.

The regression model captures the relationship between the dependent variable (the time series) and the independent variable(s) by fitting a line or curve that best represents the data. This line or curve helps to identify the overall trend and level of the time series.

While moving average, simulation method, covariance analysis, and correlation analysis are useful techniques in analyzing time series data, they are not specifically designed to estimate the level and trend in a time series. Therefore, (C) regression analysis is the most appropriate method for estimating the level and trend in a time series.

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If we move one unit to the right from (0,-1), we get the point (1,-33). This is the ordered pair that represents an input (x=1) and a corresponding output (y=-33) on the graph of the function y=−32x−1.

To find the ordered pair that represents an input and a corresponding output on the graph of the function y=−32x−1, we need to plot the graph first. The function is in the form of slope-intercept form, where the slope is -32 and the y-intercept is -1.

Thus, we can plot the point (0,-1) on the y-axis. Then, we can find another point by using the slope -32, which means that for every unit increase in x, y decreases by 32.

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Given:

There are given the expression:

Explanation:

According to the question:

We need to find the value of the given expression:

Then,

To find the expression, we need to use the exponent rule:

From the exponent rule:

Then,

From the expression:

Final answer:

Hence, the value of the expression is 43046721.