Evaluate 5x – 2y + (7x – y) for x = 7 and y = –2.

Answer:

From the question we are told that

   The  population mean is  \(\mu = 16\)

    The sample size is  n  =  30  

     The  sample mean is  \(\= x = 16.32\)

     The  population standard deviation is  \(\sigma = 0.8\)

      The  level of significance is  \(\alpha = 0.10\)

Step 1: State hypotheses:

The  null hypothesis is  \(H_o : \mu = 16\)

The alternative hypothesis is  \(H_a : \mu \ne 16\)

Step 2: State the test statistic. Since we know the population standard deviation and the sample is large our test statistics is

          \(t = \frac{ \= x -\mu }{ \frac{\sigma}{ \sqrt{n} } }\)

=>       \(t = \frac{ 16.32 -16 }{ \frac{0.8 }{ \sqrt{30} } }\)

=>       \(t =2.191\)

Generally the degree of freedom is mathematically represented as

          \(df = n - 1\)

=>      \(df = 30 - 1\)

=>      \(df =29\)

Step 3: State the critical region(s):

From the student t-distribution table the critical value corresponding to  \(\alpha = 0.10\)  is

         \(t = 1.311\)

Generally the critical regions is mathematically represented as  

         \(- 1.311 < T < 1.311\)

Step 4: Conduct the experiment/study:

Generally the from the value obtained we see that the t value is outside the critical region so  the decision is [Reject the null hypothesis ]  

Step 5: Reach conclusions and state in English:

  There is  sufficient evidence to show that the filling weight has to be adjusted

Step 6: Calculate the p-value associated with this test. How does this the p-value support your conclusions in Step 5?

From the student t-distribution table the probability value to the right corresponding to \(t =2.191\) at  a degree of freedom of  \(df =29\)  is

        \(P( t > 2.191) = 0.0183\)

Generally the p-value is mathematically represented as

       \(p-value = 2 * P( t > 2.191 )\)

=>    \(p-value = 2 * 0.0183\)

=>    \(p-value = 0.0366\)

Generally  looking at the value obtained we see that \(p- value < \alpha\) hence

The decision rule is

Reject the null hypothesis

Step-by-step explanation:

Answer:

88 feet. Please mark me brainliest I really need it

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given: A line passes through the points (2,4) and (5,6).

* Case 1:

If a line passes through the points (2, 4) and (5, 6)

Point slope intercept form:

for any two points  and

then the general form  for linear equations where m is the slope given by:

First calculate slope for the points (2, 4) and (5, 6);

then, by point slope intercept form;

* Case 2:

If a line passes through the points (5, 6) and (2, 4)

First calculate slope for the points (5, 6) and (2, 4);

then, by point slope intercept form;

Yes, the only equation of line from the given options  which describes the given line are;

 and

The ratio of points scored by Jennie, Sarah, and Sadie in the basketball games played last week was 1:3:5. If jenny scored 10 points last week, what was the total number of points scored by these three girls?

The ratio of points scored by Jennie, Sarah, and Sadie in the basketball games played last week was 1:3:5.

jenny scored 10 points last week game.

=> 1x, 3x, 5x.

=> 1(10), 3(10) , 5(10)

=> 10, 30, 50

Therefore, The points scored by Jennie, Sarah, and Sadie in the basketball game played last week was 10, 30, 50

The total number of points scored by these three girls are:- 10+30+50 = 90

Answer:oft-t

Step-by-step explanation:

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

Your mother

Step-by-step explanation:

[  3   9   13 ] is the Matrix showing all types of property available in key west .

A matrix is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns to represent a mathematical object or an attribute of such an entity in mathematics.

given in the table that how many types of property are there in the table

its a simple matrix which u can directly see

its a  3 x 1 matrix ...

[3  9  13] this matrix shows the required value

hope this helps...

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Answer:  [3 9 13]

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's write down all the factors of 12 and 54.

We can clearly see that the GCF (Greatest common factor) of 12 and 54 is 6.

Hence, the GCF of 12 and 54 is 6.

Answer:

The tip would be $6.00

Step-by-step explanation:

To tip 20% you move the decimal point to the left once to get 3.1. then you round to the nearest whole number which is 3. Finally, you double 3 which is 6.

I hope this helped! Have a nice day!

Answer:

Your answer is 2x³ + 7x²y + y²- x²

Step-by-step explanation:

(a) ( 2x³ + 4x²y + 5xy² - 3y² ) - ( x² - 3x²y +5xy² - 2y² ) ​

= 2x³  + 4x²y  +  5xy² - 3y² - x² + 3x²y  - 5xy² + 2y²

= 2x³ + 4x²y + 3x²y + 5xy² - 5xy² + 3y² + 2y² -  x²

= 2x³ + 7x²y + y²- x²  ans.

Hope its helpful!

Please mark me as brainlist.

Step-by-step explanation:

(a) ( 2x³ + 4x²y + 5xy² - 3y² ) - ( x² - 3x²y +5xy² - 2y² ) ​

= 2x³  + 4x²y  +  5xy² - 3y² - x² + 3x²y  - 5xy² + 2y²

= 2x³ + 4x²y + 3x²y + 5xy² - 5xy² + 3y² + 2y² -  x²

= 2x³ + 7x²y + y²- x²  ans.

Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.

The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:

tan (∅) = opposite/adjacent

We have the following:

Reference angle (∅) = 53 degrees

Length of opposite side = 21

Length of adjacent side = x

Plug in the values:

tan 53 = 21/x

x * tan 53 = 21

x = 21 / tan 53

x = 15.824

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Answer:

58.45

Step-by-step explanation:

Use BIDMAS

14.5 X 3.1 = 44.95

44.95 + 13.5 = 58.45

Answer:

58.45

Step-by-step explanation:

Here the statements 1, 2, 3, 4, 5, 7, 8, 10 are correct according to the rules of the shapes.

1: A rhombus is a quadrilateral with four equally sized sides. Each square is a rhombus since they all have four sides that are the same length. 2: Due to the parallel alignment of its opposing sides, every rhombus is a parallelogram. 3: It is true that all rectangles are parallelograms since they have two sets of parallel sides and two pairs of equal opposing sides. 4: The other is split into two equal halves by each bisector. 5: If a quadrilateral's diagonals are equal and bisect one another at right angles, it is a square. 7: Since the diagonals themselves are congruent, each bisected line segment is also congruent. 8: The diagonals split a rhombus's vertex angles into equal halves. The diagonals of a rhombus are at right angles to one another. 10: A square is a rhombus. Sometimes, this is accurate. When a rhombus has four right angles, it is true. So the statements 1,2,3,4,5,7,8,10 are correct.

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Answer:

It's written as

\(89.7 \times {10}^{9} \)

Or

\(8.97 \times {10}^{10} \)

Hope this helps you

Answer:

8.97 * 10 ^10

Step-by-step explanation:

We want one nonzero digit to the left of the decimal

8.97

We moved the decimal 10 places to the left

The exponent is positive 10 since we moved 10 places to the left

8.97 * 10 ^10

Answer:

Step-by-step explanation:

The inequality on the graph is the third option:

(2/5)*x - 3/2 ≥ y

Let's analyse the graph if the inequality.

We can see that there is a solid linear equation with a positive slope, and the shaded area is below that line, then the inequality is of the form:

y ≤ linear equation.

We know that the symbol "≤" must be used because of the solid line.

We also can see that when x = 0, y takes a velue between -1 and -2.

With that in mind the correct option is the third one:

(4/5)*x - 2y ≥ 3

Isolating y we get:

(4/5)*x - 3 ≥ 2y

(2/5)*x - 3/2 ≥ y

Changing the order:

y ≤ (2/5)*x - 3/2

That is the graphed inequality.

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Answer:

a-b-C+d-e+f-g

Step-by-step explanation:

Steps

$a-b-\left(C-\left(d-e\right)-f\right)-g$

Show Steps

$-\left(d-e\right):\quad-d+e$

$=a-b-\left(C+e-d-f\right)-g$

Show Steps

$-\left(C-d+e-f\right):\quad-C+d-e+f$

$=a-b-C+d-e+f-g$

Answer:

the answer is A

Step-by-step explanation:beacuse ik its right

Answer:

a) The margin of error for the interval is of 11.35.

b) The 98% confidence interval estimate for the population mean using the Student's t-distribution is between 298.65 and 321.35 millimeters.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 20 - 1 = 19

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 19 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.98}{2} = 0.99\). So we have T = 2.539

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 2.539\frac{20}{\sqrt{20}} = 11.35\)

In which s is the standard deviation of the sample and n is the size of the sample.

Thus, the margin of error for the interval is of 11.35.

The lower end of the interval is the sample mean subtracted by M. So it is 310 - 11.35 = 298.65 millimeters.

The upper end of the interval is the sample mean added to M. So it is 310 + 11.35 = 321.35 millimeters.

The 98% confidence interval estimate for the population mean using the Student's t-distribution is between 298.65 and 321.35 millimeters.

Answer:

at the end of the day the temperature would be -26° F

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

35 = x% of 70

35 = 1/2 of 70

x% = 50%

x = 50