Simplify each expression
1. 8x+3y-x-2y

Since, Z(0)>Z(0.1) that is 3.07>1.28. So reject H(0). So the option 1 and 3 is correct.

In the given question,

H(0): μ=18 ; H(a): μ>18

x = 19.1

Conclude whether to reject or not reject H(0), and interpret the results.

σ = 1.6

α  = 0.1 (significance level) .

The test statistic is

Z(0) = {x-μ(0)}/(σ/√n)

Z(0)= (19.1-18)/16/√20

Z(0) = 3.07

The critical value is Z(0.1) = 1.28.

As we can see that;

Z(0)>Z(0.1) that is

3.07>1.28

So reject H(0).

So the option 1 and 3 is correct.

Reject H(0), the test statistic Z(0)=3.07 is Z(0)=3.07 is greater than the critical value Z(α)=1.28, for a right-tailed test therefore there is NOT enough evidence to reject H(0) that the mean number of likes is not equal to 18 mg per generic anti-histamine dose.

And

The test statistic falls within the rejection region.

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The right question is:

Select two responses below.

Select all that apply:

(1) Reject H(0). The test statistic Z(0)=3.07 is greater than the critical value Z(α)=1.28, for a right-tailed test therefore there is NOT enough evidence to reject H(0) that the mean number of likes is not equal to 18 mg per generic anti-histamine dose.

(2) Fail to reject H(0). The test statistic Z(0)=3.07 is greater than the critical value Z(α)=1.28, for a right-tailed test therefore there is NOT enough evidence to reject H(0) that the mean number of likes is not equal to 18 mg per generic anti-histamine dose.

(3) The test statistic falls within the rejection region.

(4) The test statistics is NOT in the rejection region.

The sum can be written in logarithms as 6z log 6

What is logarithm ?

The word "logarithm" comes from the combination of the Greek words "logos," which means "principle or concept," and "arithmos," which means "number." A logarithm is the power that must be increased to obtain a given number. It is shown by a number's log.

Use of property

log (ab) = log a + log b

log a^b = b log a

Given that,

log 6^8 + log 6^z

=log 6^8 + log 6^z

=log (6^8*6^z)

=log (6^6z)

=6z log 6

Therefore, the sum can be written in logarithms as 6z log 6

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Therefore by making a line through following points we can make graph which is parabola in shape

Two things are equal, according to an equation. Like this: 9 + 2 = 11 . It will have an equivalent sign "=". According to that equation, "this equals that" is expressed as "what is on the left (9 + 2) is equal to what is on the right (11).

Here,

Given Equation : x² = 8y

Given Equation agrees with conventional equation of parabola on positive y-axis

x² = 4ay

Comparison of the two equations yields,

4a = 8 ⇒ a = 2

Focus of parabola = ( 0 , 2 ) ( 0 , 2 )

Parabola vertex equals ( 0 , 0 )

Axis of Symmetry = y-axis

To sketch its, we find some points

with x = 4 or -4 we get

4² = 8y ⇒ 16 = 8y ⇒ y = 2

So, points are ( 4 , 2 ) and ( -4 , 2 ) ( -4 , 2 )

we obtain when x = 8 or -8.

(-8)² = 8y ⇒ 64 = 8y ⇒ y = 8

So, points are ( 8 , 8 ) and ( -8 , 8 ) ( -8 , 8 )

Therefore by making a line through following points we can make graph which is parabola in shape

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The correct question is :-

Which graph represents the equation x2 = 8y?

Yes, the proof of congruence of two triangles ∆ABC ≅ ∆GHF is possible.

The convergence method which proves this congruence is SSS(side-side-side) congruence.

We have given the sketch of two triangles as seen above. We have to prove ∆ABC ≅ ∆GHF

Now , AB = √(-7+7)² + 5² = 5 in triangle ABC and FG = 5 in triangle FGH,

so, AB ≅ FG

Because AC = 3 in triangle ABC and FH = 3 in triangle FGH,

so, AC ≅ FH

To find the lengths of BC and GH , we can use distance formula.

Length of BC :

BC = √[(x₂ - x₁)² + (y₂ - y₁)²]

(x₁, y₁) = B(-7, 0) and (x₂, y₂) = C(-4, 5).

BC = √[(-4 + 7)² + (5 - 0)²]

= √[32 + 52]

= √[9 + 25]

= √34

Length of GH :

GH = √[(x₂ - x₁)² + (y₂ - y₁)²]

(x₁, y₁) = G(1, 2) and (x₂, y₂) = H(6, 5).

GH = √[(6 - 1)² + (5 - 2)²]

= √[52 + 32]

= √[25 + 9]

= √34

Conclusion :because BC = √34 and GH = √34,

=>BC ≅ GH

All the three sides of one triangle is congruent to the corresponding sides of other triangle.

By SSS congruence postulate,

ΔABC ≅ ΔFGH

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Binary Variable is  a variable that can only be 1 or 0. Binary variables are categorical variables that can take only one of two values, are usually represented as Boolean (True or False) or integer variables (0 or 1), and usually have no attributes indicates that it exists.

Binary variables have only two states, such as 0 or 1. 0 defines the variable does not exist, 1 defines the variable exists. For example, for the patient-defining variable Smoker , 1 means the patient smokes and 0 means the patient does not smoke. Binary variables can be viewed as if they were scaled by intervals, which can lead to misleading clustering results. Therefore, a method that defines binary data is essential for computing dissimilarities.

Binary data is data whose unit can take on only two possible states. These are often labelled as 0 and 1 in accordance with the binary numeral system and Boolean algebra. Binary data occurs in many different technical and scientific fields, where it can be called by different names including bit (binary digit) in computer science, truth value in mathematical logic and related domains and binary variable in statistics.

Binary data is used to represent one of two conceptually opposite values. "correct" or "incorrect".

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the interest will be $1000 IBM corporation bank.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

So simple interest will be = 10000*10*1 /100 = $1000

Hence, the interest will be $1000 IBM corporation bank.

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Answer:

The answer is b!

Step-by-step explanation:

the answer is A .

the open end of the arrow points to the bigger variable. When the variable is included there will be a line under the arrow

By using Euclidean geometry, the set of side lengths  2.5 cm, 1.8 cm, 4 cm can form a triangle.

The sum of the lengths of any two sides must be greater than the length of the third side.

a + b ≥ c

A triangle is a three-sided polygon with three straight sides. It is a basic geometric shape that is found in many areas of mathematics and geometry.

Using this rule, we can determine which of the given sets of side lengths can form a triangle:

(a) 3 cm, 4 cm, 7 cm: It is not possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (3 cm + 4 cm = 7 cm) is equal to the length of the third side.

(b) 2 cm, 3 cm, 7 cm: It is not possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (2 cm + 3 cm = 5 cm) is less than the length of the third side.

(c) 2.5 cm, 1.8 cm, 4 cm: It is possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (2.5 cm + 1.8 cm = 4.3 cm) is greater than the length of the third side.

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Answer: K=10

Step-by-step explanation:

To begin, you should multiply out the terms in front of the parentheses. This results in: 47=2k+6+3k-9

Next, we can combine like terms: 47=5k-3

Add 3 to both sides: 50=5k

Divide both sides by 5: 10=k

k=10

The value of k will be 7 by using conditions slope of the graph.

What is slope?

Slope of a line measures its steepness . Slope is calculated as "rise over run" (change in x divided by change in y).

Two ways to find the slope :

1. Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates

(rise/run or slope).

2. Differentiate the line's equation and value of dy/dx that will be value of slope .

Mathematically ,

to find slope we differentiate the graph equation :

2dy/dx = 1/7k

dy/dx = 1/14k

Given slope = 1/2

so, 1/14k = 1/2

k = 7.

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a)The value of  ∠b=64°.

b)The values of angles q, r, s, t are ∠q= 65°, ∠r=65°, ∠s=50°, ∠t=65°.

c)The value of  ∠B=72 degrees.

The same-side interior angles are additional if a transversal connects two parallel lines. Alternate interior angles are equivalent if a transversal connects two parallel lines. Corresponding angles are equal.

a) Given line PQ is parallel to ST.

   One of the theorems of parallel lines is, Corresponding angles are equal.

Here the corresponding angles are ∠a, ∠b.

so, ∠a=∠b

∴∠b=64°

b) It is given that lines B and C are parallel, according to one of the theorems of parallel lines, vertically opposite angles are equal. So, the angle opposite to 65° is also equal to 65°. Sum of the angles suspended by a line on another line is 180°. Therefore the other angle in the triangle is 180°-130°=50°.

Since the sum of interior angles in a triangle is 180°, the angle q will be:

   ∠q= 180°-(65°+50°)

    ∠q= 65°.

Vertically opposite angles are equal, therefore ∠q=∠r=65°.

∠s=180°-(65°+65°)

∠s=50°.

Corresponding angles are equal, therefore

130°=65°+∠t

∠t=65°.

c) Given lines A, and B are parallel. We know that the Corresponding angles are equal, therefore

3m=4m-24

⇒m=24

Therefore ∠B=4(24)-24

∠B=72 degrees.

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Answer:

Step-by-step explanation:

answer is a

The expected length of the piece that we are left with after breaking twice is L/4 and the variance Var(X) is 7L^2/144.

In the given question, consider a stick of length 1.

We break it at a point which is chosen randomly and uniformly over its length and keep the piece that contains the left end of the stick.

We then repeat the same process on the piece that we were left with.

We have to find expected length of the piece that we are left with after breaking twice.

In the same setting as Q7, suppose the length of the piece that we are left with after breaking twice is Y.

We also have to calculate the variance Var(Y).

Following Laws are used in the solution

Law of Iterated Expectations: E[X] = E[ E[X|Y] ]

& Law of total variance: Var(X) = E[Var(X|Y)]+Var(E[X|Y])

Now, Y = Length of the stick after we break it the first time

and X = length of the stick after we break it the second time

As both the distribution is uniformly distributed.

Now, E[Y] = L/2 and Var(Y)= l^2/12

E(x|y)[X|Y=y] = y/2 and Var(x|y)[X|Y=y] = y^2/12

As the expectation of uniform distribution over {a,b} is (b-a)/2 and variance is (b-a)^2/12

Using Law of Iterated Expectations

E[X] = E[ E[X|Y] ]

E[X] = E[ y/2 ]

E[X] = \int_{L}^{0}

E[X] = L/4

Now using Law of Total Variance

Var(X) = E[Var(X|Y)]+Var( E[X|Y] )

Var(X) = E[y^2/12]+Var(y/2)

Var(X) = (1/12)*E[Y^2]+(1/4)*Var(Y)

Var(X) = (1*12)*(Var[Y] + (E[Y])^2) + (1/4)*Var(Y)

Var(X) = (1/12)*(L^2/12+L^2/4) + (1/4)*(L^2/12)

Var(X) = 7L^2/144

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The integers in the set S:{-79, 80, 39, 40) that will make the inequality 1/0.4(m - 0.4) ≤ 1/21(m - 39) false are: S:{39, 40}​.

Determine the integers

In order to determine which integers are true and false with respect to a solution of the given inequality, we would have to test the given integers by substituting their values into the inequality as follows;

For integers (-80, 79), we have:

1/0.4(m - 0.4) ≤ 1/21(m - 39)

1/0.4(-80 - 39) ≤ 1/21(-40 - 39)

1/3(-39) ≤ 1/6(-40)

-39.6 ≤p< -40 (True).

For integers (-80, 79), we have:

1/0.4(m - 80) ≤ 1/21(m - 39)

1/3(24 - 3) ≤ 1/21(24 - 12)

1/3(27) ≤ 1/6(36)

79.6 ≤ p < 80 (False).

For integers (-40, -39), we have:

1/3(27) ≤ 1/6(36)

1/3(24 - 3) ≤ 1/21(24 - 12)

1/0.4(-80 - 39) ≤ 1/21(-40 - 39)

-39.6 ≤ -40 (True).

For integers (-80, 79), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(12 - 3) ≤ 1/6(12 - 12)

1/3(9) ≤ 1/6(0)

3 ≤ 0 (False).

For integers (12, 24), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(12 - 3) ≤ 1/6(12 - 12)

1/3(9) ≤ 1/6(0)

3 ≤ 0 (False).

1/3(m - 3) ≤ 1/6(m - 12)

1/3(24 - 3) ≤ 1/6(24 - 12)

1/0.4(-80 - 39) ≤ 1/21(-40 - 39))

79.6 ≤ p < 80  (False)

1/0.4(m - 0.4) ≤ 1/21(m - 39) false are: S:{39, 40}​.

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Answer: $144

Step-by-step explanation: To find the price she gets paid for 1 hr we need to divide the money by the hours. So, 90 / 5 = 18.

So, now we know she gets paid 18 dollars an hour. So, we need to find out how much she earns in 8 hrs. So, we would simply multiply the 18 by the 8, to get $144.

Answer:

correct answer is option b i think...

For the given expression the value of x must be 11.

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 expression is h(x) = 11. The value of x will be calculated as,

h(x)=11

h(x) = x

Compare the above equations and find the value of x,

x = 11

Therefore, for the given expression the value of x must be 11.

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Answer:

Below

Step-by-step explanation:

231469.335329 to the nearest thousand.     '1' is the thousand position

the '4' next to it says leave the '1' alone to get

231000      rounded to nearest thousand.

The measure of the spread of scores within a set of data is termed as standard deviation. Usually, we are interested in the standard deviation of a population. since, we are often presented with data from a sample only, we can estimate the population standard deviation from a sample standard deviation.

When to use the sample or population standard deviation ?

Population standard deviation is of great intrest because our population contains all the values we are interested in. Therefore, we would normally calculate the population standard deviation In two cases first when we have the entire population or second we have a sample of a larger population, but we are only interested in this sample and do not wish to generalize our findings to the population. but, in statistics, a sample is presented from which we wish to estimate (generalize to) a population, and the standard deviation is no exception to this.

Thus it can be concluded that, if we have all is a sample, but we wish to make a statement about the population standard deviation from which the sample is drawn, we need to use the sample standard deviation. There a Confusion can often arise as to which standard deviation to use due to the name "sample" standard deviation incorrectly being interpreted and not the estimate of the population standard deviation based on the sample.

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If the angle between two vectors is represented by theta and it is equal to zero or 180 degrees then the following angles would mean the vectors are parallel .

Given :

if the angle between two vectors is represented by , tell if the following angles would mean the vectors are orthogonal, parallel or neither.

if two vectors points are given then find the dot product of vectors if the result is equal to zero then the two vectors are orthogonal vectors .

If they were parallel the angle would be 0 or 180 degrees, therefore, the two vectors are not parallel.

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The interest owned and the maturity value of the loan is $217,300.

Simple interest is calculated using the following formula. PRT/100 is the formula for simple interest (SI). In this case, the principal amount is P, the interest rate is R, and the interest period is T. The total sum that must be paid consists of the principal amount plus basic interest, or P + SI.

The interest rate for the loan is denoted by this proportion. When you deposit money in a high-yield savings account, for instance, a bank will give you interest. Simple interest examples include monthly-amortized auto loans and store installment loans; both have a dipping loan balance with each monthly payment as well as a dipping interest rate.

Principal amount=205,000

Given that the interest is 6%

=205000(6/100)

=12300

The maturity amount of loan is:

=205000+12300

=$217300

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The valid conclusion is  A. We can be 90% confident that the mean amount of money spent at sporting events last year by all the students at this university is between $217 and $677.

The confidence interval used by the student researcher refers to the probability that the university's population parameter (average amount that students spent on sporting events last year) will fall between $217 and $677 for 90% of the time.

Thus, the interval measurement gives the researcher some degree of certainty that the calculated sample mean falls within the population mean most of the time.

Hence ,we can be 90% confident that the mean amount of money spent at sporting events last year by all the students at this university is between $217 and $677.

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Answer:

Step-by-step explanation:

(7, -14)

y - y1 = m(x - x1)

y - (-14) = -6(x - 7) = y + 14 = -6(x - 7)

Standard Form

y + 14 = -6x + 42

y = -6x + 28

Opposite of an integer on the number line is the same integer with opposite sign

what is number line ?

The visual representation of numbers on a straight line is called a number line. On an endless line that extends on both sides, either horizontally or vertically, this line is used to compare numbers that are spaced at equal intervals. The numbers on a horizontal number line grow as we approach towards the right side and drop as we move towards the left.

The number line's opposite of the integer "a" is "-a"; hence, the opposite of the integer "-a" is "a" on the number line, but on the other side of 0.

For example,

The number line's opposite of the integer "4" is "-4"

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The solution to the inequality expression 3/4m > −12 is m > -16

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

34m>−12

Rewrite properly

So, we have the following expression

3/4m > −12

Multiply both sides of the expression by 4

So, we have the following representation

3m > -48

Divide both sides of the expression by 3

m > -16

Hence, the solution is m > -16

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45 people used credit card on that particular day , this could be found out using simplified multiplication.

What is proportion?

A quantitative relation is an ordered try of numbers a and b, written a / b wherever b doesn't equal zero.

A proportion is Associate in Nursing equation within which 2 ratios ar set up to one another.

Main body:

We have been given that during one particular sales day, 75% of the store's customers paid with credit cards. There were 60 customers that day.

To find the number of people, who used credit card, we will find 75% of 60.

The number of people who used credit card = (75 / 100 )* 60

The number of people who used credit card = 0.75 *60

The number of people who used credit card = 45

Therefore, 45 people used credit card on that particular day.

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[tex]Answer:\ cos(\theta_1)=\boxed{-\frac{40}{41} }[/tex]

Step-by-step explanation:

[tex]\displaystyle\\sin(\theta_1)=\frac{9}{41}\ \ \ \ \ \ 90^0 < \theta_1 < 180^0\ \ \ \ \ \ \ cos(\theta_1)=?\\\\sin^2(\theta_1)+cos^2(\theta_1)=1\\\\cos^2(\theta_1)=1-sin^2(\theta_1)\\\\cos^2(\theta_1)=1-(\frac{9}{41})^2\\\\cos^2(\theta_1)=1-\frac{81}{1681} \\\\cos^2(\theta_1)=\frac{1(1681)-81}{1681} \\\\cos^2(\theta_1)=\frac{1600}{1681} \\\\[/tex]

Extract the square root of both parts of the equation:

[tex]\displaystyle\\\cos(\theta_1)=б\sqrt{\frac{1600}{1681} } \\\\\cos(\theta_1)=б\sqrt{\frac{40^2}{41^2} } \\\\\cos(\theta_1)=б\sqrt{(\frac{40}{41})^2 } \\\\\cos(\theta_1)=б\frac{40}{41}[/tex]

[tex]\displaystyle\\Since\ 90^0 < \theta_1 < 180^0, \\\\ therefore\ cos(\theta_1)=-\frac{40}{41}[/tex]

Answer:

2.1 cm

Step-by-step explanation:

All the sides of a cube are equal.

let x = side of a cube

Volume of a cube = x³

Therefore x = [tex]\sqrt[3]{9.261}[/tex] = 2.1 cm

The standard matrix of the linear transformation given in the question is

=  1/ 5  [   1  2 ]

           [   2  4 ]

The direction vector of the given line is , v = ( 1 ,2 ).

So the projection of the line will be,

projection ( x ,x ) = ( (x , y ) . v / v^2 )v

= ( ( x + 2y)/5 ) v

Therefore, the required standard matrix will be ,

 1/5    2/5

 2/5   4/5

= 1/ 5 [   1  2 ]

         [   2  4 ]

A matrix is also known as a rectangular array . The elements are arranged in the form of rows and tables forming a table . Arrays are an important part of both mathematical and computational applications.

The data in a conputer is stored in the form of an array . We can perform various operations on matrix like addition, subtraction , multiplication or division.

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