Number 67.89 is rational or irrational with explanation ​

Answer:

33°

Step-by-step explanation:

the whole angle of DAB is 57° and a line is drawn to split it into 2 parts and one part is given.

X+24°=57°

X=57-24

X=33°{angle CAD=33°}

We get that statement (B) is the situation that is represented by the expression 3 + (−7).

We are given an expression:

3 + ( - 7 )

We need to identify the statement that represents the same expression:

For the statement, "A football team lost 3 yards on one play. The team gained 7 yards on the next play.", we get the expression as:

- 3 + 7

For the statement, "A football team gained 3 yards on one play. The team lost 7 yards on the next play.", we get the expression as:

3 + ( - 7 )

For the statement, "A football team gained 3 yards on one play. The team gained 7 yards on the next play.", we get the expression as:

3 + 7

Therefore, we get that statement (B) is the situation that is represented by the expression 3 + (−7).

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Answer:

Suppose there are 1000 lockers in a school hallway and they are all closed. Only 50 students

come through the hallway and start opening and closing the lockers. The first student opened all

the lockers. The second student closed every second locker and so forth. The Third student

changes the state of every 3rd locker. The fourth student changes the state of every 4th locker,

the fifth student changes the state of every 5th locker and so on, until the 50th student.

a. What is the state of the following locker numbers: #91, #1505, #625, #1000?

i. How do you know? (please show how you know)

According to the given information the expression solution are:

An equation is referred to as an identity if it has one or more variables and is true for all alternate values of the variables for which both sides of the equation are defined.

For instance,

the equation x 2 + 2 x = x(x + 2) is an identity since it holds true for all possible replacement values for x.

A conditional equation is one that holds true only for specific replacement values of the variable.

For instance, the equation 3 x + 4 = 25 is a conditional equation because it isn't true for all possible replacement values for x.

Without specifying any limitations, an equation is claimed to be an identity, but in reality, it is only an identity for replacement values for which both sides of the identity are defined.

The trigonometric expression is 9 sec2 x (1 - sin2x)

Apply Pythagorean identity

1 - sin2 x = cos2 x9 sec2 x (1 - sin2x)

= 9 sec2 x(cos2 x)

Apply reciprocal identity cosx = 1/ secx

= 9 sec2 x(1/sec2 x)

= 9

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Answer:

a shared multiple of the denominators of several fractions

Explanation : The denominator is the number at the bottom of the fraction and when two fractions have the same number at the bottom(denominator) then they have a common denominator.

Using the given bar graph, it is found that 1675 calories per day are needed by females between 9 and 13 years old, with this lifestyle.

A bar graph shows the number of times that each observation appears in the data-set.

From the bar graph in this problem, the number of calories needed for females given the age is as follows:

Hence, 1675 calories per day are needed by females between 9 and 13 years old, with this lifestyle.

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to get the equation of any straight line, we simply need two points off of it, let's use those points from the picture below.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{4 +2}{3 -1} \implies \cfrac{ 6 }{ 2 }\implies 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{3}(x-\stackrel{x_1}{1}) \implies y +2= 3 (x -1) \\\\\\ y+2=3x-3\implies {\LARGE \begin{array}{llll} y=3x\underset{(0~~,~~-5)}{\stackrel{\stackrel{y-intercept}{\downarrow }}{-5}} \end{array}}[/tex]

The value of the expression when x = -3 is - 18

Index form is defined as the power or exponent that is raised to a number or a variable.

From the information given, we have;

-2x(to the second power)

This is expressed as;

-2x²

Now, let's substitute the value of x as -3, we get;

-2(-3)²

Take the square

-2(9)

-18

Thus, the value of the expression when x = -3 is - 18

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Answer:Tangent

A chord is a segment whose endpoints are points on a circle. A secant is a line that intersects a circle in two points. A tangent is a line in the plane of a circle that intersects the circle in exactly one point. The point is called a point of tangency.

Step-by-step explanation:

The standard deviation of the method is 0.7193.

Standard Deviation:

Standard deviation of a data set is the square root of the calculated variance of a set of data.

The formula for standard deviation is,

[tex]\sigma^2 = \dfrac{\Sigma (x_{i} - \mu)^2}{n}[/tex]

Where

xi is an individual value

μ is the mean/expected value

N is the total number of values

Given,

Data set:

20.0, 20.0, 20.0, 20.1, 20.2, 20.5, 20.5, 20.6, 20.7, 20.7, 21.0, 21.2, 21.5, 21.6, 22.1, 22.3

Here we need to find the standard deviation.

To find the standard deviation we have to identify the following from the given set,

They are,

Count, N: 16

Sum, Σx: 333

Mean, μ: 20.8125

Now we have to apply the values on the formula,

In order to solve it,

[tex]\sigma^2=\frac{[(20-20.8125)^2+....+(22.3-20.8125)^2]}{16}[/tex]

When we simplify it then we get,

[tex]\sigma^2=\frac{8.2775}{16}[/tex]

So,

σ = √0.51734375

σ =  0.7193

Therefore, the standard deviation is 0.7193.

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Using it's concept and the graph of the function, the domain and the range are given as follows:

In a graph, the domain and the range are found as follows:

For this problem, the function is given by the following rule stated in the problem:

f(x) = (x² - 4x - 12)/(x + 2).

The graph of the function is given at the end of the answer. From it, we can see that the function unexpectedly devolves into a linear function. This is because -2 is a factor of x² - 4x - 12, hence (x² - 4x - 12) = (x + a)(x + 2), and x + 2 is simplified with the denominator.

The function is defined for all real values, and also assume all real values, hence:.

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The five-number summary for the data is: 2, 3, 5, 6.5, and 9.

Given the data, 2, 2, 4, 4, 5, 5, 6, 7, 9, the five-number summary can be determined as follows:

Minimum value: this is the lowest data value, which is, 2.

First Quartile (Q1); which is the middle of the first half of the data which is, 3.

Median: center of the data set, which is, 5.

Third Quartile (Q3): which is the center of the second half of the data set, which is, 6.5.

Maximum Value: which is the highest data value of the data set, which is, 9.

Therefore, the five-number summary for the data is: 2, 3, 5, 6.5, and 9.

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Answer:

thanks for the points

Step-by-step explanation:

thanks for the points

The image of the point A after the given compositions of transformation will be (5, 1).

We are given the coordinate of the point A as:

A = (1, - 3)

Now, we have to rotate it 90° about the origin.

The rule for a rotation by 90° about the origin is given by (x, y) will become (− y, x)

So, we get for point A as:

A' = (3, 1)

Now, we have:

Translation: f(x,y)=(x+2,y)

So, for point A' we get the translation as:

A" = ( 3 + 2, 1)

A" = (5, 1)

Therefore, the image of the point A after the given compositions of transformation will be (5, 1).

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Answer:

245 + 35x = 560

Step-by-step explanation:

35 x 7 = 245 (for monday)
Then the equation should be

245 + 35x = 560

It looks like you solved it too, your answer is correct btw! Lmk if you need help with the steps, or anything

Also, how you make this equation is this, you put how much he earned for monday, and then add it to 35x (x being the amount of cars he did) make sure to do = 560 at the end so you can solve it :)

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

Step-by-step explanation:

Since he gets  35$ for every car he washes and washed seven cars on Monday, he got 35*7=245. Now, you can minus the amount from it to 315. 315/35 is 9, so nine is your answer.

To phrase it into an equation, you can do when x=amount of cars washed, 35x=560-7*35.

Hope this helped!

The correct option is A. Quantitative.

In the study Quantitative data is collected as the calculation of quantity is being done.

Quantitative data is any collection of information that may be recognized and analyzed numerically.

Some key points related to Quantitative data are-

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The complete question is-

Determine whether the data collected in the study is qualitative or quantitative:

A study is conducted to estimate the average price of gasoline in a large city. To do this, the researchers select a random sample of of 100 gas stations, and record the pump prices for both regular unleaded and premium unleaded. The average price for the 100 stations is calculated, and used as an estimate for the average price of gasoline for the entire city.

A. Quantitative

B. Qualitative

Answer:

Rotation because you can see that the shape is rotated on the other half of the graph.

Step-by-step explanation:

Answer:

x = 35

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

x + 52 + x + 2x - 12 = 180

4x + 40 = 180 ( subtract 40 from both sides )

4x = 140 ( divide both sides by 4 )

x = 35

Using the mean concept, it is found that you need at least 40 active minutes on Sunday to achieve your goal.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

In a week, there will be 7 observations, and a bar graph can represent each observation(time in minutes). They are given as follows:

15, 45, 20, 0, 60, 30 and x.

We want the mean to be of 30, hence:

30 = (15 + 45 + 20 + 0 + 60 + 30 + x)/7

170 + x = 210

x = 210 - 170

x = 40.

You need at least 40 active minutes on Sunday to achieve your goal.

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The likelihood that exactly 13 students will pursue arts in the coming year is 76.47%.

So, to find the probability:

Given:

We now want to calculate the likelihood that 13 students will pursue arts in the following year.

That is,

Therefore, the likelihood that exactly 13 students will pursue arts in the coming year is 76.47%.

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After the conversion of the given decimal number, the binary number is (1001001110100.11001101)₂.

For the decimal number 4724.80345, the binary number is (1001001110100.11001101)₂.

(Refer to the table given below for working)

Therefore, after the conversion of the given decimal number, the binary number is (1001001110100.11001101)₂.

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The correct question is given below:

Convert 4724.80345 base ten to a binary number.

The profit as a function Q is Q² + 90Q + 5000.

It should be noted total revenue = Price × Quantity = 100Q

Total cost = 5000 + 10Q + Q²

Therefore, profit will be:

= Revenue - Cost

= 100Q - (5000 + 10Q + Q²)

= -5000 -90Q - Q².

= Q² + 90Q + 5000

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The equation for the plane consisting of all points that are equidistant from the points (−7, 1, 1) and (3, 3, 5) is 20x + 4y + 8z = -9.

In order to determine the distance of this plane (x, y, z) with the given points, we would use the distance formula.

Mathematically, the distance between three (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

For these points (x, y, z) and (−7, 1, 1), the distance is given by:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Distance = √[(x₂ - (-7))² + (y₂ - 1)² + (z₂ - 1)²]

Distance = √[(x₂ + 7)² + (y₂ - 1)² + (z₂ - 1)²]

By using the algebraic formulas, the expanded expression is given by:

(a - b)² = a² - b² - 2ab

(a + b)² = a² + b² + 2ab

Distance = √[(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1)]   .......equation 1.

For these points (x, y, z) and (3, 3, 5), the distance is given by:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Distance = √[(x - 3)² + (y - 3)² + (z - 5)²]

Distance = √[(x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)]    .....equation2.

Since both distances are equidistant, we would equate eqn. 1 and eqn. 2 and then simplify:

√[(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1)] = √[(x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)]

(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1) = (x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)

x² + 14x + 49 + y² - 2y + 1 + z² - 2z + 1 = x² - 6x + 9 + y² - 6y + 9 + z² - 10z + 25

14x + 6x - 2y + 6y - 2z + 10z + 52 - 43 = 0

20x + 4y + 8z + 9 = 0

20x + 4y + 8z = -9.

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x=5 is the required equation of straight line

The steepness of a line is determined by its slope. The slope is m in the equation for a line that is typically used, y = mx + b. The term "rise over run" is also frequently used to describe it and describes how much the y-value changes as the x-value does.

According to the given value;

slope of line is Y₂-Y₁/X₂-X₁

hence slope for given line will be

3-(-2)/5-5 =5/0 = ∞

slope is infinity means straight line is vertical in nature and vertical lines are of the form x=a where a is some constant

now we can observe that 5 is constant in both the given points so x=5 is the required line which passes through (-2,-6),(-2,5)

Hence,x=5 is the required equation of straight line .

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Step-by-step explanation:

x(x-4)(x+1) is a 3 degree polynomial in factored form with zeros 0,4 and -1

Just take each zero and change its sign, then stick an x in front of it to get the 3 factors

(x-0)(x-4)(x- -1) = x(x-4)(x+1)

= x(x^2-3x-4)

= f(x) = x^3 -3x^2 -4x

f(0) = 0

f(4) = 64-3(16)-4(4) = 0

f(-1) = -1 -3(-1)^2 -4(-1) = 0

graph the polynomial and it intersects the x axis in 3 places, the origin (0,0), (4,0) and (-1,0)

The total weight of the two animals is 1.3 x 10^4 lbs.

The given parameters are

Animal 1 = 4.23 x 103 lbs.

Animal 2 = 8.7 x 103 lbs.

Rewrite the parameters properly

Animal 1 = 4.23 x 10^3 lbs.

Animal 2 = 8.7 x 10^3 lbs.

The total weight of the two animals is calculated as

Total weight = Animal 1 + Animal 2

This gives

Total weight = 4.23 x 10^3 lbs + 8.7 x 10^3 lbs.

Factor out 10^3 lbs

Total weight = (4.23 + 8.7) x 10^3 lbs.

Evaluate the sum

Total weight = 12.93 x 10^3 lbs.

Rewrite as

Total weight = 1.293 x 10^4 lbs.

Approximate

Total weight = 1.3 x 10^4 lbs.

Hence, the total weight of the two animals is 1.3 x 10^4 lbs.

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