Solve the following
simultaneous
equations using an
algebraic (not
graphical) method.
3x + 4y = 7
2x - 3y = 16

The inequality of the graph shown below is  y ≤ -x - 4

An equation is an expression that shows the relationship between two or more numbers and variables.

Inequality provides a comparison between non equal numbers and variables.

The inequality shown is a straight line passing through (-4, 0) and (0, -4). The equation of the straight line is:

y - 0 = [(-4 - 0)/(0- (-4)](x - (-4))

y = -1(x + 4)

y = -x - 4

The inequality is a thick line to the left. Hence it is  y ≤ -x - 4

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Four laws of Logarithm

Logarithm, in math refers to the power to which a number known as the base should be raised to result to a given number

Examples of some of the laws of logarithm

The product rule: this is used for multiplications

log a * log b = log (a + b)

quotient rule: the quotient is applied while dividing

log (a/b) = log a - log b

power rule: when a number is raised to power, when applied log, the power will be multiplying the log of the number

logₐ C ᵇ = b * logₐ C

identity rule: when the base and the number to find the log are equal the the log is 1

logₐ a = 1

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0. 63212  is the probability that a repair will take less than 2 hours.

What is the simple definition of probability?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                        In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.

P( X > 2 ) = 1 - P ( X/ leq2 )

             = 1 - F( 2)

             = 1 - [tex]e^{0.5 * 2}[/tex]

              = 0. 63212.

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The probability that 10 squared centimeters of dust contains more than 10140 particles is 0.1841

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

The mean asbestos particles in 1 cm2 is given as 1000, therefore in 10 cm2 of dust, the mean number of particles is given as: 1000*10 = 10,000

The number of particles here is given as:

X ~ Poisson(y = 10000)

Therefore the normal approximation here is given as:

X Nu = 10000,02 = 10000)

The probability here is computed as:

P(X > 10090)

Converting it to a standard normal variable, we get here:

10090 – 10000 P(Z > V10000

P(Z > 0.9)

Getting it from the standard normal tables, we get here:

P(Z > 0.9) = 0.1841

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Answer:

-35.4

Step-by-step explanation:

Using PEMDAS divide 63 first by 5 and u will get:

Now we have 12.6-48. If we subtract them together we will get:

Hence, the answer is -35.4

The equation that can be used to find the number of seconds in a number is [60s = m].

So, an equation that finds the number of seconds in a number of minutes.

We know that:

Then, the equation will be:

Therefore, the equation that can be used to find the number of seconds in a number is [60s = m].

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The slope of the line is 400

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

Start position = 600 feet

Rate of ascending = 400 feet per minute

The above parameters can be interpreted as

Initial position = 600 feet

Rate = 400 feet per minute

The rate is the slope

So, we have

Slope = 400

Hence, the slope is 400

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The probability is 0.2322.

From the question, we have

Probability that the person who visit her restaurant will spend at least $125 is : p = 0.4

Total number of people : n= 8

Probability that 4 will spend at least $125,

P(X=4)= 8C4(0.40)^4 (1-0.4)^4

=0.2322

Probability:

Probability is another word for possibility. This area of mathematics examines how random events happen. The value might be between 0 and 1. Mathematicians have used probability to forecast the likelihood of certain events. In general, probability relates to how likely something is to happen. You can better understand the potential results of a random experiment by using this fundamental theory of probability, which also holds true for the probability distribution. Utilize probability to ascertain how likely something is to occur. Many things are difficult to foresee with absolute confidence.

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Question 1

y = mx+7

5 = m*(-2)+7

5 = -2m+7

-2m+7 = 5

-2m = 5-7

-2m = -2

m = -2/(-2)

===============================================

Question 2

y = 2x+c

4 = 2(1)+c

4 = 2+c

4-2 = c

2 = c

The area of the given shape is 78.5 unit²

Given,

The shape is 1/4th part of circle.

The radius is given as 10 units

We have to find the area of the shape.

Here,

The area of a circle is pi times the radius squared (A = π r²).

Area of circle = π × r²

Then

Area of 1/4th part of circle = π × r² / 4

That is,

Area of 1/4th part of circle = 3.14 × 10² / 4

Area of 1/4th part of circle  = 314 / 4

Area of 1/4th part of circle = 78.5 unit²

That is,

The area of the given shape is 78.5 unit²

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Answer: a is the correct answer

Step-by-step explanation:

Answer:

50000 ppppp567765

Step-by-step explanation:

Everytime you can come over and play with your hair

When we know the population standard deviation σ, we use a standard normal distribution to calculate the error-bound EBM and construct the confidence interval.

The value of z needs to be found for that is equal to the confidence level (in decimal form) which is in the middle of standard normal deviation Z ~ N(0, 1). One doesn't know the Population Standard Deviation (SD) unless one measures the entire population data points. One can calculate SD. If one means estimating the SD of the population then we can answer that. Any dataset is measured and reported in at least two ways: Center Tendency of the data set (Mean, Median or Mode) and Variability of the data set (Range, SD, etc.)

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1. The three lengths are B. 18cm, 12cm, and 9cm which cοuld be the lengths οf the sides οf a triangle.

2. The third side D. It must be greater than οr equal tο 6 and at mοst 24.

A physical measure οf distance between twο places in space is length. It is a fundamental quantity that is emplοyed in bοth engineering and physics. The Internatiοnal System οf Units (SI) uses metres as the unit οf length (m). In geοmetry, length plays a crucial rοle in describing the size and lοcatiοn οf geοmetrical shapes in space.

Accοrding tο the Triangle Inequality Theοrem,

The tοtal οf twο sides οf a triangle must be greater than the sum οf the third side, accοrding tο this theοrem. If all three cοmbinatiοns are true, yοu will have a true triangle.

1) Yοu must gο thrοugh each οf these οptiοns οne by οne tο ensure that the triangle is feasible. Cοnsider the triangle tο have the side lengths a, b, and c, and the theοrem tο be an inequality, which states:

a+b > c, a+c > b, and b+c > a.

As per οptiοn (B),

a = 18, b = 12, and c = 9

Here, Triangle Inequality Theοrem satisfies.

Thus, the three lengths are 18cm, 12cm, and 9cm which cοuld be the lengths οf the sides οf a triangle.

2. By the prοperties οf the triangle, the sum οf the square οf twο lengths is equal tο the third side length οf the triangle.

Always remember that when yοu add twο sides tο a triangle, the sum will cοme οut tο be higher than the third side’s length.

Hence, D. It must be greater than οr equal tο 6 and at mοst 24.

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y = 500(0.7)ˣ is the equation that best captures this circumstance.

Given data,

Suppose a culture of bacteria begins with 500 cells and dies 30% each year.

y = abˣ, where an is y's starting value, b is its rate of decay, and y and x are variables, describing an exponential decay.

A = 500 because there are 500 cells in the culture at the beginning. Each year, 30% of the cells die,

Hence b = 100% - 30% = 0.7

The formula is y = 500(0.7)ˣ

Consequently, y = 500(0.7)ˣ is the equation that best captures this circumstance.

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In order to prove triangles are congruent using the sas postulate, the two sides and one angle of the one triangle should be equal to the two sides and one angle of second triangle

Here the given postulate is sas  postulate

The sas stands for Side - Angle - Side postulates

The congruent is defined as the two shapes that has same size and shape.

Two triangles can be proved congruent by using the sas, sss, asa postulates

According to sas postulate of the triangle, if two sides and one angle of the triangles must be equal to the two sides and one angle of second triangle

Hence, In order to prove triangles are congruent using the sas postulate, the two sides and one angle of the one triangle should be equal to the two sides and one angle of second triangle

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The y intercept of the line passing through the points (12,-2) and slope -1/6 is  0  .

In the question ,

it is given that ,

the slope of the line is -1/6 ,

the line passes through the points (12 , -2)

we know that the equation of the line is written as

y = mx + c

where, "m" is the slope

and c is the y intercept .

Since the line passes through point (12,-2) , it should satisfy the equation of the line , that is

-2 = (-1/6)*12 + c

-2 = -2 + c

c = -2 + 2

c = 0

So , y intercept is 0 .

Therefore , The y intercept of the line passing through the points (12,-2) and slope -1/6 is  0  .

The given question is incomplete , the complete question is

Find the y intercept of the line passing through (12,-2) and slope = -1/6 ?

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Answer:

$25.00

Step-by-step explanation:

Total amount of bill is $25.

Given information:

The amount of tip = $4.50

The percentage given = 18%

4.50 of 18% is $25

a) Using PEMDAS, the value of expression 5² - 9 ÷ 3 is 22.

b) Using PEMDAS, the value of expression 8 + 6 - 2× 2 -3² is 1.

According to the PEMDAS rule, the computation wrapped in brackets or the parenthesis comes first in the order of operation. Exponents (degrees or square roots) are then operated on, followed by multiplication and division operations, and finally addition and subtraction.

Given,

Expressions:

a) 5² - 9 ÷ 3

Using PEMDAS,

Squaring,

25 - 9 ÷ 3

Dividing,

25 - 3

Subtracting,

22

Using PEMDAS, the value of expression 5² - 9 ÷ 3 is 22.

b) 8 + 6 - 2× 2 -3²

Using PEMDAS,

Squaring,

8 + 6 - 2 × 2 - 9

Multiplying,

8 + 6 - 4 - 9

Adding,

14 - 4 -9

Subtracting,

1

Using PEMDAS, the value of expression 8 + 6 - 2× 2 -3² is 1.

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Answer:

Step-by-step explanation:

First, write it in slope-intercept form.

8x-4=y

Rearrange this to get 8x-y=4.

A=8

B=-1

C=4

It is a valid probability model when pew research center reported that among months, family size is shrinking.

Given that,

pew research center reported that among months, family size is shrinking. suppose we are to randomly select one mother (age 40 to 44) and record the number of children she has. Here is a probability model.

We have to find explain why this is a valid probability model.

We know that,

In the picture we can see,

Probability is 0.22+0.41+0.24+0.13 = 1

Since all probability are less than 1 and sum of all probability is equal to 1.

Therefore, It is a valid probability model when pew research center reported that among months, family size is shrinking.

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The sales of phones and accessories should be 6 and 12 each, correspondingly.

The data stated in question-

Let 'P' be the number of the phones sold.

Then, the accessory sold be '2P'.

The equation will form for the total cost will be;

11P  +  3(2P) = 102

11P  +  6P = 102

17P = 102

P = 102 / 17 =

P = 6  (number of sold phones)

Accessories sold = 2P = 2 x 6 = 12

Thus, the sales of phones and accessories should be 6 and 12 each, correspondingly.

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Square root of 15.625 is 3.906

What in mathematics is a square root?

A number can be generated by multiplying the square root of that number by itself. The word" square root" is represented by the symbol" sqrt" square root of, end square root. The reverse of squaring a number is chancing the square root.

How is the square root calculated?

The result of multiplying a number by itself yields its square value, while the square root of a number can be set up by looking for a number that, when squared, yields the original value. It follows that a a = b if" a" is the square root of"b."

Find the nearest perfect square, in this case 16 .

Subtract 4 from the number (15.625) (the square root of 16). The outcome is around 3.906

Calculate 3.953 by averaging 4 and 3.906. This approximate value represents the square root of 15.625.

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Answer:

450 bacteria

Step-by-step explanation:

90 percent of 100 is 90 90x5 is 450

Length of AB = 8.06 units

Length of BC = 8.94 units

Length of AC = 9.22 units

What is a Scalene Triangle?

A scalene triangle is a type of triangle with three different length sides and three interior angles that add up to 180 degrees. Scalene triangles have no equal of parallel sides , hence there is no line of symmetry. The interior angles of a scalene triangle can be acute , right or obtuse angles.

Given data ,

Triangle ABC with vertices

A( 5 , 12 ) , B( 13 , 13 ) and C( 11 , 5 )

From the coordinates , we can see that

Now ,

When two points are given P( x₁ , y₁ ) and Q( x₂ , y₂ ) , the distance between the two points is given by distance formula

D = √( x₂ - x₁)² + ( y₂ - y₁)²

So , Length of AB is given by

AB = √( 13 - 5 )² + ( 13 - 12 )²

AB = √( 64 + 1 )

AB = √65

AB ≈ 8.0622

So , Length of AB = 8.06 units

And , Length of BC is given by

BC = √ ( 11 - 15 )² + ( 5 - 13 )²

BC = √ ( 16 + 64 )

BC = √ 80

BC ≈ 8.944

So , Length of BC = 8.94 units

And , Length of AC is given by

AC = √ ( 11 - 5 )² + ( 5 - 12 )²

AC = √ ( 36 + 49 )

AC = √85

AC ≈ 9.219

So , Length of AC = 9.22 units

Since , the lengths of AB , BC and AC all are different , we can say that the triangle ABC is a scalene triangle

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Answer:

3/16

Step-by-step explanation:

Step 1) Calculate the difference

The first step is to find the absolute difference between 1/8 and 3/12. We do that by subtracting 3/12 from 1/8, like this:

1/8 - 3/12 = |1/8|

Step 2) Divide the difference by two

Next, we divide the absolute difference by two. This gives us half of the absolute difference. To do this, we divide the answer in step 1 by 2, like this:

1/8 ÷ 2 = 1/16

Step 3) Add half the difference

In the final step, we add half of the absolute difference to the lowest fraction. The lowest fraction of 1/8 and 3/12 is 1/8. Therefore, we add 1/16 to 1/8, like this:

1/8 + 1/16 = 3/16

Per our calculations above, the fraction exactly halfway between 1/8 and 3/12 is as follows:

3/16

Hope this helps! :)

There is 48% probability that the two socks will match .

The branch of mathematics concerned with the occurrence of random events. Values ​​are represented from 0 to 1. Probability was introduced into mathematics to predict the probability of an event occurring. Probability basically means how likely it is that something will happen. This is the basic theory of probability and is also used in probability distributions to learn possible outcomes of random experiments. To determine the probability of a single event occurring, we first need to know the total number of possible outcomes.

Since there are a total of 35 socks, the probability of both socks being blue is

P(blue) = 15/35 * 14/35 = 3/35 * 14/7 = 3/35 * 2 = 6/35

The probability of both being grey is

P(grey) = 20/35 * 19/35 = 19/35 * 4/7  = 76 / 245

The probability that they match is

P(blue) + P(grey) = 6/35 + 76/245  =  42+76/245 = 118/245 = 0.48 = 48%

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Answer:

15

Step-by-step explanation:

Let's try to list the factors of 60 first.

60 { 1,2,3,4,5,6,10,12,15,20,30,60}

Now, it says it's a double digit number, so these are the remaining answers.

{10,12,15,20,30,60}

Since it is a multiple of 3, these are the possibilities.

12,15,20,30,60

After that, since it says that it's odd, we only have one possible solution left.

15

Answer:

5 grams, 9.4 grams, 0.35 kilograms

Step-by-step explanation:

9.4 g and 5g are already converted so don't worry about those.

0.35 kilograms translates to 350 grams.

from smallest to largest thatd be

5, 9.4, 350