Liam is 3 years older than his little sister Carin. Together they're 31 years old. How old is Liam? Solve the problem with an equation

Let [tex]x=t[/tex]. Then

[tex]x+z = 0 \implies z = -x = -t[/tex]

[tex]x + y + z = 6 \implies y = 6 - x - z = 6 - t - (-t) = 6[/tex]

so our parametric equations for the line are

[tex]\begin{cases}x(t) = t \\ y(t) = 6 \\ z(t) = -t\end{cases}[/tex]

where [tex]t\in\Bbb R[/tex].

Final answer:

The odds against exactly 5 cars passing over the bridge in that time is calculated as 4:21

A probability must be between 0 and 1 (nothing can happen with a greater than 100% likelihood). The chances are not as limited. Odds can be any positive number; for example, a chance of 2/3 is equivalent to odds of 2/1. By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.

By dividing the odds in the first group by the odds in the second group, the odds ratio is calculated. For many clinicians, odds and odds ratios are difficult to comprehend. Odds are calculated by dividing the likelihood of an event happening by the probability that it won't.

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Answer:

Question 4x-8/2=10       Answer X=7

Step-by-step explanation:

          [tex]\frac{2\left(4x-8\right)}{2}=10\cdot \:2[/tex]

        4x-8=20

        4x-8+8=20+8

        4x=28

          [tex]\frac{4x}{4}=\frac{28}{4}[/tex]

                       X= 7                                

Hope this helps

Pls mark brainliest

According to the given statement Outliers would be any sightings that are more than 1.5 IQR below Q1 or more then 1.5 IQR above Q3.

An outlier is a value that is significantly different from the other values in a random sampling of a population. In some ways, this definition leaves it up towards the analyst (or a consensus process) to determine what is abnormal.

Identifying potential outliers is critical for such following reasons. An outlier could imply faulty data. For example, the data could have been wrongly coded, or an experiment could have been done erroneously.

An outlier is defined as an observation that is less than or more than Q3 times IQR.

We need to look for place variances in Q1 and Q3.

When we utilize the IQR approach to discover outliers outside of Q1 and Q3, we create a "fence." Outliers are any values that fall outside of the defined boundary.

To construct this fence, we take 1.5 times the IQR, deduct it from Q1, and add it to Q3.

IQR = (1.5 - Q1)

IQR = (1.5 + Q3)

This provides us with the minimum and maximum fence posts to which we can compare every observation.

the given statement Outliers would be any sightings that are more than 1.5 IQR below Q1 or more then 1.5 IQR above Q3.

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The value of A - B is - 12

It is given that A + B = 0 .......... ( Eq . 1 )

⇒ A = - B ............ ( i )

Another equation which is given is :

AB  = - 36 ........... ( Eq . 2 )

Using (i) in Eq . 2

- B ( B ) = -  36

- B ² = - 36

B ² = 36

B  = √ 36

B = 6 .......( ii )

Using B = 6 in ( i ) ,

A B = - 36

A ( 6 ) = - 36

A = -6

This implies,  A = - 6 and B = 6

Now to find the value of A - B , we need to put the values

A - B = - 6 - 6

=  - 12

Hence, the value of A - B is - 12 .

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The other three sides of the patio will be represented by one line with a slope of 2/3 and two lines with a slope of  -3/2.

The general equation of a straight line is -

y = mx + c

Given in the question is a equation that describes the one side of a rectangular patio. From the question, we can write -

Equation representing a side of Patio - y = 2/3x + 5/3

If we compare the equation representing a side of Patio with the general equation of line, we get -

y = 2/3 x + 5/3      

[y] = [m] x + [c]

From this we can conclude that -

m = 2/3 = slope of line

c = 5/3 = y - intercept

The patio is in the shape of a rectangle. Therefore, the side opposite to the line of slope → 2/3 will be equal in length and parallel to it. We know, that the slope of two parallel lines are same. So, the slope of line parallel to  y = 2/3x + 5/3  will be 2/3.

The remaining two sides are perpendicular to both the side of slope → 2/3. The remaining sides are also parallel to each other, indicating they both have same slope. The slope of a line perpendicular to a given line (L) is given by -

m [p] x m [L] = -1

m [p] = - 1 / m [L]

m [p] = - 3/2

Therefore, the remaining two sides will have slope of  -3/2.

Therefore, the other three sides of the patio will be represented by one line with a slope of 2/3 and two lines with a slope of  -3/2.

[Refer to the graph attached]

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correlation coefficient,r = 0.5497

Standard Error,[tex]SE_{r} = 0.1477[/tex]

Dopamine, also known as DA or 3,4-dihydroxyphenethylamine, is a neuromodulatory chemical with a variety of crucial functions in cells. It is an organic substance that belongs to the phenethylamine and catecholamine families. About 80% of the catecholamines in the brain are made up of dopamine. It is an amine produced by removing a carboxyl group from a molecule of L-DOPA, which is used as a precursor and is produced in the kidneys and brain. Plants and the majority of animals can produce dopamine as well. Dopamine performs the role of a neurotransmitter in the brain, which is a substance secreted by neurons (nerve cells) to communicate with other nerve cells. Although neurotransmitters are only produced in some parts of the brain, they have a systemic impact on numerous areas.

Let the random variable, X = % of dopamine receptors blocked and Y= subject's ratings of cocaine high.

The correlation coefficient, r

Given:

[tex]SS_{XY}[/tex] = 957.5

[tex]SS_{X}[/tex] = 8145.441

[tex]SS_{Y}[/tex]= 372.5

The correlation coefficient between the variables, X and Y is obtained using the following formula,

[tex]r=\frac{SS_{XY} }{\sqrt{SS_{X} \times SS_{Y} } }[/tex]

[tex]r=\frac{957.5 }{\sqrt{{8145.441} \times372.5 } } }[/tex]

r = 0.5497

The standard error for the estimate of the correlation coefficient is obtained using the following formula,

[tex]SE_{r} = \sqrt{\frac{1-r^{2} }{n-2} }[/tex]

From the scatterplot, the sample size, n = 34

[tex]SE_{r} = \sqrt{\frac{1-(0.5497)^{2} }{34-2} }[/tex]

[tex]SE_{r}=0.1477[/tex]

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The pool's new dimensions will be 10cm by 5cm, where 1 centimeter equals 5 meters.

So, scaling is a technique for resizing an object. It can either enlarge or decrease the size of the object.

Making a scale drawing of the pool in which 1cm equals 5 meters, that is:

The length:

Subtraction of both expressions 1 and 2:

In terms of width:

Obtain new width:

Therefore, the pool's new dimensions will be 10cm by 5cm, where 1 centimeter equals 5 meters.

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The correct question is given below;
A rectangular swimming pool measures 50 meters in length and 25 meters in width. Make a scale drawing of the swimming pool where 1 centimeter represents 5 meters.

We want to do a change of units of a rate, from words per minute to words per hour.

We will find that the answer is 22,200 words per hour.

The rate that we need to modify is:

370 words/minute

So the time is in the denominator.

Also, remember that:

1 hour  = 60 minutes.

Then:

1 minute = (1/60) hours.

Using the above relation, we can replace the "minute" in the denominator by (1/60) hours, so we get:

370 words/minute = 370 words/((1/60) hours.) = 60*370 words/hour

                               22,200 words/hour.

Then the rate is 22,200 words per hour.

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Answer:

We want to do a change of units of a rate, from words per minute to words per hour.

We will find that the answer is 22,200 words per hour.

The rate that we need to modify is:

370 words/minute

So the time is in the denominator.

Also, remember that:

1 hour  = 60 minutes.

Then:

1 minute = (1/60) hours.

Using the above relation, we can replace the "minute" in the denominator by (1/60) hours, so we get:

370 words/minute = 370 words/((1/60) hours.) = 60*370 words/hour

                              22,200 words/hour.

Then the rate is 22,200 words per hour.

Step-by-step explanation:

There are 56 number of possible ways are there to select two items so that at least one jeans is chosen.

Combinations:

Combinations is the number of ways in which you can choose r elements out of a set containing n distinct objects.

The combination formula that will allow you to determine the number of combinations in no time:

C(n,r) = n! / (r! (n-r)!)

where:

C(n,r) is the number of combinations;

n is the total number of elements in the set; and

r is the number of elements you choose from this set.

Given,

A shop has 5 different shirts and 7 different jeans.

Here we need to find how many number of ways ways are there to select two items so that at least one jeans is chosen.

Let's say,

First, you picked up 1 jeans and 1 shirt …

Then the number of ways to do that is

=> ⁵C₁ x ⁷C₁

=> 5 x 7

=> 35

Similarly, in second case you picked up the only 2 jeans

number of ways to do that is

=> ⁷C₂

=> 21

So the final answer will be sum of both the cases that is

=>( ⁵C₁ x ⁷C₁ ) + (⁷C₂)

=> 35+21

=> 56 ways

Therefore, there are 56 possible ways to select two items so that at least one jeans is chosen.

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The center of rotation for the polygon p is shown as the red point in the attached graph below.

A plane figure spins around a point known as the center of rotation. Throughout the rotation, this point remains stationary.

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Answer:

Well that depends

Step-by-step explanation:

Answer:

6x^2+6x

Step-by-step explanation:

2x(3x^2+5x-2)

6x^2+10x-4x

6x^2+6x

Jamaal using whole interval type of data recording to collect the data on Freddie’s on-task behavior.

One form of interval recording technique is whole interval recording. An interval recording approach involves watching to see if a behavior happens or not within predetermined intervals of time. After determining the duration of an observation session, the time is divided into shorter segments that are all of the same length. To record the incidence of behavior, ten boxes may be utilized to divide a 10-minute observational session into 1-minute intervals. A whole interval recorder uses a X for occurrence and a O for no non-occurrence to indicate if a behavior occurred during the entire interval.

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It depends on the sign of [tex]x-4[/tex].

Recall the absolute value function's definition:

[tex]|x| = \begin{cases}x & \text{if } x \ge 0 \\ -x & \text{if } x < 0\end{cases}[/tex]

Now, if [tex]x-4\ge0[/tex], then

[tex](x-4)|x-4| = (x-4)(x-4) = x^2 - 8x + 16[/tex]

On the other hand, if [tex]x-4<0[/tex], then

[tex](x-4)|x-4| = -(x-4)(x-4) = -(x-4)^2 = -x^2 + 8x - 16[/tex]

What you first suggested is incorrect. We have

[tex]x^2 - 16 = (x - 4) (x + 4)[/tex]

but [tex]|x-4| \neq x + 4[/tex].

We can show this using the definition again. If [tex]x-4\ge0[/tex], then

[tex]x-4 = x+4 \implies -4=4[/tex]

which is a contradiction; on the other hand, if [tex]x-4<0[/tex], then

[tex]-x+4 = x+4 \implies 2x = 0 \implies x =0[/tex]

holds for only one value of [tex]x[/tex].

The number of ways in which the word detail can be arranged in such a way that the vowels occupy only the odd positions is 36.

We will find the number of permutations in which the word DETAIL can be arranged such that the vowels occupy odd positions.

The vowels are E, A and I. They can occupy 1st, 3rd and 5th position in any order. Hence, the number of ways to do that is 3! = 6.

Now, the consonants D, T and L can occupy 2nd, 4th and 6th position in any order. Hence, the number of ways to do that is 3! = 6.

Hence,

Total number of ways = 3! * 3! = 6*6 = 36.

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the probability that one of the three will be elected = [tex]\frac{19}{30}[/tex]

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.

As per the question, it is given that :

Probability of John (A) = [tex]\frac{1}{8}[/tex]

Probability of Beth (B) = [tex]\frac{2}{5}[/tex]

Probability of Avery (C) = [tex]\frac{1}{3}[/tex]

The probability that one of the three will be elected :

P(A) * P(B') * P(C') + P(A') * P(B) * P(C') + P(A') * P(B') * P(C) = P(A) * (1 - P(B)) * (1 - P(C)) + (1 - P(A)) * P(B) * (1 - P(C)) + (1 - P(A)) * (1 - P(B)) * P(C).

here, P(A) = Probability of A happening

        P(A') = Probability of A not happening

= [tex](\frac{1}{8} * \frac{3}{5} * \frac{2}{3}) + (\frac{7}{8} * \frac{2}{5} * \frac{2}{3}) + (\frac{7}{8} * \frac{3}{5} * \frac{1}{3})[/tex]

= [tex]\frac{1}{20} + \frac{7}{30} + \frac{7}{20}[/tex]

= [tex]\frac{3 + 14 + 21}{60}[/tex]

= [tex]\frac{38}{60}[/tex]  =  [tex]\frac{19}{30}[/tex]

Therefore, the probability that one of the three will be elected = [tex]\frac{19}{30}[/tex]

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The area left to be tiled on Wednesday is 1/6

Let the total area to tile be 60 sq feet

We have taken 60 sq feet as the LCM of 2 and 3 is 6. So taking up 60 makes our calculation part easy.

Area tiled on Monday = 1/3*60 = 20 sq feet

Area tiled on Tuesday = 1/2*60 = 30 sq feet

Area remaining to be tiled = 10 sq feet

So, a fraction of the area left to be tiled = Area left to be tiled/Total area to be tiled

= 10/60 = 1/6

Hence, 1/6 of the area is left to be tiled

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Answer:1/6

Step-by-step explanation:

Answer:

It will be 29/1000

Step-by-step explanation:

Because each kg equal 1000 milie gram

The given statement is True.

"It is not always helpful to rewrite an equation in standard form as a first step in solving it."

In standard form, the right side of an equation should be 0 and every component on the left side should be 1. For example, x2 = 4; to express this in standard form, move the number 4 to the left side of the equation, resulting in x2 - 4 = 0.

If you are asked to find x in this circumstance, there is no need to write the equation in standard form; simply take this same real number of both of the equation's sides to find x.

Ax+By=C is the common structure for linear equations in two variables. 2x+3y=5, for example, is a simple linear equation. It is rather simple to find both intercepted communications when an equation is stated in this way (x and y). This form is indeed useful for solving two-linear equation systems.

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I understand that the question you are looking for is:

It is not always helpful to rewrite an equation in standard form as a first step in solving it.

True/False

Answer:

X=10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:27 and 13

Step-by-step explanation: 27 + 13= 40

27 x 13= 351

-10 minus -4 = -6

Solving the equation

-10 minus -4

= -10 - (-4)

= -10 + 4

= -6

-10 minus -4 = -6

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Answer:

x= -2

Step-by-step explanation:

A square number is the result when a number has been multiplied by itself

Answer:

Answer in the photo

Step-by-step explanation:

Hope this helps x :)

Answer:

i think ur saying that j=4 so the answer is 13

just 4+9

Step-by-step explanation:

Answer:x+1.5y=21

Step-by-step explanation:

We know that a pencil is $1, so let's represent that as 1x or just x. We also know that each pen costs $1.50, and let's represent this as 1.5y for the number of pens Stella bought. Your equation would be x+1.5y=21.

During this time, Helen Barnes from tri-state realty called for information about a stone listing. The assistant should give Helen the information she is asking for.

An unlicensed assistant broker does a number of responsibilities. Nonetheless, it is vital that every broker understands what an unlicensed broker is legally allowed to do when compared to a licensed assistant broker, in order to avoid getting into trouble.

Therefore, we conclude that in this question, the assistant should give Helen the information she is asking for.

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Complete question is; all of the licensees at stone realty are attending an off site conference for the afternoon. the broker’s unlicensed assistant remained at the office to answer the telephone. during this time, helen barnes from tri-state realty called for information about a stone listing. what should the assistant do?

The coordinates of the vertices of the reflected image are

A' ( 6,5) , B' ( 5,1), C' ( 8,2)

given that

a triangle has vertices A ( -6,5 ) , B (-5, 1) , C( -8,2 )

it is reflected over Y axis

we have to find the coordinates of the vertices of the reflected image

since it is reflected over Y axis then only the sign of x coordinates changes

the rule for a reflection over the Y axis is (x, y) -> ( -x , y)

the y coordinate in this case is unchanged

the vertices changes and it become

A( -6, 5) -> A' ( 6,5)

B ( -5, 1) -> B' ( 5,1)

C ( -8,2) -> C' ( 8,2)

preimage of coordinates attached below

Hence the coordinates of the vertices of the reflected image are

A' ( 6,5) , B' ( 5,1), C' ( 8,2)

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Answers:

1.) Plot the numbers on the y-axis (vertical line) and the countries on the x-axis (horizontal). Then, put "Cars (billions)" to label the y-axis and put "Country" to label the x-axis. There is an example attached.

2.) Do the same thing as #1 but label the y-axis with "People (hundreds)" and the x-axis as "Colonies".

3.) Japan because 8 is the greatest amount comparing to the other countries.

4.) Japan made 6 million more cars than Spain since 8 - 2 = 6. (We are counting the cars in millions)