If PQ=3x+8 and QR=2x + 17, find the value of x.

The number of gray squares for 15 white squares based on the given ratio will be 25.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given,

Number of white squares = 3

Number of gray squares = 5

The ratio of gray squares to white = 5/3

With maintaining the same ratio,

Let's say the number of gray squares for 15 white squares will be x.

The ratio of gray squares to white will be as x/15

Both ratios must be the same for the same pattern.

x/15 = 5/3

x = (5/3)15 = 25

Hence "On the basis of the specified ratio, there will be 25 gray squares for every 15 white squares.".

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When they decide to bid the same then the probability of Barney getting the car is 1/3. The expected profit by Barney will be the difference amount of SL and SH.

Given:

if arnie, barney and carny agree to always bid $l,

, then on any given day, what is the probability that barney gets the car for $l when it is actually worth $l to him = ?

When they choose to place identical bids, Barney has a 1/3 chance of winning the automobile. The difference between SL and SH will represent Barney's anticipated profit.

Hence we get the required answer.

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The fraction of chocolate left in the box is [tex]\frac{1}{6}[/tex].

A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction has a numerator that is less than the denominator.

Given:

Andrew eat = 1/3 of the chocolate,

Jame eats =2/5 of the chocolate

Jenny eat =1/10 of the chocolate

According to the question,

Let the total chocolate = 1

Therefore as per the question,

Chocolate left = 1 – [1/3+2/5+1/10]

[tex]=1- [\frac{1}{3} +\frac{2}{5} +\frac{1}{10} ]\\=1 - [ \frac{10 + 12+3}{30} \\=1-\frac{25}{30} \\= 1 - \frac{5}{6} \\\\= \frac{1}{6}[/tex]

Threfore, the Fraction of chocolate left in box is [tex]\frac{1}{6}[/tex].

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Answer:

[tex]u(w(2) = 19[/tex]

Step-by-step explanation:

let's evaluate w(2) first

[tex]w(2) = - 2(2) {}^{2} - 1 = - 9[/tex]

at this point let's replace thia value in u(x)

[tex]u( - 9) = - 2( - 9) + 1 = 19[/tex]

The probability that the child is not affected by  the disorder is \frac{5}{6}

Probability is simply the likelihood of something occurring.

It is an autosomal recessive disorder because all of the defective ones are recessive. So, when a 2nd generation 3rd individual marries a 2nd generation 4th individual, the probability of their child having a genetic disease is [tex]\frac{1}{6}[/tex]. The parents must be heterozygous for the child to be diseased, and the probability of an individual being heterozygous is [tex]\frac{2}{3}[/tex]. 2nd generation, 3rd individual, and the probability of disease in the child is [tex]\frac{1}{4}[/tex], so [tex]\frac{2}{3} *\frac{ 1}{4} = \frac{1}{6}[/tex].

As a result, the probability of a child having a genetic disorder is [tex]\frac{1}{6}[/tex].

then the probability of child not having any genetic disorder is [tex]1-\frac{1}{6} =\frac{5}{6}[/tex].

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Answer:

infinite solutions

Step-by-step explanation:

4x=2(2x-3)+6

4x=4x-6+6

4x=4x

these are the same lines so there are infinitely many solutions

hopes this helps

A system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased are as follows;

Let S = number of bottles of soda.

Let J = number of bottles of juice.

System of Equations:

30S + 40J = 430

J = 2 + S  

In order to write a system of linear equations to describe this situation, we would assign variables to the number of bottles of soda and number of bottles of juice respectively, and then translate the word problem into algebraic equation as follows:

Since each bottle of soda has 30 grams of sugar and each bottle of juice has 40 grams of sugar with both of them having a sum total of 430 grams of sugar, we have the following equation:

30S + 40J = 430              .....equation 1.

Wyatt purchased 2 more bottles of juice than bottles of soda;

J = 2 + S                            .....equation 2.

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The graph of the piece-wise function containing Andres's data is given by the image at the end of the answer.

A piece-wise function is a function that has different definitions, based on it's input.

The variables in this problem are given as follows:

At 6 a.m., the temperature was 60° F, hence the intercept is of:

(0,60).

For the next 9 hours, the temperature rose 2° every 3 hours, hence a line is traced connecting these two points:

(0, 60) and (9, 66).

For the next 2 hours, it rose 2° per hour, hence these two points are connected:

(9, 66) and (11,70).

The temperature then stayed steady until 6 p.m, hence these two points are connected:

(11,70) and (12,70).

For the next 2 hours, the temperature dropped 1° per hour, hence the points at:

(12,70) and (14,68).

The temperature then dropped steadily until the temperature was 66° at midnight, then the points are:

(14,68) and (18,66).

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There is  no error by Margaret identifying the different transformations of graphs

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the change of algebraic equations, it is a typical kind of algebraic problem.

Reflections, rotations, and translations are the three fundamental rigid transformations. Dilation is a fourth frequent transition.

Vertical Reflection: Mirror images are produced by reflections. Imagine the graph "folding" over the x-axis.

Horizontal reflection: Mirror images make up reflections. Imagine the graph "folding" over the y-axis.

Vertical Shift: This translation "slides" up or down in a straight line.

• The graph is translated upward by k units if k > 0.

• If k is less than 0, the graph descends by k units.

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The pace or speed of Debbie during rides with her bike is greater on the way of going to home from School.

So, her pace is faster on the way of going to home .

We have given that,

Debbie ride 1.5 miles to school in 10 minute

As we know that 10 minute = 10/60⇒1/6 hour

As we know that

Speed = distance /time or S = D/T

So, the speed at which Debbie ride to school with first route,

S=1.5/1/6 => 9 mile per hour

Now, On her way home, she took other route and

she rides, 3 mile in 15 minutes,

As 15 minutes = 15/60 => 1/4 hour

Speed of Debbie of her way home

S' = 3/1/4 => 12miles per hour

As we see that S' > S

So, Debbie rides faster on her way to home.

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Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Substituting into the slope formula, [tex]m=\frac{-2-3}{-4-6}=\frac{1}{2}[/tex].

Answer:

1/2

Step-by-step explanation:

The value of x will be;

⇒ x = 1

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 3 (6x - 2) = 2 (3x + 3)

Now,

Since, The expression is,

⇒ 3 (6x - 2) = 2 (3x + 3)

Solve for x as;

⇒ 18x - 6 = 6x + 6

⇒ 18x - 6x = 6 + 6

⇒ 12x = 12

⇒ x = 12/12

⇒ x = 1

Thus, The value of x = 1

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Answer:

x = 1

Step-by-step explanation:

Given equation,

→ 3(6x - 2) = 2(3x + 3)

Now the value of x will be,

→ 3(6x - 2) = 2(3x + 3)

→ (3 × 6x) - (3 × 2) = (2 × 3x) + (2 × 3)

→ 18x - 6 = 6x + 6

→ 18x - 6 - 6x = 6

→ 12x = 6 + 6

→ 12x = 12

→ x = 12/12

→ [ x = 1 ]

Let's check the value of x,

→ 3(6x - 2) = 2(3x + 3)

→ 3(6(1) - 2) = 2(3(1) + 3)

→ 3(6 - 2) = 2(3 + 3)

→ 3 × 4 = 2 × 6

→ 12 = 12

→ [ LHS = RHS ]

Hence, the value of x is 1.

Answer:

Median: 8.15

Mean: 7.6

Mode: 10.1

Step-by-step explanation:

10.1, 12.3, 2.4, 10.1, 4.5, 6.2

2.4, 4.5, 6.2, 10.1, 10.1, 12.3

Median:

(6.2 + 10.1)/2 = 8.15

Mean:

2.4 + 4.5 + 6.2 + 10.1 + 10.1 + 12.3 = 45.6

45.6 / 6 = 7.6

Mode:

10.1

I hope this helps!

Answer:

The correct Answer is - :

16x¹⁰ + 121

At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

The speed of an object is the ratio of distance and time it takes for the object to travel that distance.

Mathematically,

S = D/T

where

S is velocity

D is the distance traveled or distance traveled

T is the time it takes to travel that distance

Velocity is considered a scalar quantity. A scalar size only has a size. It does not provide information about the direction of object movement.

If an object moves at a constant speed, it means that the object moves the same distance in the same time interval.

Acceleration of an object is the ratio of velocity and time. vector size. Vector quantities have both magnitude and direction.

Mathematics,

a = v/t

When an object is in motion, its acceleration is never zero.

When an object moves, it moves a constant distance over time. Therefore, body positions cannot be the same from the same coordinate system.

Given in the question:

First the plane was travelling at a constant rate of 250  miles per hour.

Initial height was 20000 feet

Now,

As the speed increases and travels at a constant rate of 400 miles per hour.

Now,

   (400 /250 ) × 20000

=  1.6 × 20000

= 32000 feet

Thus, At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

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Answer:

Read carefully each step for your fully understand it.

Step-by-step explanation:

To find the equation of a line that is perpendicular to the line y = 2x - 3 and contains the point (-5, 3), we need to find the slope of the perpendicular line.

To find the slope, we use the negative reciprocal of the slope of the given line. The slope of the given line is 2, so the slope of the perpendicular line is -1/2.

We can then use the point-slope formula to find the equation of the line that is perpendicular to y = 2x - 3 and contains the point (-5, 3).

The point-slope formula is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values, we get:

y - 3 = -1/2 (x + 5)

We can then simplify this equation to get the final equation:

y = -1/2 x - 11/2

Therefore, the equation of the line that is perpendicular to y = 2x - 3 and contains the point (-5, 3) is y = -1/2 x - 11/2.

Answer:

w = 39

Step-by-step explanation:

3w + 9 + 2w - 24 = 180 , that is

5w - 15 = 180 ( add 15 to both sides )

5w = 195 ( divide both sides by 5 )

w = 39

Equation of the line  that passes through the midpoint and is perpendicular to PQ is 2x - y +1 = 0.

One way to describe a perpendicular bisector is as a line segment that cuts through another line segment at a 90 degree angle. Simply said, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle. Measuring a line segment that needs to be bisected will help you discover a perpendicular bisector.

The midway of the measured length can then be determined by dividing it by two. From this center, extend a line at a 90-degree angle. All you need to do to determine the perpendicular bisector of two points is to discover their midpoint and negative reciprocal, then enter these results into the slope-intercept form of the equation for a line.

Here points are P( -4 ,3 ) and Q ( 4,-1)

Mid -point of PQ :

[tex]=(\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )\\\\=(\frac{-4+4}{2} ,\frac{3-1}{2} )\\\\=(0,1)\\[/tex]

Slope of PQ:

[tex]m = \frac{y_{2}{-y_{1} } }{x_{2}{-x_{1} }} \\\\m =\frac{-1-3}{4+4}\\\\ m= \frac{-4}{8} \\\\m = \frac{-1}{2}[/tex]

The slope of the line is Perpendicular to PQ

so, slope 2= -1/m

slope 2 = -1/(-1/2)

slope 2 = 2

Equation of the line  that passes through the midpoint and is perpendicular to PQ

[tex]y-y_{1} =m(x-x_{1}) \\y-1 =2(x-0}) \\\\y-1=2x\\[/tex]

2x - y +1 = 0.

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Correct Question:

Find the midpoint of PQ with endpoints P (-4, 3) and Q (4,-1) . Then write an equation of the line that passes through the midpoint and is perpendicular to PQ. This line is called the perpendicular bisector.

Answer:

3,398.7 square centimeters.

Step-by-step explanation:

The area of a square is the square of the side length, so the ratio of the areas of the mirrors is equal to the ratio of the side lengths squared. If the ratio of the side lengths of Mirror A to Mirror B is 5:6, then the ratio of the side lengths squared is 5^2:6^2 = 25:36. This means that the ratio of the areas of Mirror B to Mirror C is 25:36.

The ratio of the areas of Mirror B to Mirror C is 25:36, and the ratio of the areas of Mirror B to Mirror C is 16:25, so 25:36 = 16:25. This means that the ratio of the areas of Mirror B to Mirror C is 1:1.5.

The perimeter of Mirror C is 280 centimeters, which means that each side has a length of 280/4 = <<280/4=70>>70 centimeters. The area of Mirror C is the square of this side length, or 70^2 = <<70^2=4900>>4900 square centimeters.

Since the ratio of the areas of Mirror B to Mirror C is 1:1.5, the area of Mirror B is 1.5 times the area of Mirror C, or 1.54900 = <<1.54900=7350>>7350 square centimeters.

The ratio of the side lengths of Mirror A to Mirror B is 5:6, so the side length of Mirror A is 5/670 = <<5/670=58.333>>58.333 centimeters. The area of Mirror A is the square of this side length, or 58.333^2 = <<58.333^2=3398.68>>3398.68 square centimeters. Rounding to the nearest tenth of a centimeter, the area of Mirror A is 3398.7 square centimeters. Answer: {3,398.7}.

For the given distribution the mean is 20.74  , the variance is  1.652   and the standard deviation is 1.2853   .

In the question ,

probabilities are given ,

the mean is given by the formula,

mean = [tex]\sum[/tex]x*p(x) ,

we get ,

mean = 19*0.21 + 20*0.23 + 21*0.30 + 22*0.13 + 23*0.13

= 3.99 + 4.6 + 6.3 + 2.86 + 2.99

= 20.74

For calculating the Variance we need to subtract the mean for every value x, then we square the result and multiply it by the respectively probability .

19 - 20.74 = -1.74 = (-1.74)²× 0.21 = 0.6357

20 - 20.74 = -0.74 = (-0.74)²× 0.23 = 0.1259

21 - 20.74 = 0.26 = (0.26)²× 0.30 = 0.0202

22 - 20.74 = 1.26 = (1.26)²× 0.13 = 0.2063

23 - 20.74 = 2.26 = (2.26)²× 0.13 = 0.6639

The variance = 0.6357 + 0.1259 + 0.0202 + 0.2063 + 0.6639

= 1.652

the standard deviation = √variance

= √1.652

= 1.2853

Therefore , the values are mean is 20.74  , the variance is 1.652  and standard deviation is 1.2853 .

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There are three type of bias occurs they are Sampling, record and Anchoring

What is meant by bias?

In general terms, bias refers the action of supporting or opposing a particular person or thing in an unfair way, because of allowing personal opinions to influence your judgment

Here we need to find the type of bias occurs when researchers fail to choose a representative sample of potential respondents.

The first type is, Sampling bias is the phenomenon that happens when a research take a look at layout fails to collect a representative sample of a goal populace and this generally happens due to the fact the selection standards for respondents failed to seize a wide enough sampling frame to represent all viewpoints.

Secondly, Records bias where happens at some stage in the information series step and is not unusual in studies studies that involve self-reporting and retrospective facts series and it may also result from bad interviewing strategies or differing tiers of recall from contributors. the primary types of records bias are: take into account bias.

Finally, Anchoring bias is a cognitive bias that reasons us to depend too heavily on the first piece of statistics we are given approximately a topic.

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The measure of <B is 41 degree.

The fundamental characteristics listed below make it simple to recognize parallel lines.

Given:

m<CEF = 145°

m<DCE = 104°

So, <FEC+ <CEB = 180 {Linear Pair}

<CEB = 180- 145

<CEB = 35 degree.

<BCA = < ECB= 104 {Vertically Opposite Angle}

Now, In ΔABC

< ABC+ <BAC + <CAB = 180

104+ 35 + <ABC = 180

<ABC = 180 - 139

m<ABC= 41 degree.

Hence, the measure of <B is 41 degree.

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Answer:

442 ÷ (12+5) = 26

26 × 12 = 312, 312 ppl think yoda was cuter

26 × 5= 130, 130 ppl think Porg was cuter

As per the concept of regression, the best predicted value of given that the has an IQ is 106.2

What is meant by regression?

In math, regression refers a powerful statistical method that allows you to examine the relationship between two or more variables of interest

Here we have given that suppose IQ scores were obtained for randomly selected sets of . The pairs of measurements yield , , r , P-value 0.000, and , where x represents the IQ score of the .

And we need to find the best predicted value of given that the has an IQ.

While we looking into the given question we know that the a significance level is 0.05.

Then by using regression equation

=> ŷ=14.68+0.88x​

And now we have to plug in IQ, which is x

=> 14.68 + 0.88(104)

=> 106.2

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To demonstrate that ΔKLM ≈ ΔEFG , we can use the SSS Similarity Theorem.

Given,

The ratio of the corresponding sides of the triangles ΔKLM  and ΔEFG;

KM/EG = 8/24 = 1/3

KL/EF = 6/18 = 1/3

ML/GF = 5/15 = 1/3

We have to prove that the triangles are similar using SSS or SAS similarity theorems;

SSS similarity theorem;

The two triangles are similar if all three sides of one triangle are in proportion to the three sides of another triangle.

SAS similarity theorem;

The triangles are congruent if two sides and the included angle of one triangle are equivalent to two sides and the included angle of another triangle.

Here, the sides of the triangles are in proportion.

That is,

KM/EG = KL/EF = ML/GF = 1/3

Here,

We can consider SSS similarity theorem to prove that ΔKLM ≈ ΔEFG

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The function's domain are {4.1, -2, -2.5, -4} and range are {1.1, 2, 3, 0}.

The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then:

Domain = the set of all x-coordinates = {1, 2, 3, 4}

Range = the set of all y-coordinates = {2, 3}

From the given graph, we have (4.1, 1.1), (-2, 2), (-2.5, 3), (-4, 0)

The domain of functions are={4.1, -2, -2.5, -4}

The range of functions are={1.1, 2, 3, 0}

Therefore, the function's domain are {4.1, -2, -2.5, -4} and range are {1.1, 2, 3, 0}.

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Answer:

The amount of carbon-14 in the fossil is 15% of the amount of carbon-14 in a living beetle.

This means that the amount of carbon-14 in the fossil is 0.15 * the amount of carbon-14 in a living beetle.

The age of the fossil can be found by dividing the half-life of carbon-14 by the logarithm of the ratio of the amount of carbon-14 in the fossil to the amount of carbon-14 in a living beetle.

This means that the age of the fossil is 5715 years / log(0.15).

The age of the fossil is approximately 5715 years / -1.1761.

Therefore, the age of this fossil is approximately <<4895.4683=4895>>4895 years.

Answer:

the mark up is 2$

Step-by-step explanation:

each shirt was baught for 18$ divide 7200 by 400

The required volume of the given cylinder is 1005 ft³.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid.

It is regarded as a prism with a circle as its base in basic geometry.

In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

So, the volume of cylinder formula:

V=πr²h

We have,

Height of 20 ft and diameter of 8 ft.

The radius will be 8/2 = 4 ft.

Now, calculate the volume as follows:

V=πr²h

V=π(4)²20

V=1005.30965

Rounding off: 1005 ft³

Therefore, the required volume of the given cylinder is 1005 ft³.

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109.8

just took the quiz