Solve for x. 4x + 6 = 2(2x + 3)

vector representation of the given vectors will be AB(5,6,-3).

A quantity or phenomena with independent qualities for both size and direction is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

The vector representation will be -

A(x1,x2,x3), B(x1,x2,x3) so, AB will be - (x2 - x1, y2 - y1, z2 - z1)

So, given,

A(−6,0,1)

B(1,6,−2)

AB(1+6, 6-0, -2-1)

AB (5,6,-3)

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When we compare the p-value and the significance level is given [tex]\alpha=0.01[/tex], we can see that [tex]p_v < \alpha[/tex], so we can conclude that we have enough evidence to reject the null hypothesis, which is less than 5.7 Mpa at 1% significance.

Given:

Identify the null and alternative hypotheses.

We need to test a hypothesis to see if the true mean is less than 5.7 Mpa; the hypothesis system would be:

If the sample size is 30 and we don't know the population deviation, we should use a t-test to compare the actual mean to the reference value, and the statistic is given by:

The t-test: "Is one of the most common tests for determining whether the mean is (higher, lower, or not equal) to a specified value."

Determine the statistic

We can substitute the following information in formula (1):

P-value:

The first step is to compute the degrees of freedom, which in this case are:

Because this is a one-sided lower-tailed test, the p-value would be:

Therefore, when we compare the p-value and the significance level given [tex]\alpha=0.01[/tex], we can see that [tex]p_v < \alpha[/tex], so we can conclude that we have enough evidence to reject the null hypothesis, which is less than 5.7 Mpa at 1% significance.

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The complete question is given below:
When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive (called "Smartbond") has been developed to eliminate the necessity of a dry field. However, there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. ( Trends in Biomaterials & Artificial Organs, Jan. 2003.) Tests on a sample of 10 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of x = 5.07 Mpa and a standard deviation of s = 0.46 Mpa, where Mpa = megapascal, a measure of force per unit area. Orthodontists want to know if the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa, the mean breaking strength of the composite adhesive. Conduct the appropriate analysis for the orthodontists. Use alpha= 0.01. What is the p-value?

Answer:here is ur answer

4+8x=20 8x=20-4 8x=16 x=$2.00 for a candy bar

Step-by-step explanation: i really hope this helps pls lmk if i am wrong have a good day/night (: <3

Answer:

One per candy bar: 5$

8 candy bars: 40$

Step-by-step explanation:

Take four dollars away from the drink and you end up with 40$. And, then you'll go and divide 40 divided by 8 equals 5. So, per 1 candy bar is 5$.

Answer:

Option #1, #4 & #5

Step-by-step explanation:

It's rise over run which is y-axis/intercept (up and down) over x-axis/intercept (left or right).

Hope this helps.

Answer:

Step-by-step explanation:

The carrier that has the lower initial fee is carrier B

For carrier B, we have the following equation

y = 55x + 300

Set x = 0 to determine the initial fee

y = 55 x 0 + 300

Evaluate

y = 300 ---- the initial fee of carrier B

For carrier A, we have the following points on the table

(x, y) = (3, 500), (6, 650)

The slope of the points is calculated using

m = (y2 - y1)/(x2 - x1)

This gives

m = (650 - 500)/(6 - 3)

Evaluate

m = 50

Let the initial fee of carrier B y

So, we have the following points

(x, y) = (0, y), (6, 650)

The slope of the points is calculated using

m = (y2 - y1)/(x2 - x1)

This gives

m = (650 - y)/(6 - 0)

Evaluate

m = (650 - y)/6

Substitute m = 50 in m = (650 - y)/6

50 = (650 - y)/6

This gives

300 = 650 - y

Solve for y

y = 350

So, we have:

y = 300 ---- the initial fee of carrier B

y = 350 ---- the initial fee of carrier A

300 is less than 350

Hence, the carrier that has the lower initial fee is carrier B

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Answer:

Step-by-step explanation:

hope it helps you

Based on the congruence statement triangle △SUN ≈ △FOG, the true statement is SU is Congruent to side FO.

Congruence of the triangle:

Two triangles are said to be congruent if one can be placed over the other so that they coincide (fit together). This means that congruent triangles are exact copies of each other and when fitted together the sides and angles which coincide, called corresponding sides and angles, are equal.

For example,

△ABC ≈ △DEF

then,

Side  AB  corresponds to  DE,BC  corresponds to  EF , and  AC  corresponds to  DF .

Given,

The congruence statement triangle

△SUN ≈ △FOG

Based on the congruence of the triangle rule,

Here the option

SU is Congruent to side FO.

is the correct option.

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He can make 8 party package and each package consists 4 pencils and 7 lollipops with 32 pencils and 56 lollipops .

To determine the greatest number of identical packages possible we have to determine the highest common factor of two given no. , 32 and 56

Let's determine the factors of the 32 and 56 ,

32 = 2 × 16 = 2 × 2 × 2 × 2 × 2

56 = 2 × 2 × 2 × 7

So , common factors are 2 , 2 ,2

Now , The HCF is , 2 × 2 × 2 = 8

So , total combination is 8 and in each combination , there is 4 pencils  ( 32 / 8 = 4 )and 7 ( 56/8 = 7 ) lollipops .

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Answer:

Step-by-step explanation:

2:3

Answer:

2:3.

Step-by-step explanation:

If you turn 8:12 into a fraction (8/12), then make it simplest form, it would be 2/3.

2/3 as a ratio is 2:3. Therefore, 2:3 is equivalent to 8:12.

Answer:

3

Step-by-step explanation:

The slopes of two perpendicular lines are negative reciprocals of each other

so negative reciprocal of -1/3 is 3

The simplified form of the expression is -m-2n+10

Linear equation are equation that has a linear degree of 1. Given the following expression

-3m+7-2n+3-m+3m

Collect the like terms

-3m+3m-m-2n+7+3

-m - 2n +  7 + 3

Simplify to finally have:

-m-2n+10

Hence the simplified form of the expression is -m-2n+10

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Solution : Straight line question : y= 2x-3

Straight Line:

A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.

Slope:

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Use the slope and one of the points to solve for the y-intercept (b).

One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.

Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line

1)Point (3,3) (4,5)

slope: (5-3)/(4-3) = 2/1 = 2

Y= mx+c

y -3 = 2(x-3)

y-3= 2x-6

y= 2x-6+3

y= 2x-3

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The addition of the given fractions are;

1) -3³/₅ + -1¹/₅

= -4⁴/₅

2) (-3.5) + (-4)

= -7.5

3) 4.5 + (-3)

= 1.5

4) -5³/₅ + 3¹/₅

= - 2²/₅

1) We want to add the fractions as follows;

-3³/₅ + -1¹/₅

= -3³/₅ - 1¹/₅

= -18/5 - 6/5

= -24/5

= -4⁴/₅

2) (-3.5) + (-4)

= -3.5 - 4

= -7.5

3) 4.5 + (-3)

= 4.5 - 3

= 1.5

4) -5³/₅ + 3¹/₅

= -28/5 + 16/5

= - 2²/₅

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Answer: Credit cards are safer to carry than cash and offer stronger fraud protections than debit.

Answer:

1. l

2. h

3. j

4. k

Step-by-step explanation:

Looks right to me :)

The answer for this equation would be f = 86

Answer:

18

Step-by-step explanation:

Congruent means same size and shape

So if the first one was 18 by 24 and you are given another that is congruent to it and given one side which is 24 so the other has to be 18.

The coordinates of Q will be (0, -6) if R(6, -1) is the midpoint of QS.

Let the coordiantes of point Q be (x, y).

According to the given question.

R is the midpoint of QS.

The coordinates of point R is (6, -1).

And the coordinates of point S is (12, 4).

Thereofore, the coordiantes of point Q is given by

(6, -1) = (  (x + 12)/2, (y + 4)/2 )

⇒  x + 12/2 = 6  and  y + 4/2  = -1

⇒ x + 12 = 12 and  y + 4  = -2

⇒ x = 0 and  y = -6

Hence, the coordinates of Q will be (0, -6) if R(6, -1) is the midpoint of QS.

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MO=4-3=1

OP=8-1=7

MP=16+1=17

Given:

MO= [tex]x^2-3,[/tex]

OP=[tex]4x-1[/tex]

MP= 8x+1

O is the midpoint of MP so

MO=OP

[tex]x^2-3[/tex]=[tex]4x-1[/tex]

[tex]x^2-4x-4=0[/tex]

[tex]X^2-2x-2x-4=0\\x(x-2)-2(x-2)\\(x-2)(x-2)\\x=2[/tex]

MO=4-3=1

OP=8-1=7

MP=16+1=17

A line segment's midpoint is a point that is halfway between two points. The midpoint is the same distance between the two ends.

This calculator can be used to find the midpoint, the distance between two points, or an endpoint given the midpoint and the other endpoint. Solutions for Midpoint and Endpoint Calculators

Enter two points in the form of numbers, fractions, mixed numbers, or decimals. The midpoint calculator displays the work to be done:

midpoint of two given points

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Answer: The answer is A) - 9/5, because the slope of the line is decreasing/going downward indicating that the slope is negative. The slope of the line is steep, and so the rise should be more the run.

Step-by-step explanation: hope this helps!!!!!!

Answer:

11

Step-by-step explanation:

Answer:

no. 10^0=

Step-by-step explanation:

The solution is Mean = 3.25 for the given distribution's mean and its type of skew.

A list of values, such as measurements or numbers, is used to calculate it by dividing the total number of values in the list by the total number of values in the list. Add up each value in the set to determine the mean. Next, divide the total by the number of values.

based on the facts provided;

Step 1: Presented data:

4.5, 3, 1, 2, 4, 3, 6, 4.5, 4, 5, 2, 1, 3, 4, 3, 2

Step 2:

Sum of the numbers

         = 4.5 + 3 + 1 + 2 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2

         = 52

Sum of the numbers = 52

Number of terms = 16

Step 3:

Mean=sum of the number/number of term

         =52/16

          = 3.25

Mean = 3.25

Mean of the distribution is 3.25.

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The differences between two samples are more likely to be statistically significant if the samples are and the standard deviations of the samples are: large and the standard deviations of the samples are small.

Now,

Hence, The differences between two samples are more likely to be statistically significant if the samples are and the standard deviations of the samples are: large and the standard deviations of the samples are small.

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The average speed required to reach the concert in time is 61 miles per hour.

The average speed required to reach school in time is 27.567 miles per hour.

What is the average speed?

The average speed of an object is defined as the total distance travelled by an object in a particular interval of time or average time. Mathematically, average speed = total distance / total time taken. Its SI unit is m/s.

Calculation of the average speed

We are given that a concert starts in 5 hours and is 305 miles away from the house, i.e. time = 5 hours and distance  305 miles

Then the average speed in miles per hour is given by total distance / total time

Average speed = 305 / 5

= 61 miles per hour

Further, the time taken to reach school is 37 minutes which when converted to hours becomes 37 / 60 hour

The distance between school and home is 17 miles

So, the average speed = total distance / total time

= 17 / (37 / 60)

= (17 × 60) / 37

= 27.567 miles per hour

Hence, the average speed required to reach the concert in time is 61 miles per hour.

The average speed required to reach school in time is 27.567 miles per hour.

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Answer:

area is side multiplied by side

Step-by-step explanation:

162 divided by 2x

Answer:

$98.14

Step-by-step explanation:

150.99 x 0.35. Subtract answer from total to get final price.

The complete arithmetic sequence is 1, .25, -0.5, -1.25, -2

The arithmetic sequence is given as:

1, .25, blank, -1.25, blank

Replace the blanks in the arithmetic sequence with x and y

So, we have:

1, .25, x, -1.25, y

An arithmetic sequence has a common difference (d)

The common difference is calculated using

d = T2 - T1

So, we have

d = 0.25 - 1

d = x - 0.25

d = y + 1.25

Substitute d = x - 0.25 in d = 0.25 - 1

x - 0.25 = 0.25 - 1

This gives

x = 0.25 + 0.25 - 1

Evaluate the sum

x = -0.5

Substitute d = 0.25 - 1 in d = y + 1.25

0.25 - 1  = y + 1.25

This gives

y = 0.25 - 1 - 1.25

Evaluate

y = -2

Hence, the complete arithmetic sequence is 1, .25, -0.5, -1.25, -2

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If Payton buys 3 pounds of Kiwi and 1.5 pounds of cherries, then the pounds of fruit Payton bought at 4.5 pounds.

If Payton buys x pounds of Kiwi and y pounds of cherries, the number of pounds of fruit purchased is x + y.

Payton bought 3 pounds of kiwi and 1.5 pounds of cherries. The total fruits bought is therefore:

= 3 + 1.5

= 4.5 pounds of fruit

If Payton bought x pounds of kiwi and y pounds of cherries, again the total pounds purchased is:
= x + y

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Step-by-step explanation:

there is explanation in the answer