8. The endpoints of ST are s(-3, 2) and t(5,8). Find the coordinates of the midpoint of ST. Then find ST. OA midpoint: (1,5); ST = 5 OB midpoint: (1, 4); ST = 10 с midpoint: (1, 5); ST = 10 midpoint: (2,5); ST = 10​

The matrix equation that can be solved to find all the respective costs is;

\(\left[\begin{array}{ccc}2&3&50\\4&6&100\\2&5&80\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}51\\90\\78\end{array}\right]\)

Let cost of admission for children be x.

Let cost of admission for adults be y.

Let cost of admission for carnival tickets be z.

Thus, we have the simultaneous equation as;

2x + 3y + 50z = 51

4x + 6y + 100z = 90

2x + 5y + 80z = 78

Thus, writing this in matrix form gives;

\(\left[\begin{array}{ccc}2&3&50\\4&6&100\\2&5&80\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}51\\90\\78\end{array}\right]\)

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We can conclude that only some of the ratios in Table A are greater than the ratios in Table B. (option-c)

To compare the ratios of squares to circles in the tables, we must divide the value in the Squares column by the value in the Circles column for each row in the table.

For Table A, the ratios of squares to circles are:

5/3 = 1.67

10/6 = 1.67

For Table B, the ratios of squares to circles are:

10/3 = 3.33

20/9 = 2.22

Comparing the ratios in Table A to the ratios in Table B, we see that the first two ratios are equal (1.67) and the last two ratios are different (3.33 in Table B is greater than 1.67 in Table A, and 2.22 in Table B is less than 1.67 in Table A).

Specifically, the ratio in the second row of Table B is greater than both ratios in Table A, but the ratios in the first row of each table are equal.(option-c)

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Answer:

SR

Step-by-step explanation:

The segment that has the same measure as ST is SR

Lines segments with the same measures have the same lengths

From the question, we have the following highlights

The highlight (I) above means that:

Line segments RX and SX are congruent

Given that:

Line segment I contains point S

Then it means that:

Line segments ST and SR are congruent

Hence, the segment that has the same measure as ST is SR

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To solve the equation 2y^(4) +11y^(3) + 18y" + 4ť' - 8y=0, we can first factor out a common factor of 2y: 2y(y^3 + 5y^2 + 9y + 2ť' - 4) = 0 Next, we can focus on the expression inside the parentheses, which can be written as:

y^3 + 5y^2 + 9y + 2ť' - 4

We can recognize this expression as the polynomial 2r^4 +11r^3 + 18r^2 + 4r – 8 evaluated at r=y-1/2.

So, 2r^4 +11r^3 + 18r^2 + 4r – 8 = (2r - 1)(r + 2)^3.

Finally, we can factor out a common factor of 2 and use the factored form of the polynomial:

2(y-1)(y+2)^3(2y+1) = 0

Therefore, the solutions to the original equation are:

y = 1, -2, -1/2 (multiplicity 3)
To solve the given polynomial equation, we will first rewrite it in a more accurate and coherent form by removing the irrelevant terms:

2y^4 + 11y^3 + 18y^2 + 4y - 8 = 0

We are given a hint that the equation can be factored as:

(2r - 1)(r + 2)^3

Now, we will replace r with y to match the variable in the given equation:

(2y - 1)(y + 2)^3 = 0

Now that we have the factored form of the equation, we can set each factor equal to zero and solve for y:

1) 2y - 1 = 0
2y = 1
y = 1/2

2) (y + 2)^3 = 0
y + 2 = 0
y = -2

So the solutions to the given equation are y = 1/2 and y = -2.

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Answer:

  47.5 cm

Step-by-step explanation:

You want the height of a trapezoid with bases of lengths 135 cm and 105 cm, and an area of 5700 cm².

The formula for the area of a trapezoid is ...

  A = 1/2(b1 +b2)h

Filling in the given values, we have ...

  5700 = 1/2(135 +105)h

  5700 = 120h

  h = 5700/120 = 47.5

The height of the tabletop is 47.5 cm.

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two angles that add up to 90 degrees are called complementary angles.

The value of t statistic for independent measures is option B: 2.00 by calculations using the formula, t = (X1 - X2) / (SE).

The formula for the t statistic for independent measures is given by:

t = (X1 - X2) / (SE)

where X1 - X2 is the difference between the means of two independent samples, SE is the standard error of the difference between means.

We have already been given that n = 6 in each sample produces a sample mean difference of 4 points and a pooled variance of 12, and a standard error of the mean difference of 2, we can calculate the t statistic as follows:

t = (4) / (2) (Because X1 - X2 =4)

= 2

Therefore, the value for the t statistic is 2.

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Complete question is:

An independent-measures study with n = 6 in each sample produces a sample mean difference of 4 points and a pooled variance of 12, and a standard error of the mean difference of 2. What is the value for the t statistic?

A. 0.80

B. 2.00

C. 0.67

D. 8/√12

Answer: 1865.738

Step-by-step explanation:

1,873 - 7.262 = 1865.738

The perimeter of the garden is:

90 + 30√3 feet

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

The perimeter of the garden is the sum of all the three sides of the garden.

Check the attached for the sketch of the garden.

Thus, we can say:

sin 60 = (30√3)/y

(√3)/2 =  (30√3)/y

1/2 =  30/y

y = 2 * 30

y = 60 feet

tan 30 = x/(30√3)

1/√3 = x/(30√3)

(√3) x = 30√3

x = 30 feet

perimeter = x + y + 30√3

perimeter = 30 + 60 + 30√3

perimeter = 90 + 30√3 feet

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The experimental probability of rolling a 1 or a 2 is 0.2.

Hence, Option A is correct.

We know that,

The experimental probability of an event is defined as the number of times the event occurred divided by the total number of trials.

In this case,

The event is rolling a 1 or a 3,

Which occurred ⇒  3 + 1

                           = 4 times.

Given that there are total number of trials = 20.

Therefore,

The experimental probability of rolling a 1 or a 3 = 4/20,

                                                                                = 1/5

                                                                                 = 0.2

Hence, the required probability is 0.2.

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The complete question is:

Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?

Number on cube:1,2,3,4,5,6

Number of times event occurs:3,6,1,5,3,2

A.0.2

B.0.3

C.0.6

D.0.83

Answer:

54.8

Step-by-step explanation:

41+39+48+52+46+62+54+40+96+52+98+40+42+52+60 = 822

822/15= 54.8

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The probability of each number except 3 is 1/7

The total number of outcomes= 6 (a dice has 6 numbers)

The formula of Probability = Selected outcome/ Total number of outcomes

Let the probability be represented by P(x), where x is the number whose probability is asked.

Let the probability of rolling a number except 3 be x

then, P(3) = 2x

Adding the probability of all the outcomes = x+x+2x+x+x+x

probability of all the outcomes = 7x

Total of the probability of all the outcomes of a dice =1

Then, 7x=1

x=1/7

Then the probability of each of the number appearing except 3 is 1/7

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Mark should use the volume formula to determine the number of cubic feet of soil needed to fill the planter half-full. To fill the planter half-full, he would require 18 cubic feet of soil.

In order to determine the amount of soil needed to fill the planter half-full, Mark should use the volume formula. The volume of a rectangular box is calculated by multiplying its length, width, and height. In this case, the length of the planter is 12 feet, the width is 6 feet, and the height is 3 feet. By multiplying these dimensions together (12 x 6 x 3), Mark can find the total volume of the planter, which is 216 cubic feet.

However, the question specifies that Mark needs to fill the planter only half-full. Therefore, he would require half of the calculated volume, which is 216 cubic feet divided by 2, resulting in 108 cubic feet. Therefore, Mark needs 108 cubic feet of soil to fill the planter half-full.

It's worth noting that the trick detail mentioned in the question is the requirement for the planter to be half-full. This means Mark needs to consider only half of the total volume when calculating the amount of soil required.

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It is possible to draw a graph with six vertices and degrees 5, 4, 3, 2, 2, 2. The sum of the numbers in the degree sequence is always even. It is possible to draw graphs with degree sequences 3, 3, 2, 1, 1, but not with 4, 3, 2, 1, 1.

Yes, it is possible to draw a graph with six vertices and the given degree sequence of 5, 4, 3, 2, 2, 2. Here is one example of such a graph:

In this graph, vertex 1 has degree 5, vertex 2 has degree 4, vertex 3 has degree 3, vertex 4 has degree 2, vertex 5 has degree 2, and vertex 6 has degree 2.

There can be more than one way to draw a graph with a given degree sequence. However, not all degree sequences can be realized as the degree sequence of a graph.

The sum of the numbers in the degree sequence is always even, since the sum is twice the number of edges in the graph. In the given degree sequence (5, 4, 3, 2, 2, 2), the sum is 18, which means the graph has 9 edges.

It is possible to draw a graph with the degree sequence 3, 3, 2, 1, 1. Here is one example of such a graph.

In this graph, vertices 1 and 2 have degree 3, vertex 3 has degree 2, and vertices 4 and 5 have degree 1.

It is not possible to draw a graph with the degree sequence 4, 3, 2, 1, 1, since the sum of the degrees in this sequence is 12, which is not even, and therefore cannot be the degree sequence of a graph.

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Answer:

15.6 grams of baking soda can produce 6.124 grams of water.

Step-by-step explanation:

The chemical equation for the reaction of baking soda (sodium bicarbonate) with vinegar (acetic acid) is:

NaHCO3 + CH3COOH → CO2 + H2O + NaCH3COO

From the balanced equation, we can see that for every 1 mole of NaHCO3 reacted, 1 mole of H2O is produced.

The molar mass of NaHCO3 is:

Na: 22.99 g/mol

H: 1.01 g/mol

C: 12.01 g/mol

O: 3 x 16.00 g/mol = 48.00 g/mol

Molar mass of NaHCO3 = 22.99 + 1.01 + 12.01 + 48.00 = 84.01 g/mol

Therefore, 1 mole of NaHCO3 has a mass of 84.01 grams.

To find the number of moles of NaHCO3 in 15.6 grams, we divide by the molar mass:

15.6 g / 84.01 g/mol = 0.1855 moles

Since the reaction produces 1 mole of H2O for every mole of NaHCO3, we can expect to produce 0.1855 moles of water.

The molar mass of water is:

H: 1.01 g/mol

O: 2 x 16.00 g/mol = 32.00 g/mol

Molar mass of H2O = 1.01 + 32.00 = 33.01 g/mol

Therefore, 1 mole of H2O has a mass of 33.01 grams.

To find the mass of water produced, we multiply the number of moles by the molar mass:

0.1855 moles × 33.01 g/mol = 6.124 grams of water

So, 15.6 grams of baking soda can produce 6.124 grams of water.

Answer:

4

Step-by-step explanation:

Answer:

58b - 36

Step-by-step explanation:

-11b + 15 + 69b - 51

combine 'like terms' to get:

58b - 36

Answer: 8602 is the answer to 253 x 34, do you want the other parts solved too?

Step-by-step explanation:

Answer:

4x +16 the slope is 4 because its parallel to the other equation

The solution is: the equation of the line that is parallel to the line

y - 1 = 4(x + 3) and passes through the point (4, 32) is y = 4x + 16.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have,

When two lines are parallel, their slope stays the same. thus we have y = 4x (so far)

Then use the point (4, 32) to plug in the coordinates to y = 4x + b

y = 4x + b (because y-intercept changes)

32 = 4(4) + b

32 = 16 + b

b = 32 - 16

b = 16

now, we get,

the y-intercept is 16 and the equation of the line that passes through the point (4,32) and is parallel to the line y = 4x + 13 is y = 4x + 16.

Hence, The solution is: the equation of the line that is parallel to the line

y - 1 = 4(x + 3) and passes through the point (4, 32) is y = 4x + 16.

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Answer:

Ans: 21

Step-by-step explanation:

Using BODMAS

12+36÷4

12+9

=21

Answer:

I think it's right if <xyw = <wyz

Step-by-step explanation:

\(10x - 8 = 68\)

\(10x = 68 - 8\)

\(10x = 60\)

\( \frac{10x}{10} = \frac{60}{10} \)

\(x = 6\)

Answer:

infinite ANSWERS starting below 23 towards negative side

Step-by-step explanation:

2x>12+37

2x>49

x>24.5

CONCLUSION HAS INFINITE ANSWERS

Marilyn's net pay will decrease by $18.15 if she increases her federal withholding allowances from 3 to 4.

Marilyn's gross pay is subject to Social Security, Medicare, and state taxes. The Social Security tax is 6.2% of her gross pay, the Medicare tax is 1.45% of her gross pay, and the state tax is 21% of her federal tax.The effect of increasing Marilyn's federal withholding allowances from 3 to 4 is that her federal tax will decrease. When her federal tax decreases, her state tax will also decrease because the state tax is a percentage of her federal tax. However, her Social Security and Medicare taxes will not change because they are calculated based on her gross pay.Marilyn's net pay is her gross pay minus all of the taxes that are deducted from her paycheck. Therefore, if her federal tax and state tax decrease, her net pay will increase. Conversely, if her federal tax and state tax increase, her net pay will decrease. In this case, Marilyn's net pay will decrease by $18.15 if she increases her federal withholding allowances from 3 to 4.

Marilyn's net pay will be affected by her federal withholding allowances. If she increases her allowances, her federal tax will decrease, which will result in a decrease in her state tax and net pay. Therefore, her net pay will decrease by $18.15 if she increases her federal withholding allowances from 3 to 4.

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The correct answer is option c. 95%. Reaching out two standard errors on either side of the sample proportion gives us an interval of 95% confidence.

This is due to the fact that two standard errors on either side of the sample proportion will cover around 95% of the population's cases.

We can typically determine the true proportion in the population using this range of two standard errors on either side of the sample proportion.

This is because it helps us identify any potential outliers in the population and provides a range of population proportions for which we may be 95% certain.

We are 95% certain that the true percentage is capable inside the interval if we stretch out two standard errors on either side of the sample proportion.

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\( \frac{3x + 9}{6} = x - 3 \\ \)

\(3x + 9 = 6(x - 3)\)

\(3x + 9 = 6x - 18\)

\(6x - 3x = 9 + 18\)

\(3x = 27\)

\(x = \frac{27}{3} \\ \)

answer: \(x = 9\)

The limit of (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity is 0.

To find the limit of the function (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity, we will divide both the numerator and denominator through the highest power of x. In this case, the highest power of x is x², so we can divide both the numerator & the denominator through x²:

\([(2x-1)/(x^2)] * [(3-x)/((x-1)/(x^2)(x+3))]\)

Now, as x approaches infinity, every of the fractions within the expression procedures zero except for (2x-1)/(x²). This fraction techniques 0 as x procedures infinity because the denominator grows quicker than the numerator. therefore, the limit of the expression as x strategies infinity is:

0 * 0 = 0

Consequently, When x gets closer to infinity, the limit of (2x-1)(3-x)/(x-1)(x+3) is 0.

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THE GENERAL EQUATION OF A STRAIGHT LINE IS y=mx+c

TO FIND c I WILL SUBSTITUTE THE GIVEN KNOWN POINTS.

\( - 5= \frac{1}{2} (2) + c \\ - 5= 1 + c \\ c = - 5 - 1 \\ c = - 6\)

THEREFORE WE NOW HAVE

\( y= \frac{1}{2} x - 6\)

ATTACHED IS THE SOLUTION

Answer:

y=2

because 4x2 =8 then 8-4 equals to 4 which is what your trying to get