Simplify the given expression. Show all steps. Submit your handwritten work or use the equation editor to receive credit.

The distance between the two towns is 165 kilometers

The initial speed = 100 kilometer per hour

Time taken = t hours

We know,

Speed = Distance / Time

Distance = Speed × t

Distance = 100 × t

New speed = 110 kilometer per hours

He saves 9 minutes

9 minutes = 9/60 hours

The time taken = t - 9/60

The distance = 110 × (t - 9/60)

= 110t - 33/2

Then the equation will be

100t = 110t - 33/2

110t - 100t = 33/2

10t = 33/2

t = 33/2 ÷ 10

t = 33/2 × 1/10

t = 1.65 hours

Then the distance = 100 × t

= 100 × 1.65

= 165 kilometers

Hence, the distance between the two towns is 165 kilometers

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The dimensions that minimize the cost of building the tank are r ≈ 6.5 ft and h ≈ 26 ft

What do you mean by cost?

The total cost becomes

T = ucSc + 2ucSh

   = 2ucπrh + 8ucπr²

We need to eliminate h . The volume from the question gives a way out.

4640 = 4/3πr³ + πr²h

  h = 4640/πr² - 4r/3

substitute into the formula for total cost gives, after simplifying

  T =  16ucπr²/3 +  9280uc/r²

differentiating with respect to r , we get

  dT/dr = 32/3Ucπr - 9280Uc/r²

at extrema

dT/dr = 0

⇒ 32/3Ucπr = 9280Uc/r²

 r = ∛870/π ≈ 6.5 ft

To confirm that r is a minimum value, carry out the second derivative test

   d²T/dr² = 32Ucπ/3 +  18560/r³

substituting ∛870/π, we get that d²T/dr² > 0  confirming that minimum value

To find h , recall that

 h = 4640/πr² - 4r/3

substituting r , we get h ≈ 26.0 ft as the corresponding minimum height.

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Answer:

"Gases are compressible because most of the volume of a gas is composed of the large amounts of empty space between the gas particles. At room temperature and standard pressure, the average distance between gas molecules is about ten times the diameter of the molecules themselves."

Step-by-step explanation:

Found information on Compressibility | CK-12 Foundation website

The slope of the line parallel to y = -3/2 x + 3 is -3/2.

The slope - intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).

The slope intercept form of an equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as y = mx + b.

Here , we are given that the line is parallel to y = -3/2x + 3  ---(i)

By comparing (i) with slope-intercept form of equation for a straight line. we get the slope of (i) as -3/2.

i.e., the slope of (i) is m= -3/2.

And we know that two parallel lines have same slope which gives the slope of the line parallel to (i) -3/2.

Therefore, the slope of the line parallel to y = -3/2 x + 3 is -3/2 .

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NOTE : The question given here is not complete. The complete question is given below.

Question: What is the slope of a line parallel to y= -3/2 x + 3?.

Answer:

c = 112 , d = 29

Step-by-step explanation:

c and 68 are a linear pair and sum to 180° , that is

c + 68 = 180 ( subtract 68 from both sides )

c = 112

the 3 angles 30, 3d - 5 and 68 lie on straight line AOB and sum to 180° , so

30 + 3d - 5 + 68 = 180

3d + 93 = 180 ( subtract 93 from both sides )

3d = 87 ( divide both sides by 3 )

d = 29

The equation of circle can be written as (x-4)^2+ (y+2)^2 = 6^2. The center of the circle is (4,-2) and radius is 6.

What is a circle?

A circle is locus of points which have same distance from a point known as center. Circle is a 2 dimensional figure.

We are given a equation

x^2+y^2-8x+4y-16 = 0

Using completing square method

x^2-8x+ 16+y^2+4y+4-36=0

(x-4)^2 + (y+2)^2 = 6^2

Comparing with standard equation

The center of circle is (4,-2) and and radius of the circle is 6.

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The amount of money that Alonso has invested in these accounts is given as $9000 and $21000

We have to represent the percentages as a and b, then multiply 100 at the right hand side of the equation

we would have

7a + 5b = 1680 * 100

7a + 5b = 168000 ---- 1

From the amount that Alonso has to invest we would have

a + b = 30000

where b = 30000 - a   ---- 2

We have to put the value of b in equation a

7a + 5(30000 - a) = 168000

7a + 150000 -5a = 168000

7a - 5a = 168000 - 150000

2a = 18000

a = 18000 / 2

= $9000

From equation 2

b = 30000 - 9000

= $21000

The amount that was invested in each of the accounts are

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Answer:12.5 pieces

Step-by-step explanation:2/5 as a decimal is .4.      

5/.4=12.5

The largest possible value of 10 can be calculated using factorials and the largest value would be = 3628800

Factorials is defined as the mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that is n is given as 5, then it's factorial would be =5×4×3×2×1 = 120.

Factorials is used in mathematics or statistics to denote the possibilities of an event in an outcome.

The total numbers of the two groups = 10

The factorials of 10 = 10×9×8×7×6×5×4×3×2×1

= 3,628,800.

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Answer: 15 x 9 = 135

The time required for a Ford Raptor travelling at 75mph to travel 250 mile is 10/3 hours.

The speed of the Ford Raptor traveling is 75 mi per hour

Total distance to be covered is 250 mile

We need to calculate total time required to cover the diatance of 250 miles

Total time can be found by using the speed distance formula

As per the formula

speed = total distance covered / total time taken

Let total time be x

75 = 250/x

x = 250/75

x = 10/3

Therefore, the time taken for a Ford Raptor travelling at 75mph to travel 250 mile is 10/3 hours.

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Answer:

x>-⅘ OR x<-⅘ (Can I have brainliest ;-;)

Step-by-step explanation:

1) Find x-int:

0=10x+8

-8=10x (÷10)

-⅘=x

x(-⅘;0)

2) Domain:

3) Choose 1 of those, since i cant see the graph i cant say which domain would fit the graph

The given triangle is not an isosceles triangle because all sides have different lengths. So, Anthony is incorrect.

We are given a graph. The graph shows a triangle. The vertices of the given triangle are K, L, and M. The coordinates of the vertices of the triangle are K (-4, 8), L (-7, 4), and M (-2, 1). Anthony claims that the triangle ΔKLM is isosceles. We need to check whether he is right or not. We will find the lengths of all sides of the triangle using the distance formula between two points.

KL = √[(-4 + 7)² + (8 - 4)²] = √(9 + 16) = √25

LM = √[(-7 + 2)² + (4 - 1)²] = √(25 + 9) = √34

MK = √[(-4 + 2)² + (8 - 1)²] = √(4 + 49) = √53

The lengths of all sides of the triangle are different from each other. Hence, it is a scalene triangle.

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The original width is 6 inches, and was reduced to 3 inches, which is half. Keeping this in mind, the new height should be half the original 8 inch height, being halved to 4 inches.

Answer:

Step-by-step explanation:

807

Answer:

408

Step-by-step explanation:

3 x 19 = 57

x 14 = 798

+ 18 = 816

divided by 2 = 408

Ryan will use the multiplication with 0.621 to find the speed in mile per hour.

To find the speed in mile per hour we will convert the unit from mentioned unit to desired unit. As per the known fact, 1 kilometre is 0.621 mile.

Keeping the value of mile in the place of kilometres, we will calculate the speed in miles per hour.

Speed = (100 × 0.621)/1

Performing multiplication in numerator on Right Hand Side of the equation to find the value of speed in miles per hour

Speed = 62.1 miles per hour

Thus, Ryan should multiply the value with 0.621 miles per hour and hence, the value of speed in miles per hour is 62.1.

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For the given number of shares 1,239 and cost price per share is $19.36 and selling price per share $27.93 then gain percent is equal to

44.27%( nearest hundredth place).

As given in the question,

Total number of shares = 1,239 shares

Cost price per share = $19.36

Cost price of 1,239 shares = 1,239 × 19.36

                                          = $ 23987.04

Selling price per share = $27.93

Selling price of 1,239 shares = 1,239 × 27.93

                                              = $ 34605.27

Selling price > Cost price

Gain amount = 34605.27 - 23987.04

                    = $10618.23

Gain percent = [(10618.23) /(23987.04) ] × 100

                     = 44.2665..

                     = 44.27%

Therefore, for the given number of shares 1,239 and cost price per share is $19.36 and selling price per share $27.93 then gain percent is equal to 44.27%( nearest hundredth place).

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[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=29\\ \theta = 99 \end{cases}\implies A=\cfrac{(99)\pi (29)^2}{360} \\\\\\ A=\cfrac{9251\pi }{40}\implies A\approx 726.57~cm^2[/tex]

The following is the 95% confidence interval for the standard deviation of UH students' height: CI = (1.81, 4.028) that is option B is correct.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed. The standard deviation gauges how widely the data deviates from the mean. When comparing data sets that may have the same mean but a different range, it is helpful.

Here,

The formula for the standard deviation's confidence interval is given as CI = √[(n - 1)s²/(χ²ₙ ₋ ₁, α/2)], √[(n - 1)s²/(χ²ₙ ₋ ₁, (1 - α)/2)]

Number of participants; n = 14 D F = n - 1 = 14 - 1 = 13

Deviation from the mean; s = 2.5

Significant level; = 1 - 0.95 = 0.05 

Confidence level; CL = 95% = 0.95

As a result, using an online Chi-square distribution table, we have: 

χ²₁₃, ₀.₀₂₅ = 24.736

(χ²₁₃, ₀.₉₇₅) = 5.01

CI = √[(13 * 2.5²/(24.736)], √[(13 * 2.5²/(5.01)]

CI = (1.81, 4.03) (1.81, 4.03)

The range with a 95% confidence level for the height standard deviation of UH students is as follows: CI = (1.81, 4.028), so option B is the proper one.

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Answer:

54

Step-by-step explanation:

We can divide 28 by 11 to get...

11 ÷ 28 = 2.545454

   22

     60

     55

        50

        44

           60

            55

               50

                44

                   60

                    55

                      50

                      44

                        60

The division quotient reveals that the numbers 5 and 4 repeat themselves frequently. It is a situation of a repeating decimal that does not end.

This means that in the decimal equivalent of [tex]\frac{28}{11}[/tex], the smallest group of repeating digits is composed of 54 repeating digits.

Hope this helps! :)

The value of the expression is -4.

Question:

Evaluate the expression. 4−[(11+12(−2)÷6)+1] What is the value of the expression? Enter your answer in the box.

What is an expression?

A mathematical expression is a phrase containing a minimum of two numbers or variables and a minimum of one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression)

4−[(11+12(−2)÷6)+1]

Simplify parenthesis first followed by box brackets

=4-[(11 -24÷6)+1]

=4-[(11-4+1]

=4-8=-4

So, the value of the expression is -4.

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The probability that the first is a king, the second a diamond and the third a diamond quiz let is 1/13, 1/4 and 10/52 respectively.

Now, we know that there are 52 cards in the deck of cards, and there are 13 cards of each suits i.e. diamonds, spade, heart and clubs. Also there are 12 face cards in total of the deck.

So, the probability if getting the first card is king :

King is a face card and there are 4 kings in the deck so the probability will be :

P(getting 1st card as king) = 4/52 = 1/13.

The probability of getting the second card a diamond is :

we know that there are 13 cards of the diamond in the deck so the probability will be :

P(getting the diamond card) = 13/52 = 1/4.

Now, lastly the probability if getting the diamond quiz let is :

There are 10 flashcards of the diamonds in the deck, so the probability will be :

P(getting the diamond flashcard) = 10/52.

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Answer: 50

Step-by-step explanation:

30% as a decimal is 0.3.

Let's say "what" is a variable, x.

0.3x=15

Divide both sides by 0.3 and you get x=50

Answer:50

Step-by-step explanation:30/100×x=15

x=15×100/30

x=50

Answer:

Step-by-step explanation:

32,54,52

The graph of the quadratic function y = 0.75x² is given by the image at the end of the answer.

The notation y = 0.75x² is already in vertex form, meaning that the function was vertically compressed by a factor of 3/4 from the original graph.

The definition of a quadratic equation with vertex (h,k) is given as follows:

y = a(x - h)² + k.

In which a represents the leading coefficient of the quadratic function.

In this problem the coordinates of the vertex are:

(0,0).

Hence the parameters are:

h = 0, k = 0.

Thus the equation is:

y = ax².

When x = -2, y = 3, hence the leading coefficient is given as follows:

3 = a(-2)²

4a = 3

a = 3/4

a = 0.75.

Hence the equation is:

y = 0.75x².

The multiplication by 0.75 means that the parent function y = x² is vertically compressed by a factor of 0.75.

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Answer:

f(x) = 13 [tex](3)^{x}[/tex]

Step-by-step explanation:

we require to find a and b

using ordered pairs from the table and substituting into f(x)

f(x) = a[tex](b)^x}[/tex]

using (0, 13 )

13 = a[tex]b^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , then

a = 13

f(x) = 13[tex](b)^{x}[/tex]

using (1, 39 )

39 = 13[tex]b^{1}[/tex] = 13b ( divide both sides by 13 )

3 = b

f(x) = 13 [tex](3)^{x}[/tex]

Answer:

[tex]f(x)=13(3)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

The y-intercept of a function is the y-value when x = 0.

From inspection of the table, the y = 13 when x = 0, so a = 13:

[tex]\implies f(x)=13(b)^x[/tex]

Substitute the ordered pair (1, 39) into the equation and solve for b:

[tex]\begin{aligned}f(1)=13(b)^1&=39\\13b&=39\\b&=\dfrac{39}{13}\\b&=3\end{aligned}[/tex]

Therefore, the equation for the given table is:

[tex]f(x)=13(3)^x[/tex]

Solution of expression 5²- 9 ÷ 3 using PEMDAS is 22.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are referred to as PEMDAS in this context. Teachers in the United States constantly remind their students about the acronym PEMDAS, which stands for parentheses, exponents, multiplication, division, addition, and subtraction. BODMAS, which stands for brackets, ordering, division and multiplication, and addition and subtraction, is another acronym used by educators. A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations. Parentheses, Exponents, Multiplication and Division (from Left to Right), Addition and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).

Given,

Expression:

5²- 9 ÷ 3

Using PEDMAS,

Squaring,

25 - 9 ÷3

Dividing,

25 - 3

22

Solution of expression 5²- 9 ÷ 3 using PEMDAS is 22.

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The critical value will be +- 1.96.

What is critical value?

A crucial value delimits areas of a test statistic's sampling distribution. Both confidence intervals and hypothesis tests take these values into account.

Main body:

sample size is 10.

if you use z-scores, and it appears that you have to, since you don't know the mean or standard deviation of your population, your mean is 0 and your standard deviation is 1.

at 95% confidence level, 100% - 95% is your alpha.

that makes it equal to 5%.

divide that by 2 and you have half your alpha on the left end of the confidence interval and half on the right end.

that makes it 2.5% on each end.

2.5% is the same as .025 in decimal form.

look up a z-score to the left of .025 to get a z-score of -1.959963986 which can be rounded to -1.96.

since the normal distribution is symmetric about the mean,

Therefore your critical z-score is plus or minus 1.96.

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The mean of the data calculated by the standard method is 67.4  .

The given data set is:

82, 75, 48, 78, 54

To find the mean we have to find the total value of all the data together.

Total value = 82 + 75 + 48 + 78 + 54 = 337

frequency of data(total number of independent data) = 5

Mean = total value / frequency

or, mean = 337 / 5 = 67.4

The mean is one of the metrics of central tendency, along with the mode and median. The mean is just the average of the values in the specified set. It suggests that values in a specific data set are evenly distributed.

In order to find the mean, the total values provided in a datasheet must be added, and the sum must be divided by the total number of values.

Therefore the mean of the data set is 67.4.

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