Find a general solution of y" + 4y = 0.

Answer:

229.17 kilo-calories

Step-by-step explanation:

We have been given that 240 ml of orange juice (1 cup) provides about 110 kcal.

First of all, we will divide 500 by 240 to find amount of cups in 500 ml.

[tex]\text{Number of cups}=\frac{500}{240}[/tex]

[tex]\text{Number of cups}=2.08333[/tex]

Now, we will multiply 2.08333 by 110 to find amount of k-cal in orange juice.

[tex]\text{Number of k-cal}=2.08333\times 110\text{ k-cal}[/tex]

[tex]\text{Number of k-cal}=229.16666\text{ k-cal}[/tex]

[tex]\text{Number of k-cal}\approx 229.17\text{ k-cal}[/tex]

Therefore, there are approximately 229.17 kilo-calories in 500 ml of orange juice.

Final answer:

To find the number of kcalories in 500 ml of orange juice, set up a proportion using the known ratio of 240 ml to 110 kcal. Cross multiply and solve for the unknown value to find that there are approximately 229 kcalories in 500 ml of orange juice.

Explanation:

To calculate the number of kcalories in 500 ml of orange juice, we can use the ratio method. First, we know that 240 ml (1 cup) of orange juice provides 110 kcal. We can set up a proportion to find the number of kcalories in 500 ml of orange juice.

240 ml / 110 kcal = 500 ml / x kcal

Cross multiplying, we get 240x = 55000. Dividing both sides by 240, we find that x is approximately equal to 229.17. Therefore, there are about 229 kcalories in 500 ml of orange juice.

Answer:

50%

Step-by-step explanation:

29 right and 29 wrong. 29+29=58

Divide 29 by 58 and you get .5

Move the decimal over two to the right, and there’s the 50%.

You could also multiply .5 by 100 and you’ll still get 50!

Answer:

Step-by-step explanation:

1. Find the total number of problems, incorrect and correct. 29 incorrect problems + 29 correct problems is 58 total problems.

2. Find the total number of correct problems divided by the total number of problems. 29 incorrect problems divided by 58 total problems. This is simplified to 1/2.

3. Finally, convert 1/2 into a fraction. We can do this by multiplying the fraction by 50/50 to get a fraction of 50/100, and we know that 50/100 50 percent.

Answer:

b) 15,90,24.133,20

c) New average = 19.4, New Median = 20

d) 8

e) 40%

f) Wednesday

Step-by-step explanation:

a)                    Mon  Tue  Wed  Thu  Fri    

     Week 1      17      16     20     24   22

     Week 2     15      21    25     17    90

     Week 3      16      17    22     20   20

This is a 3×5 matrix where the rows gives us the weeks(Week 1, Week 2, Week 3) and the columns are the weekdays(Mon, Tue, Wed, Thu, Fri).

b)The shortest duration out of the data given for fifteen days is 15 minutes.

The longest duration is 90 minutes.

To calculate the average of given data, we use the following formula:

Average  = [tex]\frac{\text{Sum of all observations}}{\text{Total no of observations}}[/tex]

=[tex]\frac{17+16+20+24+22+15+21+25+17+90+16+17+22+20+20}{15}[/tex]

=[tex]\frac{362}{15}[/tex]

=24.133

Median = the value that divides the data into two equal parts]

Ascending order: 15,16,16,17,17,17,20,20,20,21,22,22,24,25,90

Median = [tex](\frac{n+1}{2})\text{th term}[/tex] = 8th term = 20

c)                   Mon  Tue  Wed  Thu  Fri    

     Week 1      17      16     20     24   22

     Week 2     15      21    25     17     19

     Week 3      16      17    22     20   20

New average = [tex]\frac{\text{Sum of new observations}}{\text{Total no of observations}}[/tex]

=[tex]\frac{17+16+20+24+22+15+21+25+17+19+16+17+22+20+20}{15}[/tex]

=[tex]\frac{362}{15}[/tex]

=19.4

New Median

Ascending order: 15,16,16,17,17,17,19,20,20,20,21,22,22,24,25

Median = [tex](\frac{n+1}{2})\text{th term}[/tex] = 8th term = 20

d) In order to know how many times we commute for 20 minutes or more, we check the entries that are greater than or equal to 20 minutes. We have 8 such entries. Thus, 8 times the commute was 20 minutes or more longer.

e)  Percent of commutes less than 18 minutes = [tex]\frac{\text{Commutes that are less than 18 minutes}}{\text{Total number of commutes} }[/tex]× 100%

=[tex]\frac{6}{15}[/tex]×100% = 40%

f) Average  = [tex]\frac{\text{Sum of all observations}}{\text{Total no of observations}}[/tex]

Average time spent in commuting on Monday = 16

Average time spent in commuting on Tuesday = 18

Average time spent in commuting on Wednesday = 22.3

Average time spent in commuting on Thursday = 20.3

Average time spent in commuting on Friday= 20.3

On Wednesday, we spent the most on commute time.

Final answer:

To find the percentage of students who voted for the athlete, divide the number who voted for the athlete (25) by the total number of students (100), and multiply by 100%. Therefore, 25% of the students voted for the athlete.

Explanation:

To calculate the percentage of students who voted for the athlete, we divide the number of students who voted for the athlete by the total number of students who voted, and then multiply the result by 100 to convert it to a percentage.

Total number of students = 25 (voted for the athlete) + 75 (voted for the actor) = 100 students

Now, to find the percentage who voted for the athlete:

Percentage voting for the athlete = (Number of students voting for the athlete ÷ Total number of students) × 100%

Percentage voting for the athlete = (25 ÷ 100) × 100%

Percentage voting for the athlete = 0.25 × 100%

Percentage voting for the athlete = 25%

25% of the students voted for the athlete.

Answer:  -8

Step-by-step explanation:

The slope of a line passing through two points (a,b) and (c,d) is given by:-

[tex]m=\dfrac{d-b}{c-a}[/tex]

Given : A line passes through the points ( 3 , -14 ) and ( x , 6 ) with a slope of -4, then we have

[tex]-4=\dfrac{6-(-14)}{x-3}\\\\\Rightarrow\ (x-3)(-4)=6+14\\\\\Rightarrow\ -4(x-3)=20\\\\\Rightarrow\ (x-3)=\dfrac{20}{-4}=-5\\\\\Rightarrow\ x-3=-5\\\\\Rightarrow\ x=-5-3=-8[/tex]

Hence, the value of x= -8

Answer: If we have a set defined as the difference of two sets, this is

A = B - C, then A = B - B∩C

So this is defined as, if you subtract the set C to the set B, then you are subtracting the common elements between C and B, from the set B.

so if A = {a,b,c} - {a,b,d}, the common elements are a and b, so: A = {c}

Answer:

. . . False

Step-by-step explanation:

5 is not among the elements of the given set.

__

The symbol ∈ means "is an element of ...".

Answer:

a) 0.0202

b)The seller's claim is not correct.

c) If the seller's claim is true we cannot have individual length of 72.15 inch.

Step-by-step explanation:

In the question it is given that

population mean, μ = 72 inch

Population standard deviation, σ = 0.5 inch

Sample size, n = 47

Sample mean, x =72.15 inch

a) z score = [tex]\frac{x-\mu}{\sigma/\sqrtr{n}}[/tex] = [tex]\frac{72.15-72}{0.5/\sqrt{47}}[/tex] = 2.0567

P(x ≥ 72.15) = P(z ≥ 2.0567) = 0.5 - 0.4798 = 0.0202

We calculated the probability with the help of standard normal table.

b) The sellers claim that the machine cuts the lumber with a mean length of 72 inch is not correct as we obtained a very low probability.

c)If we assume that the seller's claim is true that is the machine cuts the lumber into mean length of 72 inch then we cannot have an individual length 72.15.

Standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex] = 0.0729

Because it does not lie within the range of two standard errors that is (μ±2 standard error) = (71.8541,72.1458)

Answer:

5 = radius

Step-by-step explanation:

According to one of the Circle Equations, (X - H)² + (Y - K)² = R², you take the square root of your squared radius:

√25 = √R²

5 = R

* When we are talking about radii and diameters, we want the NON-NEGATIVE root.

I am joyous to assist you anytime.

Answer:

x=-5+2t, y=-6+3t, z=-6+9t

Step-by-step explanation:

We need to find parametric equations for the line through the point ( - 5, - 6, - 6) and perpendicular to the plane 2x + 3y + 9z = 17 .

If a line passes through a point [tex](x_1,y_1,z_1)[/tex] and perpendicular to the plane [tex]ax+by+cz=d[/tex], then the Cartesian form of line is

[tex]\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}[/tex]

and parametric equations are

[tex]x=x_1+at,y=y_1+bt,z=z_1+ct[/tex]

For the given information, [tex]x_1=-5,y_1=-6,z_1=-6,a=2,b=3,c=9[/tex]. So, the Cartesian form of line is

[tex]\frac{x+5}{2}=\frac{y+6}{3}=\frac{z+6}{9}[/tex]

Parametric equations of the line are

[tex]x=-5+2t[/tex]

[tex]y=-6+3t[/tex]

[tex]z=-6+9t[/tex]

Therefore the parametric equation for the line are x=-5+2t, y=-6+3t, z=-6+9t.

Final answer:

The parametric equations for the line are found using the point (-5, -6, -6) and the normal vector of the plane (2, 3, 9) as the direction vector, resulting in the equations x = -5 + 2t, y = -6 + 3t, and z = -6 + 9t.

Explanation:

To find a parametric equation for the line through the point (-5, -6, -6) and perpendicular to the plane 2x + 3y + 9z = 17, we use the fact that the normal vector of the plane (2, 3, 9) gives the direction of the line that is perpendicular to the plane. The general form of a parametric equation of a line is x = [tex]x_{0}[/tex] + at, y = [tex]y_{0}[/tex] + bt, and z = [tex]z_{0}[/tex] + ct, where [tex](x_{0},y_{0},z_{0})[/tex] is a point on the line and (a, b, c) is the direction vector of the line. In this case, the point given is (-5, -6, -6) and the direction vector is (2, 3, 9), so the parametric equations of the line are x = -5 + 2t, y = -6 + 3t, and z = -6 + 9t.

Step-by-step explanation:

If X is a finite Hausdorff space then every two points of X can be separated by open neighborhoods. Say the points of X are [tex]x_1, x_2, ..., x_n[/tex]. So there are disjoint open neighborhoods [tex]U_{12}[/tex] and [tex]U_2[/tex], of [tex]x_1[/tex] and [tex]x_2[/tex] respectively (that's the definition of Hausdorff space). There are also open disjoint neighborhoods [tex]U_{13}[/tex] and [tex]U_3[/tex] of [tex]x_1[/tex] and [tex]x_3[/tex] respectively, and disjoint open neighborhoods [tex]U_{14}[/tex] and [tex]U_4[/tex] of [tex]x_1[/tex] and [tex]x_4[/tex], and so on, all the way to disjoint open neighborhoods [tex]U_{1n}[/tex], and [tex]U_n[/tex] of [tex]x_1[/tex] and [tex]x_n[/tex] respectively. So [tex]U=U_2 \cup U_3 \cup ... \cup U_n[/tex] has every element of [tex]X[/tex] in it, except for [tex]x_1[/tex]. Since [tex]U[/tex] is union of open sets, it is open, and so [tex]U^c[/tex], which is the singleton [tex]\{ x_1\}[/tex], is closed. Therefore every singleton is closed.

Now, remember finite union of closed sets is closed, so [tex]\{ x_2\} \cup \{ x_3\} \cup ... \cup \{ x_n\}[/tex] is closed, and so its complemented, which is [tex]\{ x_1\}[/tex] is open. Therefore every singleton is also open.

That means any two points of [tex]X[/tex] belong to different connected components (since we can express X as the union of the open sets [tex] \{ x_1\} \cup \{ x_2,...,x_n\}[/tex], so that [tex]x_1[/tex] is in a different connected component than [tex]x_2,...,x_n [/tex], and same could be done with any [tex]x_i[/tex]), and so each point is in its own connected component. And so the space is totally disconnected.

For part (a) and (b) suposse [tex]A\subset B[/tex].

To prove part (a) observe that we already have that [tex]B\subset A\cup B[/tex]. So we will prove that [tex]A\cup B \subset B[/tex]. Let [tex]x\in A\cup B[/tex], then [tex]x\in A[/tex] or [tex]x\in B[/tex]. If  [tex]x\in B[/tex] we finish the proof, and if [tex]x\in A[/tex] implies  [tex]x\in B[/tex] because we assume [tex]A\subset B[/tex], and the proof is complete.

For part (b) we always have [tex]A\cap B\subset A[/tex]. We finish the proof showing [tex]A\subset A\cap B[/tex]. Let [tex]x\in A[/tex], then [tex]x\in B[/tex] by the asumption that [tex]A\subset B[/tex]. So, we have both [tex]x\in A[/tex] and  [tex]x\in B[/tex], that implies [tex]x\in A\cap B[/tex]. Therfore [tex]A\subset A\cap B[/tex], which completes the proof.

Answer: [tex]0.070<\sigma< 0.128[/tex]

Step-by-step explanation:

Confidence interval for population standard deviation :-

[tex]s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, n-1}}}<\sigma<s\sqrt{\dfrac{n-1}{\chi^2_{1-\alpha/2, n-1}}}[/tex]

Given : Significance level : [tex]\alpha: 1-0.90=0.10[/tex]

Sample size : n= 17

Sample standard deviation: [tex]s= 0.09[/tex]

Then by using the chi-square distribution table, we have

[tex]\chi^2_{1-\alpha/2, n-1}}=\chi^2_{0.95, 16}=7.96[/tex]

[tex]\chi^2_{\alpha/2, n-1}}=\chi^2_{0.05, 16}=26.30[/tex]

Confidence interval for population standard deviation will be :-

[tex]( 0.09)\sqrt{\dfrac{16}{26.30}}<\sigma<( 0.09)\sqrt{\dfrac{16}{7.96}}\\\\0.070197981837<\sigma<0.12759861690\\\\\approx0.070<\sigma< 0.128[/tex]

Hence, 90% confidence interval of the standard deviation of the skating performance test.: [tex]0.070<\sigma< 0.128[/tex]

90% confidence interval of the standard deviation of the skating performance test is [tex]0.070 < \sigma < 0.127[/tex]

It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.

The formula for finding the confidence interval for population standard deviation as follow:

[tex]\rm s \sqrt{\dfrac{n-1}{\chi ^2_{\alpha /2,n-1}}} < \sigma < s \sqrt{\dfrac{n-1}{\chi ^2_{1-\alpha /2,n-1}}}[/tex]

Where [tex]\rm s[/tex] is the standard deviation.

[tex]\rm n[/tex] is the sample size.

[tex]\rm{\chi ^2_{\alpha /2,n-1[/tex]  and  [tex]\rm\chi ^2_{1-\alpha /2,n-1[/tex] are the constant based on the Chi-Square distribution table.

[tex]\rm\alpha[/tex] is the significance level.

[tex]\rm\sigma[/tex] is the confidence interval for population standard deviation.

Calculating the confidence interval for population standard deviation:

We know significance level = 1 - confidence level

[tex]\rm \alpha = 1 - 0.90 = 0.10[/tex]

[tex]\rm n = 17[/tex]

[tex]\rm s = 0.09[/tex]

By the chi-square distribution table, the values of constants are below:

[tex]\rm \chi ^2_{1-\alpha/2,n-1} = \chi ^2_{0.95,16} = 7.96\\\rm \chi ^2_{ \alpha /2,n-1} = \chi ^2_{0.05,16} = 26.30[/tex]

putting all values in the above formula we will get the confidence interval for population standard deviation:

[tex]\begin{aligned} \rm (0.09) \sqrt{\dfrac{17-1}{26.30}}} & < \sigma < (0.09) \sqrt{\dfrac{17-1}{7.96}}}\\\\\rm s \sqrt{\dfrac{16}{26.30}}} & < \sigma < s \sqrt{\dfrac{16}{7.96}}\\\\\rm 0.0701197 & < \sigma < 0.12759 \\\\\end{aligned}\\[/tex]

or [tex]\approx 0.070 < \sigma < 0.127[/tex]

Thus, 90% confidence interval of the standard deviation of the skating performance test is [tex]0.070 < \sigma < 0.127[/tex]

Learn more about the confidence interval for population standard deviation here:

https://brainly.com/question/6654139

Answer:

1536 tiles

Step-by-step explanation:

Given,

The length of kitchen = 10 ft,

Width of the kitchen = 8 ft,

∵ The shape of floor of kitchen must be rectangular,

Thus, the area of the kitchen = 10 × 8 = 80 square ft = 11520 in²

( Since, 1 square feet = 144 square inches )

Now, the length of a tile = 2.5 in and its width = 3 in,

So, the area of each tile = 2.5 × 3 = 7.5 in²,

Hence, the number of tiles needed = [tex]\frac{\text{Area of kitchen}}{\text{Area of each tile}}[/tex]

[tex]=\frac{11520}{7.5}[/tex]

= 1536

Approximately 1536 tiles are needed to cover a kitchen floor that is 10 feet by 8 feet using tiles that are 2.5 inches by 3 inches.

To determine how many tiles are needed to cover a kitchen floor that is 10 feet long and 8 feet wide with tiles that are 2.5 inches by 3 inches, we first need to convert the dimensions of the kitchen to inches because the tile dimensions are given in inches. There are 12 inches in a foot, so the kitchen is 120 inches long (10 feet × 12 inches/foot) and 96 inches wide (8 feet  × 12 inches/foot).

We now calculate the area of the kitchen floor: Area = Length ×  Width = 120 inches × 96 inches = 11520 square inches.

Next, we calculate the area of one tile: Tile Area = Length × Width = 2.5 inches × 3 inches = 7.5 square inches.

Now, to find the number of tiles needed, we divide the total area of the kitchen floor by the area of one tile: Number of Tiles = Kitchen Area / Tile Area = 11520 square inches / 7.5 square inches ≈ 1536 tiles.

Therefore, approximately 1536 tiles are needed for the kitchen.

Answer:

The present value of K is, [tex]K=251.35[/tex]

Step-by-step explanation:

Hi

First of all, we need to construct an equation system, so

[tex](1)K=\frac{169}{(1+i)} +\frac{169}{(1+i)^{2}}[/tex]

[tex](2)K=\frac{225}{(1+i)^{2}} +\frac{225}{(1+i)^{4}}[/tex]

Then we equalize both of them so we can find [tex]i[/tex]

[tex](3)\frac{169}{(1+i)} +\frac{169}{(1+i)^{2}}=\frac{225}{(1+i)^{2}} +\frac{225}{(1+i)^{4}}[/tex]

To solve it we can multiply [tex](3)*(1+i)^{4}[/tex] to obtain [tex](1+i)^{4}*(\frac{169}{(1+i)} +\frac{169}{(1+i)^{2}}=\frac{225}{(1+i)^{2}} +\frac{225}{(1+i)^{4}})[/tex], then we have [tex]225(1+i)^{2}+225=169(1+i)^{3}+169(1+i)^{2}[/tex].

This leads to a third-grade polynomial [tex]169i^{3}+451i^{2}+395i-112=0[/tex], after computing this expression, we find only one real root [tex]i=0.2224[/tex].

Finally, we replace it in (1) or (2), let's do it in (1) [tex]K=\frac{169}{(1+0.2224)} +\frac{169}{(1+0.2224)^{2}}\\\\K=251.35[/tex]

Answer:

8 ten-thousands is 80 thousands.

Step-by-step explanation:

To find : How do I write 8 ten-thousands?

Solution :

We have to write 8 ten thousand,

We know that, according to numeric system

[tex]\text{Thousand is 1000}[/tex]

[tex]\text{Ten-Thousand is 10,000}[/tex]

[tex]\text{8 ten thousand is}\ 8\times 10000[/tex]

[tex]\text{8 ten thousand is 80000}[/tex]

Therefore, 8 ten-thousands is 80 thousands.

Answer:

Functions with straight lines have this sort of equation: Y = mx + b where the m is called slope and b, the y-intercept. As you don't have the slope you have to find out. In this case, the slope if 10, so when u have the m, just replace with one of your points to get the b, (y-intercept). The final equation for this function is, Y= 10x+35

Step-by-step explanation:

Answer:

See picture below

Step-by-step explanation:

The total area of the sheet of paper is 80, so we can divide the sheet of paper into 4 different sections, each one of them with area 20 (you can verify this by counting the squares in each section, there are 20 squares per section).

In the picture below we can see that the perimeter of each of the sections are from left to right:

The first one is a rectangle, with sides 5 and 4. Therefore the perimeter is 2(5) + 2(4) = 18.

The next section is irregular so we sum up the sides: 2 + 6 + 5 + 1 + 2 + 1 + 5 + 4 = 26.

For the next section we also sum up the sides: 3 + 7 + 2 + 1 + 1 + 6 = 20.

For the bottom section, we will sum up the sides too: 2 + 1 + 6 + 1 + 2 + 1 + 10 + 3 = 26.

So the perimeters are 8, 26, 20 and 26. This satisfies the condition of no more than two sections having the same perimeter.

Answer:

Part 1) The distance is [tex]d=7.3\ units[/tex]

Part 2) The measure of angle 2 is 121°

Part 3) The coordinates of endpoint V are (7,-27)

Part 4) The value of x is 10

Step-by-step explanation:

Part 1) Find the distance between M(6,16) and Z(-1,14)

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute the given values in the formula

[tex]d=\sqrt{(14-16)^{2}+(-1-6)^{2}}[/tex]

[tex]d=\sqrt{(-2)^{2}+(-7)^{2}}[/tex]

[tex]d=\sqrt{53}\ units[/tex]

[tex]d=7.3\ units[/tex]

Part 2) Find the measure m∠2

we know that

If two angles are supplementary, then their sum is equal to 180 degrees

In this problem we have

m∠1+m∠2=180°

substitute the given values

[tex](4y+7)\°+(9y+4)\°= 180\°[/tex]

Solve for y

[tex](13y+11)\°= 180\°[/tex]

[tex]13y= 180-11[/tex]

[tex]13y=169[/tex]

[tex]y=13[/tex]

Find the measure of  m∠2

[tex](9y+4)\°[/tex]

substitute the value of y

[tex](9(13)+4)=121\°[/tex]

Part 3) The midpoint of UV is (5,-11). The coordinates of one endpoint are U(3,5) Find the coordinates of endpoint V

we know that

The formula to calculate the midpoint between two points is

[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

we have

[tex]M(5,-11)[/tex]

[tex](x1,y1)=(3,5)[/tex]

substitute and solve for (x2,y2)

[tex](5,-11)=(\frac{3+x2}{2},\frac{5+y2}{2})[/tex]

so

Equation 1

[tex]5=(3+x2)/2[/tex]

[tex]10=3+x2[/tex]

[tex]x2=7[/tex]

Equation 2

[tex]-11=(5+y2)/2[/tex]

[tex]-22=(5+y2)[/tex]

[tex]y2=-27[/tex]

therefore

The coordinates of endpoint V are (7,-27)

Part 4) GI bisects ∠DGH so that ∠DGI is (x-3) and ∠IGH is (2x-13) Find the value of x

we know that

If GI bisects ∠DGH

then

∠DGI=∠IGH

Remember that bisects means, divide into two equal parts

substitute the given values

[tex]x-3=2x-13[/tex]

solve for x

[tex]2x-x=-3+13[/tex]

[tex]x=10[/tex]

Answer:

The graph of given inequality is shown below.

Step-by-step explanation:

The given linear inequality is

[tex]x>7[/tex]

We need to graph the region of solution of the given linear inequality.

The related equation of given linear inequality is

[tex]x=7[/tex]

We know that x=a is a vertical line which passes through the point (a,0).

Here, a =7. So x=7 is a vertical line which passes through the point (7,0).

Relate line is a dotted line because the sign of inequality is >. It means the points on the line are not included in the solution set.

Shaded region is right side of the related line because the solution set contains all possible values of x which are greater than 7.

Answer:

the dimension called by the specification is larger

Step-by-step explanation:

Data provided in the question:

micrometer reading = 7.5 in

Dimension called by the specifications = 7.59 in

Now,

Subtracting the Micrometer reading from the dimension called by specification , we get

 7.59

- 7.5

--------

0.09

since, the result is positive thus,

the dimension called by the specification is larger

The specification of 7.59 inches is larger than the micrometer reading of 7.57 inches. Therefore, the part does not meet the required specification.

To determine whether the micrometer reading or the specification is larger, we need to compare the two values. The micrometer reading is 7.57 inches, and the specification calls for a dimension of 7.59 inches.

When comparing these two measurements:

Clearly, 7.59 inches is larger than 7.57 inches.

This comparison shows that the specification is larger than the micrometer reading.

Answer:

Step-by-step explanation:

Given is a phrase

"I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times."

This implies instead of attempting so many things without depth one thing indepth training is very much good and feared by others.

This applies to knowledge and also the subject Mathematics

Instead of practising many sums without getting answers, learning one concept and trying to get the difficult problem will help go a long way in learning.

In depth learning helps to master other allied concepts also very easily and this helps extending to other topics

Answer:

we over weighted suitcase will be 46.9889 pound

Step-by-step explanation:

We have given the average weight of passenger's suitcase [tex]\mu =45\ pounds[/tex]

Standard deviation [tex]\sigma =2\ pounds[/tex]

16 % of the suitcase are overweight so 100-16 =84 % of the suitcase will pass without any problem

So probability [tex]p=0.84[/tex]

From z table at p =0.84 z will be z=0.99445

We know that [tex]z=\frac{x-\mu }{\sigma }[/tex]

[tex]0.99445=\frac{x-45}{2}[/tex]

x = 46.9889 pound

So we over weighted suitcase will be 46.9889 pound

Using standard deviation formula to solve the problem. Then the overweighted suitcase is 46.9889 pounds.

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.

Given

The average [tex](\mu )[/tex] weight of an airline passenger’s suitcases is 45 pounds.

The standard deviation [tex](\sigma)[/tex] of 2 pounds.

16% of the suitcase are overweight. So,

[tex]100 - 16 = 84\%[/tex]

The suitcase will pass without any problem. So the probability will be

[tex]\rm P = 0.84[/tex]

From z table at P = 0.84 will be

z = 0.99445

We know that

[tex]\begin{aligned} z &= \dfrac{x - \mu}{\sigma}\\0.99445 &= \dfrac{x - 45}{2}\\x &= 46.9889\end{aligned}[/tex]

Thus, the overweighted suitcase is 46.9889 pounds.

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Answer:

(1) [tex]y=(\frac{2}{a+bx})^3[/tex]

By differentiating w.r.t. x,

[tex]\frac{dy}{dx}=3(\frac{2}{a+bx})^2\times \frac{d}{dt}(\frac{2}{a+bx})[/tex]

[tex]=3(\frac{2}{a+bx})^2\times (-\frac{2}{(a+bx)^2})[/tex]

[tex]=-\frac{24}{(a+bx)^4}[/tex]

(2) [tex]y=(at^3-3bt)^3[/tex]

By differentiating w.r.t. t,

[tex]\frac{dy}{dt}=3(at^3-3bt)^2\times \frac{d}{dt}(at^3-3bt)[/tex]

[tex]=3(at^3-3bt)^2 (3at^2-3b)[/tex]

[tex]=9t^2(at^2-3b)^2(at^2-b)[/tex]

(3) [tex]y=(t^b)(e^\frac{b}{t})[/tex]

Differentiating w.r.t. t,

[tex]\frac{dy}{dt}=t^b\times \frac{d}{dt}(e^\frac{b}{t})+\frac{d}{dt}(t^b)\times e^\frac{b}{t}[/tex]

[tex]=t^b(e^\frac{b}{t})\times \frac{d}{dt}(\frac{b}{t}) + bt^{b-1}(e^\frac{b}{t})[/tex]

[tex]=t^be^\frac{b}{t}(-\frac{b}{t^2})+bt^{b-1}e^{\frac{b}{t}}[/tex]

(4) [tex]z = ax^2.sin (4x)[/tex]

Differentiating w.r.t. x,

[tex]\frac{dz}{dt}=ax^2\times \frac{d}{dx}(sin (4x))+sin (4x)\times \frac{d}{dx}(ax^2)[/tex]

[tex]=ax^2\times cos(4x).4+sin (4x)(2ax)[/tex]

[tex]=4ax^2cos (4x)+2ax sin (4x)[/tex]

1. Y-axis. 2. X-axis. 3. X-axis

Step-by-step explanation:

1. Look at the shapes, is it reflecting vertically (y axis) or horizontally (x axis)? Take the shape, and mentally flip it over over each axis. If it lines up with the reflection provided, the answer is the axis you flipped over.

Answer:

53.69 kilograms.

Step-by-step explanation:

You had 454 grams of shrimp per square feet in a tank.

Converting square feet in square meter.

1 square foot = 0.092903 square meter

Means you had 454 grams of shrimp per 0.093 square meter in a tank.

The bottom area of the tank is 11 square meter.

So, grams of shrimp in 11 square meter = [tex]\frac{454\times11}{0.093}[/tex]

= 53698.92 grams

In kg it will be [tex]\frac{53698.92}{1000}[/tex] = 53.69 kg

The distribution function for the length of the time that the first to arrive has to wait for the other is given by a triangular shape. This comes from the continuous uniform distribution nature of their arrival time. More probable waiting times are represented by the peak of the triangle.

This problem relates to the mathematical concept of a continuous uniform distribution. In the meeting scenario of Mr. Warren Buffet and Mr. Zhao Danyang, each person arrives between 12 pm and 1 pm at random with a uniform probability. This means there is equal likelihood for each time interval within the hour for them to arrive.

We are interested in the length of time the first person to arrive has to wait for the second. Let's denote the time of arrival of Mr. Buffet by X and that of Mr. Zhao by Y, both from 0 (12:00 pm) to 1 (1:00 pm). The time the first to arrive has to wait is |X - Y|. The distribution function of this waiting time (W = |X - Y|) is a triangle with its peak at W = 0 (no waiting time). The two ends of the base of the triangle fall at -1 and 1. This triangular shape comes from the fact that shorter waiting times (near the peak) are more probable because there is more overlap between X and Y.

Therefore, the cumulative distribution function for the waiting time, W, is given by:

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Answer:

Mean = 86.067

Median = 85

Step-by-step explanation:

The given data set is

{ 93, 94, 95, 89, 85, 82, 87, 85, 84, 80, 78, 78, 84, 87, 90 }

Number of observations = 15

Formula for mean:

[tex]Mean=\frac{\sum x}{n}[/tex]

where, n is number of observations.

Using the above formula, we get

[tex]Mean=\frac{93+94+95+89+85+82+87+85+84+80+78+78+84+87+90}{15}[/tex]

[tex]Mean=\frac{1291}{15}[/tex]

[tex]Mean\approx 86.067[/tex]

Therefore the mean of the given data set is 86.067.

Arrange the given data set in ascending order.

{ 78, 78, 80, 82, 84, 84, 85, 85, 87, 87, 89, 90, 93, 94, 95 }

Number of observation is 15 which is an odd term. So

[tex]Median=(\frac{n+1}{2})\text{th term}[/tex]

[tex]Median=(\frac{15+1}{2})\text{th term}[/tex]

[tex]Median=8\text{th term}[/tex]

[tex]Median=85[/tex]

Therefore the median of the data set is 85.

Answer:

a) MAX--> PC (R,P) = 0,3R+ 0,5P

b) Optimal solution: 40.000 units of R and 10.000 of PC = $17.000

c) Slack variables: S3=1000, is the unattended demand of P, the others are 0, that means the restrictions are at the limit.

d) Binding Constaints:

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

Step-by-step explanation:

I will solve it using the graphic method:

First, we have to define the variables:

R : Regular Gasoline

P: Premium Gasoline

We also call:

PC: Profit contributions

A: Grade A crude oil

• R--> PC: $0,3 --> 0,3 A

• P--> PC: $0,5 --> 0,6 A

So the ecuation to maximize is:

MAX--> PC (R,P) = 0,3R+ 0,5P

The restrictions would be:

1. 18.000 A availabe (R=0,3 A ; P 0,6 A)

2. 50.000 capacity

3. Demand of P: No more than 20.000

4. Both P and R 0 or more.

Translated to formulas:

Answer d)

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

To know the optimal solution it is better to graph all the restrictions, once you have the graphic, the theory says that the solution is on one of the vertices.

So we define the vertices: (you can see on the graphic, or calculate them with the intersection of the ecuations)

V:(R;P)

• V1: (0;0)

• V2: (0; 20.000)

• V3: (20.000;20.000)

• V4: (40.000; 10.000)

• V5:(50.000;0)

We check each one in the profit ecuation:

MAX--> PC (R,P) = 0,3R+ 0,5P

• V1: 0

• V2: 10.000

• V3: 16.000

• V4: 17.000

• V5: 15.000

As we can see, the optimal solution is  

V4: 40.000 units of regular and 10.000 of premium.

To have the slack variables you have to check in each restriction how much you have to add (or substract) to get to de exact (=) result.  

To maximize the total profit contribution, a linear programming model is formulated with decision variables, objective function, and constraints. The model is: Maximize 0.30x + 0.50y, Subject to: 0.3x + 0.6y ≤ 18,000, x + y ≤ 50,000, y ≤ 20,000, x, y ≥ 0.

To formulate a linear programming model, we need to define the decision variables, objective function, and constraints. Let's assume that x represents the number of gallons of regular gasoline produced and y represents the number of gallons of premium gasoline produced.

The objective function is to maximize the total profit contribution, which can be expressed as: 0.30x + 0.50y.

The constraints are:

So, the linear programming model can be formulated as:

Maximize 0.30x + 0.50y

Subject to:

0.3x + 0.6y ≤ 18,000

x + y ≤ 50,000

y ≤ 20,000

x, y ≥ 0

The expression 4d + 6 + 2d is equivalent to the expression (3d + 3) + (3d + 3). Then the correct option is C.

The equivalent is the functions that are in different forms but are equal to the same value.

The expression is given below.

→ 4d + 6 + 2d

Then the expression can be written as

→ 6d + 6  

→ 2(3d + 3)

→ (3d + 3) + (3d + 3)

Thus, the correct option is C.

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Final answer:

Choices A and C, which evaluate to 2(3d+3) and (3d+3)+(3d+3) respectively, are equivalent to the original expression 4d+6+2d.

Explanation:

The student is asking to identify which expressions are equivalent to 4d+6+2d. To solve this, we combine like terms in the original expression.

4d + 2d + 6 = 6d + 6.

Now let's analyze the provided choices:

(Choice A) 2(3d+3) simplifies to 6d + 6, which is the same as the original expression.

(Choice B) 6(d+6) simplifies to 6d + 36, which is not equivalent to 6d + 6.

(Choice C) (3d+3) + (3d+3) simplifies to 3d + 3 + 3d + 3, which simplifies further to 6d + 6, equivalent to the original expression.

Choices A and C are equivalent to 4d+6+2d.