The slopeof a linear function h(x) is 2. Suppose the function is translated 8 units up to get d(x). How can h(x) be translated to the left or right to represent the same function d(x)?

Answer:

Line A is represented by the function f(x) = 2x + 1.

Step-by-step explanation:

This can be solved by trial and error. What it means? It means that we are going to replace the ordered pairs in the function, and the equality must be satisfied.

Line A

(-2,-3)

When x = -2, f(x) = -3. Does it happen in the function?

[tex]f(x) = 2x + 1[/tex]

[tex]-3 = 2(-2) + 1[/tex]

[tex]-3 = -3[/tex]

The first equality is OK. Let's see the second

(2,5)

When x = 2, y = 5.

[tex]f(x) = 2x + 1[/tex]

[tex]5 = 2(2) + 1[/tex]

[tex]5 = 5[/tex]

Also OK.

So line A is represented by the function f(x) = 2x + 1.

Now let's see why the other lines are not represented by this function.

Line B

(-2,-4)

[tex]f(x) = 2x + 1[/tex]

[tex]-4 = 2(-2) + 1[/tex]

[tex]-4 = -3[/tex]

False

Line C

(-2,-5)

[tex]f(x) = 2x + 1[/tex]

[tex]-5 = 2(-2) + 1[/tex]

[tex]-5 = -3[/tex]

False

Line D

(0,-4)

[tex]f(x) = 2x + 1[/tex]

[tex]-4 = 2(0) + 1[/tex]

[tex]-4 = 1[/tex]

False

Answer:

line a

Step-by-step explanation:

Answer:

The rounded number is 0.06006 to the hundred-thousandths place.

Step-by-step explanation:

Consider the provided number.

0.0600609

Here we need to round the number to the nearest hundred-thousandths.

Rounding to the hundred-thousandths means that there should be maximum 5 digits after the decimal point.

Here, the provided number 0.0600609 contains 7 digit after the decimal point and we want only 5 digits after decimal. So we will remove the last 3 digit.

For this we need to round the number to the nearest hundred thousands place.

The rule of rounding a number is:

If 0, 1, 2, 3, or 4 follow the number, then no need to change the rounding digit.

If 5, 6, 7, 8, or 9 follow the number, then rounding digit rounds up by one number.

The 6th digit after the decimal is 0, so there is no need to change the rounding digit.

So, the rounded number is 0.06006 to the hundred-thousandths place.

Answer and Step-by-step explanation:

To find the angles between the lines, we can use the formula:

tanα = |ms - mr| / | 1 + ms.mr|

where ms and mr are the linear coefficients of the lines you want to find. It always finds the smaller angle formed.

Let's find all the angles from the triangles formed.

y=x     ms = 1

y=2x   mr = 2

tanα = |1 - 2| / | 1 + 1.2|

tanα = |-1| / | 1 + 2|

tanα = |-1/3|

tanα = 1/3

α = tan⁻¹1/3

α = 18.4°

y=x     ms = 1

y=-4   mr = 0

tanα = |1 - 0| / | 1 + 1.0|

tanα = |1| / | 1 + 0|

tanα = |1/1|

tanα = 1

α = tan⁻¹1

α = 45°

y=2x     ms = 2

y=-4     mr = 0

tanα = |2 - 0| / | 1 + 2.0|

tanα = |2| / | 1 + 0|

tanα = |2/1|

tanα = 2

α = tan⁻¹2

α = 63.4°

As these 2 lines are in both triangles, the suplement of this angle is also asked, so, 180° - 63.4° = 116.6°

For y=2x and y=-4, it's the same: α = 63.4°  

y=2x     ms = 2

y=-2x     mr = -2

tanα = |2 - (-2)| / | 1 + 2.(-2)|

tanα = |4| / | 1 - 4|

tanα = |4/3|

tanα = 4/3

α = tan⁻¹ 4/3

α = 53.1°

Final answer:

To find angles ABC and ABD in the intersecting lines problem, analyze the slopes of the lines and their intersections.

Explanation:

Triangles can be formed by the intersection of lines with given equations. In this case, the lines are y=x, y= 2x, y=-2x, and y=-4. To find angles ABC and ABD, one must analyze the slopes of these lines and their intersections.

Angle ABC= arctan(∣ m2 −m 1 ∣)

Angle ABC = arctan(∣2−1∣)

Angle ABC = 45 degree

Angle ABD:

This angle is formed by the lines

Angle ABD= arctan (∣m 2 −m 1 ∣)

Angle ABD = arctan(∣−2−1∣)

Angle ABD ≈ 71.57 degree

The 99% confidence interval for the true mean time to change a water pump is approximately (14.650, 20.850) minutes, based on the recorded times.

To find the 99% confidence interval for the true mean time it takes to change a water pump, follow these steps in Excel:

Compute the sample mean [tex](\(\bar{x}\))[/tex] using the AVERAGE function and the sample standard deviation (s) using the STDEV.S function for the recorded times.

Calculate the degrees of freedom (n - 1) using the COUNT function to count the number of samples and subtracting 1.

Use the T.INV.2T function to find the critical value for the 99% confidence level with the obtained degrees of freedom.

Compute the margin of error using the formula:

[tex]\(t_{\alpha/2} \times \frac{s}{\sqrt{n}}\)[/tex], where [tex]\(t_{\alpha/2}\)[/tex] is the critical value, s is the sample standard deviation, and n is the sample size.

Determine the confidence interval by subtracting and adding the margin of error to the sample mean.

Round the lower and upper bounds of the confidence interval to three decimal places.

Following these steps, the 99% confidence interval for the true mean time to change a water pump is approximately (14.650, 20.850) minutes based on the given recorded times.

Answer:3 9 15 21

Step-by-step explanation:

3+6=9

9+6=15

15+6=21

or think of it as 3+3+3+3+3+3+3=21

Final answer:

Adam's number pattern starts with 3, and by adding 6 to each previous term, the first four terms are 3, 9, 15, and 21.

Explanation:

The student is asking about creating a number pattern based on a given rule. In this instance, the pattern begins with the number 3, and the rule is to add 6 to the previous term to get the next term. To determine the first four terms of Adam's pattern, we start with the number 3 and repeatedly add 6.

First term: 3 (starting number)

Second term: 3 + 6 = 9

Third term: 9 + 6 = 15

Fourth term: 15 + 6 = 21

Therefore, the first four terms of Adam's number sequence are 3, 9, 15, and 21.

Answer:

Step-by-step explanation:

If you have to choose 25 days, you have to think how many months there are.

The year has 12 months, so, if you divide 25 days /12 months =2,08333. (more than 2--> 3)

So if you happen to choose 2 of every month you have 24 days chosen, you have to pick one extra day and will add 3 to the month it belongs.

In any way you choose, you an be sure there is at least one month with 3 or more days chosen.

Answer:

D) The variable is discrete because it is countable.      

Step-by-step explanation:

Both discrete and continuous falls under the numeric category.

Discrete variables are the variable that are countable and cannot be expressed in decimal form.

Example: Tosses of a coin, Number of rooms in an house.

Continuous variables on the other hand cannot be counted, they are countable and can be expressed in the form of decimals. Its value can be expressed in the form of interval.

Example: Time, Length.

Now, number of students in a class is a discrete variable since students are countable and they cannot be expressed in decimal form.

So the correct option is D) The variable is discrete because it is countable.

Final answer:

The number of students in a class is a quantitative discrete variable because student numbers are countable and would always be a whole number.

Explanation:

The number of students in a class is a quantitative discrete variable. This is because the number of students can be counted, and would always be a whole number. There is no situation in which you could have a fraction of a student. Discrete random variables like this are countable, as opposed to continuous random variables which result from measurements and can take on any value in a range, including decimals and fractions. For instance, if we were discussing the heights of students, which can vary in continuous increments, we would be talking about a continuous variable.

Therefore, the correct option for the provided question is: D. The variable is discrete because it is countable.

Answer: So, if m divides n then n/m = x, and x is integer.

then -n/m = (-1*n)/m = -1*n/m = -1*x = -x.

So if x is integer, -x also is integer, then -n/m is integer and then m divides -n.

Where you used that in the integers set each number a has a opposite (also in the set ) such that a + b= 0, and b = -a = -1*a.

0 = 0% probability that Saturday is the day after Wednesday.

---------------------------------------------

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, we have to consider that:

Thus, 0 = 0% probability that Saturday is the day after Wednesday.

A similar question is given at https://brainly.com/question/16763692

the correct answer is 1/7.

To determine the probability that Saturday is the day after Wednesday, let's consider the days of the week in order:

1. List the days of the week**: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.

2. Identify the position of Wednesday**: Wednesday is the 4th day of the week.

3. Determine the position of Saturday, the day after Wednesday: Saturday is the 6th day of the week.

4. Calculate the probability:

  - There are 7 days in total.

  - Wednesday is followed by Thursday, Friday, and then Saturday, making Saturday the 6th day after Wednesday.

5. Probability calculation:

  - There is only one Saturday in the week.

  - Therefore, the probability that Saturday is the day after Wednesday is [tex]\( \frac{1}{7} \).[/tex]

Answer: 100 miles, 4 gallons used

Step-by-step explanation:

Dist = rate * time = 50 mi/hr * 2 hr = 100 mi

Miles = gallons * miles/gallon. 100 = gallons*25mpg. Gallons = 100/25 = 4

Answer:

-B9C

Step-by-step explanation:

Hi!

Firstly,

1) Start dividing -2972 : 16 = -185 (quotient) *(16) -12 Remainder

2) Do it again! Divide -185 for 16 = -185 / 16 = -11 (quotient) *(16) - 9 Remainder

3) Divide = -11/16 there's no integer result (since it's 0.68) we put it 0*16 -11 (Remainder) = 11

(Since the result gave us a 0 as integer. We had to lower it one unit the Remainder to satisfy the division algorithm which says = a:b=q*b +r,

11 =0*16+11

4) Gathering all Remainders from bottom to top: 12912

Comparing with the Table (below), from the last remainder to the first, and checking it with the table:

Decimal = Hex (multiplying by minus 1 since it's negative):

-11912 =-B9C

Answer:

x = 2.4 or 12/5 or 2 and 2/5

Step-by-step explanation:

4(8x + 7) = 17x - 8

4 * 8x = 32x

4 * 7 = 28

32x + 28 = 17x - 8

-28             - 28

32x = 17x - 36

-17x       -17x

15x = -36

----      ----

15       15

x = 2.4 or 12/5 or 2 and 2/5

Hey!

---------------------------------------------------

Solution:

4(8x + 7) = 17x - 8

32x - 28 =  17x - 8

32x - 28 + 28 = 17x - 8 + 28

32x = 17x + (-36)

32x - 17x = 17x - (36) - 17x

15x = -36

15x/15 = -36/15

x = -36/15 or -12/5

---------------------------------------------------

Answer:

x = -12/5

---------------------------------------------------

Hope This Helped! Good Luck!

Answer: There are 18 sets of five marbles including at least two red ones.

Step-by-step explanation:

Since we have given that

Number of red marbles = 3

Number of green marbles = 3

Number of lavender marbles = 1

total number of marbles = 3+3+1+1 = 8

We need to find the sets of five marbles including at least two red ones.

so, it becomes,

[tex]^3C_2\times ^4C_3+^3C_3\times ^4C_2\\\\=18[/tex]

hence, there are 18 sets of five marbles including at least two red ones.

To determine the total number of sets of five marbles that include at least two red ones, you need to figure out the total number of ways you can choose 5 marbles out of the 8 in the bag, and then calculate combinations for cases with at least 2 red ones and add them up.

To determine the total number of sets of five marbles that include at least two red ones, you need to use combinatorics, which is a branch of Mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints, such as those posed by questions concerning the possibility of constructing.

Firstly, you need to figure out the total number of ways you can choose 5 marbles out of the 8 in the bag. This is calculated using the combination formula: C(n, k) = n! / [k!(n-k)!]. Where n is the total number of items, and k is the number of items to choose. For this case, n is 8 (total marbles) and k is 5 (marbles we want to choose), so total possible combinations will be C(8, 5).

We want sets that include at least two red marbles, so the sets can have 2, 3 or all red marbles. So, calculate combinations for each case and add them up, like this:

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Answer:

The total resistance of these three resistors connected in parallel is [tex]1.7143\Omega[/tex]

Step-by-step explanation:

The attached image has the circuit for finding the total resistance. The circuit is composed by a voltage source and three resistors connected in parallel: [tex]R_1=6\Omega [/tex], [tex]R_2=3\Omega [/tex] and [tex]R_3=12\Omega [/tex].

First step: to find the source current

The current that the source provides is the sum of the current that each resistor consumes. Keep in mind that the voltage is the same for the three resistors ([tex]R_1[/tex], [tex]R_2[/tex] and [tex]R_3[/tex]).

[tex]I_{R_1}=\frac{V_S}{R_1}[/tex]

[tex]I_{R_2}=\frac{V_S}{R_2}[/tex]

[tex]I_{R_3}=\frac{V_S}{R_3}[/tex]

The total current is:

[tex]I_S=I_{R_1}+I_{R_2}+I_{R_3}=\frac{V_S}{R_1}+\frac{V_S}{R_2}+\frac{V_S}{R_3}=\frac{R_2\cdot R_3 \cdot V_S+R_1\cdot R_3 \cdot V_S+R_1\cdot R_2 \cdot V_S}{R_1\cdot R_2\cdot R_3}[/tex]

[tex]I_S=V_S\cdot \frac{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}{R_1\cdot R_2\cdot R_3}[/tex]

The total resistance ([tex]R_T[/tex]) is the source voltage divided by the source current:

[tex]R_T=\frac{V_S}{I_S}[/tex]

Now, replace [tex]I_S[/tex] by the previous expression and the total resistance would be:

[tex]R_T=\frac{V_S}{V_S\cdot \frac{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}{R_1\cdot R_2\cdot R_3}}[/tex]

Simplify the expression and you must get:

[tex]R_T=\frac{R_1\cdot R_2\cdot R_3}{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}[/tex]

The last step is to replace the values of the resistors:

[tex]R_T=\frac{(6\Omega )\cdot (3\Omega)\cdot (12\Omega)}{(3\Omega)\cdot (12\Omega)+(6\Omega)\cdot (12\Omega)+(6\Omega)\cdot (3\Omega)}=\frac{12}{7}\Omega=1.7143\Omega [/tex]

Thus, the total resistance of these three resistors connected in parallel is [tex]1.7143\Omega[/tex]

The total resistance of a parallel circuit with resistors of 6 ohms, 3 ohms, and 12 ohms is calculated using the parallel resistance formula, resulting in approximately 1.71 ohms.

The subject of your question falls under Physics, where we need to calculate the total resistance of a parallel circuit with three different resistors.

To find the total resistance in a parallel circuit, we use the formula:

1/Rtotal = 1/R1 + 1/R2 + 1/R3

For the given values, R1 = 6 ohms, R2 = 3 ohms, and R3 = 12 ohms. Plugging in these values:

1/Rtotal = 1/6 + 1/3 + 1/12

1/Rtotal = 2/12 + 4/12 + 1/12

1/Rtotal = 7/12

Rtotal = 12/7 ohms

Rtotal ≈ 1.71 ohms

Thus, the total resistance of the parallel circuit is approximately 1.71 ohms.

Answer:

Irrational numbers are not closed under addition.

Step-by-step explanation:

Irrational numbers are the numbers that cannot be expressed in the form of a fraction [tex]\frac{x}{y}[/tex]. In other words we can say that irrational number,s decimal expantion does not cease to end.

The closure property of addition in irrational numbers say that sum of two irrational number is always a rational number, But this is not true. It is not necessary that the sum is always irrational some time it may be rational.

This can be understood with the help of an example:

let (2+√2) and (-√2) be two irrational number. Their sum is (2+√2)+(-√2) = 2, which is clearly a rational number.

Hence, irrational numbers are not closed under addition.

To give a dose of 40 μg of Digoxin using a solution with a concentration of 0.1 mg/mL, you should administer 0.4 mL of the solution. This is achieved by first converting the dose to the same units as the concentration, then applying the formula: Volume (mL) = Dose (mg) / Concentration (mg/mL).

To determine how many milliliters would provide a dose of 40 μg of Digoxin, we first need to convert the dose from μg to mg because the concentration provided is in mg/mL. 1 mg is equivalent to 1000 μg. Hence, 40 μg would be the same as 0.04 mg.

Since the concentration of the Digoxin solution is 0.1 mg/mL, this means that every 1 mL of the solution contains 0.1 mg of Digoxin. Therefore, the volume in milliliters that would provide a dose of 0.04 mg (or 40 μg) can be calculated by the following equation: Volume (mL) = Dose (mg) / Concentration (mg/mL).

In this case, the calculation is: Volume = 0.04 mg / 0.1 mg/mL = 0.4 mL. Therefore, 0.4 mL of the solution will provide a dose of 40 μg of Digoxin.

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To provide a dose of 40 μg using a concentration of 0.1 mg/mL, 2.5 mL of the digoxin solution is needed.

To find the volume of digoxin (Lanoxin) needed to provide a dose of 40 μg, we can use the formula:

C₁V₁ = C₂V₂

Given:

C₁ = 0.1 mg/mL (0.1 mg per 1 mL)

C₂ = 40 μg (0.04 mg)

V₂ = ? mL (unknown volume)

Rearranging the formula, we get:

V₂ = (C₁V₁) / C₂

Substituting in the given values:

V₂ = (0.1 mg/mL) / (0.04 mg) = 2.5 mL

Therefore, 2.5 milliliters of the digoxin solution would provide a dose of 40 μg.

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Answer:

a) There is a 83.06% probability that all orders are shipped on time.

b) There is a 15.90% probability that exactly one order is not shipped ontime.

c) The probability of at least two orders being late is 1.02% + 0.02% = 1.04%.

Step-by-step explanation:

Probability:

What you want to happen is the desired outcome.

Everything that can happen iis the total outcomes.

The probability is the division of the number of possible outcomes by the number of total outcomes.

In our problem, there is:

-A 6% probability that a customer's order is not shipped on time.

-A 94% probability that a customer's order is shipped on time.

We have these following orders:

O1 - O2 - O3.

(a) What is the probability that all are shipped on time?

The probabilities that each order is shipped on time are O1 = 0.94, O2 = 0.94 and O3 = 0.94. So:

[tex]P = (0.94)^{3}[/tex] = 0.8306

There is a 83.06% probability that all orders are shipped on time.

(b) What is the probability that exactly one is not shipped ontime?

The order's can be permutated. What this means? It means that we can have O1 late and O2,03 on time, O2 late and O1,O3 on time and O3 late and O1, O2 on time. We have a permutation of 3 elements(the orders) with 2 and 1 repetitions(2 on time and one late).

The probability that an order is late is:

[tex]P = (0.94)^{2}(0.06)[/tex] = 0.053 for each permutation

Considering the permutations:

[tex]P = 0.053*p^{3}_{2,1} = 0.053\frac{3!}{2!*1!} = 0.053*3 = 0.1590[/tex]

There is a 15.90% probability that exactly one order is not shipped ontime.

(c) What is the probability that two or more orders are not shipped on time?

P = P1 + P2, where P1 is the probability that two orders are late and P3 is the probability that all three orders are late.

P1

Considering the permutations, the probability that two orders are late is:

[tex]P_{1} = p^{3}_{2,1}*(0.94)*(0.06)^{2} = 3*(0.94)*(0.06)^{2} = 0.0102[/tex]

There is a 1.02% probability that two orders are late

P2

[tex]P_{2} = (0.06)^3 = 0.0002[/tex]

There is a 0.02% probability that all three orders are late.

The probability of at least two orders being late is 1.02% + 0.02% = 1.04%.

Answer:

1. Precise

2.Both

3.Precise

5.Neither

Step-by-step explanation:

Accuracy is the closeness of a measured value to a standard value.

Precision is the closeness of two or more measurements to each other.

1.The norm is 45 sit-ups in a minute.The students did, 64, 69,65 and 67. Values are not accurate compared to standard value 45.

Values are precise

Answer--Precise

2. Average score is 89.5

  Scores are 89,93,91,87

  Values are precise i.e a difference of 2 from each score

  Values are accurate because the average score is 90 thus compared to      the known average score of 89.5 they are accurate.

Answer-Both

3. Yesterday temperature=89

   Tomorrow=88

    Next day=90

   Average =75

   Values are precise i.e. difference of ± 1°

   Values are not accurate compared to the average temperatures of 75 F

   Answer---Precise

5. The jar contained 568 pennies

   The 6 people guessed the numbers as

    735,209,390,300,1005, 689

  The values are not precise

  The values are not accurate

  Answer---Neither

Accuracy refers to the closeness of a measurement to the true value, while precision is about the repeatability of measurements. The student examples show diverse cases where results can be accurate, precise, both, or neither. Without the actual value or other measurements, assessment of accuracy and precision is often not possible.

The terms accuracy and precision have distinct meanings in science. Accuracy refers to how close a measurement is to the correct or accepted value. In contrast, precision indicates how close a set of measurements are to each other, demonstrating the consistency of the measurements.

Answer:

2

Step-by-step explanation:

1. solve for the multiplication (3x4)= 12

2. solve for (7+9-10) take 7+9 which =16 and then subtract by 10. (16-10=6)

3. take the 12 and divide by 6

To solve the expression (3×4)÷(7+9-10), perform the operations inside the brackets first, then multiply and divide according to BODMAS/BIDMAS rules. The correct answer after simplifying is 2.

To solve the problem (3×4)÷(7+9-10), you should follow the steps of BEDMAS/BIDMAS (Brackets, Exponents/Indices, Division and Multiplication, Addition and Subtraction), also known as the order of operations.

Always remember to check the answer to see if it is reasonable by reviewing your calculation steps.

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Answer:

1.2 grams.

Step-by-step explanation:

We have been given that an oral concentrate of sertraline hydro-chloride (Zoloft) contains 20 mg/mL of the drug.

First of all, we will find number of mg in 60 mL container of the concentrate as:

[tex]\frac{\text{20 mg}}{\text{ml}}\times \text{60 ml}[/tex]

[tex]\text{20 mg}\times 60[/tex]

[tex]\text{1200 mg}[/tex]

We know 1 gram equals 1000 mg.

[tex]\text{1200 mg}\times \frac{\text{1 gram}}{\text{1000 mg}}[/tex]

[tex]1.2\times\text{1 gram}[/tex]

[tex]1.2\text{ grams}[/tex]

Therefore, 1.2 grams of sertraline hydrochloride are in each 60-mL container of the concentrate.

Answer:

The probability that the sample mean would differ from the population mean by greater than 2.2 kilograms is 0.0104 .

Step-by-step explanation:

The mean weight of an adult is 62 kilograms with a variance of 144

i.e. [tex]\mu = 62 \\\sigma^2 = 144[/tex]

We are supposed to find probability that the sample mean would differ from the population mean by greater than 2.2 kilograms

i.e. [tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=1-P(59.8<\bar{x}<64.2)[/tex]

Using formula : [tex]\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=1-P(59.8<\bar{x}<64.2)[/tex]

[tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=1-P(\frac{59.8-62}{\frac{12}{\sqrt{195}}}<\frac{64.2-62}{\frac{12}{\sqrt{195}}})[/tex]

[tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=1-P(-2.56<z<2.56)[/tex]

[tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=1-{P(z<2.56)-P(z<-2.56)}[/tex]

Refer the z table

[tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=1-{0.9948-0.0052}[/tex]

[tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=0.0104[/tex]

Hence The probability that the sample mean would differ from the population mean by greater than 2.2 kilograms is 0.0104 .

0.0104 or 1.04% is the probability that the sample mean weight of 195 adults will differ from the population mean .

We have to  use the central limit theorem.

Given the mean weight (62 kg) and variance (144 kg²) of the population, we first calculate the standard deviation:

Step 1: Calculate the population standard deviation.

Step 2: Calculate the standard error of the mean.

Step 3: Find the z-scores corresponding to ±2.2 kg difference from the mean.

Step 4: Use the standard normal distribution to find the probabilities.

Step 5: Calculate the total probability.

Therefore, the probability that the sample mean differs from the population mean by more than 2.2 kg is approximately 0.0104 or 1.04%.

Answer:

His daily fat intake is 40.824g.

His daily Vitamin D intake is 290.304 IU.

Step-by-step explanation:

The first step to solve this problem is finding the daily kcal intake of the dogs.

Each cup has 324 kcal, and he eats 3.5cups a day. So:

1 cup - 324 kcals

3.5 cups - x kcals

[tex]x = 324*3.5[/tex]

[tex]x = 1134[/tex] kcals.

His daily intake is of 1134 kcals.

The food contains 3.6 g of fat in 100 kcals of energy. what is his daily fat intake?

There are 3.6g of fat in 100 kcals of energy. How many g of fat are there in 1134 kcals?

3.6g - 100 kcals

xg - 1134 kcal

[tex]100x = 1134*3.6[/tex]

[tex]x = \frac{1134*3.6}{100}[/tex]

[tex]x = 11.34*3.6[/tex]

[tex]x = 40.824[/tex]g

His daily fat intake is 40.824g.

The food contains 25.6 IU of Vitamin D3 in 100 kcals of energy. what is his daily Vitamin D inake?

Similar logic as above.

25.6IU - 100 kcals

x IU - 1134 kcal

[tex]100x = 1134*25.6[/tex]

[tex]x = \frac{1134*25.6}{100}[/tex]

[tex]x = 11.34*25.6[/tex]

[tex]x = 290.304[/tex]IU

His daily Vitamin D intake is 290.304 IU.

Answer:

The upper limit of the confidence interval is 3127 $/day.

Step-by-step explanation:

With the new sample we can estimate the one-sided 95% confidence interval.

For this interval (one sided, 95% of confidence), z=1.64.

The number of observations (n) is 45 days.

The mean is 2984 and the standard deviation is 585.

We can estimate the upper limit of the confidence interval as

[tex]UL=X+z*s/\sqrt{n} \\UL = 2984 + 1.64*585/\sqrt{45}=2984+ 959.4/6.708=2984+143=3127[/tex]

Answer:

a)  1.6180339875

b) 2.7182818

Step-by-step explanation:

a) Golden ratio is the ratio that divides a quantity in such a manner that when the larger quantity is divided by the smaller quantity, it is equal to the value when the whole quantity is divided by the larger quantity. It is also known by the name golden mean or divine ratio.

It is generally denoted by [tex]\phi[/tex]

Its numeric value is: 1.6180339875

b) Approximate value of e can be calculated with the help of taylors expansion of [tex]e^x[/tex] at x = 1.

Approximate value of e upto 6 decimal places: 2.7182818

Answer:

This proof can be done by contradiction.

Let us assume that 2 - √2 is rational number.

So, by the definition of rational number, we can write it as

[tex]2 -\sqrt{2} = \dfrac{a}{b}[/tex]

where a & b are any integer.

⇒ [tex]\sqrt{2} = 2 - \dfrac{a}{b}[/tex]

Since, a and b are integers [tex]2 - \dfrac{a}{b}[/tex] is also rational.

and therefore √2 is rational number.

This contradicts the fact that √2 is irrational number.

Hence our assumption that 2 - √2 is rational number is false.

Therefore, 2 - √2 is irrational number.

By assuming 2 - √2 is rational and showing this leads to a contradiction as both a and b would have to be even, which violates the initial condition that they have no common factors other than 1, it has been proven that 2 - √2 is irrational.

To show that 2 - √2 is irrational, we shall assume the opposite, that 2 - √2 is rational, and look for a contradiction. By definition, if 2 - √2 is rational, it can be expressed as a fraction of two integers, say √2 = a/b, where a and b are integers with no common factors other than 1, and b is not zero.

We can rearrange the equation to obtain √2 = 2 - a/b. Multiplying both sides by b gives us b√2 = 2b - a. Squaring both sides of this equation gives us 2b² = (2b - a)² = 4b² - 4ab + a².

Rearranging to solve for a² gives us a² = 2b², implying that a² is an even number, and hence a must be even. Let's say a = 2k for some integer k. Substituting this back into the equation gives us (2k)² = 2b², which simplifies to 4k² = 2b², and further to 2k² = b². This implies that b² is also even, which means b is even as well.

However, this is a contradiction because we assumed that a and b have no common factors other than 1; yet, we've just shown that both must be even, so they have at least a factor of 2 in common. This contradiction shows that the assumption that 2 - √2 is rational is false, and therefore 2 - √2 must be irrational.

Answer:

33 feet

22 feet

Step-by-step explanation:

Let the longer piece be x

Therefore the shorter piece is (2/3)x

x + (2/3)x  = 55                  Combine the left 2 terms.

(3/3)x + (2/3)x = 55           Add  

(5/3)x = 55                        Multiply both sides by (3/5)

(3/5) * (5/3)x = (3/5)*55

x = 33

The larger piece is 33 feet

The smaller piece is (2/3) * 33 = 22 feet

Answer:

He own 200 shares of stock A and 100 shares of stock B.

Step-by-step explanation:

Let x be the number of shares of stock A and y be the number of shares of stock B.

Current value of a share of stock A = $40

Current value of a share of stock B = $60

A person has 14000 invested in stock A and stock B.

[tex]40x+60y=14000[/tex]

Divide both sides by 20.

[tex]2x+3y=700[/tex]            .... (1)

Stock B doubles in value and stock A goes up 50%, his stock will be worth 24,000.

New value of a share of stock A = $40 + (50% of 40)= $40 + $20 = $60

New value of a share of stock B = $60 × 2 = $120

[tex]60x+120y=24000[/tex]

Divide both sides by 60.

[tex]x+2y=400[/tex]            .... (2)

Solve equation (1) and (2) by elimination method.

Multiply 2 on both sides in equation (2).

[tex]2x+4y=800[/tex]       .... (3)

Subtract equation (3) from equation (1).

[tex]2x+3y-2x-4y=700-800[/tex]

[tex]-y=-100[/tex]

[tex]y=100[/tex]

The value of y is 100.

Substitute y=100 in equation (1).

[tex]2x+3(100)=700[/tex]

[tex]2x+300=700[/tex]

Subtract 300 from both sides.

[tex]2x=700-300[/tex]

[tex]2x=400[/tex]

Divide both sides by 2.

[tex]x=200[/tex]

The value of x is 200.

Therefore he own 200 shares of stock A and 100 shares of stock B.

Answer:

40.53%

Step-by-step explanation:

[tex]Percentage Increase = \frac{New Value - Old Value}{Old Value}\times100[/tex]

Here, New Value = 960÷100,000

Old Value = 190÷ 100,000

∴ [tex]Percentage Increase = \dfrac{\frac{960}{100,000} - \frac{190}{100 ,000} }{\frac{190}{100,000}}\times100[/tex]

⇒ Percentage Increase = 40.53%

Thus, percent increase in the male incarceration rate during given period is 40.53%.

Answer:

Your velocity is 10 miles per hour.

Step-by-step explanation:

This can be solved as a simple rule of three problem.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Here, our measures are:

- The distance you ran, in miles

- The time you spent running.

As the time increases, so does the distance, it means there is a direct relationship between the measures.

Each hour has 60 minutes. You ran 3 miles in 18 minutes. So how many miles you ran in 60 minutes?

3 miles - 18 minutes

x miles - 60 minutes

18x = 180

[tex]x = \frac{180}{18}[/tex]

x = 10 miles.

Your velocity is 10 miles per hour.

To find the mass of water that fell on the city, multiply the volume of the rainstorm by the density of water.

To calculate the amount of water that fell on the city, we first calculate the volume of water by multiplying the width, length, and height of the rainstorm. Using the given values of 1.0 cm of rain, 4 km wide, and 8 km long, we find that the volume is 1.5 × 1018 m³. Since water has a density of 1 ton per cubic meter, we can calculate the mass by multiplying the volume by the density, which gives us 1.5 × 1018 metric tons.

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