m grade> Y.4 Area and perimeter: word problems JFR
A rectangular garage is 6 meters wide and 7 meters long. What is its perimeter?

Answer:

To evaluate this limit, we can factor out the highest power of x from the numerator and denominator, which is x^14. Then, we can divide both the numerator and denominator by x^14. This gives:

lim x→∞ (6x^14 + 8x^11 + 37x^14) / x^14

= lim x→∞ (6x^14 / x^14 + 8x^11 / x^14 + 37x^14 / x^14)

= lim x→∞ (6 + 8 / x^3 + 37)

= 6 + 0 + 37 (since as x approaches infinity, 8/x^3 approaches zero)

= 43

Therefore, the value of the limit is 43.

Answer: Linear

Step-by-step explanation:

Since the difference between consecutive values of f(x) is constant, this suggests that the function could be linear. To confirm this, we can calculate the differences between consecutive values:f(1) - f(0) = -15 - (-18) = 3

f(2) - f(1) = -12 - (-15) = 3

f(3) - f(2) = -9 - (-12) = 3

f(4) - f(3) = -6 - (-9) = 3

Since the differences are constant and equal to 3, this confirms that the function is linear.

To find the equation of the linear function, we can use the slope-intercept form of a linear equation:

y = mx + bwhere m is the slope and b is the y-intercept.

We can use the first two points (0, -18) and (1, -15)  to find the slope:

m = (change in y) / (change in x) = (-15 - (-18)) / (1 - 0) = 3

Now we can use the slope and one of the points to find the y-intercept:

y = mx + b

-18 = 3(0) + b

b = -18

Therefore, the equation of the linear function is:

f(x) = 3x - 18

So the function type that could represent the values in the table is linear.

The prοbability that mοre than twο machines need cοrrecting is apprοximately 0.0826 οr 8.26%.

Binοmial distributiοn is a prοbability distributiοn that describes the number οf successes in a fixed number οf independent trials, where each trial can οnly have twο οutcοmes: success οr failure.

Accοrding tο questiοn:

Let X be the number οf machines that need cοrrecting adjustments during a day's prοductiοn run, and let p = 0.2 be the prοbability that any οne machine needs cοrrecting.

Then, X fοllοws a binοmial distributiοn with parameters n = 6 (the number οf machines) and p = 0.2 (the prοbability οf a machine needing cοrrecting).

The prοbability οf X is:

P(X > 2) = 1 - P(X <= 2)

Tο calculate P(X <= 2), we can sum the prοbabilities οf X taking οn the values 0, 1, and 2:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = 0) = (6 chοοse 0) * 0.2⁰ * 0.8⁶ = 0.2621

P(X = 1) = (6 chοοse 1) * 0.2¹ * 0.8⁵ = 0.3932

P(X = 2) = (6 chοοse 2) * 0.2²* 0.8⁴ = 0.2621

Therefοre,

P(X <= 2)

= 0.9174

And

P(X > 2)

= 1 - P(X <= 2)

= 1 - 0.9174

= 0.0826

Sο the prοbability that mοre than twο machines need cοrrecting is apprοximately 0.0826 οr 8.26%.

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Answer: 5kg

Step-by-step explanation:

If Ms. Walker has 15 kilograms of clay that she wants to distribute evenly among 3 students, all you need to do is divide 15 by 3. Doing so, we get:

15 kg / 3 = 5 kg

Therefore, each student will receive 5 kilograms of clay.

The mass of clay that each student will get is 5kg.

Here, the given questions ask for a solution that deals with the concept of  the basic principle of division. hence implementing the principle we can see that,

The given total amount of clay by Ms. walker is 15 kilograms(kg).

Furthermore, this total amount of clay needs to be divided equally between the  3 students.

Then, let the mass of clay given to each student equally be denoted by M in  the equation to find out the solution can be written as

M = Total amount of clay ÷ Total number of students

Then,

M = 15 ÷ 3

M = 5 kg

Therefore, The mass of clay that each student will get is 5kg.

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Gina finished making sugar cookies at 1:30 P.M.

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

To find out what time Gina finished making sugar cookies, we need to add the time it took her to make them to the starting time.

Starting time: 12:15 P.M.

Time it took to make cookies: 1 hour and 15 minutes

To add the time, we first convert 1 hour and 15 minutes to hours by dividing the minutes by 60:

1 hour and 15 minutes = 1 + 15/60 hours = 1.25 hours

Now we can add 1.25 hours to 12:15 P.M.:

12:15 P.M. + 1.25 hours = 1:30 P.M.

Hence, Gina finished making sugar cookies at 1:30 P.M.

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Complete question:

Gina started making sugar cookies for her friends at 12:15 P.M. It took her 1 hour and 15 minutes to make. By what time Gina finished making sugar cookies?

Answer:

B: 9

Step-by-step explanation:

The prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and 23.

Answer:

bottom two

Step-by-step explanation:

if "=", equation

if no "=", expression

Answer:

The ones without an equal sign.

Hope this helps!

Step-by-step explanation:

4x - 7 = 5

4x - 7 is the expression

4x, 7, and 5 are terms

4x - 7 = 5 is the equation

Answer:

5683200

Step-by-step explanation:

Move the decimal 4 places to the right because [tex]10^4[/tex] has 4 zeros.

Answer:

3x + 4 < 13

2y - 5 > 7

6n - 1 ≤ 23

8m + 2 ≥ 18

4a - 7 < 5a + 2

9b + 3 > 6b + 10

Step-by-step explanation:

I dunno if this is what you're asking for

Answer:

ok.....

x + 2 < 5

|x - 4| > 4

x + 7 [tex]\geq[/tex] 8

-x < -5

x - 5 < 9

5x + 18 > 2

|3x - 1| < 8

Answer:

x=-1/3

Step-by-step explanation:

3x-4+2x+6+x=0

6x+2=0

6x=-2

x=-2/6

x=-1/3

Hence, x has a value of 36 as the sum of the supplementary angles 3x and 2x must equal 180 degrees .

Angles in mathematics are used to quantify how much two intersecting surfaces or lines rotate relative to one another. Angles can be measured in degrees, radians, or various ways. Degrees, which divide a whole rotation into 360 equal parts, are the most popular unit of measurement for angles. Angles are a fundamental idea in geometry and trigonometry and have practical uses in a number of industries, including physics, engineering, and navigation.

given

The sum of the supplementary angles 3x and 2x must equal 180 degrees. Which is:

3x + 2x = 180

Putting similar phrases together on the left side, we get:

5x = 180

When we multiply both sides by 5, we get:

x = 36

Hence, x has a value of 36 as the sum of the complementary angles 3x and 2x must equal 180 degrees .

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In Bermuda, there are a total of 90 telephones for each 100 people. Also there are a total of 3,76,000 telephones in use in Luxembourg according to simple calculations.

Here, they given that a telephone symbol is equal to 5 telephones.

Then according to the given diagram,

1. There are:

= (5 + 5 + 5 + 3) 5 telephones

= ( 18 ) 5 telephones

= 90 telephones.

Therefore, there are a total of 90 telephones for each 100 people.

2. In 2005, the population of Luxembourg was 470,000.

According to the given diagram, there are 80 telephones available for every 100 people.

For 4,70,000:

100 -------------- 80

4,70,000 ------ (x)

After cross multiplication,

x * 100 = 80 * 470000

x = 8 * 47000

x = 3,76,000

Therefore, there are total of 3,76,000 telephones in use in Luxembourg.

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Step-by-step explanation:

the perimeter is the sum of the lengths of all outside sides.

at the top is a triangle.

at the bottom is a rectangle.

the triangle looks like an isoceles triangle (both legs are equal), but the given measurement tells us otherwise.

if it were isoceles, the height would split the baseline into 2 equal halves (20/2 = 10ft).

per Pythagoras the 12 ft Hypotenuse would be

Hypotenuse² = 10² + 10² = 100 + 100 = 200

Hypotenuse = sqrt(200) = 14.14213562... and NOT 12 ft.

so, we need to calculate the actual part of the 20ft baseline (again Pythagoras) :

12² = 10² + part²

144 = 100 + part²

44 = part²

part = sqrt(44) = 6.633249581... ft

that means the 2nd part of the baseline is

20 - 6.633249581... = 13.36675042... ft

and we get the second leg of the large triangle again via Pythagoras :

leg² = 10² + 13.36675042...² = 100 + 178.6700168...

leg² = 278.6700168...

leg = sqrt(278.6700168...) = 16.69341238... ft

we need to sum up both legs of the triangle, 2 widths and one length of the rectangle, as the triangle base line and the second length of the rectangle cover each other up, and are not visible to the outside of the combined object.

P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈

≈ 64.69 ft

Explanation:

Any company that has an online presence (eg: website) needs to take cybersecurity seriously. This is safeguard their customers against online criminals, and also keep their employees safe. Cybersecurity isn't limited to government roles or defense contractor roles only.

the value of variable x in the rhombus is Option (c) 25.

A parallelogram is a particular instance of a rhombus. opposite sides and angles of the rhombus are parallel and equal. The rhombus has equal-length sides on each side, and its diagonals meet at right angles to form its shape as square. The rhombus is sometimes called as a diamond or rhombus.

Let O be the intersection point of the line AC and the line BD in the rhombus.

This two lines intersect at a 90° angle in the center. ( Property of Rhombus)

∠AOD=90°

∠AOD+∠OAD+∠ODA=180° (triangle sum property)

90°+x+x+40°=180°

2x=180°-130°

x=25

Hence the value of x=25.

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The amount and the compound interest on a sum of Rs. 62500 are Rs. 65625 and Rs. 3125, respectively.

Given:

Principal amount (P) = Rs. 62500

Rate of interest (R) = 5%

Time period (t) = 1 year

Interest is compounded yearly.

Formula for calculating compound interest is given as:

A = P(1 + R/100)ᵗ

where A is the amount.

Using this formula, we can find the amount (A) after one year:

A = 62500(1 + 5/100)¹

A = 65625

Therefore, the amount after one year is Rs. 65625.

To find the compound interest, we can subtract the principal from the amount:

Compound Interest = A - P

= 65625 - 62500

= 3125

Therefore, the compound interest is Rs. 3125.

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Note that,
the encrypted message for "OK" is the pair of numbers (616, 2385).
and the final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).

To encrypt a message using RSA, we need to first represent the message as numbers using a suitable encoding scheme. For simplicity, we can use the ASCII code for each character, which is a standard encoding scheme for text.

a) To encrypt "OK", we first convert each letter to its corresponding ASCII code:

"O" = 79

"K" = 75

Next, we use the RSA encryption formula:

C ≡ [tex]M^{e}[/tex] (mod n)

For "O", we have C ≡ 79¹¹ (mod 2911) ≡ 616 (mod 2911)

For "K", we have C ≡ 75¹¹ (mod 2911) ≡ 2385 (mod 2911)

Therefore, the encrypted message for "OK" is the pair of numbers (616, 2385).

b) To encrypt "HELP", we break it up into two blocks:

Block 1: "HE"

Block 2: "LP"

For block 1, we have:

"H" = 72

"E" = 69

Using the RSA encryption formula, we get:

C1 ≡ 72¹¹ (mod 2911) ≡ 738 (mod 2911)

C2 ≡ 69¹¹ (mod 2911) ≡ 1277 (mod 2911)

Therefore, the encrypted message for "HE" is the pair of numbers (738, 1277).

For block 2, we have:

"L" = 76

"P" = 80

Using the RSA encryption formula, we get:

C3 ≡ 76¹¹ (mod 2911) ≡ 1479 (mod 2911)

C4 ≡ 80¹¹ (mod 2911) ≡ 2252 (mod 2911)

Therefore, the encrypted message for "LP" is the pair of numbers (1479, 2252).

The final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).

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Answer:

Step-by-step explanation:

Your sister can use the formula for calculating the present value of an annuity to determine how much she can withdraw each year.

The formula for the present value of an annuity is:

PV = Payment x (1 - (1 + r)^-n) / r

Where:

- PV is the present value of the annuity

- Payment is the amount of each withdrawal

- r is the annual interest rate

- n is the number of periods (in this case, 25 years)

We can rearrange this formula to solve for Payment:

Payment = PV x r / (1 - (1 + r)^-n)

We know that your sister has R375 000 to start with, and she wants to end up with zero in 25 years. So, her present value (PV) is R375 000, and we can assume her future value (FV) is zero.

Using the future value formula, we can calculate the interest rate she needs to earn in order to end up with zero in 25 years:

FV = PV x (1 + r)^n

0 = 375000 x (1 + r)^25

(1 + r)^25 = 1

1 + r = (1)^1/25

r = 0

This means that your sister needs to withdraw all of her money over the 25 years in order to end up with zero at the end.

Her withdrawal each year would be:

Payment = PV x r / (1 - (1 + r)^-n)

Payment = 375000 x 0.08 / (1 - (1 + 0.08)^-25)

Payment = R34,028.82 per year

Your sister can withdraw R34,028.82 at the beginning of each year for the next 25 years, and she will end up with zero at the end, assuming she earns an 8% return on her invested funds.

The interest that is paid on the loan in 6 years will be $4,200.

The amount of interest that is saved is $2,100.

The simple interest is a linear function of the number of years of the loan, value of the loan and the duration of the loan. The higher either of these values are, the higher the simple interest.

Simple interest = loan x time x interest rate

Simple interest if the loan is paid off after 6 years: $12,500 x 6 x 0.056 = $4,200

Simple interest if the loan is paid off after 3 years: $12,500 x 3 x 0.056 = $2100

Interest saved = $4200 - $2100 = 2100

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Answer:

2 hope that helps

Step-by-step explanation:

The formula for the normal approximation to the binomial with a correction for continuity is

P(X ≤ x) ≈ Φ(z), where z = (x + ½ - μ)/σ

In this case, μ is the expected number of left-handed people in the sample, which is 0.14*190 = 26.6

σ is the standard deviation of the sample, which is (0.14*(1-0.14))^0.5*190 = 5.58

x is the desired number of left-handed people in the sample, which is 24.5 (since fewer than 25)

Therefore, z = (24.5 + ½ - 26.6)/5.58 = -1.03

The probability that fewer than 25 people in the sample are left-handed is then Φ(-1.03) = 0.1545, to at least 3 decimal places.

Answer:

Therefore, the maturity value of the loan is $2568.75.

Step-by-step explanation:

To calculate the maturity value of the loan, we need to add the interest to the principal.

First, we need to find out how much interest Ricardo will owe for the 180-day period.

The formula for calculating ordinary interest is:

Interest = Principal x Rate x Time

where:

Principal = $2500

Rate = 7.8% = 0.078 (expressed as a decimal)

Time = 180/360 (since the interest is for a 180-day period and the rate is an annual rate)

Time is expressed as a fraction of a year because the rate is an annual rate. In this case, the time is 180/360 because the loan is for 180 days, which is half of a year.

Using the formula above, we can calculate the interest as follows:

Interest = $2500 x 0.078 x 180/360 = $68.75

Therefore, Ricardo will owe $68.75 in interest for the 180-day period.

To find the maturity value of the loan, we add the interest to the principal:

Maturity Value = Principal + Interest = $2500 + $68.75 = $2568.75

Therefore, the maturity value of the loan is $2568.75.

The first thing we must do for this case is to find the surface area of the rectangular prism.

We have then:

[tex]A = 2 \times (l \times h) + 2 \times (h \times w) + 2 \times (w \times l)[/tex]

Where,

w: width

l: long

h: height

Substituting values we have:

[tex]A = 2 \times (10 \times 8) + 2 \times (8 \times 8) + 2 \times (8 \times 10)[/tex]

[tex]A = 448 \ in ^ 2[/tex]

Answer:

the least amount of wrapping paper needed to wrap the gift box answer is:

A = 448 in²

The nearest ten thousand of the digits  14509 is 14, 000.

The rule for rounding to the nearest ten thousand is to look at the last four digits.

If the last four digits of the number is greater than 5000, we have to round the value up but if the number is below 5000 we have to round below.

For example let's round up 27567 to the nearest ten thousands.

Therefore, 7567 is above 5000, Hence, we have to round up. The nearest ten thousand of 27567 is 30000.

Let's round 14509 to the nearest ten thousand.

The nearest ten thousand of 14509 is 14, 000

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Answer: Answer is below <3

The quotient of three times a number and 7: 3n/7

The difference between 5 and a number is x:  5 - n = x

The product of 3 times a number and 7:  (3n)(7)

Two times the sum of a number and 9:  2 (n + 9)

The sum of twice a number and 9:  2n + 9

5 less than a number is x:  x = n - 5

Answer:

The probability of winning second prize in a 5/45 lottery is 1 in 8,145. This is calculated by taking the total number of possible combinations (8,145) and dividing it by the total number of possible outcomes (1).

Answer:

[tex]9 + 15 = 24 > 13[/tex]

[tex]9 + 13 = 22 > 15[/tex]

[tex]15 + 13 = 28 > 9[/tex]

So the lengths 13, 15, and 9 can form a triangle.

The system is inconsistent and has no solution. Therefore, the answer is "inconsistent".Since the last row is of the form [0 0 0 | b], where b is nonzero (b=7

To determine whether the system of equations represented by the given matrix has a solution, we can use row operations to put the matrix into reduced row echelon form. If the resulting matrix has a row of the form [0 0 ... 0 | b], where b is nonzero, then the system is inconsistent and has no solution. If there are any free variables in the reduced row echelon form, then the system has infinitely many solutions and is dependent. If there are no free variables and no rows of the form [0 0 ... 0 | b], then the system has a unique solution and is independent.

Using row operations, we can put the given matrix into reduced row echelon form as follows:

[tex][1 -3 1 4 | 4] (R1)[3 2 1 | 3] (R2)[-6 -4 -2 | 1] (R3)[/tex]

([tex]R2 - 3*R1) - > R2:[/tex]

[tex][1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[-6 -4 -2 | 1] (R3)(R3 + 6*R1) - > R3:[1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[0 -22 4 | 25] (R3)(R3 + 2*R2) - > R3:[1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[0 0 0 | 7] (R3)[/tex]

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