Divide £88 in the ratio 1:7

Let L be the length of the rectangular garden.

The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

Substituting the given values, we get:

328 = 2L + 2(67)

Simplifying the equation, we get:

328 = 2L + 134

2L = 328 - 134

2L = 194

L = 194/2

L = 97

Therefore, the length of the rectangular garden is 97 meters.

Answer:

angle w = 50; angle y = 130

Step-by-step explanation:

because of supp. angles, y + w = 180

12x-2+4x+6=180

16x+4=180

16x=176

x=11

to calculate, sub 11 in

w = 4(11) + 6 = 50

y = 12(11) - 2 = 130

All possible numbers that are co-primes with the following numbers are mentioned below in detail. The possible co-primes of 390 are 1, 7, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, and 49.

Co-prime numbers are pairs of numbers that only share the factor 1 in common. They are additionally referred to as reasonably prime numbers.

In the given question,

(a) 390

The prime factors of 390 are 2, 3, 5, and 13. All of the numbers that are co-prime with 390 are those that do not share any of these prime factors. This includes the numbers 1, 7, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, and 49.

(b) 210

The prime factors of 210 are 2, 3, 5, and 7. All of the numbers that are co-prime with 210 are those that do not share any of these prime factors. This includes the numbers 1, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, and 49.

(c) 49335

The prime factors of 49335 are 5, 7, 11, and 13. All of the numbers that are co-prime with 49335 are those that do not share any of these prime factors. This includes the numbers 1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, and 49.

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Let's call the radius of the circle "r". The formula for the area of a sector of a circle is given by:

(θ/360) * π * r^2,

where θ is the central angle of the sector in degrees.

In this case, we know that the central angle is 315° and the area of the sector is 504π, so we can set up an equation as follows:

(315/360) * π * r^2 = 504π

Solving for r, we can isolate it on one side of the equation:

r^2 = 504 / (π * (315/360))

To simplify the expression on the right-hand side, we can divide both the numerator and denominator by 45 (which is a factor of both 315 and 360):

r^2 = 504 / (π * (7/8))

Finally, taking the square root of both sides gives us:

r = sqrt(504 / (π * (7/8)))

So the radius of the circle is approximately 17.14 inches.

The missing length of the triangle is the hypotenuse which is given by 12.08

Pythagorean theorem states that the sum of the square of the opposite and adjacent sides of a triangle is equal to the square of the hypotenuse.

a² + b² = c²

c = √a² + b²

a = 11

b = 5

c = √a² + b²

= √11² + 5²

= √121 + 25

= √146

c = 12.08304597359

Approximately,

c = 12.08

Consequently, the hypotenuse of the triangle is approximately 12.08

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Plugging in our known values, we get h = 12,560/3.14(10)^2 = 40.16 feet. Therefore, height of the water tower is 40.16 feet tall.

To calculate the height of the water tower, we can use the formula for the volume of a cylinder. This formula is V = πr^2h, where V is the volume, π is the constant pi (3.14), r is the radius of the cylinder, and h is the height of the cylinder. In this case, the radius of the cylinder is 10 feet and the volume of the cylinder is 12,560 gallons. We can rearrange the formula to solve for h, giving us h = V/πr^2. Plugging in our known values, we get h = 12,560/3.14(10)^2 = 40.16 feet. Therefore, the water tower is 40.16 feet tall.

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Answer:

The statement "A = (1/2) (B)(B + 5)" represents the area of a triangle, where B is the base of the triangle and (B + 5) is the height. This formula is used by the carpenter to calculate the area of a triangle with a given base and height.

Step-by-step explanation:

The slope of the line that passes through the points (0, - 4) and (30, -9) is -1/6.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope, m = (-9 + 4)/(30 - 0)

Slope, m = -5/30

Slope, m = -1/6.

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Answer:

(126, 101), (127, 100), (128, 99).

Step-by-step explanation:

The profit from selling one adult ticket is $10.00 and from selling one children's ticket is $5.00.

The total profit from selling A adult tickets and C children's tickets can be represented as 10A + 5C.

The goal is to find combinations of A and C that meet the following conditions:

10A + 5C >= 3750

A + C <= 500

One way to solve this problem is to use a brute force approach and try different values of A and C until we find three combinations that meet the conditions. Another way is to use a more efficient method and find the values of A and C that maximize the number of adult tickets while still meeting the profit and seating limit conditions.

Let's start by finding the maximum number of adult tickets that can be sold while still meeting the profit goal:

10A + 5C >= 3750

10A >= 3750 - 5C

A >= 375 - 0.5C

Since C must be an integer, we can round down the value of A to the nearest integer.
For example, if C = 100, then A >= 125. If we round down A to 125, then the profit from selling 125 adult tickets and 100 children's tickets would be:

10 * 125 + 5 * 100 = 1250 + 500 = 1750

which is less than the profit goal of 3750.

If we increase C by 1, then A would increase by 0.5, and the profit would increase by 5.
So, to reach the profit goal, we need to increase C until the profit is at least 3750.

Let's try C = 101. Then A >= 125.5, which we can round down to 126.

The profit from selling 126 adult tickets and 101 children's tickets would be:

10 * 126 + 5 * 101 = 1260 + 505 = 1765

which is greater than or equal to the profit goal of 3750.

So, the first combination of adult and children's tickets that meets the profit and seating limit conditions is (126, 101).

We can repeat the same process to find the second and third combinations.

For example, the second combination could be (127, 100), and the third combination could be (128, 99).

The final answer is (126, 101), (127, 100), (128, 99).

Answer:

250 $3 tickets and 100 $2 tickets were sold.

Step-by-step explanation:

3(350 – y) + 2y = 950

1050 – 3y + 2y = 950

3y – 2y = 1050 – 950

y = 100

Substitute y = 100 into equation 1

x + 100 = 350

x = 250

a. The greatest number of packages the teacher can make using all the paintbrushes and paint is 8

b. The number of paintbrushes in each package would be 3 and the number of tubes of paints would be 5

In order to determine the greatest number of packages the teacher can make using all the paintbrushes and paint, we have to determine the highest common factor of the number of brushes and the number of tubes of paint

Highest common factor is the highest factor that is common to two or more numbers:

Factors of 24 = 1,2,3,4,6,8,12 and 24

Factors of 40 = 1, 2, 4, 5, 8, 10, 20 and 40.

Common factors of 24 and 40 = 1, 2, 4, 8

Therefore, the highest common factor is 8.

The number of paintbrushes in each package:

= Number of brushes / number of package

= 24/8

= 3 brushes

The number of tubes of paint:

= number of tubes of paints / number of package

= 40 / 8

= 5 tubes of paints

Full question "An art teacher is making packages of paint brushes and paint for his. He has 24 brushes and 40 tubes of paint. Each package will have the same number An art teacher is making packages of paintbrushes and paint for his students. of brushes and the same number of tubes of paint. Part a. What is the greatest number of packages that the art teacher can make using all the paintbrushes and paint? Show your work Part b. How many paintbrushes and tubes of paint are in each package?​".

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Answer:

see explanation

Step-by-step explanation:

A segment joining the midpoints of two sides of a triangle is

parallel to the third side

∠ 1 and 144° are same- side interior angles and sum to 180° , so

∠ 1 + 144° = 180° ( subtract 144° from both sides )

∠ 1 = 36°

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

∠ 2 and 56° are corresponding angles and are congruent , so

∠ 2 = 56°

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

∠ 3 and 56° are a linear pair and sum to 180°

∠ 3 + 56° = 180° ( subtract 56° from both sides )

∠ 3 = 124°

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

the sum of the 3 angles in a triangle = 180° , then

∠ 1 + ∠ 2 + ∠ 4 = 180° , that is

36° + 56° + ∠ 4 = 180°

92° + ∠ 4 = 180° ( subtract 92° from both sides )

∠ 4 = 88°

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

∠ 5 and ∠ 1 are corresponding angles and are congruent , so

∠ 5 = 36°

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

Answer:

m∠1 = 36° , m∠5 = 36° , m∠4 = 88°  , m∠3 = 124° , m∠2= 56°

Step-by-step explanation:

m∠1 and 144° are Co-Interior angles, or the angles which are on the same side of the transveral

m∠1 + 144°  = 180°

m∠1 = 36°

angle 5 and 144° are in a linear pair-
144 °+ angle 5 = 180°

m∠5 = 36°

angle 5 + 56° + angle 4 = 180°        because addition of angles of a triangle is 180°

36° + 56° + angle 4 = 180°
angle 4 = 180° - 92°
angle 4 = 88°

56° and angle 3 are in a linear pair

56° + angle 3 = 180°
angle 3 = 124°

angle 3 and angle 2 are Co-Interior angles

angle 3 + angle 2 = 180°
124° + angle 2 = 180°
angle 2 = 56°

Hope it helped and you understood it :)

The area of the lawn in the scale drawing is approximately 996 square feet.

1. Measure the length and width of the lawn in inches on the scale drawing.

Length = 16.5 inches

Width = 15.5 inches

2. Convert the measurements to feet by dividing the inches by 12.

Length = 16.5/12 = 1.375 feet

Width = 15.5/12 = 1.291 feet

3. Calculate the area of the lawn by multiplying the length and width.

Area = 1.375 x 1.291 = 1.75 square feet

4. Multiply the area by the scale factor (in this case, 560) to get the actual area.

Area = 1.75 x 560 = 996 square feet

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Answer:

minimum is $14.40

maximum is $18

she can get 9 ice cream cups

Step-by-step explanation:

Answer:

260

Step-by-step explanation:

Substitute: (-2 · 7)² – 2 x (-2)⁵

Remove parenthesis: (2 · 7)² + 2 · 2⁵

Calculate the first two terms: 14ײ + 2 × 2⁵

Calculate the power: 196 + 2 × 32

Calculate the first two terms: 196 + 64

Calculate the first two terms: 260

Answer: 260

Answer:

D

Step-by-step explanation:

The 6 represents the initial value of 6000.  The cases are going down 5,000 a month.

According to the given question,  when m=5 and n=4, the value of the expression 10m + 4n²/4 is 66.

A mathematical expression is a phrase having a minimum of two numbers or variables and at least one mathematical operation. This mathematical operations may be add, subtraction, multiply, or divide. An expression's basic components are as follows: (Math Operator, Number/Variable, Expression)

Keep in mind that words can be variables, constants, or coefficients. Therefore, 1+1 is a straightforward example of an expression. This equation has two constant terms and one operation (addition). x³ is another illustration.

To evaluate the expression 10m + 4n²/4 when m=5 and n=4, we substitute these values into the expression and simplify:

10m + 4n²/4

= 10(5) + 4(4^2)/4

= 50 + 4(16)/4

= 50 + 16

= 66

Therefore, when m=5 and n=4, the value of the expression 10m + 4n^2/4 is 66.

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Answer:

1/4

Step-by-step explanation:

On a graph that's up 1 over 4 and its rise over run or (rise/run)

Answer:

see explanation

Step-by-step explanation:

the cost C(x) is the total of the number of erasers made and the fixed cost

(a)

let x be the number of erasers

C(x) = 0.16x + 455

(b)

substitute x = 3000 into C(x) for total cost

C(3000) = 0.16(3000) + 455 = 480 + 455 = 935

total cost = $935

1) Given that the perimeter of the rectangle is at least 40 cm, the  inequality and show that it reduces to x ≥ 3 2/3 is:  12x - 4 >= 40

2) The smallest possible value of x is 4

3) The area of the rectangle is  57 cm²

(i) The perimeter of a rectangle is given by the formula P = 2(l + b), where l is the length and b is the breadth. Substituting the given values, we get:

P = 2(4x + 3 + 2x - 5) cm

P = 2(6x - 2) cm

P = 12x - 4 cm

We are given that the perimeter is at least 40 cm, so we can write the inequality:

12x - 4 ≥ 40

Simplifying this inequality, we get:

12x ≥ 44

Dividing both sides by 12, we get:

x ≥ 11/3

x ≥ 3 2/3

So the inequality reduces to x ≥ 3 2/3

II) Note that if x is a perfect square, the smallest possible value of x is 4, because 4 is the smallest perfect square.

III) Substituting x = 4 in the length and breadth of the rectangle, we get:

Length = 4x + 3 = 19 cm

Breadth = 2x - 5 = 3 cm

Therefore, the area of the rectangle is:

Area = Length x Breadth = 19 cm x 3 cm = 57 cm²

Thus, it is correct to state that the area of the rectangle is 57cm².

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Answer:

lower quartile = 75

Step-by-step explanation:

the lower quartile Q₁ is situated at the left side of the box.

lower quartile Q₁ = 75

Answer:

p + (m × 1) = t

If a plant is already ___cm tall and it will grow one cm every month, an equation to find out how much the plant grew in __ months is this:

(Let t = total number of centimeters, m = number of months, and p = the length of the plant already.)

Therefore, the equation you can use is p + (m × 1) = t.

When the outside temperature is 30°F, the sales is $414.13

When the sale is $1,993.33, the outside temperature is 78°F

Since the equation y = 32.9x - 572.87 can be used to model the relationship between sales at a local ice cream shop, y, in dollars, and the outside temperature, x, in degrees Fahrenheit (F).

Thus, when the outside temperature is 30°F, the sales can be estimated by substituting x = 30°F into the equation and solving for y. That is:

y = 32.9x - 572.87

y =  32.9(30) - 572.87

y = 987 - 572.87

y = $414.13

Thus, when the sale is $1,993.33, the outside temperature can be estimated by substituting y = $1,993.33 into the equation and solving for x. That is:

y = 32.9x - 572.87

1,993.33 = 32.9x - 572.87

32.9x = 1,993.33 + 572.87

32.9x = 2566.2

x = 2566.2/32.9

x = 78°F

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The equation of the line that passes through (18, 16) and has a slope of 11/8 is 8y = 11x - 70.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables. Depending on the facts at hand, there are different ways to find a line's equation. Several techniques include:

Form of point slope, Form of a slope-intercept, Two-point form for intercepting.

The point slope form is given as:

(y - y1) = m (x - x1)

The point is (18, 16) and the slope is 11/8.

Substituting the values we have:

y - 16 = 11/8 (x - 18)

8(y - 16) = 11(x - 18)

8y - 128 = 11x - 198

8y = 11x - 70

Hence, the equation of the line that passes through (18, 16) and has a slope of 11/8 is 8y = 11x - 70.

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The sequence is a geometric sequence with a common ratio of 4.

What is a geometric sequence?

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed non-zero number called the common ratio (r).

To determine whether the sequence is arithmetic or geometric, we can look at the differences between consecutive terms.

The difference between the second and first terms is 2 - 0.5 = 1.5.

The difference between the third and second terms is 8 - 2 = 6.

The difference between the fourth and third terms is 32 - 8 = 24.

The difference between the fifth and fourth terms is 148 - 32 = 116.

Since the differences are not constant, the sequence is not arithmetic.

To determine if it is a geometric sequence, we can look at the ratios of consecutive terms.

The ratio of the second and first terms is 2/0.5 = 4.

The ratio of the third and second terms is 8/2 = 4.

The ratio of the fourth and third terms is 32/8 = 4.

The ratio of the fifth and fourth terms is 148/32 = 4.

Since the ratios are constant, the sequence is geometric with a common ratio of 4.

Therefore, the sequence is a geometric sequence with a common ratio of 4.

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The soap used by the machine last year is 5399.76 gallons.

The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage." This percent symbol can always be changed to a fraction or decimal equivalent by using "divided by 100."

Let the soap used last year = x.

Then, according to the given condition:

4,508.8 = x (1 - 16.5%)

4,508.8 = x (83.5/100)

x = 4,508.8(100) / 83.5

x = 5399.76

Hence, the soap used by the machine last year is 5399.76 gallons.

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There is a 0.06% chance that a randomly selected individual from the population would have the same genotype as the evidence sample at the FGA locus.

As a forensic scientist, one of your important tasks is to determine the likelihood that a particular piece of evidence matches a specific individual.

To determine the random match probability for the evidence sample at the FGA locus, you will need to compare it to the reference sample. The reference sample is typically obtained from a suspect or a known individual who is not a suspect in the crime. The reference sample for the FGA locus has a genotype of 16,17.

The random match probability is the probability that a randomly selected individual from the population would have the same genotype at a specific locus as the evidence sample. To calculate this probability, you will need to use the allele frequency of the FGA locus in the population. This frequency is typically obtained from a large database of individuals.

Let's assume that the allele frequency for the FGA locus is 0.03 for the 16 allele and 0.02 for the 17 allele. To calculate the random match probability, you will need to multiply these two frequencies together since the evidence sample has both alleles present. This gives us a probability of 0.0006 or 0.06%.

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Complete Question:

You are a forensic scientist and you are able to obtain the following 3 CODIS STR genotypes from an evidence sample found at a crime scene:

Locus       Evidence Genotype

D55818    6,10

FGA         16,17

VWA        11,12

Based on the reference sample, what is the random match probability for the evidence sample at the FGA locus?

If a least square regression line fits the data well, the characteristic should the residual plot exhibit is random scatter

The least squares regression line fits the data well.

The least squares regression is defined as the method that used to find the regression line or best suitable line for the given pattern

So if the data shows a linear relationship between the two given variable so such line will be called least squares regression line

The residual plot is the measure that vertical line how much misses from the data point

Here the least square-square regression lines fits the data well so the characteristics will be random scatter

Therefore, the characteristic that the residual plot exhibit is random scatter

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The probability of winning $2 without getting below $0 at any time is 1/4  or 0.25.

To calculate the probability of winning $2 without getting below $0 at any time, we can use a branching diagram to track the possible outcomes.

Starting from $0, there are two possible outcomes for the first flip: heads or tails. If the first flip heads, the outcome is $1 and there are two possible outcomes for the second flip: heads or tails. If the second flip heads, the outcome is $2 and we have won the game. If the second flip is tails, the outcome is back to $0 and we have to start over. If the first flip is tails, the outcome is $-1 and we also have two possible outcomes for the second flip: heads or tails. If the second flip heads, the outcome is back to $0 and we have to start over. If the second flip is tails, the outcome is $-2 and we have lost the game.

Putting all of the possible outcomes together, we get the following branching diagram:

              H                              T

         /          \                       /     \

       H             T                  H      T

     /     \          /                      \

    H      T     T                        H

   $2    $0   -$1                       -$2

The only way to win $2 without getting below $0 at any time is to get two heads in a row. This can only happen along the top branch of the diagram, which has a probability of (1/2) * (1/2) = 1/4.

Therefore, the probability of winning $2 without getting below $0 at any time is 1/4 or 0.25.

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