math complementary angles

The profit for one small cake is £1.31.

Let's first determine the overall count of parts demonstrated in the ratio 5:7:12, which is equal to 24. Subsequently, each part would hence correspond to a quantity of nine cakes as per the equation below:

216 cakes / 24 = 9 cakes

5 parts x 9 cakes/part = 45 cakes

Likewise, similarly calculating the number of medium cakes leads us to 63 cakes, while that of large cakes sums up to 108 cakes:

7 parts x 9 cakes/part = 63 cakes

12 parts x 9 cakes/part = 108 cakes

Considering what the profit for one small cake is denoted by "x", and similarly, the profit for one medium cake is "2x" and the profit for one large cake is "3x", we can express the total gain as follows:

45x + 63(2x) + 108(3x) = 648.45

After similifying and solving for "x", we obtain an answer of £1.31 after rounding it off to two decimal places:

495x = 648.45

x = 1.31 (rounded to two decimal places)

Thus, the income earned from selling one single small cake is estimated at £1.31.

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Answer:

y- intercept = - 14

Step-by-step explanation:

the y- intercept is the point on the y- axis where the line crosses.

at any point on the y- axis, the x- coordinate is zero.

let x = 0 in the equation and solve for y , the y- intercept

5(0) - 2y = 28

0 - 2y = 28

- 2y = 28 ( divide both sides by - 2 )

y = - 14 ← y- intercept

Answer:  Option C

Step-by-step explanation: To compare the rates at which the pipes are leaking, we can find the amount of water each pipe leaks per minute.

For Pipe A:

3/4 gallon ÷ 30 minutes = 1/40 gallon per minute

For Pipe B:

1 1/4 gallon ÷ 45 minutes = 5/36 gallon per minute

For Pipe C:

1/2 gallon ÷ 20 minutes = 1/40 gallon per minute

Therefore, Pipes A and C are leaking at the same rate, which means option C is true. Option A and D are false, as Pipe B has the fastest leak rate. Option B is false, as both Pipe A and Pipe C are leaking at the same rate.

Answer: -0.25

Step-by-step explanation:

Start by undoing with PEMDAS (order of operations, P-parenthesis, E-exponents, etc)

+3 on both sides of equal sign, which gives you

8n=-2

then divide by 8 on both sides (undo the times 8)

n=-0.25

Answer: -0.25

Step-by-step explanation:

Start by undoing with PEMDAS (order of operations, P-parenthesis, E-exponents, etc)

+3 on both sides of equal sign, which gives you

8n=-2

then divide by 8 on both sides (undo the times 8)

n=-0.25

The domain of the ellipse is [-7, 7].

The range of the ellipse is [-4, 4].

In mathematics, the domain of a function is the set of all possible input values for which the function is defined. In other words, it is the set of all values of the independent variable (usually denoted by x) for which the function produces a valid output (usually denoted by y).

In mathematics, the range of a function is the set of all possible output values that the function can produce for a given set of input values. In other words, it is the set of all values of the dependent variable (usually denoted by y) that can be obtained from the function.

To find the domain and range of an ellipse, we need to identify the minimum and maximum x-coordinates and y-coordinates of the points on the ellipse.

The center of the ellipse is the midpoint of its major axis, which is the line segment connecting its vertices (-7,0) and (7,0). The midpoint is ((-7+7)/2, (0+0)/2), or (0,0). This means the center of the ellipse is at (0,0).

The semi-major axis is the distance from the center of the ellipse to one of its vertices, which is 7. The semi-minor axis is the distance from the center of the ellipse to one of its co-vertices, which is 4.

So, the equation of the ellipse can be written in standard form as:

(x - 0)²/7² + (y - 0)²/4² = 1

Simplifying, we get:

x²/49 + y²/16 = 1

To find the domain and range, we need to consider the x-coordinates and y-coordinates separately.

For the x-coordinates, we can rearrange the equation as:

x² = 49 - 49y²/16

This tells us that the minimum and maximum values of x occur when y is at its extremes, which are -4 and 4. Substituting these values, we get:

x² = 0 and x² = 49

Taking the square root, we get:

x = 0 and x = ±7

So, the domain of the ellipse is [-7, 7].

For the y-coordinates, we can rearrange the equation as:

y² = 16 - 16x²/49

This tells us that the minimum and maximum values of y occur when x is at its extremes, which are -7 and 7. Substituting these values, we get:

y² = 0 and y² = 16

Taking the square root, we get:

y = 0 and y = ±4

So, the range of the ellipse is [-4, 4].

Therefore, the domain of the ellipse is [-7, 7], and the range of the ellipse is [-4, 4].

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The middle 95% of Jace's finishing times in the 400 meter race is between 82 and 92 seconds.

Approximately 68% of the data falls within 1 standard deviation of the mean (i.e., between μ - σ and μ + σ).

Approximately 95% of the data falls within 2 standard deviations of the mean (i.e., between μ - 2σ and μ + 2σ).

Approximately 99.7% of the data falls within 3 standard deviations of the mean (i.e., between μ - 3σ and μ + 3σ).

We want to find the interval of times that represents the middle 95% of Jace's finishing times, which means we want to find the interval that falls between μ - 2σ and μ + 2σ.

Substituting the given values, we get:

μ - 2σ = 87 - 2(2.5) = 82

μ + 2σ = 87 + 2(2.5) = 92

Therefore, the middle 95% of Jace's finishing times in the 400 meter race is between 82 and 92 seconds.

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If a single letter from the word SLEEPLESS is chosen, the probability of choosing a P or an S as a fraction in lowest terms is 5/8.

To find the probability of choosing a P or an S from the word SLEEPLESS, we need to first determine the total number of letters in the word and then count how many of those letters are P's or S's.

There are 8 letters in the word SLEEPLESS, so there are 8 possible outcomes when selecting a single letter at random. Of these 8 letters, 2 are P's and 3 are S's.

Therefore, the probability of choosing a P or an S is the sum of the probabilities of choosing a P and choosing an S:

P(P or S) = P(P) + P(S)

P(P) = 2/8 = 1/4, since there are 2 P's out of 8 total letters.

P(S) = 3/8, since there are 3 S's out of 8 total letters.

P(P or S) = 1/4 + 3/8

P(P or S) = 5/8, which is the final probability expressed as a fraction in lowest terms.

Alternatively, we can convert the fraction to a decimal and round to the nearest millionth:

P(P or S) = 0.625

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Points are (0,-8) and (-6,-3) Slope m = rise/run = Δy/Δx. [(-3 - (-8)]/[-6 - 0] = 5/-6 = -5/6

y = mx + b Using the (0,-8) point: -8 = 0x + b, so b = -8

The line is y = -5x/6 - 8 or (-5/6)x - 8. You can check via the Desmos Graphing Calculator site

I used the slope-intercept form, but you could also use the point-slope form (y2 - y1) = m(x2 - x1)

Answer:

[tex]2 \dfrac{1}{2}[/tex]     OR     [tex]\dfrac{5}{2}[/tex]

Step-by-step explanation:

We can see that there are 2 whole shaded circles, and there is 1 half shaded circle.

Therefore, we can represent the shaded area as [tex]\bold{2 \dfrac{1}{2}}[/tex] circles.

We can convert this mixed number to an improper fraction by multiplying the whole number by the denominator and adding the resulting value to the numerator.

[tex]2 \dfrac{1}{2}[/tex]

[tex]= \dfrac{(2 \times 2) + 1}{2}[/tex]

[tex]= \dfrac{5}{2}[/tex]

The height of the thrown bottle becomes zero at the t = 1/2 that is half a second and at t = 3 seconds

An equation is formed by expressing the relationship between two or more mathematical expressions. It can be formed by using mathematical symbols, operations, and variables. Typically, equations are used to solve problems or find unknown quantities by setting up an equation that represents the problem and then manipulating the equation using algebraic operations until the solution is obtained. For example, to solve the equation 2x + 3 = 7, you would use algebraic operations to isolate the variable x on one side of the equation, giving you the solution x = 2.

To find when the height of the thrown bottle is equal to 0, we need to solve the given equation:

h = -16t² + 56t - 24 = 0

Takin -8 common out we get,

-8(2t² - 7t + 3) = 0

Now we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero:

-8 = 0 or 2t² - 7t + 3 = 0

But -8 ≠ 0, so we only possible one is,

2t² - 7t + 3 = 0

(2t - 1)(t - 3) = 0

Using the zero product property, we get,

2t - 1 = 0 or t - 3 = 0

Solving for t we get,

t = 1/2 or t = 3

Therefore, the height of the thrown bottle is equal to 0 at t = 1/2 seconds and t = 3 seconds.

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The height of the thrown bottle becomes zero at the t = 1/2 that is half a second and at t = 3 seconds

An equation is formed by expressing the relationship between two or more mathematical expressions. It can be formed by using mathematical symbols, operations, and variables. Typically, equations are used to solve problems or find unknown quantities by setting up an equation that represents the problem and then manipulating the equation using algebraic operations until the solution is obtained. For example, to solve the equation 2x + 3 = 7, you would use algebraic operations to isolate the variable x on one side of the equation, giving you the solution x = 2.

To find when the height of the thrown bottle is equal to 0, we need to solve the given equation:

h = -16t² + 56t - 24 = 0

Takin -8 common out we get,

-8(2t² - 7t + 3) = 0

Now we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero:

-8 = 0 or 2t² - 7t + 3 = 0

But -8 ≠ 0, so we only possible one is,

2t² - 7t + 3 = 0

(2t - 1)(t - 3) = 0

Using the zero product property, we get,

2t - 1 = 0 or t - 3 = 0

Solving for t we get,

t = 1/2 or t = 3

Therefore, the height of the thrown bottle is equal to 0 at t = 1/2 seconds and t = 3 seconds.

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The probability that the distance between two points on a circle of radius 1 is at most 1.5 is approximately 0.477 or 47.7%, which corresponds to the range of central angles less than or equal to 3 radians out of the total central angle of 2π radians.

Let's consider two points on a circle of radius 1, labeled A and B. The distance between A and B is given by the length of the arc AB on the circle, which is a fraction of the circumference of the circle. The circumference of a circle of radius 1 is 2π, so the length of the arc AB is given by

d = θ/2π * 2πr = θ

where d is the distance between A and B, θ is the central angle between A and B (in radians), and r is the radius of the circle (which is 1 in this case).

To find the probability that the distance between A and B is at most 1.5, we need to find the range of central angles that correspond to arc lengths less than or equal to 1.5. Let's call this range of angles θ₁. We have

θ₁ = 2d/r = 2(1.5)/1 = 3

This means that the central angle between A and B must be less than or equal to 3 radians for the distance between A and B to be at most 1.5. Since the total central angle of the circle is 2π radians, the probability of selecting two points with a central angle less than or equal to 3 radians is

P(θ ≤ 3) = θ/2π = 3/2π ≈ 0.477

Therefore, the probability that the distance between two points on a circle of radius 1 is at most 1.5 is approximately 0.477 or 47.7%.

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Answer:

The formula for the surface area of a cylinder is:

SA = 2πr^2 + 2πrh

where r is the radius and h is the height.

Since the diameter of the tube is 2 cm, the radius is 1 cm.

Substituting the given values, we get:

SA = 2π(1^2) + 2π(1)(8)

SA = 2π + 16π

SA = 18π

To find the surface area in square centimeters, we need to multiply by the conversion factor (1 cm)^2/(1 π) = 1 cm^2/3.14.

SA = 18π × (1 cm^2/3.14)

SA ≈ 18 × 0.3185

SA ≈ 5.73 cm^2

Rounding to the nearest whole number, we get:

SA ≈ 6 cm^2

Therefore, the answer is B. 57 cm^2.

Step-by-step explanation:

a)0.2407 is the point estimate of the proportion.

b) The 95% confidence interval for the proportion that beat estimates is (0.4858, 0.6746).

c) A sample size of 754 is needed to achieve a desired margin of error of 0.05.

(a) What is the point estimate of the proportion?

The point estimate of the proportion that fell short of estimates is 39/162 = 0.2407. Rounded to four decimal places, this is pshort = 0.2407.

(b) How to determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates?

To determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates, we need to first find the point estimate and standard error of the proportion that beat estimates.

The point estimate of the proportion that beat estimates is 94/162 = 0.5802.

The standard error can be calculated as:

SE = √(p×(1-p)/n)

where p is the point estimate of the proportion that beat estimates and n is the sample size. Substituting the values we get:

SE = √(0.5802×(1-0.5802)/162) = 0.0482

To calculate the margin of error, we use the formula:

ME = zSE

where z is the z-score corresponding to the desired confidence level. For a 95% confidence level, z* = 1.96 (from the standard normal distribution table).

Substituting the values we get:

ME = 1.96×0.0482 = 0.0944

Therefore, the margin of error is 0.0944. To find the 95% confidence interval, we add and subtract the margin of error from the point estimate of the proportion that beat estimates:

CI = 0.5802 ± 0.0944

CI = (0.4858, 0.6746)

Therefore, the 95% confidence interval for the proportion that beat estimates is (0.4858, 0.6746).

(c) How large a sample is needed if the desired margin of error is 0.05?

To find the sample size needed for a desired margin of error of 0.05, we use the formula:

n* = (z*/ME)² × p×(1-p)

where z* is the z-score corresponding to the desired confidence level (we use 1.96 for a 95% confidence level), ME is the desired margin of error (0.05), and p is an estimate of the proportion (we use the point estimate of 0.5802 for the proportion that beat estimates).

Substituting the values we get:

n* = (1.96/0.05)² × 0.5802×(1-0.5802) = 753.16

Rounding up to the next integer, we get n* = 754. Therefore, a sample size of 754 is needed to achieve a desired margin of error of 0.05.

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Answer:

x=70°

Step-by-step explanation:

angles on straight line add to 180 so...

180-120=60°

angles in triangle add to 180° so...

180°-50°-60°=70°

so x=70°

The data item in this distribution corresponding to a z-score of -7 will be 290.

Here, we have,

The standard score in statistics is the number of standard deviations that a raw score's value is above or below the mean value of what is being observed or measured.

Raw scores that are higher than the mean have positive standard scores, whereas those that are lower than the mean have negative standard scores.

The Z-score measures how much a particular value deviates from the standard deviation.

The Z-score, also known as the standard score, is the number of standard deviations above or below the mean for a given data point.

The standard deviation reflects the level of variability within a particular data collection.

Here,

z=(X-μ)/σ

-7=(X-500)/30

-210=X-500

X=290

The data item in this distribution that corresponds to we given z-score

z equals to -7 will be 290.

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Answer:

29.2

Step-by-step explanation:

10.30+18.90=29.2

Answer:

$29.20

Step-by-step explanation:

$10.30

+$18.90

=$29.20

On adding the measurement of "4-boards", the total length of the 'four-boards" is  154 inches.

In order to add the lengths of these four boards, we first need to convert all the measurements to the same units.

So, Let us convert all the measurements to inches:

(i) 3 feet 4 inches = (3×12) + 4 = 40 inches,    ...because 1 feet = 12 inch;

(ii) 27 inches = 27 inches;

(iii) 1(1/2) yards = (1.5 × 3 × 12) = 54 inches;

(iv) 2(3/4) feet = (2.75 × 12) = 33 inches;

Now, we can add the lengths of the four-boards:

⇒ 40 + 27 + 54 + 33 = 154 inches,

Therefore, the total length of all four boards is 154 inches.

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Answer: 2 Radians

Step-by-step explanation:

    A full circle is 2 full radians, also known as 2π. Half of a circle is equal to 180 degrees, which is equal to one radian, π.

    I have attached a picture of the unit circle below, this picture comes form www.remind.com, but you can find many online.

Answer: 288.62

Step-by-step explanation:

10.4^2 + 15.3^2 = 342.25,

c^2 = 342.25

c (hypotenuse of the right triangle & length of rectangle) = 18.5

7(8) + 10.4(15.3) = 288.62

Answer:

The answer is A. $1,166.40

Step-by-step explanation:

Answer:

40 students are in the class :)

Step-by-step explanation:

35%=14

1%=14/35=0.4

0.4*100=40=100%

If Mrs. Smith's oatmeal cookie recipe calls for 2/5 of a cup of sugar to make a full batch of cookies, then to make half a batch of cookies, she will need half the amount of sugar.

So, to find out how much sugar Mrs. Smith needs to make half a batch of cookies, we can use the following calculation:

Sugar needed for half a batch = (2/5 cup sugar) x (1/2 batch)

Simplifying this expression, we get:

Sugar needed for half a batch = 2/10 cup sugar

Which can be further simplified to:

Sugar needed for half a batch = 1/5 cup sugar

Therefore, Mrs. Smith will need 1/5 cup of sugar to make half a batch of oatmeal cookies.

Perimeter = 28 yards

Area 49 square yards.

Answer:

Step-by-step explanation:

A is correct

The situations that represent a proportional relationship are:

A). Natalia is selling fresh eggs at the local farmer's market. She sells 6 eggs for $3.12, a dozen eggs for $6.24, and eighteen eggs for $9.36.

C). Graph 1 provided in the pictures. This graph shows a straight line passing through the origin, which indicates a proportional relationship.

D). Graph 2 provided in the pictures. This graph also shows a straight line passing through the origin, which indicates a proportional relationship.

E). Azul bought several different packages of 8-inch by 10-inch art canvases for a craft project at her family reunion. The number of canvases in a package and the cost of the package is shown in the table.

Therefore, the situations A, C, D, and E represent proportional relationships.

A proportional relationship is a relationship between two quantities where one quantity is a constant multiple of the other quantity. In other words, if one quantity increases or decreases by a certain factor, then the other quantity will increase or decrease by the same factor. This relationship can be represented by a straight line passing through the origin on a graph.

For example, if the price of gasoline is proportional to the number of gallons purchased, then buying twice as many gallons would cost twice as much money. Similarly, if the distance traveled is proportional to the time taken, then traveling twice as long would cover twice the distance.

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The area of a trapezoid =1/2× (sum of the parallel sides)×h

=1/2×(a + b)×h=1/2×(3+6)×4=9×2= 18 square units.

A trapezoid is a geometric shape with four sides, where two of the sides are parallel and the other two sides are not parallel. The parallel sides are called bases, and the non-parallel sides are called legs. The height or altitude of the trapezoid is the distance separating the two bases.

There are two main types of trapezoids: isosceles and non-isosceles. In an isosceles trapezoid, the legs are congruent, and the base angles (the angles formed between each base and a leg) are also congruent. In a non-isosceles trapezoid, the legs and base angles are not congruent.

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The word that describes the probability that Janelys reaches in without looking and pulls out a strawberry chew is "the probability of selecting a strawberry chew randomly from the bag".

The word or phrase that describes the probability of pulling out a strawberry chew without looking is "the probability of selecting a strawberry chew at random" or "the probability of picking a strawberry chew by chance".

This probability is calculated by dividing the number of strawberry chews in the bag by the total number of chews in the bag, since each chew is equally likely to be selected.

In this case, there are 15 strawberry chews and 5 cherry chews, so the probability of selecting a strawberry chew at random is 15/(15+5) or 3/4, which is approximately 0.75 or 75%.

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In increasing order according to their capacity:

The capacity of a container, such as a cup, bottle, or tank, is the amount of fluid or material it can hold. It is usually stated in volume quantities such as liters, milliliters, gallons, or ounces.

Capacity is a necessary concept in engineering, manufacturing, and transportation, where it is used to design and run systems involving the storage, movement, and processing of fluids or materials.

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Answer:

Volume L× W × H

Volume 4 × 3 × 2

4 × 3 × 2 =24

If the fish poke is 6 feet long and she has a rectangular prism of 24 since 4 × 3 ×2 equals 24 then yes she can store the fishing pole in the box

24