Lewis was driving at 90 km per hour when he sneezed.
During the sneeze, his eyes were closed for half a second.
Work out how many metres he travelled in this time.​

Answer:

136°

Step-by-step explanation:

The whole of the cake angle = 360°

Half of it = 180°

Therefore; if 44° angle is eaten out of the half i.e 180°

Then what's left = 180° - 44° = 136°

Using simplification, if the total ticket sales was $1316, then 70 children, 78 students and 35 students attended.

From the given question,

We know that the capacity of movie theater is 183.

The theater charges $5.00 for children, $7.00 for students and $12.00 of adults.

There are half as many adults as there are children.

If the total ticket sales was $1316, then we have to find how many children, students, and adults attended.

Let the number of children that attended = x

Since, there are half as many adults as children.

Therefore number of adults = 1/2x =0.5x

We know there are total of 183 tickets

Therefore number of students = 183 - x - 0.5x

number of students = 183 - 1.5x

Each children ticket costs = $5

Then the price of children tickets = 5x

Similarly for adults each ticket costs = $12

So total cost of adult ticket = 12×0.5x = $6x

Now the cost of student tickets = 7(183 - 1.5x)

As given that

Total cost of all tickets = $1316

So the expression should be

5x + 6x + 7(183 -1.5x) = 1316

Simplifying

11x + 1281 - 10.5x = 1316

Subtract 1281 on both side

11x + 1281 - 10.5x-1281 = 1316-1281

Simplifying

0.5x = 35

Divide by 0.5 on both side we get

x = 70 children

Now finding the number of adults

= 0.5x

= 0.5×70

= 35 adults

Now finding the number of students

= 183 - 1.5x

= 183 - 1.5×70

= 183 - 105

= 78 students

Hence, If the total ticket sales was $1316, then 70 children, 78 students and 35 students attended.

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Answer:

a=60°

b=300°

Step-by-step explanation:

the triangle is equilateral so all angles are 60 °

a = 60°

b=360 - 60 =300°

Answer:

A is 60°, B is 300°

Step-by-step explanation:

If you look closely, you can tell that this circle is divided into 6 triangles, but there is only one showing. This triangle is 1/6 of the circle.

You can find B by find 1/6 of 360° and subtracting that from 360, (a full circle is 360°)

1/6 of 360° is 60°

360° - 60° = 300°, so B is 300°

Now lets find A. Triangles are 180°. This triangle is obviously an equilateral triangle, so the measurements will all be the same.

180 ÷ 3 is 60, so A is 60°

I hope this helped, please mark Brainliest, thank you!

The biconditional statement,

→ If a polygon is a triangle, then the polygon has exactly three sides.

→ If a polygon has exactly three sides then it is a triangle.

Given statement;

If a polygon has three sides, then it is a triangle. If a polygon is a triangle, then it has three sides.

The biconditional of the given statement is,

→ If a polygon is a triangle, then the polygon has exactly three sides.

→ If a polygon has exactly three sides then it is a triangle.

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Answer:

15 multiple choice 5 true false

Plzzzzz give me Brainliest!!!!!  

I) f is continuous at x=2

II) f is differentiable at x=2

These both f (function ) are true

The given limit can be recognized as the definition of the derivative of f at x=2. Specifically, it states that the derivative of f at x=2 is equal to 5.

Using this information, we can make the following conclusions:

I) We cannot say for sure whether f is continuous at x=2 based on the given limit alone. While a function being differentiable at a point implies that it is also continuous at that point, the converse is not necessarily true. Therefore, we would need additional information to determine whether f is continuous at x=2.

II) The given limit implies that f is differentiable at x=2, since the limit exists and is finite. Specifically, we can say that the derivative of f at x=2 exists and is equal to 5.

III) The given limit also implies that the derivative of f is continuous at x=2. This is because the limit defines a continuous function at x=2, and it is well-known that if a function is differentiable at a point, then it is also continuous at that point.

Therefore, the correct answers are II and III.

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Answer:

2296 unit^2

Step-by-step explanation:

The area is the sum of the  6 rectangles in the net.

= 38*10 + 38*16 + 38*10 + 38*16 + 10*16 + 10*16

= 380 + 608 + 380 + 608 + 160 + 160

= 2296.

The population will grow the fastest at half of the carrying capacity, which is 250 crabs.

In the logistic growth equation, the population growth rate is highest when the population is at half of the carrying capacity. This is because, at this point, there is a balance between birth rates and death rates, maximizing the net population growth.

For the given logistic growth equation with a carrying capacity of 500 crabs, the population will grow the fastest at half of the carrying capacity, which is 250 crabs.

Regarding the second question, to determine the initial population size of widowbirds when tracking started, we can use the equation λ = (births - deaths) / initial population.

Given that 150 individuals were born and 75 birds died during the tracking period, and λ is equal to 2, we can solve the equation for the initial population.

2 = (150 - 75) / initial population

Multiplying both sides by the initial population:

2 * initial population = 150 - 75

2 * initial population = 75

Dividing both sides by 2:

initial population = 75 / 2

initial population = 37.5

Since population size cannot be a decimal, we round down to the nearest whole number.

Therefore, when tracking the population of widowbirds, the initial population size would be approximately 37 birds.

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Answer:

y = 3x - 7

Step-by-step explanation:

Please let me know if you want me to write an explanation for my answer :)

Answer:

10 years old

Step-by-step explanation:

Answer: The formula is C=2 π r

Step-by-step explanation: Hope this helps

Answer:

Degrees = Radians x 180/π

or

Degrees = 57.2958  x radians

Step-by-step explanation:

1 radian = 180/π degrees

1 radian = 57.2958 degrees

Multiply radians by this factor of 57.2958  to get the equivalent measure in degrees

π radians = 180°

2π radians = 360° which is the number of degrees in a circle

For anything greater than 2π radians you will have to subtract 360°

For example, 7 radians using the formula is 7 x (57.2958  ) ≈ 401.07°

But this still falls in the first quadrant, so relative to the x-axis it is
401.07 - 360 = 41.07°

Here since the ratios are not all equal, we can conclude that x and y are not in a proportional relationship.

What is meant by ratios?

Ratios are a mathematical tool used to compare the sizes of two or more quantities, expressed as a ratio of their values. Ratios can be simplified, converted to fractions or decimals, and used to solve problems in various fields.

What is meant by proportional?

Proportional refers to the constant relationship between two or more quantities where their ratio remains the same. Scaling one quantity by a certain factor requires scaling the other quantity by the same factor to maintain the proportion.

According to the given information

To determine if x and y are in a proportional relationship, we need to check if the ratio of y to x is constant.

Let's calculate the ratio of y to x for each pair of corresponding values:

y/x for (1, 2.5) = 2.5/1 = 2.5

y/x for (2, 5) = 5/2 = 2.5

y/x for (3, 7.5) = 7.5/3 = 2.5

y/x for (6, 12) = 12/6 = 2

Since the ratios are not all equal, we can conclude that x and y are not in a proportional relationship.

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Answer:

86

Step-by-step explanation:

Just multiply the mean by how many numbers

21.5 x 4 = 86

Answer:

35 pets

Step-by-step explanation:

11+4+1+3+4+12=15+4+16=19+16=35

Answer:

I got in total you have 35 pets

Step-by-step explanation:

I added \(~_~)/

According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same. The formula for this property can be expressed in real numbers a, b and c. If a × c = b × c.

Property of Equality:

The equivalence property describes the relationship between two equal quantities. If you apply a math operation to one side of the equation, you must also apply it to the other side of the equation to maintain balance.

That is, a property that does not change the truth value of an equation or does not affect the equivalence of two or more quantities is called an equality property. These equality properties help solve various algebraic equations and define equivalence or equilibrium relationships.

Multiplicative Property of Equality:

According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same.

The formula for this property can be expressed as for the real numbers a, b, and c.

If a × b, then, a × c = b × c.

In algebra, the multiplicative property of an equation helps extract unknown terms from an equation. Because multiplication and division are opposites of each other.

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Answer:

a =13

Step-by-step explanation:

180= (44+16-23)+11a

143=11a

143÷11= 13

Labor content (labor dollar per unit) is the total cost of labor required to produce one unit of a product. It can be calculated by dividing the total labor cost by the number of units produced.

In this scenario, we are given that an employee produces 17 parts during an 8-hour shift and earns $109 per shift.

To calculate the labor content, we first determine the labor cost per hour. This is done by dividing the total amount earned in the 8-hour shift by 8.

Labor cost per hour = $109 ÷ 8 = $13 per hour

Next, we calculate the number of parts produced per hour by dividing the total number of parts produced (17) by the duration of the shift (8 hours).

Parts produced per hour = 17 ÷ 8 = 2.125 parts per hour

Finally, we calculate the labor cost per part by dividing the labor cost per hour by the number of parts produced per hour.

Labor cost per part = $13 ÷ 2.125 = $6.12 per part

Therefore, the labor content (labor dollar per unit) of the product is $6.12 per part.

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An investment strategy with an expected return of 14 percent and a standard deviation of 8 percent has the potential for higher returns, but also comes with a higher level of risk. It is important to carefully consider the trade-off between risk and return before making an investment decision.

An investment strategy with an expected return of 14 percent and a standard deviation of 8 percent means that the investment has a higher potential for return, but also a higher risk.

The standard deviation is a measure of the variation or dispersion of a set of data values. In this case, the standard deviation of 8 percent indicates the degree of variation in the investment returns. A higher standard deviation means that the investment returns are more spread out and there is a higher chance of extreme values, both positive and negative.

In terms of investment strategy, it is important to consider the trade-off between risk and return. While a higher expected return is desirable, it often comes with a higher level of risk. Therefore, it is important to carefully consider the standard deviation and the potential risks associated with an investment before making a decision.

In conclusion, an investment strategy with an expected return of 14 percent and a standard deviation of 8 percent has the potential for higher returns, but also comes with a higher level of risk. It is important to carefully consider the trade-off between risk and return before making an investment decision.

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A ratio variable should be transformed into a dichotomous variable represented with dummy coding when the research question or analysis requires a simplified comparison between two distinct groups, the relationship between the ratio variable and the outcome variable is non-linear, there is a meaningful cutoff or threshold value, or specific statistical methods necessitate dichotomous variables.

A ratio variable may be transformed into a dichotomous variable represented with dummy coding under the following conditions:

Simplification of Analysis: When the research question or analysis requires a simplified comparison between two distinct groups or categories based on the ratio variable.

Nonlinearity: If the relationship between the ratio variable and the outcome variable is non-linear, it may be beneficial to dichotomize the ratio variable to capture the presence or absence of a certain condition or threshold.

Practical Interpretation: When there is a meaningful and interpretable cutoff or threshold value for the ratio variable that divides the population into two distinct groups.

Statistical Analysis Requirements: Certain statistical methods or models may require dichotomous variables for analysis, and transforming a ratio variable into a dichotomous variable allows for the use of these methods.

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The size around the circular edge of the plate is 37.68 inches

The circumference of a circle can be solved as follows:

The ant is standing at the centre of a perfectly circular plate and it walks to the edge of the plate .

The centre of the plate to the edges is 6 inches. Therefore, the radius of the circular plate is 6 inches.

Hence, the distance around the edge of the plate is the circumference of the plate.

Therefore,

circumference of the circular plate = 2πr

circumference of the circular plate = 2 × π × 6

circumference of the circular plate = 12π

circumference of the circular plate = 12 × 3.14

circumference of the circular plate = 37.68 inches

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Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

Answer:

2x-1= p

Step-by-step explanation:

dude srsly

The sample autocorrelation function is ρ(k) = (1/n) ∑(t=k+1)ⁿ 3(t - 1) (3t-k)

To compute the sample autocorrelation function for our time series, we can use the following formula:

ρ(k) = (1/n) ∑(t=k+1)ⁿ (3t - 3) (3t-k - 3)

where ρ(k) represents the autocorrelation at lag k, n represents the number of observations (which in our case is 100), 3 represents the sample mean of the time series, and the summation is taken over all t=k+1 to n.

Then the function is written as,

=> ρ(k) = (1/n) ∑(t=k+1)ⁿ 3(t - 1) (3t-k)

Once we have computed the sample autocorrelation function, we can plot it to visualize the pattern of correlation between the time series and its lagged values.

The plot will have lag on the x-axis and autocorrelation on the y-axis. The plot will help us identify any significant correlations that exist between the time series and its lagged values.

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The percentage of published studies that supported the tested hypothesis has changed from 70 to 85% over the past 25 years.

Hypothesis testing:

A hypothesis testing means investigates a proposed mathematical model to determine whether there is sufficient evidence from a sample of data to reject the defined null hypothesis.

Given,

The percentage of published studies that supported the tested hypothesis has changed from _____ to _____ over the past 25 years.

Here we need to find the change in the percentage for the past 25 years.

Based on the details, the percentage of published studies that supported the tested hypothesis has changed from 70 to 85% over the past 25 years.

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Answer:

we know that sum of angle a and b is 180

so a+b= 180

a= 34 (given)

b= 180-34

b= 146 degrees

Answer:

146 degrees

Step-by-step explanation:

Why?

Angle A and B together = 180 because they make up that one line and a line = 180 degrees and it says that angle A =34 so...

180 - 34 =  (B)

146 = (B)

Since n•u is not equal to 0, we conclude that the vector u is not in the plane spanned by the columns of A.

A vector u is in the plane spanned by the columns of a matrix A if and only if the dot product between u and the normal vector of the plane is equal to 0.

In this case, let A = [5 -2 1; -3 6 1]. To determine if u = [-12, 36, 8] is in the plane spanned by the columns of A, we can calculate the dot product between u and the normal vector of the plane, which can be found by taking the cross product of the two columns of A.

Since the cross product of two columns in A gives the normal vector of the plane spanned by the columns, we have:

n = (5, -2, 1) × (-3, 6, 1) = (18, -26, -11)

Next, we calculate the dot product of n and u:

n•u = (18, -26, -11) • [-12, 36, 8] = 18 * -12 - 26 * 36 - 11 * 8 = -816 - 936 - 88 = -1840

Since n•u is not equal to 0, we conclude that the vector u is not in the plane spanned by the columns of A. In other words, u is not orthogonal to the normal vector of the plane and therefore, is not in the plane.

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a. The equation that represents the given data is y = 700x + 2,000.

b. The average daily attendance at Disneyland on its 80th anniversary is 58,000.

We are given the data about average daily attendance at Disneyland's anniversary celebrations. At Disneyland's 40th anniversary, the average daily attendance was 30,000 people. On the 60th anniversary, the average daily attendance was 44,000 people. We need to create an equation that would represent y, the average daily attendance, based on x, the number of years after Disneyland opened.

We can write the data in the form of points on the coordinate axes. The coordinates of the points are (40, 30,000) and (60, 44,000). We can use the two-point form to write an equation.

(y - y1) = [(y2 - y1)/(x2 - x1)]*(x - x1)

(y - 30,000) = [(44,000 - 30,000)/(60 - 40)]*(x - 40)

(y - 30,000) = [(14,000)/(20)]*(x - 40)

(y - 30,000) = (700)*(x - 40)

y = 700x - 28,000 + 30,000

y = 700x + 2,000

Now, we need to find out the average daily attendance at Disneyland on its 80th anniversary.

y = 700*80 + 2,000

y = 56,000 + 2,000

y = 58,000

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Answer:

32 degrees

Step-by-step explanation:

Answer:

55!

Step-by-step explanation:

y= 100-45!

exterior angle in equal to sum of interior angles 100° = y +45°

The planned order releases for each item are as follows: A: 20 units in period 1, B: 10 units in period 1, C: 40 units in period 3, D: No planned order release, E: 100 units in period 5, F: 100 units in period 5

To determine the planned order releases for all items, we need to calculate the net requirements for each period based on the given information. We will start with the highest-level item and work our way down the bill of materials.

Item A:

Period 1: Gross requirement of 20 units.

Since A uses lot-for-lot (L4L) as the lot-sizing technique, we release an order for 20 units of A.

Item B:

Item B is a component of A, and each A requires 2 units of B.

We need to calculate the net requirements for B based on the planned order release for A.

Period 1: Gross requirement of 20 units * 2 (requirement multiplier for B) = 40 units.

B has a scheduled receipt of 30 units in period 1.

Net requirement for B in period 1: 40 units - 30 units = 10 units.

Since B also uses L4L as the lot-sizing technique, we release an order for 10 units of B.

Item C:

Item C is a component of A, and each A requires 3 units of C.

We need to calculate the net requirements for C based on the planned order release for A.

Period 1: Gross requirement of 20 units * 3 (requirement multiplier for C) = 60 units.

C has a lead time of two periods, so we need to account for that.

Net requirement for C in period 3: 60 units - 20 units (scheduled receipt for A in period 1) = 40 units.

Since C uses L4L as the lot-sizing technique, we release an order for 40 units of C.

Item D:

Item D is a component of C, and each C requires 1 unit of D.

We need to calculate the net requirements for D based on the planned order release for C.

Period 3: Gross requirement of 40 units * 1 (requirement multiplier for D) = 40 units.

D has a lead time of one period, so we need to account for that.

Net requirement for D in period 4: 40 units - 60 units (scheduled receipt for C in period 3) = -20 units (no requirement).

Since the net requirement is negative, we do not release any planned order for D.

Item E:

Item E is a component of C, and each C requires 1 unit of E.

We need to calculate the net requirements for E based on the planned order release for C.

Period 3: Gross requirement of 40 units * 1 (requirement multiplier for E) = 40 units.

E has a lead time of two periods, so we need to account for that.

Net requirement for E in period 5: 40 units - 0 units (no scheduled receipt for E) = 40 units.

Since E requires a multiple of 100 to be purchased, we release an order for 100 units of E.

Item F:

Item F is a component of B and C, and each B requires 1 unit of F, while each C requires 2 units of F.

We need to calculate the net requirements for F based on the planned order releases for B and C.

Period 1: Gross requirement for B = 10 units * 1 (requirement multiplier for F) = 10 units.

Period 3: Gross requirement for C = 40 units * 2 (requirement multiplier for F) = 80 units.

F has a lead time of two periods, so we need to account for that.

Net requirement for F in period 5: 10 units + 80 units - 0 units (no scheduled receipt for F) = 90 units.

Since F requires a multiple of 100 to be purchased, we release an order for 100 units of F.

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