mr crates, the principal at a local middle school, made a rule that there must be 1 adult for every 4 students attending a feild trip.

Answer:

Step-by-step explanation:

Answer:

[tex]a_1=-4, \,a_n=a_{n-1}+4[/tex]

Step-by-step explanation:

Clearly, our common difference is [tex]d=4[/tex], and we can see that the first term if we work backward from [tex]a_4[/tex] is [tex]a_1=-4[/tex].

Hence, by using the recursive formula [tex]a_n=a_{n-1}+d[/tex], we have our final formula as [tex]a_n=a_{n-1}+4[/tex]

Answer: B

Step-by-step explanation:

"When students are taking a test, they should keep their eyes on their own paper" is grammatically correct and the best sounding out of the others.

The total amount of money Jose made on 5 shares is given by the equation A = $ 101.70

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of money Jose made on 5 shares be A

Now , the equation will be

The amount at which Jose buys the share = $ 114.95

The amount at which Jose sells the share = $ 135.29

So , the amount of money Jose made = amount at which Jose sells the share - amount at which Jose buys the share

Substituting the values in the equation , we get

The amount of money Jose made = $ 135.29 - $ 114.95

On simplifying the equation , we get

The amount of money Jose made = $ 20.34

Now , the amount of money Jose made on 5 shares = 5 x amount of money Jose made

On simplifying the equation , we get

The amount of money Jose made on 5 shares A = 5 x 20.34

The amount of money Jose made on 5 shares A = $ 101.70

Hence , the amount of money Jose made is $ 101.70

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The number of 3-digit numbers that can be formed is: 216.

The numbers that are less than 500 is: 120.

The number of 3-digit numbers that can be formed from the digits 2, 3, 4,5, 6 and 9 is calculated as:

6 * 6 * 6 = 216

This is because each digit can be chosen from the six available digits in 6 ways.

Out of these 216 numbers, those that are less than 500 have the hundreds digit equal to 2, 3, 4, or 5, and the first two digits can be chosen from any of the available digits in any order.

So, there are 4 * 6 * 5 = 120 numbers less than 500.

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For the function y = ( x² + 5 )² and x = 2 and dx = 0.3 then the value of differential dy is equal to 21.6.

y = (x² + 5)²

Calculate the differential dy with respect to x  we get,

dy / dx = d /dx (x² + 5)²

⇒ dy / dx = 2 ( x² + 5 )²⁻¹ × ( 2x )

⇒ dy = 4x ( x² + 5 ) dx

Now substitute the value of  x = 2, and dx = 0.3 to get the value of differential dy we get,

dy = 4( 2 ) ( 2² + 5 ) ( 0.3 )

⇒ dy = 8 × 0.3 × ( 9 )

⇒ dy = 21.6

Therefore, the value of the differential function dy for the function          y = ( x² + 5 )²  is equal to 21.6.

The above question is incomplete, the complete question is :

Let y = (x² + 5)². find the differential dy when the value of x = 2 and dx = 0.3.

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The probability that one selects a green marble and then a yellow marble from a bag of 3 red, 1 green, and 3 yellow marbles without replacement is 7.15%.

Probability refers to the chance or odds of making a selection with an expected outcome.

In probability, many possible outcomes are being considered with an expected event.

The number of red marbles = 3

The number of green marbles = 1

The number of yellow marbles = 3

The odds of selecting a green marble = 1/7

The likelihood of selecting a red marble = 3/7

The chance of selecting a yellow marble = 3/7

The probability of selecting a green (1/7) and then a yellow without replacement (3/6) = 0.0715 (0.143 x 0.5)

= 7.15%

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Answer:

second option

Step-by-step explanation:

vertical angles are situated opposite each other at a vertex. For this reason they are often called vertically opposite angles.

from the diagram the vertical angles opposite to each other at vertex E are

∠ 1 ≅ ∠ 3 and ∠ 2 ≅ ∠ 4

Answer:

∡1 ≅ ∡3 and ∡2 ≅ ∡4

Explanation:

Definition of vertical angles: Each of the pairs of opposite angles made by 2 intersecting lines.

By definition, vertical angles are on opposite sides of the intersection, and are always equal.

Since the pairs ∡1,∡3 and ∡2,∡4 are on opposite sides of the intersection, they are equal.

Proof for the Vertical Angles Theorem:  https://www.cuemath.com/geometry/vertical-angles/

Answer:

When you rotate a figure around a center point other than the origin, the resulting image is translated or shifted from the original figure's position. This happens because the center of rotation affects the position of the figure after the rotation is performed.

If you rotate a figure around a center point that is not the origin, the figure will still undergo a rotation, but the position of the rotated figure will depend on the location of the center point. The center point of rotation acts as a pivot point and determines the new location of the rotated figure.

In summary, rotating a figure around a center point other than the origin will result in a translated image that is shifted from the original position of the figure. The amount of translation will depend on the location of the center of rotation.

Answer:

between D and A of it might be c

The amount of money that Lisa would have after 9 years is equal to $5,183.2.

Mathematically, compound interest can be calculated by using this formula:

A(t) = P(1 + r/n)^{nt}

Where:

Substituting the given parameters into the compound interest formula, we have;

Future value, A(t) = 4,000(1 + 0.029/2)^{2 × 9}

Future value, A(t) = 4,000(1 + 0.0145)^{18}

Future value, A(t) = 4,000(1.0145)^{18}

Future value, A(t) = 4,000(1.2957968642629875)

Future value, A(t) = $5,183.2.

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The p-value is less than 0.01 so we reject the null hypothesis.

Formulating Hypotheses:

Whenever formulating the null and alternative hypotheses, we also consider that the null hypothesis is true. Therefore, it is always a statement of equality and by definition, the alternative hypothesis is contrary to the null hypothesis.

Null hypothesis

H0: σ1² ≤ σ2²

Alternative hypothesis

H1: σ1² > σ2²

We have the level of significance = 0.01

Test statistic

F = S1²/S2²

F= 170²/100²

F= 28900/10000

F = 2.89

Df = degrees of freedom

Df1 = n1 - 1

= 26-1

Df1= 25

Df2 = n2 - 1

= 25-1

DF2= 24

B. We get the p-value using the f distribution

Fdist(2.89,25,24)

P value = 0.0057

The p-value is less than 0.01 so we reject the null hypothesis.

So we can conclude that automobiles that are of 4 years have variances larger In annual repair costs than those that are of 2 years.

Reasonableness: we expect this since 4byears old automobiles are more likely to have more expenses during repair leading to greater variances.

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Answer: jasmine

Step-by-step explanation: this problem is actually pretty easy when you solve it!

all you have to do is divide 8 by 10 to find Joe’s rate, which would be 2 songs per min

then divide 12 by 15 to find jasmines rate which would be .8 songs per minute!

so because Jasmine download songs at a rate of .8 songs per minute, Jasmine is faster.

Answer:

Juan can fill 4 mugs.

Step-by-step explanation:

Take the total amount of hot chocolate and divide by the amount each mug will hold.

1/2 ÷ 1/8

Copy dot flip.

1/2 * 8/1

8/2

4

Juan can fill 4 mugs.

Answer:

4 mugs

Step-by-step explanation:

If each mug holds 1/8 of a quart, and Juan has 1/2 of a quart of hot chocolate, then he can fill:

[tex]\sf:\implies{1/2 ÷ 1/8 = 4 \: mugs.}[/tex]

So, Juan will be able to fill 4 mugs.

The rate for a ratio of the two different quantities is; ¹⁸/₃ puppies per liter

Two quantities can be referred to as proportional provided that they can be represented in the general form y = kx,

where k is a constant of proportionality

Now, we have the parameters as;

Number of Puppies = 18 puppies

Number of Litters = 3 litters

Thus, the rate for the ratio between the two quantities is expressed as;

18 puppies/3 Litters

= ¹⁸/₃ puppies per liter

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The equation is 2000=5[tex](L-10)^{2}[/tex] to find the dimensions of the original cardboard piece.

If she is using a square piece of cardboard, then have in mind that we are dealing with a square of unknown length "L".

Now, consider that you are removing from each corner of that square a smaller square of surface 5 . Once the small 5 in size square pieces are cut, the four flaps that are left (see attached image) are bent through the lines pictured in grey so they form the final box.

Notice that the dimensions of this box will be:

Notice as well that the height of the box will be exactly 5 inches (the length of the square cutting).

⇒Volume of the box =Length*Breadth*Height.

⇒2000=(L-10)*(L-10)*5

⇒2000=5[tex](L-10)^{2}[/tex]

Therefore, the equation is 2000=5[tex](L-10)^{2}[/tex] to find the dimensions of the original cardboard piece.

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The perimeter of shed is, (6x+ 4)

The area of the shed is, (2x² + 5x + 3)

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

Shirley is building a shed. The length is 2x + 3 feet long and the width is

x + 1 feet long.

Now, We know that;

The perimeter of rectangle = 2 (Length + Width)

Substitute all the values, we get;

⇒ Perimeter = 2 (2x + 1 + x + 1)

⇒ Perimeter = 2 (3x + 2)

⇒ Perimeter = (6x + 4)

And, Area of rectangle = Length × Width

Substitute all the values , we get;

⇒ Area = (2x + 3) × (x + 1)

⇒ Area = (2x² + 2x + 3x + 3)

⇒ Area = (2x² + 5x + 3)

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A simple method for adding and subtracting fractions with unlike denominators:

Find a common denominator: The first step is to find a common denominator that is a multiple of both denominators. The smallest common denominator is usually the least common multiple (LCM) of the two denominators.

Convert the fractions to equivalent fractions with the common denominator: Once you have a common denominator, you can convert each fraction to an equivalent fraction with the same denominator by multiplying the numerator and denominator by the same number.

Add or subtract the numerators: Once both fractions have the same denominator, you can add or subtract the numerators to get the numerator of the resulting fraction.

Simplify the resulting fraction: Finally, simplify the resulting fraction by dividing both the numerator and denominator by their greatest common factor, if possible.

Here is an example:

To add 1/3 + 1/4, we first find a common denominator:

The LCM of 3 and 4 is 12, so we multiply both the numerator and denominator of each fraction by 4 to get 12/12 as the common denominator:

1/3 * 4/4 = 4/12

1/4 * 3/3 = 3/12

Next, we add the numerators:

4/12 + 3/12 = 7/12

Finally, we simplify the fraction:

7/12 = (7 ÷ 1) / (12 ÷ 1) = 7/12.

So the result is 7/12.

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The length of x to the nearest 10th of an inch is 7.1 inches.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

We have law of sine of triangle, which states that,

sin X / x = sin Y / y = sin Z / z

where X, Y and Z are three angles of a triangle and x, y and z are the sides opposite to X, Y and Z respectively.

Using this,

Sin V / v = Sin W / w = Sin X / x

Given that, m ∠V = 76° and m ∠W = 44°

m ∠V + m ∠W + m ∠X = 180°

76° + 44° + m ∠X = 180°

m ∠X = 180° - ( 76° + 44° )

m ∠X = 60°

Also, given that, v = 7.9 inches

Sin V / v = Sin X / x

sin (76°) / 7.9 = sin (60°) / x

x = [sin (60°) × 7.9] / sin (76°)

x = [0.866 × 7.9] / 0.970

x = 7.051 ≈ 7.1

Hence the length of the x is 7.1 inches to the nearest 10th of an inch.

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Answer:

Expression: 0.75m + 4.50

$8.25

Step-by-step explanation:

0.75m + 4.50

0.75(5) + 4.50

3.75 + 4.50

8.25

The diameter of the middle shelf is solved using similar triangle to get

The middle shelf is in the mid segment hence Using the concept of similar triangle the proportions are as follows

The proportions

1 / 2 = x / 15

cross multiplying

15 = 2x

rearranging the equation

2v = 15

isolating x by dividing through by 2

2v / 2 = 15 / 2

x = 7 1/2

x = 7.5

The diameter of the middle shelf is equal to x which is calculated to be 7.5

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If A is a m × n matrix, with columns a1, . . . , an, and if b is in R

m,

then the matrix equation

Ax = b

has the same solution set as the vector equation

x1a1 + x2a2 + · · · + xnan = b

which, in turn, has the same solution set as the system of linear

equations whose augmented matrix is

a1 a2 · · · an b.

The equation Ax = b is consistent if−2b1 + b3 = 0.

(equation of a plane in R3)

x1a1 + x2a3 + x3a3 = b

if and only if b3 − 2b1 = 0.

Columns of A span a plane

in R3 through 0

Instead, if any b in R3

(not just those lying on a particular line or

in a plane) can be expressed as a linear combination of the

columns of A, then we say that the columns of A span R3

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The probability that in the next ten days, exactly three are rainy days will occur is 0.25028.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%

Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

The formula for probability states that the possibility of an event happening, or P(E), equals the ratio of the number of favorable outcomes to the number of total outcomes. Mathematically, it looks like this: P(E) = favorable outcomes/total outcomes​

Probability p of a rainy day is 0.25

Using binomial theorem,

The Probability that in the next ten days, exactly three are rainy days will occur:

= 10c₃  p³(1-p)¹⁰⁻³

= 10c₃  (0.25)³(0.75)⁷

= 0.25028

Thus, The probability that in the next ten days, exactly three are rainy days will occur is 0.25028.

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Answer: 120 inches cubed

Step-by-step explanation:

There are 214 distinct paths from (-1,2,0) to (1,3,7) in Euclidean three-space.

We can approach this problem using a combinatorial approach.

Let's say that there are a total of n moves from the starting point (-1,2,0) to the ending point (1,3,7). Then, the number of H moves is nh, the number of V moves is nv, and the number of A moves is na, where nh + nv + na = n.

The starting point (-1,2,0) is (1,1,7) moves away from the ending point in the x, y, and z directions, respectively. Therefore, we have the following constraints:

   nh ≥ 1 (to move from x = -1 to x = 1)

   nv ≥ 1 (to move from y = 2 to y = 3)

   na ≥ 7 (to move from z = 0 to z = 7)

The number of distinct paths from (-1,2,0) to (1,3,7) is simply the number of ways to choose nh, nv, and na moves from n total moves such that the constraints are satisfied. This is equivalent to finding the number of solutions to the equation nh + nv + na = n subject to the constraints.

Using the stars and bars technique, the number of solutions can be calculated as:

C(n - 1, 2) = C(n - 1, n - 3) = C(n - 1, na - 1)

where C(n, k) is the binomial coefficient representing the number of ways to choose k items from a set of n items.

Since na ≥ 7, we can start by setting na = 7 and then increasing it by one to see if there are additional solutions. For na = 7, n = 7 + nh + nv. Therefore, n >= 8 and n <= 14. The number of solutions for each value of n can be calculated using the formula above, and the total number of solutions can be obtained by summing up the results for each value of n.

For example, when n = 8, there are C(7, 2) = 21 solutions, when n = 9, there are C(8, 2) = 28 solutions, and so on. The final answer is the sum of all the solutions, which is:

21 + 28 + 35 + 35 + 28 + 21 + 13 + 6 = 214

Therefore, there are 214 distinct paths from (-1,2,0) to (1,3,7) in the Euclidean three-space.

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The limit of this expression as δt approaches zero is 7t5

The limit is a concept in mathematics that represents the value that a function approaches as the input approaches a certain value.

To find the limit, we will simplify the expression and cancel out δt wherever possible.

First, we can simplify the expression inside the parentheses,

=> (t+δt)2 − 7(t+δt) 5.

We can rewrite this as

=> (t2x δt2) - (7 x t5 x δt).

Then, we can simplify the second part of the expression,

=> (δt x t2) - (δt * 7t5)

Finally, we can subtract these two expressions and simplify further,

=> (t2 x δ t2) - (7 x t5 x δ t) - (δt x t2) + (δt * 7t5).

Since δt is a small value that approaches zero, we can assume that delta t2 approaches zero.

This means that we can simplify the expression to

=> δt * 7t5.

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Answer:

10q + 5

Step-by-step explanation:

6q+7-2+4q

=10q+5

:]

Hope this helps

The gradiant of the line which passes through the given points is 1

A straight line's steepness may be determined by looking at its gradient. A line's gradient does not have to be a whole integer and might be positive or negative.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two separate locations on a line is calculated using the slope of a line formula.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

The points on the line :

x: -5, -4, -3, -2, -1

y : 1,2,3,4,5

The gradiant of the line :

(y₂ - y₁)/(x₂ - x₁) = (5 - 4)/(-1 + 2) = 1

The gradiant of the line which passes through the given points is 1

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The distance between two points A (3, 2) and B (9, 7) is [tex]\sqrt{61}[/tex] units.

The midpoint between a celestial body's greatest and smallest separations from its primary.

The metre is the SI unit for distance (m). Long distances can be measured in kilometres, whereas little distances can be gauged in millimetres (cm) (km).

For instance, you might measure the distance in centimetres between the bottom and top of a piece of paper and the kilometres between your home and school.

You are a long way from anything in space or time if you are far away from it, cannot see it, or cannot recall it.

I need to keep my mum at a distance if I want to manage.

Distance between P and Q if two points are given P([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and Q([tex]x_{2}[/tex], [tex]y_{2}[/tex]) , PQ = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Given:

A (3,2) and B (9,7) are the two points in a plane. We have to find the distance between A and B. Here, [tex]x_{1}[/tex] = 3, [tex]x_{2}[/tex] = 9, [tex]y_{1}[/tex] = 2 and [tex]y_{2}[/tex] = 7.

AB = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

AB = [tex]\sqrt{(9 - 3)^2 + (7 - 2)^2}[/tex]

AB = [tex]\sqrt{(6)^2 + (5)^2}[/tex]

AB = [tex]\sqrt{36 + 25}[/tex]

AB = [tex]\sqrt{61}[/tex] units.

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Cost of 9 miles ride = $19.25

Cost of m miles ride = $3.50 + $1.75m

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Taxi charges $3.50 for pickup and $1.75 per mile.

Total charges can be expressed as

y = $3.50 + $1.75m

where m is the  number of miles

For 9 miles

cost y = $3.50 + $1.75×9

          = $3.50 + $15.75

          = $19.25

Hence, $19.25 will cost for 9 miles ride

For m miles ride will cost $3.50 + $1.75m.

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