There are 43 children at a school. they want to make teams with 8 children on each team for kickball. one of the children goes home. how many complete teams can they​ make? explain.

The typical method of solving this question... (School method)

The required value of the a, b, and c is 1, 18, and -3 respectively,

Given that,
The equation y=ax2+bx+c goes through the coordinates (-6, 15), (0, -3), and (2, 7). What are the values of a, b, and c is to be determined.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
In the given expression put x = 0 and y = -3 as ordered pair (0, -3).
-3 = 0 + 0 + c
c = -3
Similarly,
Put other ordered pair in the given equation and c from above to evaluate a and b as 1 and 18 respectively.

Thus, the required value of the a, b, and c is 1, 18, and -3 respectively,

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Answer: 1/50

Step-by-step explanation:

Step 1: We need to multiply the numerator and denominator by 100 since there are 2 digits after the decimal.

0.02 = (0.02 × 100) / 100

= 2 / 100 [ since 0.02 × 100 = 2 ]

Step 2: Reduce the obtained fraction to the lowest term

Since 2 is the common factor of 2 and 100 so we divide both the numerator and denominator by 2.

2/100 = (2 ÷ 2) / (100 ÷ 2) = 1/50

To determine how many scarves Maddie can make and still have at least 3.5 ounces of yarn left over, we can use division and subtraction.

First, we need to figure out how much yarn Maddie will use to make two pairs of mittens:

2 pairs of mittens x 2 mittens per pair x 2.25 ounces of yarn per mitten = 9 ounces of yarn

Next, we can subtract the amount of yarn needed for the mittens from the total amount of yarn Maddie has:

28.14 ounces of yarn - 9 ounces of yarn = 19.14 ounces of yarn remaining

Now, we can divide the remaining amount of yarn by the amount needed for each scarf to find out how many scarves Maddie can make:

19.14 ounces of yarn ÷ 5.25 ounces of yarn per scarf ≈ 3.64 scarves

Since Maddie can't make a fraction of a scarf, we need to round down to the nearest whole number. Therefore, Maddie can make 3 scarves and still have at least 3.5 ounces left over to make two pairs of mittens.

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Answer:

135

Step-by-step explanation:

if you think about it al cicle = 360 so its 360- 225= 135

The weight of the truck,  When a loaded truck pulls onto it, the boat sinks an additional 5.00cm into the river is  11,788 N.

To discover the weight of the truck, we ought to utilize the concept of buoyancy.

When the truck pulls onto the vessel, it uproots a sum of water that breaks even with its claimed weight. The weight of this uprooted water makes an upward buoyant constraint on the pontoon.

The watercraft sinks an extra 5.00 cm, which suggests that the buoyant constraint breaks even with the weight of the truck furthermore the weight of the uprooted water, and this adds up to the weight causing the boat to sink assist.

Let's accept that the thickness of water is 1000 kg/m³ (this can be ordinary esteem for new water). The volume of water uprooted by the pontoon is rise to its length times its width times the profundity it sinks into the water:

V = (6.00 m)(4.00 m)(0.05 m) = 1.20 m³

The weight of this uprooted water is:

Wwater = Vρg = (1.20 m³)(1000 kg/m³)(9.81 m/s²) ≈ 11,788 N

where ρ is the thickness of water and g is the speeding up due to gravity.

Since the buoyant drive is broken even with the weight of the truck furthermore the weight of the uprooted water, we have:

Wtruck + Wwater = Fbuoyant

where Wtruck is the weight of the truck and Fbuoyant is the buoyant drive. Ready to improve this condition to illuminate for the weight of the truck:

Wtruck = Fbuoyant - WWater

The buoyant drive is broken even with the weight of the water uprooted by the watercraft, which we calculated prior to being around 11,788 N. In this manner:

Wtruck = 11,788 N - 0

 Wtruck ≈ 11,788 N

So, the weight of the truck is around 11,788 N. 

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The full question is

A small ferryboat is 4.00m wide and 6.00m long. When a loaded truck pulls onto it, the boat sinks an additional 5.00cm into the river. What is the weight of the truck?

Answer:

4 radians

Step-by-step explanation:

Arc Length (Radians) = rθ

Given Arc Length XY  = 40cm and radius, r = 10cm,

we will substitute these 2 values into the formula to find θ.

(10)θ  = 40

θ = 40 / 10

= 4 radians

Answer:

A

Step-by-step explanation:

the length of arc XY is calculated as

arc = circumference of circle × fraction of circle

      = 2πr × \(\frac{0}{2\pi }\) ( r is radius and Θ is central angle )

here arc = 40 and r = 10 , then

2π × 10 ×\(\frac{0}{2\pi }\) = 40

20π × \(\frac{0}{2\pi }\) = 40 ( cancel 20π and 2π by 2π )

10Θ = 40 ( divide both sides by 10 )

Θ = 4 radians

Answer:

Step-by-step explanation:

You want the objective function, its maximum value, and the variable values that give that maximum based on the model shown in the graph.

The problem statement tells you the profit function is ...

  1.00x +1.50y . . . . . . objective function

Since the objective is to maximize profit, this is the objective function.

The integer values nearest the vertex of the feasible region farthest from the origin are (x, y) = (69, 70). These are the numbers of 'economy' and 'best' brushes that maximize the profit.

The maximum profit for these numbers of brushes will be ...

  p = x +1.5y = 69 +1.5(70) = 69 +105

  p = 174 . . . . maximum profit

The maximum profit of the situation is $174

From the question, we have the following parameters that can be used in our computation:

Profit function = $1 for x and $1.50 for y

This means that the objective function is

P(x, y) = x +1.5y

Also, the graph is given where we have:

Optimal point, (x, y) = (69, 70)

Substitute these points in the profit function

So, we have

P(x, y) = 69 +1.5 * 70

Evaluate

P(x, y) = 174

Hence, the maximum profit is $174

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Answer:

B

Step-by-step explanation:

You had a balance of $535.07 from the previous month and only paid $450.00 so you didn’t pay off your balance in full.

The smallest number of eggs that could have been in the box is 1134

The problem is to find the smallest number of eggs that could have been in the box, given the remainder when taking them out by different numbers. Here are the moves toward tackling it:

Allow n to be the quantity of eggs in the container. Then we have the accompanying arrangement of congruences:

n ≡ 1 (mod 2)

n ≡ 1 (mod 3)

n ≡ 1 (mod 4)

n ≡ 1 (mod 5)

n ≡ 1 (mod 6)

n ≡ 0 (mod 7)

For this problem, we have k = 6 k = 6, a i = {1,1,1,1,1,0} a_i = {1,1,1,1,1,0}, M i = {1260,840,630,504,420,720} M_i = {1260,840,630,504,420,720}, and y i = {−1,−2,−3,-4,-5,-6} y_i = {-1,-2,-3,-4,-5,-6}.

Plugging these values into the formula and simplifying modulo 5040, we get:

n = (−1260 + −1680 + −1890 + −2016 + −2100 + 0) mod 5040

n = (−8946) mod 5040

n = (−3906) mod 5040

n = 1134 mod 5040

Therefore, the smallest number of eggs that could have been in the box is 1134

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Answer:

Step-by-step explanation:

Because angle NRM is vertical to angle QRP, they are congruent. That means that arc NM is congruent to arc PQ, making arc MQ and arc NP congruent. That means that arc NP is also 162. Since the outside of a circle measures 360 regardless of how big or small the circle is, we can find the measures of arcs MN and PQ by doing some simple math.

Arc MN = Arc PQ = 360 - 162 - 162 = 36 and divide that in half to get

Arc MN = Arc PQ = 18°. As we all know, the measure of a central angle is congruent to the measure of the arc it intercepts, so the measure of angle NRM is 18°. That gives us the angle we need for the formula:

\(AL=\frac{\theta}{360}*2\pi r\) where θ is the measure of the central angle, 18°:

\(AL=\frac{18}{360}(3.1415)(8)\) which gives us

AL = 1.26 feet (Note: arc length is in distance measures, like feet, inches, meters, etc., while arc measure will always be in degrees!)

Answer:

2

Step-by-step explanation:

Answer:

B. Combine like terms

Step-by-step explanation:

Inside the parenthesis, they combined -2 and 6 to get a total of 4x

1.) 17x3-55

2.) 54x2-109+-3

3.) (−80+100)×−0.20

Answer:

16t + 10c > 110

Step-by-step explanation:

Cost of tutoring per hour = $16

So, cost of tutoring t hours = $16t

Cost of clearing tables per hour = $10

So, cost of clearing tables c hours = $10c

Since, Isaiah must earn at least $110 this week.

Therefore, the required inequality will be given as:

16t + 10c > 110

Answer:

When we have a rectangular point (x, y), the angle between the x-axis and a ray that connects the origin with this point is given by:

Tan(θ) = y/x.

Cos(θ) = x/(√(x^2 + y^2))

Sin(θ) = y/(√(x^2 + y^2))

So for the point (-4,3) we have:

x = -4

y = 3

√( (-4)^2 + 3^2) = √(16 + 9) = √25 = 5

Then:

Tan(θ) = 3/-4 = -(3/4)

Sin(θ) = 3/5

Cos(θ) = -4/5

And for the other 3 trigonometric functions (the inverses of the 3 above ones) we have:

Ctg(θ) = 1/Tan(θ) = -4/3

Csc(θ) = 1/Sin(θ) = 5/3

Sec(θ) = 1/Cos(θ) = -4/5

Answer:

3

Step-by-step explanation:

Unit conversion is a way of converting some common units into another without changing their real value. The number of pounds that Karen will get is £216.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

The amount that is left with Karen = $750 - $(95×5)

                                                          = $750 - $475

                                                          = $275

Now, since the Bank would only accept her money to the nearest 10 USD. Therefore, the amount that the bank will accept is $270.

Further, the exchange rate is  £1 = $1.25, therefore, the number of pounds that Karen will get in the number of dollars is,

Number of Pounds = £275/1.25 = £216

Hence, the number of pounds that Karen will get is £216.

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In our proof, as the trapezium are congruent and the rest of the sides are equal ∴AC = BD. Hence, the cyclic trapezium is isosceles and its diagonals are equal.

Step 1:

The diagonals are AC and BD, and the line CE is parallel to AD.

We know that a parallelogram's opposite angles are equal.

∠D = ∠AEC......(1)

We also know that the sum of a cyclic quadrilateral's opposite angles is 180 degrees.

∠D + ∠ABC = 180..........(2)

We can deduce from (1) and (2) that

AEC + ABC = 180....... (3)

AEC and CEB are now a linear pair.

AEC + CEB = 180................. (4)

We can conclude from (3) and (4) that,

CEB = ABC

The sides opposite the equal angles are also equal, as we know.

CEB = ABC

CE = CB ... (5)

However, because AECD is a parallelogram, opposite sides must be equal.

∴CE = AD ... .(6)

From equation (5) and (6), we can conclude that

AD = CB ......(7)

As a result, the cyclic trapezium ABCD is isosceles.

Step 2:

Establishing that its diagonals are equal.

We have AC and BD as diagonals.

In triangle DBA and CBA,AD = CB from (7)⇒AB = AB (common side).

ADB + ACB (angles in the same segment of a circle are equal). As a result of the SAS rule, ABD and ABC are congruent.

Because they are congruent and the other sides are equal, AC = BD. As a result, a cyclic trapezium is isosceles and has equal diagonals.

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The value of a is given by the third root of the function.

The function for this problem is defined as follows:

f(x) = x(x - 2)(x - a).

According to the Factor Theorem, the function is defined as a product of it's linear factors, hence the roots of the function are given as follows:

Hence the value of a is the third root of the function, which is the value on the graph at which the function crosses the x-axis along with x = 0 and x = 2.

The problem is incomplete, hence the general procedure to obtain the value of a is presented.

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Answer:

f(2) = 32

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define

f(x) = 3x² + 2x + 16

f(2) is x = 2

Step 2: Evaluate

And we have our answer!

The probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 90 inches, and a standard deviation of 14 inches.

z score is given by,

z = (x - μ)/(σ/√n) = (92.8 - 90)/(14/√49) = 2.8/2 = 1.4

The  required probability is,

p(z < 1.4) = 0.9192, by standard normal table.

Hence, the  probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is,  0.9192.

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Central tendency, is the term that relates to the way data tend to cluster around some middle or central value.

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution. Mode in statistics is the number of times a number is repeated. The number which is repeated maximum times in a series of data is known as the modular number. The mode is used to compare data that has extreme figures. Central tendency simply means most scores in a normally distributed set of data tend to cluster near the center of a distribution.

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It should be noted that to determine whether an angle with an unknown measure is acute, obtuse, or right, you need to measure the angle or know its degree measure.

Here are the definitions of each type of angle:

Acute angle: an angle that measures less than 90 degrees

Obtuse angle: an angle that measures greater than 90 degrees but less than 180 degrees

Right angle: an angle that measures exactly 90 degrees

Once you have the degree measure of the angle, you can determine its type using the following rules:

If the angle measures less than 90 degrees, it is acute.

If the angle measures exactly 90 degrees, it is a right angle.

If the angle measures between 90 and 180 degrees, it is obtuse.

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Answer:

slope: -3; y-intercept: (0,15)

Step-by-step explanation:

The slope is -3, simply move 3x to the right side for slope intercept form, the y-intercept is where x =0 so set x equalt to zero. 3(0)+y=15, y=15

Answer:

The answer is D 1/8th

Step-by-step explanation:

The theoretical propability is 50% of the time, he only flipped heads 3/8 of the time. Comparing the two fractions we get this-

3/8 = 0.375

1/2 = 0.5

Add 1/8th and we have a 50 percent chance!

Enjoy!

It gradually decreases as alcohol is metabolized. The function C(t)=0.135 t e^{-2.802 t}models the mean BAC measured in g/mL.

The maximum average BAC during 3 hours is 0.0001358 g/mL.

f(t) = α t e−βt --(1)

Let's rewrite this in a simple form:

f(t)= α eˡⁿ ᵗ e⁻βt = αe^(ln t −βt)

Since e^x is strictly increasing and it will be maximized exactly when its argument is maximized, so we can maximize instead:

g(t)=ln t −βt

differentiating with respect to t , and g'(t) = 0

g′(t)=1/t − β = 0

=> t =1/β

we have given a function

C(t)=0.135 t e⁻²·⁸⁰²ᵗ

if we compare it with (1) we get

β = 2.802, 0.135 = α

For it's maximized we need to check the second order condition, and that of g will differentiate again , g′′(t)= −1/t² < 0

We have to compute the derivative of C(t):

C′(t) = 0.135 t⋅(−2.802)e⁻²·⁸⁰²ᵗ + 1.35e⁻²·⁸⁰²ᵗ

For optimum at t₀ if C′(t₀)=0 and C′′(t₀)≠0. Here, we have

C′(t₀) = 0.135t₀⋅(−2.802)e⁻²·⁸⁰²ᵗ₀+ 0.135e⁻²·⁸⁰²ᵗ₀ =e⁻²·⁸⁰²ᵗ₀(−0.135* 2.802t₀+ 0.135)=0

It is clear that e⁻²·⁸⁰²ᵗ₀ not equal to zero for all t₀∈R, so that

=> −0.135* 2.802t₀+0.135=0

=> t₀ = 1/2.802 ≈0.36

let us consider t is in hours, so that it makes t₀ =0.36h≈21.41min. This is the only optimum and one should verify it is indeed a maximum, i.e. C′′(t₀)<0.

Now, easily compute the maximum average BAC, which is C(t₀)=C(0.36) = 0.135 (0.36)e⁻²·⁸⁰²⁽⁰·³⁶⁾

= 0.0486(0.3678) = 0.01787508

Hence, the maximum average BAC, is 0.017 g/dL.

Maximum average BAC during the first 3 hours,

t = 3 , C(t)=C(3) = 0.135 (3)e⁻²·⁸⁰²⁽³⁾ = 0.0001358 g/mL

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The amount of money that you will have in eight years from today is $29,315.79 (rounded to 2 decimal places).

To find out the amount of money that you will have in eight years, you need to use the future value formula, which is:FV = PV × (1 + r)n

Where, FV = future value

PV = present value (initial investment) r = annual interest rate (as a decimal) n = number of years

First, you need to find the future value of the gift amount of $17,000 in two years.

Since it's a gift and not an investment, we can assume an interest rate of 0%.

Therefore, the future value would simply be:

PV = $17,000r = 0%n = 2 years

FV = $17,000 × (1 + 0%)2FV = $17,000

Now, you will loan that amount at 9.75% interest for six more years.

So, you need to find the future value of $17,000 after 6 years at an annual interest rate of 9.75%.

PV = $17,000

r = 9.75%

n = 6 years

FV = $17,000 × (1 + 9.75%)6

FV = $29,315.79

Therefore, the amount of money that you will have in eight years from today is $29,315.79 (rounded to 2 decimal places).

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Answer:

We can start by isolating the variable "h".

5 8 h + 1 1 2 = 5

Subtracting 11/2 from both sides:

5 8 h = 5 - 1 1 2

Simplifying:

5 8 h = 8 1 2

Dividing both sides by 5/8:

h = 8 1 2 ÷ 5 8

Converting the mixed number to an improper fraction:

h = (8 x 8 + 1) ÷ 5 8

h = 65/8

Now, we can convert this fraction to a mixed number:

h = 8 1/8

Brigid has already picked for 8 1/8 hours, so the amount of time needed to pick the remaining strawberries is:

5 - (1 1/2 + 5/8 x 8) = 5 - (3 5/8) = 1 3/8

Therefore, Brigid still needs to pick for 1 3/8 hours to fill 5 bushels of strawberries. The answer is 1 and 3/8 hours or 2 and 3/16 hours (if simplified).

Step-by-step explanation:

Answer:

1. A

2. C

Step-by-step explanation:

1. A

2. C

Answer:

B, F, G

Step-by-step explanation:

Answer:

B, F, G

Step-by-step explanation: