a random sample of teenagers were surveyed about their favorite sport. the bar graph below displays their responses. which of the following statements is correct?

Step-by-step explanation:

y = ax^n + bx^(n-1) ... + z

(0, 1) tells us that the constant term z = 1.

because x = 0 eliminates all other terms. and as the sum is 1, that means z = 1.

for the other pairs I strongly suspect

(-1, 3) : 2×(-1)² + 1 = 2×1 + 1 = 3

(-2, 9) : 2×(-2)² + 1 = 2×4 + 1 = 9

so, the fitting equation is

y = 2x² + 1

Answer:

14+14 + 4pi= 28 + 4pi

\(\pi\)

answer is 170

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

50% of 850 = 425

30% of 850 = 255

425 + 255 = 680

850 - 680 = 170

There are 170 kg mass of parsnips left after distributing to the local market and local supermarket.

To calculate the mass of parsnips left after distributing them to the local market and the local supermarket, we need to subtract the quantities allocated to these places from the total harvest.

The farmer harvested 850 kg of parsnips.

30% of the harvest goes to the local market, which is (30/100) * 850 kg = 0.3 * 850 kg = 255 kg.

50% of the harvest goes to the local supermarket, which is (50/100) * 850 kg = 0.5 * 850 kg = 425 kg.

To find the mass of parsnips left, we subtract the quantities allocated to the market and supermarket from the total harvest:

Total harvest - (Quantity for market + Quantity for supermarket)

= 850 kg - (255 kg + 425 kg)

= 850 kg - 680 kg

= 170 kg.

Therefore, there are 170 kg of parsnips left after distributing to the local market and local supermarket.

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The number of roots of the equation 1/x = x² + 1 is given as follows:

One.

The number of solutions of the system of equations is given by the number of times which the two functions intersect.

When the two functions intersect, we have that:

1/x = x² + 1

Hence:

1/x  - (x² + 1) = 0.

Which is the number of roots of the equation.

From the graph, the two functions intersect at one point, hence the number of roots is of one.

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Answer:

6/7 x 21 = 18

Answer:

the answer is 18 hope this helped :)))

Step-by-step explanation:

\( - 3(2x + 4) + 4x = 3x + 10\)

or,

\( - 6x - 12 + 4x = 3x + 10\)

or,

\( - 12 - 10 = 3x + 6x - 4x\)

or,

\( - 22 = 5x\)

or

\( - 22 \div 5 = x\)

or

\(x = - 22 \div 5 \: \: ans\)

The general Solution to the differential equation is

\(y(t) = y_h(t) + y_p(t) = c_1e^{7t} + c_2e^{-3t} + (1/25)e^{-3t}e^{4t}\)

To find the general solution to the differential equation\(y'' - 4y' - 21y = e^{-3t}e^{4t}\)

First, we find the homogeneous solution to the differential equation by solving the characteristic equation:

\(r^2 - 4r - 21 = 0\)

The roots of this quadratic equation are:

r = 7, -3

So the homogeneous solution is:

\(y_h(t) = c_1e^{7t} + c_2e^{-3t}\)

Next, we find a particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients and assume a particular solution of the form:

\(y_p(t) = Ae^{-3t}e^{4t}\)

Taking the derivatives of this function, we get:

\(y_p'(t) = (-3A + 4Ae^{-3t})e^{4t}y_p''(t) = (9A - 24Ae^{-3t} + 16Ae^{-6t})e^{4t}\)

Substituting these derivatives and the assumed form of y_p(t) into the original differential equation, we get:

\((9A - 24Ae^{-3t} + 16Ae^{-6t})e^{4t} - 4(-3A + 4Ae^{-3t})e^{4t} - 21Ae^{-3t}e^{4t} = e^{-3t}e^{4t}\)

Simplifying this equation, we get:

\((25A - 24)e^{4t} = e^{-3t}e^{4t}\)

So, we have:

A = 1/25

Therefore, the particular solution is:

\(y_p(t) = (1/25)e^{-3t}e^{4t}\)

Thus, the general solution to the differential equation is

\(y(t) = y_h(t) + y_p(t) = c_1e^{7t} + c_2e^{-3t} + (1/25)e^{-3t}e^{4t}\)

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The simplified expression is a⁸b¹²c⁴.

To simplify the expression (a³b¹²c²)(a⁵c²)(b⁵c⁴)⁰, we can use the following rules of exponents:

1. When multiplying terms with the same base, we add the exponents.

2. Any term raised to the power of 0 is equal to 1.

Using these rules, let's simplify the expression step by step:

(a³b¹²c²)(a⁵c²)(b⁵c⁴)⁰

First, let's simplify the term (b⁵c⁴)⁰:

Since any term raised to the power of 0 is equal to 1, we have:

(b⁵c⁴)⁰ = 1

Now we have:

(a³b¹²c²)(a⁵c²)(1)

Next, let's multiply the terms with the same base by adding the exponents:

a³ * a⁵ = a⁽³⁺⁵⁾ = a⁸

b¹² * 1 = b¹²

c² * c² = c⁽²⁺²⁾ = c⁴

Putting it all together, we get:

(a³b¹²c²)(a⁵c²)(b⁵c⁴)⁰ = a⁸ * b¹² * c⁴ * 1 = a⁸b¹²c⁴

Therefore, the simplified expression is a⁸b¹²c⁴.

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Answer:

We know the diameter is 3 inches. We need the radius to find the area. By dividing the dimater by 2, we get the radius of 1.5 inches. The answer is 7 inches squared.

Brainliest would be great.

Answer:

6x+12y

Step-by-step explanation:

I hope this helps, and STAYYY!!!!!! Fresh!

Answer:

55/7 in simplest form is 7 6/7

Answer:

8/3

Step-by-step explanation:

If we multiply it the subtraction will cut off and 8 will mulitply to 8/3.

Answer:

The Value of Payments is  P18,557.15

Step-by-step explanation:

The quarterly payment is an annuity payment.

Use the following formula to calculate the present value of the payments.

PV of Annuity = Annuity Payment x ( 1 - ( 1 + interest rate )^-Numbers of periods ) / Interest rates

Where

Annuity Payment = Quarterly payment = P1,300

Interest rate = 5.12% x 3/12 = 1.375%

Numbers of periods = 4 years x 12/3 = 16 quarters

PV of Annuity = Value of Payments  = ?

Placing values in the formula

Value of Payments = P1,300 x ( 1 - ( 1 + 1.375% )^-16 ) / 1.375%

Value of Payments =  P18,557.15

9514 1404 393

Answer:

  4.17 hours

Step-by-step explanation:

The speed of light is about 670,616,629.4 miles per hour, so the travel time to Neptune is ...

  (2,798,842,000 mi)/(670,616,629.4 mi/h) ≈ 4.17 h

It takes about 4.17 hours for light to travel from the sun to Neptune.

Answer:

The probability that a randomly selected group of four trees can be used as timber is 4.5 × 10⁻⁵

Step-by-step explanation:

The given parameters are;

Mean = 34 cm

The standard deviation = 8 cm

The mean

The Z score is \(Z=\dfrac{x-\mu }{\sigma }\), which gives;

For x  = 30 we have;

\(Z=\dfrac{30-34 }{8 } = -0.5\)

P(x>30) = 1 - 0.30854 = 0.69146

For x = 40, we have

\(Z=\dfrac{40-34 }{8 } = 0.75\)

P(x < 40) = 0.77337

Therefore, the probability that the mean of four trees is between 30 and 40 is given as follows;

P(30 < x < 40) = 0.77337 - 0.69146 = 0.08191

The probability that a randomly selected group of four trees can be used as timber is given as follows;

Binomial distribution

\(P(X = 4) = \dbinom{4}{4} \left (0.08191\right )^{4}\left (1-0.08191 \right )^{0} = 4.5 \times 10^{-5}\)

Answer:

9 3/5

Step-by-step explanation:

4 cups is 8 times the amount, so multiply 1 1/5 by 8 which gets you to 9 3/5

hope this helps

Answer:

40cm

Step-by-step explanation:

A box is normally in the shape of a cube

formula of volume of a cube;

We want to find the height(tallness)

Volume=LengthxWidthxHeight

10000=25x10xHeight

10000=250H. (divide both side by 250 to remain with H only)

10000/250=250H/250

40cm=Height

Answer:

Alternate Interior- 9 and 7, 13 and 3, 8 and 10, 14 and 4

Alternate Exterior- 11 and 5, 6 and 12, 2 and 16, 1 and 15

Corresponding Angles - 6 and 10, 5 and 9, 11 and 7, 12 and 8, 2 and 14, 15 and 3, 1 and 13, 16 and 4

Vertical Angles- 13 and 15, 14 and 16, 1 and 3, 4 and 2, 5 and 7, 6 and 8, 9 and 11, 10 and 12

The probability of getting either 1 or 6 more than two times is P(T)=121/1296

To find the probability we use the binomial distribution.

Here we have 4 independent experiments. Each time, the sample space is (1,2,3,4,5,6) so the prob of getting a 6 is 1/6.

so p=1/6

prob of coming 6 and q= 1-p = 1-(1/6)=5/6

prob of not coming 6 is 5/6

p= prob of success. here our success event is getting 6

q= prob of failure. here our failure event is not getting 6

no of trials n=4

now using the binomial distribution formula:

ncr(p)^n(1-p)^r

here we want at least two 6, desirable outcomes are two 6 or three 6, or four 6 because at least two 6 doesn't mean that we can't get more than two 6 .

so r in these cases take the value of 2,3,4 respectively.

so for r=2

c(4,2)*(1/6)^2*(5/6)^2

P(A)=  150/1296

for r=3

c(4,3)*(1/6)^3*(5/6)^1

P(B)= 20/1296

for r = 4

c(4,4)*(1/6)^4*(5/6)^0

P(C)= 1/1296

here we will add these prob ..Getting two 6 fulfills our condition so we will stop and calculate the prob and keep it aside

now adding these we get P(T)=P(A)+P(B)+P(C).

(150/216) +(20/216) + (1/216)

P(T)= 171/1296

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Based on the given information, the estimate for the number of cells in a T75 flask can be calculated by comparing the number of cells in the picture to the field of view area and then scaling it up to the size of the T75 flask.

Given that there are 55 cells in the picture, we can use this information to estimate the density of cells in the field of view. The field of view has dimensions of 1.85 mm x 1.23 mm, which gives an area of 2.7095 square millimeters (\(mm^2\)). To calculate the cell density, we divide the number of cells (55) by the area (2.7095 \(mm^2\)), resulting in an approximate cell density of 20.3 cells per \(mm^2\).

Now, to estimate the number of cells in a T75 flask, we need to know the size of the flask's growth area. A T75 flask typically has a growth area of about 75 \(cm^2\). To convert this to \(mm^2\), we multiply by 100 to get 7500 \(mm^2\).

To estimate the number of cells in the T75 flask, we multiply the cell density (20.3 cells/\(mm^2\)) by the growth area of the flask (7500 \(mm^2\)). This calculation gives us an approximate estimate of 152,250 cells in the T75 flask. It's important to note that this is just an estimate, and actual cell counts may vary depending on various factors such as cell size, confluency, and experimental conditions.

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Given:

The pair of expressions in the options.

To find:

The pair that shows equivalent expressions.

Solution:

We have,

\(2\left(\dfrac{2}{5}x+2\right)\)

By using distributive property, we get

\(2\left(\dfrac{2}{5}x+2\right)=2\left(\dfrac{2}{5}x\right)+2(2)\)

\(2\left(\dfrac{2}{5}x+2\right)=\dfrac{4}{5}x+4\)

So, option A is incorrect and option B is correct.

We have,

\(2\left(\dfrac{2}{5}x+4\right)\)

By using distributive property, we get

\(2\left(\dfrac{2}{5}x+4\right)=2\left(\dfrac{2}{5}x\right)+2(4)\)

\(2\left(\dfrac{2}{5}x+4\right)=\dfrac{4}{5}x+8\)

So, options C and D both are incorrect.

Therefore, the correct option is B.

The correct pair of equivalents expressions is B.

To solve the question, one must have knowledge about the multiplication of expressions.

When you have an expression being multiplied by a value, you multiply all the terms of the expression by that value, so that:

                                     \(a (x + y) = ax + ay\)

Thus, performing this multiplication for all alternatives we have:

a) \(2 (\frac{2}{5}x + 2) = \frac{4}{5}x + 4\)

b) \(2 (\frac{2}{5}x + 2) = \frac{4}{5}x + 4\)

c) \(2 (\frac{2}{5}x + 4) = \frac{4}{5}x + 8\)

d) \(2 (\frac{2}{5}x + 2) = \frac{4}{5}x + 8\)

So, the only expression that correctly corresponds to the answer is that of alternative B.

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It is true that the A shift is a type of permutation where elements in a sequence or set are moved to the right or left by a certain number of positions.

For example, shifting the sequence (1,2,3,4,5) to the right by 2 positions would result in the sequence (4,5,1,2,3). This can be represented mathematically as (1,2,3,4,5) → (4,5,1,2,3), which is a permutation of the original sequence. Shifts can be useful in various applications, such as cryptography or data compression, where rearranging elements in a sequence can improve efficiency or security.

True. A shift is a specific type of permutation. In general, a permutation refers to the arrangement of objects in a particular order. A shift, also known as a cyclic permutation, involves moving elements of a set in a fixed direction, such that the order is maintained, but the elements change positions. In a shift, the first element moves to the last position, while all other elements move one position forward. This maintains the relative order of the elements and results in a new arrangement. Therefore, a shift is a type of permutation, as it represents an altered ordering of the elements in a set.

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Answer:

654321

Step-by-step explanation:

Answer:

P = 11 + (1/2)π(11) = 11 + 5.5π = 28.279 cm

Letting π = 3.142:

P = 11 + (1/2)(3.142)(11) = 28.281 cm

Answer: (2.4, -12.8)

Step-by-step explanation:

Answer:

1hr= 550 miles

Answer:

CP = 4500

SP = 5400

Loss = -900

Profit % = 20%

Step-by-step explanation:

CP = cost price

SP = sale price

CP = purchase price + overhead

     = 3700 + 800

     = 4500

SP = cost price + profit

     = 4500 + 900

     = 5400

Loss = CP - SP

        = 4500 - 5400

        = -900

Profit % = (profit ÷ cost price) × 100%

             = (900 ÷ 4500) × 100%

             = 20%

Answer:

c= sqrt149; 12.2 rounded

Step-by-step explanation:

Pythagorean Theorem to find c(hypotenuse): a^2+b^2=c^2

7^2+10^2=149

sqrt149= 12.2 rounded

Answer: you answer is

Step-by-step explanation: