A recipe had 4 tablespoons of seasoning to 6 cups of flour. So there is _____ of a tablespoon of seasoning for each cup of flour.

Answer:

El camión lleva 3000 cajas de patatas

Step-by-step explanation:

Proporciones

La capacidad de carga de un camión es de 68.25 Toneladas de patatas.

Como 1 tonelada es equivalente a 1000 Kg, expresamos la capacidad en Kg:

68.25 * 1000 = 68250 Kg

Cada caja de patatas pesa 22.75 Kg, luego el número de cajas que caben en el camión son:

68250/22.75 = 3000 cajas

El camión lleva 3000 cajas de patatas

Answer:

between 21 and 30 pounds in shelter A between 18 and 28 pounds in shelter B

Step-by-step explanation:

One half of the dogs in each shelter points at the the upper 50% of the dog weight. This point is marked by the median value up to the maximum weight value.

The median value is the point marked inside the box on a boxplot and the maximum value is the upper end or the endpoint of the whisker.

For SHELTER A:

Median = 21

Maximum = 30

Hence, For shelter A, it is the interval between 21 and 30

For shelter B:

Median = 18

Maximum = 28

Hence, it is the interval between 18 and 28

Answer:

it's c

Step-by-step explanation:

:)

Answer:

28 square meters

Step-by-step explanation:

7 x 4= 28

28 square meters

Answer:

x=1,9

Step-by-step explanation:

First, we expand the equation into the form ax^2+bx+c=0

2(x-5)^2=32

2(x^2-10x+25)-32=0

2x^2-20x+18=0

x^2-10x+9=0 (divide both sides by 2)

(x-1)(x-9)=0

x=1,9

There are 462 ways to choose 5 books from a shelf of 12, if you cannot choose two adjacent books.

To solve this problem, we can use a technique called "complementary counting." First, let's find the total number of ways to choose 5 books from a shelf of 12. This is simply 12 choose 5, which is:
12! / (5! × 7!) = 792
Now, let's count the number of ways to choose 5 books from a shelf of 12 where two adjacent books are chosen. We can do this by treating the adjacent books as a single unit, and then choosing 4 more books from the remaining 11. This gives us:
11 choose 4 = 330
So, there are 330 ways to choose 5 books from a shelf of 12 where two adjacent books are chosen.
Finally, we can subtract this number from the total number of ways to choose 5 books to get the number of ways to choose 5 books where no two adjacent books are chosen:
792 - 330 = 462
Therefore, there are 462 ways to choose 5 books from a shelf of 12, if you cannot choose two adjacent books.

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The measures in the circle given in the image above are calculated as:

1. m<PSQ = 130°;   2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.

In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.

1. m<PSQ = m<PAQ

Substitute:

m<PSQ = 130°

2. Find m<PBQ:

m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]

Substitute:

m<PBQ = 1/2(130 + 2(35))

m<PBQ = 100°

m<AQS = 180 - [m<BAQ + m<PBQ]

Substitute:

m<AQS = 180 - [(180 - 130) + 100]

m<AQS = 30°

3. m(QR) = m<QAR

Substitute:

m(QR) = 100°

4. m(PS) = 180 - m(RS)

Substitute:

m(PS) = 180 - 2(35)

m(PS) = 110°

5. m(RS) = 2(35)

m(RS) = 70°

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Step-by-step explanation:

40 strawberries in the farm

Answer:

46

Step-by-step explanation:

There are 46 of straws on the farm

Answer:

Option A :- if finding lateral surface area

Other information

radius r = 6 m

height h = 8 m

slant height s = 10 m

volume V = 301.592895 m3

lateral surface area L = 188.495559 m2

base surface area B = 113.097336 m2

total surface area A = 301.592895 m2

Step-by-step explanation:

Using the formulas

A=πrl+πr²

l=√r²+h²

Solving forA

A=πr(r+√h²+r²)=π · 6 · (6+√8²+6²)≈301.59289

Answer:x=4

Step-by-step explanation:

To reduce the effects of outliers on linear least squares fitting, we can use an adaptive weighting scheme. The approach involves initializing all weight values to 1.0 and placing them as diagonal values of an n × n matrix W. All off-diagonal values of W are set to zero. We then initialize the line coefficients to large real values.

Next, we use an iterative approach to update the weights and re-estimate the line coefficients. In each iteration, we calculate the residuals (i.e., the difference between the observed and predicted values) and use them to update the weights. Specifically, we set wi = 1/(residuali^2), where residual is the residual for the ith data point. We then update the weight matrix W with the new weight values.

We then solve the weighted least squares problem for coefficients c using the normal equations approach. This involves multiplying the transpose of the design matrix X with the weight matrix W and the response vector y and then solving for c using the resulting equation: (X^T)WXc = (X^T)Wy.

We repeat the above steps until convergence or until we reach a predetermined maximum number of iterations. Finally, we output the coefficients c of the initial fit and of the final fit. The initial fit is obtained using the original weight matrix with all values set to 1.0, while the final fit is obtained using the converged weight matrix with updated weight values.

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Answer:

1.1. 3(2a-7)

1.2. 3x(2x+3)

Step-by-step explanation:

Put the common factor on the outside of the parentheses.

1.1. 6a-21

The lowest common factor for 6a and -21 is 3.

     3(2a-7)

1.2. \(6x^{2} +9x\)

The lowest common factor for \(6x^{2}\) and 9x is 3x.

      3x(2x+3)

The nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

Given the 13th unit requires 87 minutes and 26th unit requires 64 minutes.To find the estimated time required by the 50th unit, we need to use the equation of the linear equation of the line.Let's find the value of m (slope).`m = (64 - 87)/(26 - 13)m = -23/13`Let's find the value of b (y-intercept).`b = 87 - (-23/13) × 13b = 87 + 23b = 110`

Therefore, the equation of the line can be written as:y = -23/13 x + 110Let's substitute the value of x as 50 and find the value of y (time required by the 50th unit).`y = -23/13 × 50 + 110y = 47.31`Rounded to the nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

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The dimensions of the cubes are 10 inches, 8 inches, and 6 inches.

Let's assume the lengths of the edges of the cubes are x, x-2, and x-4, where x is the largest edge length.

The surface area of a cube is given by the formula 6s^2, where s is the edge length.

According to the problem, the total surface area of the three cubes is 900 square inches. Therefore, we can set up the equation:

6x^2 + 6(x-2)^2 + 6(x-4)^2 = 900.

Simplifying the equation:

6x^2 + 6(x^2 - 4x + 4) + 6(x^2 - 8x + 16) = 900.

Expanding and combining like terms:

6x^2 + 6x^2 - 24x + 24 + 6x^2 - 48x + 96 = 900.

18x^2 - 72x + 120 = 900.

Dividing both sides by 6 to simplify:

3x^2 - 12x + 20 = 150.

Rearranging the equation:

3x^2 - 12x - 130 = 0.

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. After solving the equation, we find the solutions:

x = 10 and x = -4/3.

Since the dimensions of the cubes must be positive even integers, we discard the solution x = -4/3.

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Answer: \(5^{\circ}\)

Step-by-step explanation:

Given

\(\angle DIE=(18x-2)^{\circ}\\\angle DIH=15^{\circ}\\\angle FIG=103^{\circ}\)

from the figure

\(\angle HIE=\angle GIF\quad [\text{vertically opposite angles}]\\\angle HID+\angle DIE=\angle GIF\\15^{\circ}+(18x)^{\circ}-2^{\circ}=103^{\circ}\\(18x)^{\circ}=103^{\circ}-13^{\circ}\\\\x=\dfrac{90^{\circ}}{18}\\\\x=5^{\circ}\)

The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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Answer:

Number of special bagel sandwiches = 37

Step-by-step explanation:

Let \(x,y\) denote number of special bagel sandwiches and plain bagels respectively.

The bagel shop sold 100 items.

\(x+y=100\\y=100-x\)

Also, The bagel shop made $385.

\(7x+2y=385\)

Put \(y=100-x\) in \(7x+2y=385\)

\(7x+2(100-x)=385\\7x+200-2x=385\\5x=385-200\\5x=185\\x=\frac{185}{5}\\x=37\)

So,

Number of special bagel sandwiches = 37

The group that would best represent the sample population is; D: Every fifth person walking down the street in several different locations..

A sample population is simply a subset of the main population. Now, in this question we see that a poll is being taken on Wednesday to predict which movie will be the most popular at the city’s movie theaters the next weekend.

Now, since we are looking for sample population, the one that will best represent it will be Option D. This is because - Different locations through out the city at Different time has maximum randomness.

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The solutions to the quadratic equation are;

\(x = \frac{ \sqrt{10} + 5 }{2} \)

\(x = \frac{ - \sqrt{10} + 5 }{2} \)

The correct answer choice is option A and E

4x² - 20x + 25 = 10

Equate the equation to 0

4x² - 20x + 25 - 10 = 0

4x² - 20x + 15 = 0

Solve the quadratic equation using formula

\(4x^2 - 20x + 15 = 0\)

using Quadratic Formula where,

a = 4,

b = -20, and

c = 15

\(x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\)

\(x = \frac{ -(-20) \pm \sqrt{(-20)^2 - 4(4)(15)}}{ 2(4) }\)

\(x = \frac{ 20 \pm \sqrt{400 - 240}}{ 8 }\)

\(x = \frac{ 20 \pm \sqrt{160}}{ 8 }\)

\(x = \frac{ 20 \pm 4\sqrt{10}\, }{ 8 }\)

\(x = \frac{ 20 }{ 8 } \pm \frac{4\sqrt{10}\, }{ 8 }\)

\(x = \frac{ 5}{ 2 } \pm \frac{ \sqrt{10}\, }{ 2 }\)

Therefore, the solution to the quadratic equation using formula is

\(x = \frac{ 5}{ 2 } \pm \frac{ \sqrt{10}\, }{ 2 }\)

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Answer: 8:1

Step-by-step explanation:

To find the simplest ratio of 4 kg of metal to 500g of plastic, we need to convert both quantities to the same unit of measurement. Let's convert 4 kg to grams:

Now we have 4000 g of metal and 500 g of plastic. To simplify the ratio, we can divide both quantities by their greatest common factor (GCF), which is 500:

Therefore, the simplest ratio of 4 kg of metal to 500g of plastic is 8:1.

________________________________________________________

The total weight of metal and plastic in the ratio 8:1 is indeed 4.5 kg.

The total weight of metal and plastic is:

The simplest ratio of metal to plastic is found by dividing both quantities by their greatest common factor.

The greatest common factor of 4 kg and 0.5 kg is 0.5 kg. Dividing both quantities by 0.5 kg gives:

\(\therefore\) The simplest ratio of metal to plastic is 8:1.

To check, we can verify that:

So the total weight of metal and plastic in the ratio 8:1 is indeed 4.5 kg.

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The greatest area that can be covered with the given tiles is 63 square inches using the 1x9 arrangement.To find the greatest area that can be covered with the given tiles, we need to determine how to arrange the tiles to maximize the area.

The tiles measure 3 and 1/2 inches long and 2 inches wide. Let's assume that the tiles can be arranged in a rectangular shape.

To maximize the area, we want to find the dimensions that allow us to use all nine tiles without leaving any gaps. Since the tiles are rectangular, we need to find a whole number of rows and columns that multiply to nine (the number of tiles).

Possible arrangements for nine tiles are:

1 row and 9 columns (1x9)

3 rows and 3 columns (3x3)

To calculate the area, we multiply the length by the width:

For the 1x9 arrangement:

Area = 3.5 inches * (2 inches * 9) = 63 square inches

For the 3x3 arrangement:

Area = (3.5 inches * 3) * (2 inches * 3) = 31.5 square inches

Therefore, the greatest area that can be covered with the given tiles is 63 square inches using the 1x9 arrangement.

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We can use the result from Problem 1 to find the Fourier series for g(x), which will give us the Fourier series for f(x).

To find the Fourier series for the function defined by f(x) = 0, -1 < x < 0 and f(x) = 1, 0 < x < π, we can use the result obtained from Problem 1.

In Problem 1, we found the Fourier series for a periodic function f(x) defined on the interval (-π, π).

The function defined in Problem 2 is periodic with period 2π, so we can extend it to be defined on the interval (-π, π) by repeating the pattern. Therefore, we have:

f(x) = 0, -π < x < -1

f(x) = 1, -1 < x < 0

f(x) = 1, 0 < x < π

To obtain the Fourier series for this function, we can subtract the average value of f(x) from f(x) to make it a periodic function with zero average. Let I denote the average value of f(x). Then we have:

I = ∫[0,π] f(x) dx = ∫[0,π] 1 dx = π

Next, we subtract I from f(x) to obtain:

g(x) = f(x) - I

For the given function, g(x) will be:

g(x) = 0 - π, -π < x < -1

g(x) = 1 - π, -1 < x < 0

g(x) = 1 - π, 0 < x < π

Now we can use the result from Problem 1 to find the Fourier series for g(x), which will give us the Fourier series for f(x).

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Answer:

Step-by-step explanation:

m∠2 = 52° [Alternate interior angles]

m∠1 + m∠2 = 180° [Linear pair of angles are supplementary]

m∠1 = 180° - 52°

m∠1 = 128°

m∠3 = 47° [Alternate interior angles]

m∠5 + 52° + 47° = 180° [Sum of linear angles is 180°]

m∠5 = 180° - 99°

        = 81°

m∠4 + 47° = 180° [Sum of consecutive interior angles is 180°]

m∠4 = 180° - 47°

m∠4 = 137°

Answer:

A

Step-by-step explanation:

Since the prices START at 20,000 it means 20k is included.

The problem also stated that ALL cars cost LESS than 35,000 which mean 35k is not included.

Let the total number of goats that McDonald had be x. After evenly dividing them between Lilly and Hawk, each of them would have received x/2 goats. However, Lilly lost 35 goats, so she was left with (x/2 - 35) goats. Similarly, Hawk lost 40 goats and was left with (x/2 - 40) goats.

When Lilly sold each goat for $80, she earned (x/2 - 35) * $80 = 80x/2 - 35*80 = 40x - 2800 dollars. When Hawk sold each goat for $60, he earned (x/2 - 40) * $60 = 60x/2 - 40*60 = 30x - 2400 dollars.

Given that Lilly earned $1100 more than Hawk, we can set up the equation:

40x - 2800 = 30x - 2400 + 1100

Solving for x, we get x = 400. Therefore, McDonald had a total of 400 goats.

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The answer is

Step-by-step explanation:

Since there is 3 even numbers and 3 odd numbers it makes a 50/50 chance when spun once. If you spin it 60 times you will have spun it 30 times theoretically.

Ndidi rides y km at 10 km/hr, then walks 0.5y km at 3 km/hr. She is away from. home less than 4hours.Range of the values of Y is =24/7

Let's call the total time spent riding and walking t hours. We know that t is less than 4 hours, so:

t = time spent riding + time spent walking < 4 hours

The time spent riding is given by y / 10 km/hr and the time spent walking is given by 0.5y / 3 km/hr. So, we can write the inequality as:

t = y / 10 + 0.5y / 3 < 4

Expanding and simplifying the expression on the left side gives:

7/6y < 4 * 6/7

Multiplying both sides by 6/7 gives:

y < 4 * 6/7 * 6/7 = 24/7

So, the range of values of y is 0 < y < 24/7 km. This means that Ndidi rode less than 24/7 km, but more than 0 km.

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Answer: 5 gallons per hour.

Step-by-step explanation: To find the unit rate, divide "gallons" by "hours." As we said, we need to find the unit rate. We want a unit rate where 1 is in denominator, so we divide the top and bottom by 6. (Remember, unit means 1.)

\(\frac{30/6}{6/6}=\frac{5}{1}\)

Therefore, our answer is 5.