question attached above ​

Answer:

Step-by-step explanation:

(-3.1 - 4.92)/2 = -8.02/2 = -4.01

(-2.8 - 3.3)/2 = -6.1/2= -3.05

(-4.01. -3.05) the midpoint

Answer:

1. Wooden spoons

2. kitchen shears

3.cutting board

4. measuring spoons

5. measuring cups

6. Rubber spatulas

7. whisk

8. rotary beater

9. whisk

10. colander

Answer:

y=-2x+b

Step-by-step explanation:

The slope ("m") is 2... rise over run, the line goes up two, and then to the side once, which is 2/1 (aka 2). Since the line is going downhill, it is negative.

Answer:

15.6 answer

marks as branilist

Answer:

is 736 units

Step-by-step explanation:

my explanation is that I got it wrong because of the answer above of me an the right answer was 736 not 706

The surface area of the rectangular prism below with height as 8 units, length as 19 units and breadth as 8 units is A) 736 square units.

The surface area of a rectangular prism is the total area of all the faces of the prism. The rectangular prism below has 6 faces, each of which is a rectangle.

The area of a rectangle is given by:

area = length * breadth

The surface area of the rectangular prism is then given by:

surface area = 2 * (length * breadth + breadth * height + height * length)

Plugging in the values for the length, breadth, and height, we get:

surface area = 2 * (19 * 8 + 8 * 8 + 19 * 8) = 2 * (152 + 64 + 152) = 2 * 368 = 736 square units

Therefore, the surface area of the rectangular prism is A) 736 square units.

Here is a breakdown of the surface area of each of the faces:

Front face: 19 * 8 = 152 square units

Back face: 19 * 8 = 152 square units

Top face: 8 * 8 = 64 square units

Bottom face: 8 * 8 = 64 square units

Left face: 19 * 8 = 152 square units

Right face: 19 * 8 = 152 square units

The total surface area is the sum of the areas of all 6 faces, which is 736 square units.

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Answer:

450 considering Blue appears 45 times in 100 spins.

Step-by-step explanation:

Let us assume that frequency of Blue is 45 times in 100 spins.

So we have to calculate the number of times the spinner lands on blue in 1000  spins.

It simply can be calculated as

Expected number of landing on blue:

Expected frequency = probability × number of trials

= (45/100)×1000

= 450 times

So, Expected number of landing on blue = 450

Answer:450

Step-by-step explanation:

Answer:

The value of x = 40.

Step-by-step explanation:

From the figure, it is clear that given a transversal line cuts two parallel lines m and n, thus making the corresponding congruent angles 120° and 3x°.

Here, 120° is corresponding to 3x°.

As corresponding angles are congruent.

so

3x° = 120°

Divide both sides by 3

3x/3 = 120 / 3

x = 40

Therefore, the value of x = 40.

Answer:

7/12 for white sock. 5/12 black sock. 1/4 navy

Step-by-step explanation:

(white) 24-10=14 so then 14/24=7/12

(black) 10/24=5/12

(navy) 6/24=1/4

a. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis. b. the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

a) Rachel's budget line equation can be written as follows:

Budget = (Price of Hamburger * Quantity of Hamburgers) + (Price of Figs * Quantity of Figs)

Since the price per hamburger is $3 and the price per bag of figs is $2, the equation becomes:

Budget = 3x + 2y

Where x represents the quantity of hamburgers and y represents the quantity of bags of figs. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis.

b) If the price of figs increases to $3, the new budget line equation becomes:

Budget = 3x + 3y

The graph of the new budget line would show a steeper slope compared to the original budget line. This indicates that the relative price of figs has increased, making them relatively more expensive compared to hamburgers.

c) In this scenario, Rachel has an income of $50, the price per hamburger is $3, the price per bag of figs is $3, and she receives an additional $10 in cash from a friend. The new budget line equation can be written as:

Budget = (3x + 3y) + 10

The graph of the new budget line would shift upward parallel to the original budget line. The additional cash from Rachel's friend increases her purchasing power, allowing her to afford more hamburgers and/or bags of figs.

d) Now, Rachel's friend gives her a gift basket containing 3 free bags of figs. In this case, the budget line equation remains the same as in part c:

Budget = (3x + 3y) + 10

However, since Rachel receives 3 free bags of figs, she can allocate more of her budget towards purchasing hamburgers. This would cause the budget line to rotate outward from the y-intercept, resulting in a flatter slope. The new budget line would reflect Rachel's ability to purchase more hamburgers with the same income and price of figs.

In summary, the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

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The probability of selecting a pen from the first box is 1/8 (since there is only 1 pen out of 8 items in the box). The probability of selecting a crayon from the second box is 3/6 (since there are 3 crayons out of 6 items in the box).

To find the probability of both events happening together, we multiply the probabilities:

P(pen and crayon) = P(pen) x P(crayon)

P(pen and crayon) = (1/8) x (3/6)

Simplifying the fraction 3/6 to 1/2:

P(pen and crayon) = (1/8) x (1/2)

Multiplying the numerators and denominators:

P(pen and crayon) = 1/16

Therefore, the probability of selecting a pen from the first box and a crayon from the second box is 1/16.

Answer:

  C) The difference between the 75th and 25th percentiles is 12 inches.

Step-by-step explanation:

The interquartile range is the length of the "box" in a "box and whisker" plot. One end is the 25th percentile, and the other end is the 75th percentile. It is the difference between the maximum and minimum of the middle 50% of the data.

For the baker's loaf-length data set, the interquartile range being 12 inches means the loaves in the 75th percentile are 12 inches longer than the loaves in the 25th percentile. This could be described by choice C.

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

I really like cake and made a cake not to long ago.

The coordinate vector of p(t) in basis B is a' = [1/2(a - c)  1/2(a + b)  1/2(b - c)].

In linear algebra, a coordinate vector is a representation of a vector in terms of its components with respect to a specific coordinate system or basis. It provides a way to express a vector as a tuple of numbers.

Given the following ordered bases

B = {1,1-t, t-t²} and

C = {1, t, t²} for P₂.

Let p(t) = ax² + bx + c be a polynomial in P₂.

We have to find:

(a) The change of coordinates matrix from C to B.

(b) The coordinate vector of p(t).SOLUTION

(a) The change of coordinates matrix from C to B.

The matrix is formed as:

[B]C = [C to B] =  [1  -1  1] [1  0  0][0  1  0] [-1  1  -1][0  0  1] [0  -1  1]

Therefore, the matrix is [B]C = [1  0  -1][1  1  0][-1  1  1]

(b) The coordinate vector of p(t).In order to find the coordinate vector of p(t) in basis B,

we have to use the change of coordinates matrix [B]C which is:

[1  0  -1][1  1  0][-1  1  1][a'] = [B]C [a]

To solve for the coordinate vector a', we multiply both sides of the equation by the inverse of [B]C which is:

[1/2   -1/2   1/2][1/2    1/2   0][-1/2   1/2   1/2][a'] = [1  0  -1][1  1  0][-1  1  1][a][a'] = [1/2(a - c)     1/2(a + b)][1/2(a + b)     b][1/2(a - c)     1/2(b - c)]

Therefore, the coordinate vector of p(t) in basis B is a' = [1/2(a - c)  1/2(a + b)  1/2(b - c)].

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Answer:

Step-by-step explanation:

20x+21=0

20x=-21

x=-1.05

Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

answer:

5/3 m

Step-by-step explanation:

because 3/3=1 so teacher choose boys

Answer:

7/8 mile

Step-by-step explanation:

3/4 = 6/8

6/8+ 1/8 = 7/8

324 is the maximum value of the product of these three numbers

What is maxima and minima?

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, and minima will be its lowest.

The extrema of a function are the maxima and minima. The maximum and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, over its full range.

Let the three nonnegative numbers are x,y,z

According to the question

x+y+z=36

and y=2x

therefore, 3x+z=36--------------------------------------------------(1)

z=36-3x

Let 3xz= u--------------------------------------------------------------(2)

differentiating equation 2

du/dx=3z + 3xdz/dx

or

du/dx= z + xdz/dx

differentiating equation 1

3 + dz/dx = 0

dz/dx = -3

du/dz = 36-3x + x(-3)

du/dx = 12 - 2x--------------------------------------------------------------(3)

for maxima put du/dx = 0

x=6-------------------------------------------------------------------------------(4)

again differentiating du/dx = 12 - 2x

d2u/dx2=-2

which means 3xz= u is maximum at x=6

from equation 1 and 4

we get 18+z=36

z=18

Therefore 3xz= 3(6)(18)=324

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The dimension which this rug should have is 23 feet × 13 feet.

Mathematically, the area of a rectangle can be calculated by using this formula;

A = LW

Where:

Let x represent the width of this rug.

Also, the dimension of this rug is given by:

299 = (29 - 2x) × (19 - 2x)

299 = (29 - 2x)(19 - 2x)

Evaluating the equation, we have:

299 = 551 - 58x - 38x + 4x²

4x² - 58x - 38x + 551 - 299 = 0

4x² - 96x + 252 = 0

Dividing all through by 4, we have:

x² - 24x + 63 = 0

x² - 21x - 3x + 63 = 0

x(x - 21) - 3(x - 21) = 0

(x - 3)(x - 21) = 0

x = 3 or 21 feet.

Note: The plausible solution is x = 3.

Therefore, the width and length of this rug is given by:

Length = 29 - 2(3)

Length = 29 - 6

Length = 23 feet.

Width = 19 - 2(3)

Width = 19 - 6

Width = 13 feet.

In conclusion, the dimension of this rug is 23 feet × 13 feet.

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According to the given figure, angle 1 is a right triangle, it means that it measures 90°.

Regarding angle 2, we can use the triangle sum theorem to find it. It states that the sum of the interior angles of a triangle is 180°.

The answers are:

m-angle1=90°

m-angle2=63°

The vectors that join the center of a clock to the hours :

At 1:00: (cos(π/6), sin(π/6)) = (√3/2, 1/2)

At 2:00: (cos(π/3), sin(π/3)) = (1/2, √3/2)

At 3:00: (cos(π/2), sin(π/2)) = (0, 1)

What is Vector?

A vector is a object that has both magnitude (size) and direction. In other words, a vector is a quantity that can be represented by an arrow or line segment, where the length of the arrow corresponds to the magnitude of the vector.

To find the vectors that join the center of a clock with radius 1 unit to the hours 1:00, 2:00, and 3:00, we can use basic trigonometry.

First, we can find the angle (in radians) between the 12:00 position and each of the desired hour positions. Since there are 12 hours on a clock and the circle has a circumference of 2πr = 2π(1) = 2π, the angle between each hour mark is:

2π/12 = π/6 radians

Therefore, the angles between the center of the clock and the hour marks are:

At 1:00, the angle is π/6 radians clockwise from the 12:00 position.

At 2:00, the angle is 2π/6 = π/3 radians clockwise from the 12:00 position.

At 3:00, the angle is 3π/6 = π/2 radians clockwise from the 12:00 position.

Next, we can use the cosine and sine functions to find the x and y components of each vector. The x-component of each vector is given by the radius times the cosine of the angle, and the y-component is given by the radius times the sine of the angle.

Therefore, the vectors that join the center of the clock to the hours 1:00, 2:00, and 3:00 are:

At 1:00: (cos(π/6), sin(π/6)) = (√3/2, 1/2)

At 2:00: (cos(π/3), sin(π/3)) = (1/2, √3/2)

At 3:00: (cos(π/2), sin(π/2)) = (0, 1)

Note that these vectors are unit vectors, meaning that they have a length of 1 unit.

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Answer:

I would assume that 100 would be 100 minutes in the air, if -100 represents 100 minutes before take-off.

Step-by-step explanation:

Thus, the general solution of the given differential equation is: y = c1 + c2e^(-x/8) where c1 and c2 are constants determined by the initial or boundary conditions.

To find the general solution of the given differential equation, we first need to find the characteristic equation by assuming a solution of the form y = e^(rt), where r is a constant.

Substituting this into the differential equation, we get:

8(e^(rt))'' + (e^(rt))' = 0

Simplifying, we get:

8r^2e^(rt) + re^(rt) = 0

Factoring out e^(rt), we get:

e^(rt)(8r^2 + r) = 0

Solving for r, we get:

r = 0 or r = -1/8

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Step 3 is unnecessary (the statement is already given, plus you haven't proven the triangle is isosceles anyway).

After, omit step 5 and jump straight to 6.

After this, step 6 is the statement that used to be step 5, which is true by CPCTC.

Then, you can prove the required statement by definition from this.

The head start program provides a wide range of services to low-income children up to the age of 5 years and their families. Its goals are to provide services to improve social and learning skills and to improve health and nutrition status so that the participants can begin school on an equal footing with their more advantaged peers.

The distribution of ages for participating children is as follows 12% five-year-olds, 47% four-year-olds, 33% three-year-olds, and 8% under three years. When the program was assessed in a particular region, it was found that of the 215 randomly selected participants, 17 were 5 years old, 101 were 4 years old, 60 were 3 years old, 37 were under 3 years old. Perform a test to see if there sufficient evidence at αα = 0.10 that the region's proportions differ from the national proportions. The correct hypotheses are:H0:H0: The regional distribution is a good fit to the national distribution.HA:HA:

The regional distribution is not a good fit to the national distribution.(claim)The null hypothesis is represented by H0, which states that the regional distribution is a good fit to the national distribution.

The alternative hypothesis is represented by HA, which states that the regional distribution is not a good fit to the national distribution (claim).The distribution of ages for participating children in the national program is 12% for five-year-olds, 47% for four-year-olds, 33% for three-year-olds, and 8% for children under the age of three. The number of participants of a specific age range in the region differs from the national program.

The observed and expected frequencies are obtained below:| Age Range | Observed Frequency | Expected Frequency |5 | 17 | 26.1 |4 | 101 | 100.3 |3 | 60 | 71.1 |<3 | 37 | 17.6 |The expected frequency is computed from the national distribution as shown below;

Observed Frequency × (Total number of Participants /100) = Expected FrequencyWe can evaluate the goodness of fit using the chi-square distribution with k - 1 degrees of freedom, where k is the number of categories. We'll use α = 0.10 as the significance level for this test.The test value is 13.299.The p-value is 0.004.There is sufficient evidence at α=0.10 that the region's proportions differ from the national proportions.

The correct hypotheses are H0: The regional distribution is a good fit to the national distribution and HA: The regional distribution is not a good fit to the national distribution. The p-value is 0.004 and the test value is 13.299. There is sufficient evidence at α=0.10 that the region's proportions differ from the national proportions.

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Answer:

x=o and y= -6

Step-by-step explanation:

12-2x = - 2(y-x)

or,12-2x = -2y + 2x

or, 12 = - 2y + 4x

or, 12/2= 2x - y

or, 2x - y = 6

• 2x -6= y.....eqn_1

-2x=-2y+2x -12

or,4x +2y= -12

or,4x + 2(2x-6)= -12

or, 4x+4x-12=-12

or, 8x= 0

• x= o

putting the value of x in eqn...3

o=(y-0)+6

or, o= y + 6

•y = -6

Magnitude and coordinate direction angles of F1 and F2:

\(\theta_x1= 35.53 degrees\)

\(\theta_y1 = -30.96 degrees\)

\(\theta_z1 = 26.57 degrees\)

\(\theta_x2 = -21.91 degrees\)

\(\theta_y2 = -39.47 degrees\)

\(\theta_z2 = 16.85 degrees\)

To determine the magnitude and coordinate direction angles of F1 and F2, we first need to calculate the magnitude of each vector:

\(|F1| = \sqrt((60)^2 + (-50)^2 + (40)^2) = 86.6 N\)

\(|F2| = \sqrt((-40)^2 + (-85)^2 + (30)^2) = 100.5 N\)

Next, we can calculate the direction angles of each vector:

\(\theta_x1 = arctan(F1_x/F1) = arctan(60/86.6) = 35.53 degrees\)

\(\theta_y1 = arctan(F1_y/F1) = arctan(-50/86.6) = -30.96 degrees\)

\(\theta_z1 = arctan(F1_z/F1) = arctan(40/86.6) = 26.57 degrees\)

\(\theta_x2 = arctan(F2_x/F2) = arctan(-40/100.5) = -21.91 degrees\)

\(\theta_y2 = arctan(F2_y/F2) = arctan(-85/100.5) = -39.47 degrees\)

\(\theta_z2 = arctan(F2_z/F2) = arctan(30/100.5) = 16.85 degrees\)

Finally, we can sketch each force on an xyz reference:

z                    z

  ^                    ^

  |                    |

  |                    |

F1|         F2         |F1

  |                    |

  |                    |

  +---------> y        +---------> y

 /                     /

/                     /

x                     x

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After solving the equation the linear equation is x = 27/5 , y = 7/5.

What do you mean by linear equation?

Equations with the highest degree of 1 are called linear equations. This means that the exponent of the variable in the linear equation is greater than 1. The graph of a linear equation is always a straight line.

A linear equation is an algebraic equation in which each term has exponent 1, and the graph of this equation is always a straight line. For this reason, it is called a "linear equation".

Given system of equation:

7x - 7y = 28 ..........(1)

2x - 7y = 1 .............(2)

Solve this system of linear equation. Find the value of 7y from equation (1) and substitute in equation(2)

7x - 7y = 28

7x - 28 =7y .............(3)

Substitute this value in equation (2)

2x - (7x - 28) = 1

2x - 7x + 28 = 1

-5x + 28 = 1

5x = 28 - 1

5x = 27

x = 27/5

Substitute this value in equation (3)

7y = 7(27/5) - 28

7y = 189/5 - 28

7y = 49/5

y = 7/5

Therefore, x = 27/5 , y = 7/5

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