Triangle ABC has its vertices at the following coordinates:

A(-4, 1) B(0, 2) C(-11, 3)

Give the coordinates of the image triangle A'B'C' after a 90° counterclockwise rotation about the origin.

Answer

12 large baskets can hold 360 ears of corn and 20 small baskets can hold 120 ears of corn so all the baskets can hold 480 ears of corn

There are two solutions: x = -3 and x = -7.

Let's analyze each equation to determine the number of solutions and provide explanations:

x² - 144 = 0

This equation can be rewritten as (x - 12)(x + 12) = 0. It is a quadratic equation in the form of (x - a)(x + a) = 0, where a is a constant. In this case, a = 12.

Since we have two factors that multiply to give zero, either (x - 12) = 0 or (x + 12) = 0 must be true for the equation to hold.

Thus, there are two solutions: x = 12 and x = -12.

x² + 1440

This equation does not contain an equal sign, so it is not an equation. It is an expression. Therefore, it does not have any solutions.

x (x - 5) = 0

This equation is a product of two factors equal to zero. Either x = 0 or (x - 5) = 0 must be true for the equation to hold. Thus, there are two solutions: x = 0 and x = 5.

(x - 8)² = 0

This equation is a perfect square trinomial. The square of any number is always non-negative, and it only equals zero when the number itself is zero. Thus, the equation (x - 8)² = 0 has only one solution: x = 8.

(x + 3)(x + 7) = 0

This equation is a product of two factors equal to zero. Either (x + 3) = 0 or (x + 7) = 0 must be true for the equation to hold. Thus, there are two solutions: x = -3 and x = -7.

To summarize:

x² - 144 = 0 has two solutions: x = 12 and x = -12.

x² + 1440 does not have any solutions.

x (x - 5) = 0 has two solutions: x = 0 and x = 5.

(x - 8)² = 0 has one solution: x = 8.

(x + 3)(x + 7) = 0 has two solutions: x = -3 and x = -7.

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Answer:

3.141592653

Step-by-step explanation:

That's all I know

Answer:

Circumference = 2 x 3.14 x radius = 27 (in)

=> radius = 27/(2 x 3.14) = 4.3 (in)

=> Area = 3.14 x radius^2 = 3.14 x 4.3^2 = 58.1 (in2)

Answer:

58 inches^2

Step-by-step explanation:

The formula for the area of a circle is \(\pi *radius^{2}\)

To work out the area of this circle you would first need to divide the circumference of 27 by pi, this gives you 8.594. This is because the formula for the circumference is: \(\pi *diameter\\\) and so by dividing the circumference by pi we are isolating the value of the diameter.

Then now that we have worked out the diameter we can now begin to work out the area, however in order to work out the area we must work out the radius. You can do this by dividing the diameter by 2, which gives you 4.297.

Then to work out the area you would multiply pi by the radius of 4.297 squared, this gives you 58.01 \(inches^{2}\).

The next step is to round it to the nearest whole number, this gives you 58.

1) Divide 27 by pi.

\(27/\pi =8.594\)

2) Divide 8.594 by 2.

\(8.594/2=4.297\)

3) Multiply pi by 4.297 squared.

\(\pi *4.297^{2} =58.01\)

4) Round to the nearest whole number.

58 square inches

4) reflexive property

5) SSS

The area of the new square is 128 square feet larger than the area of the original square.

When the side lengths of a square are tripled, the new square will have side lengths of 12 feet (4 feet multiplied by 3). To find the area of the original square, we use the formula A = s^2, where A is the area and s is the side length. Thus, the area of the original square is 4^2 = 16 square feet.

Similarly, the area of the new square with side lengths of 12 feet is 12^2 = 144 square feet. To determine how much larger the area of the new square is than the area of the original square, we subtract the area of the original square from the area of the new square: 144 - 16 = 128 square feet.

Therefore, the area of the new square is 128 square feet larger than the area of the original square. This means that the new square is three times nine times six times larger in terms of area compared to the original square.

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Step-by-step explanation:

what do you mean lf speed is not given what we have tofind

Answer:

v = d/t, perhaps.

Step-by-step explanation:

Velocity (speed) is defined as distance traveled divided by the time it takes to travel that distance.

This gives an average speed.  For example, I'll be taking a trip tomorrow of about 150 miles.  If it takes me 3 hours, my average speed is v = 150/3 = 50 miles per hour.

That does not mean my speed is constantly 50 miles per hour; I sometimes go slower than that (maybe even stopping for red lights!), and sometimes I'll be going faster than that.

A lot of school math problems assume a constant speed.

The value of h(0) is 10, and h(4) is 16 because the function is a piecewise function.

We have a piecewise function shown in the graph:

When x = 0

h(x) = 2x² -3x + 10,  0 ≤ x , 4

h(0) = 2(0)² -3(0) + 10

h(0) = 10

And,

When x = 4

h(x) = 2ˣ

h(4) = 2⁴ = 16

Thus, the value of h(0) is 10, and h(4) is 16 because the function is a piecewise function.

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Complete question =

Consider function h.

What are the values of the function when x = 0 and when x = 4 ?

The composite function is \(f\circ g(x) = x^8+x^6+x^4\)

Given that \(f(x)=x^4+x^3+x^2\) and \(g(x)=x^2\).

We need to calculate \(f\circ g(x)\) which is a composite function.

If two functions are given and we create another function by using the given functions, then the new function is called composite function.

So to calculate the composite function, put the value of \(g(x) = x^2\) in the function \(f(x)\).

\(f\circ g(x) = (x^2)^4+(x^2)^3+(x^2)^2\)

\(f\circ g(x) = x^8+x^6+x^4\)

Hence the composite function is \(f\circ g(x) = x^8+x^6+x^4\).

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The df that will be used if a simple main effect is examined from a-two factor ANOVA with two levels in each factor and n = 4 individuals in each level is 1, 12. So, the correct option is option c. 1,12.

If a simple main effect is examined from a two-factor ANOVA with two levels in each factor and n = 4 individuals in each level, the degrees of freedom (df) that will be used are:

For the main effect of one factor (either Factor A or Factor B), the df will be calculated as follows:

1. Between-group df: number of levels - 1 = 2 - 1 = 1
2. Within-group df: (number of levels * (n - 1)) = 2 * (4 - 1) = 2 * 3 = 6

So, the df for the main effect of one factor is 1 (between-group) and 6 (within-group).

Now, let's calculate the error df for the interaction effect between the two factors:

Error df = (Factor A levels - 1) * (Factor B levels - 1) * n = (2 - 1) * (2 - 1) * 4 = 1 * 1 * 4 = 4

Therefore, df = 1, 12. So, the correct answer is option c. df-1, 12.

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Answer:

24 degrees

Step-by-step explanation:

90-66=24

a)1. True

2.False

3.True

4).False

b)Without knowing the sample size and standard deviation, we cannot determine the exact 90% confidence interval.

(a) For the content loaded Central Middle School data:

1. True: There is a 95% probability that μ (mean height) is between 54 and 58 inches.

This is the correct interpretation of the 95% confidence interval.

2. False: The confidence interval doesn't tell us the probability of the true mean or the margin of error being exactly as given. It only tells us the range where the true mean is likely to fall with 95% confidence.

3. True: If we took many additional random samples of the same size and from each computed a 95% confidence interval for μ, approximately 95% of these intervals would contain μ. This is the definition of a 95% confidence interval.

4. False: It's incorrect to say that μ would fall between 54 and 58 95% of the time. The correct interpretation is that if we computed multiple 95% confidence intervals, approximately 95% of those intervals would contain the true mean height.

(b) To determine the 90% confidence interval based on the same data:

Without knowing the sample size and standard deviation, any of the above answers could be the 90% confidence interval. Confidence intervals depend on the sample size, standard deviation, and desired confidence level. With the information given, we cannot determine the exact 90% confidence interval.

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a) The forecasted number of disk drives to be made next year is 210.

b) The mean squared error (MSE) when using linear regression is 160.

c) The mean absolute percent error (MAPE) when using linear regression is approximately 7.51%.

Let's calculate the linear regression line using the given data points. We will use the least squares method to find the equation of the line:

Year (x)     Disk Drives (y)

1                   140

2                 160

3                 190

4                 200

5                210

Now calculate the means of x and y:

X = (1 + 2 + 3 + 4 + 5) / 5 = 3

Y= (140 + 160 + 190 + 200 + 210) / 5 = 180

The deviations from the means (dx and dy):

dx = (1 - 3, 2 - 3, 3 - 3, 4 - 3, 5 - 3) = (-2, -1, 0, 1, 2)

dy = (140 - 180, 160 - 180, 190 - 180, 200 - 180, 210 - 180)

= (-40, -20, 10, 20, 30)

The sums of squares (Sxx and Sxy):

Sxx = Σ(dx²) = (-2)² + (-1)² + 0² + 1² + 2² = 10

Sxy = Σ(dx × dy) = (-2× -40) + (-1 × -20) + (0 × 10) + (1 × 20) + (2× 30)

= 100

Now find the slope (b):

b = Sxy / Sxx = 100 / 10 = 10

Find the intercept (a):

a = Y - (b × X) = 180 - (10 × 3)

= 180 - 30

= 150

Now we have the equation of the regression line:

y = a + bx

y = 150 + 10x

To forecast the number of disk drives to be made next year (year 6), we substitute x = 6 into the equation:

y = 150 + 10×6

y = 150 + 60

y = 210

Therefore, the forecasted number of disk drives to be made next year is 210.

b) To compute the mean squared error (MSE) when using linear regression.

we need to calculate the residuals (differences between the actual and predicted values) for each data point, square them, and find the average.

Let Year (x), Disk Drives (y), Predicted (Y), Residual (d = y - Y), Residual Squared (d²)

X        y         Y          d            d²

1       140      160        -20      400

2      160      170        -10        100

3       190     180         10         100

4       200    190         10         100

5        210    200        10         100

MSE = Σ(d²) / n

= (400 + 100 + 100 + 100 + 100) / 5

= 800 / 5

= 160

(c)To compute the mean absolute percent error (MAPE), we need to calculate the absolute percent error for each data point, find the average, and express it as a percentage.

Year  Disk Drives  Predicted  Absolute Error  Percent Error

1              140               160             20                     14.29%

2             160               170             10                       6.25%

3             190               180             10                       5.26%

4             200              190             10                       5.00%

5             210              200             10                        4.76%

MAPE = Σ(|d| / y × 100) / n

= (14.29% + 6.25% + 5.26% + 5.00% + 4.76%) / 5

= 7.51%

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The even integers are 10,12 and 14.

Concept:  An integer is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.

Let x,x+2,x+4 be the least, middle and greatest integer respectively.

According to the question,

15< x+x+2+x+4< 21

(3x+6)/2> 15      and    (3x+6)/2< 21

30< 3x+6                      3x+6> 42

24<3x                            3x<36

8<x                                x>12

x=10

x+2=12

x+4=14

Hence, The even integers are 10,12 and 14.

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Answer:

A

Step-by-step explanation:

Table A

input is 5 and output is 9

Using the 2 given rules

Increase the input by 4 to get output , then

5 + 4 = 9 ← correct output

Multiply input by 2 and subtract 1 to get output , then

2 × 5 - 1 = 10 - 1 = 9 ← correct output

Table A works for both rules

Answer:c

Step-by-step explanation:

Answer:

I think it is 19.7

Step-by-step explanation:

Answer:

19 feet tall

Step-by-step explanation:

The square root √(5/75) expression when simplified is 1/15√15

Given the expression:

square root of 5 divided by 75

This is a radical expression

Mathematically, this can be expressed as

√(5/75)

To simplify the square root of 5 divided by 75, we can first simplify the denominator:

75 = 15 x 5

So, the expression becomes:

√(5/75) = √(5/15 * 5)

√(5/75) = √(1/15)

√(5/75) = 1/√15

To simplify further, we can rationalize both the numerator and denominator

So we have

√(5/75) = 1/√15 * √15/√15

Evaluate

√(5/75) = 1/15√15

Therefore, the simplified expression is 1/15√15

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The measure of angle ABD is 20 degrees and this can be determined by using the properties of the angle bisector.

Given :

ABC = 40 and BD is the angle bisector of angle ABC.

The following steps can be used in order to determine the angle ABD:

Step 1 - According to the given data, BD is the angle bisector of angle ABC.

Step 2 - An angle bisector bisects the angle into two equal parts.

Step 3 - So, the measure of angle ABD is calculated as:

So, the measure of angle ABD is 20 degrees.

This criterion can be defined based on the desired level of accuracy or when the change in the estimated parameters falls below a certain threshold.

When implementing a program for a nonlinear problem using the least square adjustment technique, it is essential to determine a termination condition. This condition dictates when the program should stop iterating and provide the final estimated parameters. A common approach is to set a convergence criterion, which measures the change in the estimated parameters between iterations.

One possible criterion is to check if the change in the estimated parameters falls below a predetermined threshold. This implies that the adjustment process has reached a point where further iterations yield minimal improvements. The threshold value can be defined based on the desired level of accuracy or the specific requirements of the problem at hand.

Alternatively, convergence can also be determined based on the objective function. If the objective function decreases below a certain tolerance or stabilizes within a defined range, it can indicate that the solution has converged.

Considering the chosen termination condition is crucial to ensure that the program terminates effectively and efficiently, providing reliable results for the nonlinear problem.

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Answer:

Diagram is not so perfect

OR = distance travelled by the jet plane.

Step-by-step explanation:

Let point J be the jet plane and OJ be the constant height at jet plane is flying and OR be the distance jet plane is travelling.

h =

\(1700 \sqrt{3} \)

Now,

From the figure i drew (1st)

taking 60 as reference angle,

tan60° = p/b

or,

\(tan60 = 1700 \sqrt{3} \div b\)

\(b \: = 1700 \sqrt{3} \div tan60\)

so, b = 1700m

inital distance = 1.7km(OR)

now,

tan 30 = p/b

\(tan30 = 1700 \sqrt{3} \div b \\ or \: b = 1700 \sqrt{3} \div tan30\)

so, b = 5100 m

so, final distance = 5.1 km(OR)

Now,

distance travelled = final distance - initial distance

distance travelled = 5.1 km - 1.7km

distance travlled = 3.4 km

Now,

time = 17 seconds

= 0.00472 hour.

Now,

speed = d/t

or, speed = 3.4/0.00472

so, speed = 720.3389km/hr

so, speed = 720 km/hr approximately

The volume of the piñata is

1152 cubic in

The volume is solved by breaking the composite shape into two prisms

The volume is solved individually and then added together

Volume of square prism

= area x thickness

= 12 x 12 x 6

= 864 square in

Volume of triangular prism

= area x thickness

= 1/2 x 8 x 12 x 6

= 288 square in

The volume of the piñata

= 864 square in + 288 square in

= 1152 cubic in

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The formula NEXT = NOW - 8 is neither recursive or explicit.

In a recursive fοrmula, we can find the value οf a term in the sequence using the value οf the previοus term. Hοwever, in an explicit fοrmula, we can find the value οf a term in the sequence using its pοsitiοn. Hence, this is anοther difference between recursive and explicit.

Recursive formula = \(\rm a_{n}=a_{n-1}+ d\)

Explicit formula = \(\rm a_n= a_1 + (n - 1) d\)

Here, NEXT = NOW - 8 resembles Recursive formula, but the value of Next isn't given. Even if it starts at 50, The value of n isn't specified.

Therefore, The formula NEXT = NOW - 8 is neither recursive or explicit.

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Complete question:

Is the formula recursive, explicit, or neither?

NEXT = NOW - 8, starting at 50.

Here, we are supposed to find the value of the stock. Let's begin by determining the expected dividends: Expected dividends1st year dividend (D1)

= $1.55(1 + 26.56%)

= $1.96Second-year dividend (D2) = $1.96(1 + 26.56%) = $2.48Third-year dividend (D3)

= $2.48(1 + 26.56%)

= $3.

= D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4...∞Where r

= required rate of return Let us substitute the values now PV of the future dividends

= $1.96/(1 + 14.40%)^1 + $2.48/(1 + 14.40%)^2 + $3.14/(1 + 14.40%)^3 + $3.25/(1 + 14.40%)^4...∞PV of the future dividends = $1.96/1.1440^1 + $2.48/1.1440^2 + $3.14/1.1440^3 + $3.25/1.1440^4...∞PV of the future dividends

= $1.72 + $1.92 + $2.04 + $1.86...∞PV of the future dividends

= $7.54We know that the value of the stock is the present value of the expected dividends, so we can calculate it as follows: Value of the stock

= PV of the future dividends Value of the stock

= $7.54

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The factors indicated, are classified according to whether it is associated with a movement along the aggregate demand curve or a shift of the aggregate demand curve.

Movement along the aggregate demand curve

Shift of the aggregate demand curve

An aggregate demand curve depicts the total domestic expenditure on goods and services at each price level.

The AD curve is trending higher due to rising economic prosperity. People's spending grows as their income rises, leading to an increase in AD and vice versa. As a result of the positive link between income and AD, the AD curve slopes higher.

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Full Question:

Classify each factor according to whether it is associated with a movement along the aggregate demand curve or a shift of the aggregate demand curve.

Answer:

3: 67 5:200% 6: 50% 7: 32 8) 20

Step-by-step explanation:

Answer:

Answer:

\(Area \: of \: rhombus = \frac{pq}{2} \)

Where p is diagonal 1 and q is diagonal 2

Step-by-step explanation:

Different formulas to find the area of a rhombus are:

Formulas to Calculate Area of RhombusUsing DiagonalsA = ½ × d1 × d2

Using Base and HeightA = b × h

Using TrigonometryA = b2 × Sin(a)

Area = d1×d2÷2