The sum of two consecutive integers is 187. Find the integers.​

The Approximate the solution to the equation using three iterations of successive approximation is option b: 27/8.

In the equation given:

Note that:

x²-3x+2 = square root √x-2 + 2

Therefore:

x⁴-6x³+9x²= square root x-2

x² = 3.375

Convert 3.35 into fractions and will get 27/8. So, The Approximate the solution to the equation using three iterations of successive approximation is option b: 27/8.

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Answer:

3.398

Step-by-step explanation:

log(10) 2500 = log(10) (5^2*10^2) = log(10) 5^2 + log(10) 10^2 = 2*log(10) 5 + 2=3.398

Factors such as an increase in disposable income, a decrease in taxes, an increase in consumer confidence, and an increase in wealth can lead to an upward shift in the consumption function.

An increase in disposable income, a decrease in taxes, a decrease in interest rates, or an increase in consumer confidence would lead to an upward shift in the consumption function. These factors would increase consumer spending and shift the consumption function upwards.

To predict an upward shift in the consumption function, consider the following factors:

An increase in disposable income: When people have more disposable income, they are more likely to spend money, leading to an upward shift in the consumption function.

A decrease in taxes: Lower taxes mean more disposable income for consumers, resulting in higher consumption.

An increase in consumer confidence: When consumers feel confident about their economic future, they are more likely to spend money, causing the consumption function to shift upward.

An increase in wealth: When consumers' wealth increases, they are more likely to spend, leading to an upward shift in the consumption function.

In summary, factors such as an increase in disposable income, a decrease in taxes, an increase in consumer confidence, and an increase in wealth can lead to an upward shift in the consumption function.

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Answer:

The area of the red carpet is 1057 ft²

Step-by-step explanation:

The area of the red carpet is 112.35 ft².

Given that, the width of the stage =63 ft and the length of the stage =10 2/3 ft.

The area of a rectangle is obtained by multiplying its length and width. Thus, the formula for the area, 'A' of a rectangle whose length and width are 'l' and 'w' respectively is the product "l × w".

Now, the width of the red carpet is 1/6 of the width of the floor = (1/6) × 63

=10.5 ft

Here, 10 2/3 can be written as 10.66 ≈ 10.7 ft

The area of the red carpet = length × width = 10.7 × 10.5

=112.35 ft²

Therefore, the area of the red carpet is 112.35 ft².

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At a discount rate of 20%, the present value of your aunt’s offer of $22,000 in 17 years is approximately $190.46.


To calculate the present value of your aunt’s offer, we use the discount rate of 20%. The formula for present value is PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods. Plugging in the values, we have PV = $22,000 / (1 + 0.20)^17, which gives us approximately $190.46.

For the investment scenarios, we use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial investment), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values for each case, we calculate the final amounts.
a. A = $12,500(1 + 0.07/1)^(1*8) ≈ $19,956.77.
b. A = $12,500(1 + 0.10/1)^(1*17) ≈ $46,426.32.
c. A = $12,500(1 + 0.12/2)^(2*20) ≈ $73,785.59.
Therefore, if you invest $12,500 today, you will have approximately $19,956.77 in 8 years at 7%, $46,426.32 in 17 years at 10%, and $73,785.59 in 20 years at 12% compounded semiannually.

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Answer:

76.

Step-by-step explanation:

It is given that N is a 2-digit number.

Last two digits of N^2 is the same as N.

We know that, a number is even if it ends with 0,2,4,6,8.

\(2^2=4,4^2=16,6^2=36,8^2=64\)

If 0 is in end then we get two zeros in the square of that number.

It is clear that, number should ends with 6 to get the same number at the end.

\(16^2=256\)

\(26^2=676\)

\(36^2=1296\)

\(46^2=2116\)

\(56^2=3136\)

\(66^2=4356\)

\(76^2=5776\)

\(86^2=7396\)

\(96^2=9216\)

It is clear that last two digits of (76)^2 is the same as 76.

Therefore, the required number is 76.

The Laplace transform of the motion equation is mx(t) + dx(t) + kx(t) = f(t).

Given: Motion equation is mx(t) + dx(t) + kx(t) = f(t); X(s) and

F(s) be the Laplace transforms of the position x(t) and external force f(t) respectively.

Transfer function is G(s)= X(s)/F(s) = 1/ms² + ds + k

To derive a transfer function of a mass-spring-damper system from its equation of motion, we have to follow these steps:

Step 1: Take the Laplace transform of the motion equation.

Laplace Transform of the given equation is,  mX(s)s² + dX(s)s + kX(s) = F(s)

Step 2: Write X(s) in terms of F(s)X(s) = F(s) / m s² + d s + k

Step 3: Now the transfer function can be derived using the ratio of X(s) to F(s).

Transfer Function = G(s) = X(s) / F(s)G(s) = 1 / ms² + ds + k

Hence, the transfer function of a mass-spring-damper system from its equation of motion is G(s) = 1 / ms² + ds + k. 

In order to derive a transfer function of a mass-spring-damper system from its equation of motion, the following steps are necessary:

  Take the Laplace transform of the motion equation.

The Laplace transform of the motion equation is mx(t) + dx(t) + kx(t) = f(t).

X(s) and F(s) are the Laplace transforms of the position x(t) and external force f(t), respectively.

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First, we can use the points (4,3) and (20,15) to find the slope of the line:

Now we can find the relation function using the point (4,3) and the slope s=3/4

therefore, the equation to describe the relationship between J and M is m=3/4j

Answer:

0.03215.

Step-by-step explanation:

The best graph for the cancer registrar to use in displaying the ten-year survival rates of breast cancer patients at the hospital would be a line graph. The answer is: c.

Line graphs are particularly useful for displaying trends over time, making them suitable for representing the ten-year survival rates of breast cancer patients. The x-axis can represent the years, while the y-axis can represent the survival rates.

Each point on the graph represents the survival rate for a specific year, and connecting these points with lines shows the overall trend over the ten-year period.

Line graphs are effective in illustrating changes and patterns in data, making them well-suited for displaying the progression of survival rates over time. They allow for a clear visualization of how survival rates may have increased, decreased, or remained stable over the ten-year period.

Hence, the correct option is c. Line graph.

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The total money earned for taking care of the pets by Tamera is 7h + 30.

Equation is an expression used to show the relationship between one or more numbers and variables.

Let y represent the total money earned for x hours. Hence:

y = 7h + 15 * 2

y = 7h + 30

The total money earned for taking care of the pets by Tamera is 7h + 30.

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Answer:

28.84

Step-by-step explanation:

the figure is just a square made up of squares so to find the side of a square you use the \sqrt{52} to find one side then multiply times 4 for each side

A parent function is the simplest function of a family of functions which preserves the shape of all other functions in that family.

Notice that the function:

Comes from certain transformations applied to the parent function absolute value:

Answer:

a = - 8

Step-by-step explanation:

A polynomial divided by factor (x - h) has a remainder given by f(h)

Here the divisor is (x - 2), thus f(2) gives the remainder, that is

2³ + 2(2)² - 7(2) + a = 4 ← 4 being the remainder

8 + 8 - 14 + a = 4, that is

12 + a = 4 ( subtract 12 from both sides )

a = - 8

Answer:

B. 60%

Step-by-step explanation:

Formula to be used:

Percent of Increase/Decrease = Final Price ÷ Original Price x 100

Substitute

510 ÷ 850 = 0.6

Turn into percentage

0.6 x 100 = 60%

The monthly payment if the interest rate was 11% will be $45.63.

The remaining amount is calculated as,

P = (1 - 0.20) x $925

P = 0.80 x $925

P = $740

The monthly payment is calculated as,

MP = [$740 + ($740 x 0.11)] / 18

MP = $821.4 / 18

MP = $45.63

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The monthly payment is $49.69.

We have,

The amount of the down payment is:

0.20 x $925 = $185

So the amount financed is:

$925 - $185 = $740

Using the formula for the monthly payment on a loan:

= (Pr(1+r)^n) / ((1+r)^n - 1)

where:

P = principal or amount financed = $740

r = monthly interest rate = 11%/12 = 0.0091667

n = total number of payments = 18

Plugging in the values, we get:

Monthly payment

= ($7400.0091667 x (1+0.0091667)^18) / ((1 + 0.0091667)^18 - 1)

= $49.69 (rounded to the nearest cent)

Therefore,

The monthly payment is $49.69.

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Answer:

x=32

Step-by-step explanation:

sum of interior angles of a triangle = 180

add up all angles and equate to 180

(4x-13)+(x+18)+15=180

5x=160

x=160/5=32

x+18  =   32+18    = 50

4x-13  =  4x32-13 = 128-13 = 115

add up all to check whether ans = 180;  15+50+115=180

step 1 solve for x step 2 after getting the value of x ,substitute and get the value of angles

Answer:

the answer is 6.63

the one on the left is (2,2) the one on the right is (8,2)

In the novel, "The Outsiders," Ponyboy is the main character, who belongs to a gang of greasers and struggles with their existence. One night, Ponyboy's situation was unfortunate, and his relationship with Darry was rocky, but they were able to overcome their problems and grow as individuals.

which upset Darry. He slapped Ponyboy in anger, which made him even more frustrated and resulted in him running away with his best friend, Johnny.The novel revolves around two distinct classes, the rich, privileged, and entitled "socs" (short for socials), and the working-class "greasers." Ponyboy and his brothers are greasers, and they often encounter trouble from socs.

Darry was terrified and worried sick about Ponyboy and didn't mean to hurt him. Johnny and Ponyboy were equally scared and confused about what to do. However, they realized that running away wouldn't solve anything and returned home, where they had a heart-to-heart conversation with Darry, who apologized for hitting Ponyboy. In conclusion,

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15. Length of the radius is 4√11 inches.16.

16. Length of the chord is 6√51 cm.17

17.  Length of AB is 117.4 cm.

15. Given a chord is 20 inches long and is 24 inches from the center of the circle.

Let O be the center of the circle, and AB is the chord which is 20 inches long. Also, let OP be perpendicular to AB. Hence, OP is the perpendicular bisector of AB. Therefore, AO = BO = 12 inches. Hence, we have to find radius OP.

Using Pythagoras theorem, we have  \($OP=\sqrt{OA^2-AP^2}=\sqrt{12^2-10^2}=4\sqrt{11}$\) inches

Answer: Length of the radius is 4√11 inches.16. Given the diameter of a circle is 30 cm long and the distance from the chord to the center of the circle is 9 cm.

We know that the distance of the chord from the center of the circle is 9 cm and diameter is 30 cm.

The distance of the chord from the center of the circle bisects the chord i.e., PE = EF. We have to find the length of chord CD.

Now, we know that OP = 15 cm (half of diameter)and OE = 9 cm

Therefore, we have, EP = OP - OE = 6 cm

Triangle EPC is a right-angled triangle using Pythagoras theorem, we have, \($EC = \sqrt{PC^2+EP^2}=\sqrt{15^2-6^2}=3\sqrt{51}$\)

Similarly, triangle FPD is a right-angled triangle, using Pythagoras theorem, we have, \($FD = \sqrt{PD^2+PF^2}\\=\sqrt{15^2-6^2}\\\=3\sqrt{51}$\)

Therefore, we have, CD = EF = EC + FD = $3\sqrt{51}+3\sqrt{51}=6\sqrt{51}$ cm

Answer: Length of the chord is 6√51 cm.17. Given in circle O, the radius is 36 cm long and mAB = 140°.

We know that the angle subtended at the center of a circle is twice the angle subtended at the circumference of the circle.

Therefore, \($\angle AOB = 2\angle ABB=280$\)°

We know that angle in a semicircle is a right angle.

Therefore, \($\angle AOB = 90$\)°

So, 280° + 90° = 370° is the total angle in circle O

Therefore, we have 370° = \($2\pi r$\) (circumference of circle)

where r is the radius of the circle.

We know that \($\pi=\frac{22}{7}$\)

Hence, \($370=2\frac{22}{7}r$\)

Solving the above equation, we have,

\($r = \frac{370\times 7}{44}= 62.5$\) cm

So, the length of AB = 2r sin (AB/2)

= \($2\times 62.5 \sin(70)$\)

= \($2\times 62.5 \times 0.9397$\)

= 117.4 cm (approx)

Answer: Length of AB is 117.4 cm (approx).

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Answer:

i am almost positive its 448

Step-by-step explanation:

The surface area of the box is 448 square inches so that is the least amount of paper needed to cover the box. A gift box is the shape of a rectangular prism measures 8 inches by 8 inches by 10 inches.

Answer:138

Step-by-step explanation:

Answer:

49 coins.

Step-by-step explanation:

It takes 10 dimes to equal a dollar, therefore fourty dimes equals four dollars.

Eight more dimes for the eighty cents, and one nickel for the 5 cents.

Answer:

300

Step-by-step explanation:

3 :  15 :: 60 : x

Product of extremes  = Product of  means

3 * x = 15 * 60

    \(x = \frac{15 * 60}{3}\\\\x = 5*60\\\\x = 300\)

Or Do in this way

\(\frac{3}{15}=\frac{60}{x}\\\\\)

\(\frac{3*20}{15*20}=\frac{60}{x}\)

x = 15* 20 = 300

Answer:

300

Step-by-step explanation:

Answer:

p = 6 is the answer

Step-by-step explanation:

Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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Answer:

- The graph is decreasing over its entire domain

- The graph is symmetrical about the origin

Step-by-step explanation:

The graph has an unremovable discontinuity at X=0, therefore all continuity answers are incorrect.

The graph is neither symmetrical about the x-axis nor y-axis, but if it were to be rotated around the origin, it would be symmetric.

On both sides of the graph, the slope is decreasing.

Therefore:

- The graph is decreasing over its entire domain

- The graph is symmetrical about the origin