sriraman, b; & english, l. (2010). problem solving for the 21st century. in sriraman & english (eds) theories in mathematics education: seeking new frontiers (pp. 263-286). heidelberg, germany, springer.

Answer:

1

2,3,4

Step-by-step explanation: to

when the number of football is 1 is less expensive than basketball

Answer:

# = number of tiles + 2

Step-by-step explanation:

So It would be 3,5,7 but your would add 2 to each number of tiles increased.

There were 0 tiles in step 0

Answer:

It can be observed that there is a pattern

Step 1

Step 2

Step 3

Step 4

Step n

Answer:

b. 22

Step-by-step explanation:

1.6 x 14 = 22.4

22.4 rounded is 22

The evaluation of the limit is lim a-x a+x = 2a.

Student's work:

lim a-x a+x = lim a-x a+x

= 0

Mistake 1: The student incorrectly states that lim a-x a+x is equal to 0. This is incorrect and is not a valid step.

To correct this, the problem:

Corrected solution:

Given the expression lim a-x a+x as x approaches a. To evaluate this limit correctly,  the fact that the limit of the sum is equal to the sum of the limits. So we can split the expression as follows:

lim a-x a+x = lim a-x a + lim a-x x

evaluate each part of the limit separately:

lim a-x a: As x approaches a, the term a does not depend on x. Therefore, the limit of a with respect to x is simply a.

lim a-x x: This is the limit as x approaches a of the variable x. Since x is approaching a, the limit of x is also equal to a.

substitute the evaluated limits back into the original expression:

lim a-x a+x = lim a-x a + lim a-x x

= a + a

= 2a

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x = 8

PR = 18

measure of angle PQT = 30°

Explanation:

The parallel sides of a parallelogram are congruent. SO we equate them together.

20 is parallel to 4x - 12

20 = 4x - 12

add 12 tio both sides

20 + 12 = 4x

32 = 4x

32/4 = 4x/4

x = 8

The diagonals bisect each other at the center. Thus dividing it equally.

PR is divided into two equally:

5y - 36 is congruent to y

5y - 36 = y

collect like terms:

5y - y = 36

4y = 36

4y/4 = 36/4

y = 9

PR = 5y - 36 + y

PR = 6y - 36

PR = 6(9) - 36

PR = 18

Since the diagonals bisect the angles at the 4 corners. The angles at each corner are divided into equal halves.

angle PQR is divided into two equal parts. on eo f the angle is given as 30°.

angle PQT = angle RQT

angle RQT = 30°

Hence, angle PQT is 30°

The integral of the function f(x) =\(0.2 + 25x + 200x^2 - 675x^3 + 900x^4 - 400x^5\)from 0 to 0.8 is approximately 0.3074.

To find the definite integral of the given function analytically, we can use the standard rules of integration. By applying these rules, we obtain the result of approximately 0.3074.

When performing the numerical evaluations, we can use various methods. The first method is the trapezoidal rule. Using this rule, we divide the interval [0, 0.8] into subintervals and approximate the area under the curve using trapezoids.

The true error represents the difference between the actual integral value and the approximation, while the estimated error provides an estimate of the true error.

Applying the trapezoidal rule, we find the value of the integral to be approximately 0.319.

Next, we can improve the approximation by applying the trapezoidal rule with multiple subintervals (n=4). By dividing the interval into four subintervals and using the trapezoidal rule on each subinterval, we obtain a more accurate approximation.

The true error is reduced to approximately 0.009, and the estimated error is around 0.002.

Another method is the Simpson \(\frac{1}{3}\) rule, which approximates the integral using quadratic polynomials.

Applying this rule, we find that the value of the integral is approximately 0.3122. The true error is around 0.004, while the estimated error is approximately 0.0005.

Furthermore, the Simpson \(\frac{3}{8}\) rule can be utilized to further refine the approximation. This rule employs cubic polynomials to estimate the integral.

Applying the Simpson \(\frac{3}{8}\) rule, we obtain a value of approximately 0.3073 for the integral. The true error is approximately 0.0001, while the estimated error is around 0.00002.

Finally, we can enhance the accuracy by employing the Simpson \(\frac{1}{3}\) rule with multiple subintervals (n=4). By dividing the interval into four subintervals and applying the Simpson \(\frac{1}{3}\) rule on each subinterval, we obtain a more precise approximation.

The true error is reduced to approximately 0.00002, and the estimated error is around 0.000003.

In summary, the value of the integral of the given function from 0 to 0.8 can be evaluated analytically as approximately 0.3074. Numerically, we can approximate it using various methods, such as the trapezoidal rule, Simpson \(\frac{1}{3}\) rule, and Simpson \(\frac{3}{8}\) rule, both with and without multiple subintervals.

These numerical methods provide increasingly accurate approximations and help us understand the true and estimated errors associated with each method.

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Answer:

163°

...............

Answer:

163

Step-by-step explanation:

Answer:

Step-by-step explanation:

That is (16/50) * 100

= 16 * 100/50

= 16 *2

= 32%.

Answer: 32%

Step-by-step explanation:

put it into a fraction, 16/50 then multiply by 2 to get 32/100 now you can turn that into a percent to get 32%

The AAA (angle-angle-angle) similarity theorem can be used to express it as follows: two triangles have equal corresponding angles if and only if their corresponding sides are proportionate.

The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that “If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar”.

Proof:

Consider two triangles ABC and DEF, such that ∠A = ∠D, ∠B = ∠E and ∠C = ∠F as shown in the figure.

Now, cut DP= AB and DQ= AC and join PQ. Hence, we can say that a triangle ABC is congruent to the triangle DPQ.

(i.e) ∆ ABC ≅ ∆ DPQ, which gives ∠B = ∠P = ∠E and also, the line PQ is parallel to EF.

Therefore, by using the basic proportionality theorem, we can write

DP/PE = DQ/QF.

(i.e) AB/DE = AC/DF. …(1)

Similarly,

AB/DE = BC/EF …(2)

From (1) and (2), we can write:

AB/DE = BC/EF = AC/DF.

Therefore, the two triangles ABC and DEF are similar.

Hence, AAA(Angle-angle-angle) is proved.

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The number of  boys and girls in a class of 150 students is 90 and 60 respectively.

RATIO:

Comparing two quantities of the same units and determining the ratio tells us how much of one quantity is in the other.

i.e., it shows how many times a number contains another.

Total number of students = 150

ratio of boys to girls = 3 : 2

B:G = 3 : 2

now

3x + 2x = 150

5x = 150

x = 30

the number of boys = 3x = 3 X 30 = 90 boys.

the number of girls = 2x = 2 X 30 = 60 girls.

The number of  boys and girls in a class of 150 students is 90 and 60 respectively.

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The area of the region enclosed by one loop of the curve r = sin(10θ) is π/40.

We have to find the area of the region enclosed by one loop of the curve.

The given curve is:

r = sin(10θ)

Consider the region r = sin(10θ)

The area of region bounded by the curve r = f(θ) in the sector a ≤ θ ≤ b is

A = \(\int^{b}_{a}\frac{1}{2}r^2d\theta\)

Now to find the area of the region enclosed by one loop of the curve, we have to find the limit by setting r=0.

sin(10θ) = 0

sin(10θ) = sin0   or    sin(10θ) = sinπ

So θ = 0             or      θ = π/10

Hence, the limit of θ is 0 ≤ θ ≤ π/10.

Now the area of the required region is

A = \(\int^{\pi/10}_{0}\frac{1}{2}(\sin10\theta)^2d\theta\)

A = \(\frac{1}{2}\int^{\pi/10}_{0}\sin^{2}10\theta d\theta\)

A = \(\frac{1}{2}\int^{\pi/10}_{0}\frac{(1-\cos20\theta)}{2}d\theta\)

A = \(\frac{1}{4}\int^{\pi/10}_{0}(1-\cos20\theta)d\theta\)

A = \(\frac{1}{4}\left[(\theta-\frac{1}{20}\sin20\theta)\right]^{\pi/10}_{0}\)

A = \(\frac{1}{4}\left[(\frac{\pi}{10}-\frac{1}{20}\sin20\frac{\pi}{10})-(0-\frac{1}{20}\sin20\cdot0)\right]\)

A = \(\frac{1}{4}\left[(\frac{\pi}{10}-\frac{1}{20}\sin2\pi)-(0-\sin0)\right]\)

A = 1/4[(π/10-0)-(0-0)]

A = 1/4(π/10)

A = π/40

Hence, the area of the region enclosed by one loop of the curve r = sin(10θ) is π/40.

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Answer:

N = 40S

Step-by-step explanation:

Number of cookies made = 40 times the number of cups of sugar.

Example:

N = 120, S = ?. How much sugar was used?

120 = 40S

3 = S

Graph:

Plot point 1 at (0,0) because 0 cups of sugar is 0 cookies.

Plot points then at (40,1), (80,2) etc. Then draw a line.

Hope that helps

An inequality that represents the number of hot dogs per minute joey could eat for the last 9 minutes to break his record is: 9d +  \(11\frac{1}{4}\) > 72

For given question,

Joey chestnut is trying to break his own record for eating the most whole hot dogs in 10 minutes.

He needs to eat more than 72 hot dogs to break his record.

After 1 minute, joey has eaten \(11\frac{1}{4}\) hot dogs.

let d represent the number of hot dogs joey eats per minute for the next 9 minutes.

9d +  \(11\frac{1}{4}\) is the expression that shows how many hot dogs he will eat in total.

9d being how much he'll eat in the remaining 9 minutes, and \(11\frac{1}{4}\) being the number of hot dogs he's already eaten in the first minute.

Since it has to beat his former record of 72, it has to be greater than 72. The inequality would be

9d +  \(11\frac{1}{4}\) > 72

Therefore, an inequality that represents the number of hot dogs per minute joey could eat for the last 9 minutes to break his record is:

9d +  \(11\frac{1}{4}\) > 72

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Answer:

  the can with the 5-inch radius will cost more

Step-by-step explanation:

The cost will be given by the formula ...

  cost = 1.40 × (top & bottom area) + 0.90 × (lateral area)

In terms of radius and height the areas are ...

  top & bottom area = 2πr²

  lateral area = 2πrh

So, the total cost of a can with radius r and height h is ...

  c(r, h) = 1.40·2πr² +0.90·2πrh

Filling in the given values and doing the arithmetic, we find the costs to be ...

  c(4, 5) = $253.84

  c(5, 4) = $333.01

The cost of the can with the 5-inch radius is the greatest.

Answer:

The cylinder with radius of 5 inches and height of 4 inches costs more to manufacture.

Step-by-step explanation:

First Can:

Top and Bottom Surface Area = 2(pi(4)^2) = 2(16pi) = 32 pi = 100.53 square inches

Cost for top and bottom surface area = 1.40 * 100.53 = $140.74

Curved Surface Area = 2pi*r*h = 2*pi*4*5 = 40 pi = 125.66 square inches

Cost for Curved Surface Area = 125.66 * 0.90 = $113.10

Total Cost = $140.74 + $113.10 = $253.84

Second Can

Top and Bottom Surface Area = 2(pi(5)^2) = 2(25pi) = 50 pi = 157.08 square inches

Cost for top and bottom surface area = 1.40 * 157.08 = $219.91

Curved Surface Area = 2pi*r*h = 2*pi*5*4 = 40 pi = 125.66 square inches

Cost for Curved Surface Area = 125.66 * 0.90 = $113.10

Total Cost = $219.91 + $113.10 = $333.01

So, the cylinder with radius of 5 inches and height of 4 inches costs more to manufacture.

Answer:

the one gonna truend into two

at th down the two truend into one y is the meaning that connot has issue with fractions

Answer:

(-2,2)

Step-by-step explanation:

Answer:    12 min

Step-by-step explanation:

Volume = Bh      Where

B=Area of Base = 480 cm²

h = height = 15 cm

Volume = 480 x 15

Volume = 7200 cm³

Convert the volume to Liters Given(1 L=1,000 cm³)

Volume = ( 7200 cm³)(1 L/1,000 cm³)

Volume = 7.2 L

They want to know how long it will take to empty the tank with

Volume=7.2 L container    

But it is being filled and emptied at the same time.

Filled at rate, X=1.5 L/min      and

Emptied at rate, Y=2.1 L/min

After 1 min :  Filled to 8.7 but resulted in emptying to 6.6

After 2 min : Filled to 8.1  but resulted in emptying to 6

After 3 min : Filled to 7.5 but resulted in emptying to 5.4

You can see that this results in emptying at a rate of .6 L/min

So if we divided Volume by .6 L/min that will give us how many min it takes

Time = Volume/rate

Time = (7.2 Liters) / (.6 L/min)

Time = 12 min

Given:

Radius of circle is 13 cm

Height of triangle is 5 cm

To find:

Value of 'a' and 'b'

Steps:

To find value of 'a', we will use Pythagoras theorem as the triangle is a right angle triangle,

A² + B² = C²

\(a^{2} + 5^{2} = 13^{2}\)

\(a^{2} + 25 = 169\)

\(a^{2} = 169 - 25\)

\(a^{2} = 144\)

\(\sqrt{a^{2}}=\sqrt{144}\)

\(a = 12\)

Now to find the value of 'b', i will use law of cosine,

\(c=\sqrt{a^{2}+b^{2}-2ab(cos\beta ) }\)

\(12 = \sqrt{13^{2}+5^{2}-2(5)(13)(cos\beta )}\\12=\sqrt{169 + 25-130(cos\beta )}\\12=\sqrt{194-130(cos\beta )}\\144 = 194 - 130(cos\beta )\\50 = 130(cos\beta )\\cos\beta = 0.3846\\\beta = cos^{-1}(0.3846)\\\beta = 67.38\)

Therefore, the values of 'a' and 'b' is 12 and 67.38 respectively

Happy to help :)

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Answer:

congruent

Step-by-step explanation:

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

so yes, they are congruent because they have the same angle

Answer:

To convert 2 Bigha into Kattha:

If 1 Bigha = 20 Kattha:

2 Bigha = 2 * 20 Kattha = 40 Kattha

If 1 Bigha = 16 Kattha:

2 Bigha = 2 * 16 Kattha = 32 Kattha

Answer:

X = 4.47  Y = 8.94

Step-by-step explanation:

2\(\sqrt{5}\)= 2.23606798

2.23606798 x 2 = 4.47213596

-------

4.47213596

4.47213596^2 + 4.47213596^2 = 8.94427192^2

8.94427192^2 = 80

Square root of 80 is 8.94

Answer: D

Step-by-step explanation:

i did the test

There will be approximately 0.05 liters of water left in the bowl after the cats drink their average daily amount of water.

To determine the amount of water left after the cats drink their average daily amount, we need to know the average daily water consumption per cat. Let's assume that each cat drinks 0.4 liters of water per day.

The total water consumption for the three cats would be 3 cats * 0.4 liters/cat = 1.2 liters.

Since the initial amount of water in the bowl is 1.25 liters, we can subtract the total water consumption from the initial amount to find the remaining water:

Remaining water = Initial amount - Total water consumption

Remaining water = 1.25 liters - 1.2 liters

Remaining water = 0.05 liters

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Answer:

the sum of 10+16 multiplied by 49

Step-by-step explanation:

Answer:

The Third number is 19

Step-by-step explanation:

7 + 2 = 11 then add 19=

11 + 19 = 30 After divide by three because there are 3 numbers

30.6 ÷ 3 = 10

Remember: To find the mean you add all the numbers together and divide by how many numbers are there.

For example: you have 2, 5, 8 you add them together which is 15. There are 3 numbers so you divide 15 by 3 which is 5.

Answer:

$278.40

Step-by-step explanation:

Note: "...an additional 10% off any shoe item, once the first discount has been applied." (emphasis added).

Note that the customer is buying 3 pairs of shoes for $120 each: 120 x 3 = $360

The first discount is the 20% discount  (on every single item), the second discount is the 10% discount coupon of of any item (which signifies one item only).

Solve for the first discount:

$360 x 0.20 = $72

$360 - 72 = $288.

Next, divide $288 by 3 (to get the individual prices of the shoes:

$288/3 = $96.

The customer then uses a birthday coupon for one of the shoes, which gives an additional 10% off.

$96 x 0.10 = 9.6

$96 - 9.6 = $86.4

Remember, the other two shoes still cost $96 each. Add the price together:

$96 + $96 + $86.4 = $278.40

$278.40 will be the total.

~

Answer:

278.40

Step-by-step explanation:

Answer:

2^2

Step-by-step explanation:

(2^7)/(2^5) = 2^(7 - 5) = 2^2

0.529 is the probability that a student does not have a college degree.

From the information given, we know that:

The formula for conditional probability:

P(A|B) = P(A and B) / P(B)

Let A be the event of not having a college degree, and B be the event of being married. We want to find P(A).

Using these values, we can calculate:

P(college degree and B) = (1/2) * (400/850) = 0.235

P(A and B) = 310/850 - 0.235 = 0.07

Finally, we can calculate P(A) using the formula for total probability:

P(A) = 1 - P(college degree)

= 1 - (400/850)

= 0.529

Therefore, the probability that a student does not have a college degree is 0.529.

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Answer:

5

Step-by-step explanation:

A function

\(a \times {b}^{x} \)

where a is the initial value and b is the multiplicative rate of change.

In the function,

\(f(x) = 2 \times {5}^{x} \)

5 is the value of b so

5 is the multipicative rate of change

The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

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