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2 years ago

Prajna is listing squares of two-digit numbers in such a way that the digit in their units place is 6.

Mathematics

1 answer:

dem82 [27]2 years ago

6 0

Answer:

2 (option B)

Question:

Prajna is listing squares of two-digit numbers in such a way that the digit in their units place is 6.

How many numbers should he have listed?

a) 9 b) 2 c)18 d) 20

Step-by-step explanation:

We would find the perfect squares that are two digit numbers

For two digit perfect squares:

Largest two digit number= 81 = 9²

Smallest two digit number= 16 = 4²

Total Two digit number perfect squares = Highest number - lowest number + 1

= 9-4+1 = 6

There are 6 two digit perfect squares

Next, we have to find how many of them have 6 in their units place.

The rule to be applied: If a number has 4 or 6 in the unit place, then its square has 6 in the units place.

Following this, the possibilities are 4², 6².

We have two of such numbers.

Therefore, he would have listed 2 numbers.

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Mr. Abraham is 36 years old. His wife is 6 years younger than him and their son is 24 years old younger than his wife. What is t

sesenic [268]

Hi!
We know that Mr. Abraham’s wife is 6 years younger than him, which is 36-6, which means his wife is 30 years old.

We also know that Mr A’s son is 24 years younger than his wife, which is 30-24, which is 6.

As of right now, we now know that:
Mr. A is 36
Mr. A’s wife is 30
Mr. A’s son is 6

It’s asking for the ratio of Him:Wife:Son, so 36:30:6.

BUT, it’s asking for simplest form, so divide each of those numbers by 6.

Your answer is: 6:5:1

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2 years ago

Find the point (x,y) of x2+14xy+49y2=100 that is closest to the origin and lies in the first quadrant.

Gala2k [10]

Notice that

$x^2+14xy+49y^2=(x+7y)^2$

so the constraint is a set of two lines,

$(x+7y)^2=100\implies\begin{cases}x+7y=10\\x+7y=10\end{cases}$

and only the first line passes through the first quadrant.

The distance between any point $(x,y)$ in the plane is $\sqrt{x^2+y^2}$ , but we know that $\sqrt{f(x,y)}$ and $f(x,y)$ share the same critical points, so we need only worry about minimizing $x^2+y^2$ . The Lagrangian for this problem is then

$L(x,y,\lambda)=x^2+y^2+\lambda(x+7y-10)$

with partial derivatives (set equal to 0)

$L_x=2x+\lambda=0$

$L_y=2y+7\lambda=0$

$L_\lambda=x+7y-10=0$

We have

$L_y-7L_x=2y-14x=0\implies y=7x$

which tells us that

$x+7y-10=0\iff x+49x=10\implies x=\dfrac15\implies y=\dfrac75$

so that $\left(\dfrac15,\dfrac75\right)$ is a critical point. The Hessian for the target function $x^2+y^2$ is

$H(x,y)=\begin{bmatrix}2&0\\0&2\end{bmatrix}$

which is positive definite for all $x,y$ , so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is $\sqrt{\left(\dfrac15\right)^2+\left(\dfrac75\right)^2}=2$ .

3 0

2 years ago

During a sale, 20-cent candy bars were sold at 3 for 50 cents. How much is saved on 9 bars?

Mazyrski [523]

Answer:

Step-by-step explanation:

$0.30

Step-by-step explanation:

1 bar of candy = $0.20

3 bars of candy = $0.50

To solve, multiply for both:

If you pay for each candy bar individually, they each cost $0.20. Multiply 9 with 0.20:

9 x 0.20 = $1.80

If you pay for the candy bars by 3's, they cost $0.50 each pack. Divide 9 with 3, then multiply by 0.50:

9/3 = 3

3 x 0.50 = $1.50

Subtract the total cost of the individual from the pack:

$1.80 - $1.50 = $0.30

. $0.30 is your answer.

8 0

2 years ago

Jody bought 20 shares of amazon at the close price of $121.00. She bought 20 more shares a year later at the price of $127.00. T

hjlf

Answer:

Jody made $210 after all of these transactions.

Step-by-step explanation:

Jody bought 20 shares of amazon at the price of $121.00

= 121.00 × 20 = $2,420

After one year she bought 20 more shares at the price of $127.00

= 127.00 × 20 = $2,540

Her broker charges $50.00 for each transaction = 50 × 2 = $100

Total cost of all shares = 2,420 + 2,540 + 100 = $5,060

She sold all of her shares at the price of $133.00

= 133 × 40 = $5,320

She gave broker charge for this transaction = $50.00

Total selling amount = 5,320 - 50 = $5,270

Profit = Selling amount - cost

Profit = 5,270 - 5,060 = $210

Jody made $210 after all of these transactions.

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2 years ago

Read 2 more answers

A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past

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Answer: We reject the null hypothesis, and we use Normal distribution for the test.

Step-by-step explanation:

Since we have given that

We claim that

Null hypothesis : $H_0:\mu\geq 50000$

Alternate hypothesis : $H_1:\mu$

There is 5% level of significance.

$\bar{X}=46800\\\\\sigma=9800\\\\n=29$

So, the test statistic would be

$z=\dfrac{\bar{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\z=\dfrac{46800-50000}{\dfrac{9800}{\sqrt{29}}}\\\\z=-1.75$

Since alternate hypothesis is left tailed test.

So, p-value = P(z≤-2.31)=0.0401

And the P-value =0.0401 is less than the given level of significance i.e. 5% 0.05.

So, we reject the null hypothesis, and we use Normal distribution for the test.

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2 years ago