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2 days ago

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Terrence finished a word search in 3/4 the time it took Frank. Charlotte finshed the word search in 2/3 the time it took Terrenc

e. Frank finished the word search in 32 min. How long did it tack Charlott to finish the word search

1 answer:

Zina [3.9K]2 days ago

6 0

Answer: Charlotte completed the word search in 16 minutes.

Step-by-step explanation:

Frank took 32 minutes to finish the word search.

Terrence completed the word search in three-quarters of the time Frank used, which is:

3/4 × 32 = 24 minutes.

Charlotte finished it in two-thirds the time Terrence took, leading to:

2/3 × 24 = 16 minutes for Charlotte.

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Find the inverse of y=x2-10x

AnnZ [3877]

<span>This is quite challenging, but here’s the solution:
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y = x^2 - 10x + 25 - 25

<span> y = (x-5)^2 - 25</span>

<span> y + 25 = (x-5)^2</span>

<span> x - 5 = ±sqrt(y+25)</span>

<span> You will derive TWO inverses:</span>

<span> x = 5 + sqrt(y+25),</span> for x ≥ 5

<span> x = 5 - sqrt(y+25),</span> for x ≤ 5

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12 days ago

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Explain how to estimate the quotient using compatible numbers. 27 and two-thirds divided by 3 and StartFraction 9 over 10 EndFra

AnnZ [3877]

Answer:

The first fraction comes between 27 and 28, leaning towards 28. The second fraction lies between 3 and 4, leaning towards 4. Compatible numbers in division consist of figures that are simple to calculate mentally. 28 divided by 4 results in 7. The estimated quotient will be approximately 7.

Step-by-step explanation:

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6 days ago

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Mike earned x dollars the first week of his new job. He earned 5% more the second week than the first week. Which expression rep

zzz [4022]

The expression indicates that the total earnings of Mike over the two weeks amount to 2.05x dollars

Solution:

It is given that Mike earned x dollars during the first week at his new job,

While in the second week, he earned 5% more than the earnings of the first week.

To determine: Total earnings over the two weeks

From the information provided,

Earnings in the first week = "x" dollars

Earnings in the second week = 5% more than first week earnings

Thus,

Earnings in the second week = x + 5% of x

$\rightarrow x + 5 \% \times x\\\\\rightarrow x + \frac{5}{100} \times x\\\\\rightarrow x + 0.05x = 1.05x$

Therefore, earnings in the second week equal to 1.05x dollars

The total earnings over the two weeks:

Total earnings = Earnings from first week + Earnings from second week

$Total\ Amount = x + 1.05x = 2.05x$

Thus, the expression for the total earnings of Mike for both weeks is 2.05x dollars

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4 days ago

Find the point on the circle x^2+y^2 = 16900 which is closest to the interior point (30,40)

Leona [4166]

Response-

(78,104) represents the point closest to the interior.

Explanation-

The equation defining the circle,

$\Rightarrow x^2+y^2 = 16900$

$\Rightarrow y^2 = 16900-x^2$

$\Rightarrow y = \sqrt{16900-x^2}$

Since the point lies on the circle, its coordinates must be,

$(x,\sqrt{16900-x^2})$

The distance "d" from the point to (30,40) can be calculated as,

$=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$=\sqrt{(x-30)^2+(\sqrt{16900-x^2}-40)^2}$

$=\sqrt{x^2+900-60x+16900-x^2+1600-80\sqrt{16900-x^2}}$

$=\sqrt{9400-60x-80\sqrt{16900-x^2}}$

Next, we need to determine the value of x for which d is minimized. The minimum distance occurs when $9400-60x-80\sqrt{16900-x^2}$ is at its lowest value.

Let’s set up the equation,

$\Rightarrow f(x)=9400-60x-80\sqrt{16900-x^2}$

$\Rightarrow f'(x)=-60+80\dfrac{x}{\sqrt{16900-x^2}}$

$\Rightarrow f''(x)=\dfrac{1352000}{\left(16900-x^2\right)\sqrt{16900-x^2}}$

We find the critical points,

$\Rightarrow f'(x)=0$

$\Rightarrow-60+80\dfrac{x}{\sqrt{16900-x^2}}=0$

$\Rightarrow 80\dfrac{x}{\sqrt{16900-x^2}}=60$

$\Rightarrow 80x=60\sqrt{16900-x^2}$

$\Rightarrow 80^2x^2=60^2(16900-x^2)$

$\Rightarrow 6400x^2=3600(16900-x^2)$

$\Rightarrow \dfrac{16}{9}x^2=16900-x^2$

$\Rightarrow \dfrac{25}{9}x^2=16900$

$\Rightarrow x=\sqrt{\dfrac{16900\times 9}{25}}=78$

$\Rightarrow x=78$

Then,

$\Rightarrow f''(78)=\dfrac{1352000}{\left(16900-78^2\right)\sqrt{16900-78^2}}=\dfrac{125}{104}=1.2$

Since f''(x) is positive, the function f(x) achieves its minimum at x=78

When x is set to 78, the corresponding y value will be

$\Rightarrow y = \sqrt{16900-x^2}=\sqrt{16900-78^2}=104$

This leads us to conclude that the closest point is (78,104)

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8 days ago

A factory received a shipment of 38 sprockets, and the vendor who sold the items knows there are 5 sprockets in the shipment tha

tester [3916]

Answer:

a) 0.00019923%

b) 47.28%

Step-by-step explanation:

a) To determine the likelihood that all sockets in the sample are defective, we can use the following approach:

The first socket is among a group that has 5 defective out of 38, leading to a probability of 5/38.

The second socket is then taken from a group of 4 defective out of 37, following the selection of the first defective socket, resulting in a probability of 4/37.

Extending this logic, the chance of having all 5 defective sockets is computed as: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%.

b) Using similar reasoning as in part a, the first socket has a probability of 33/38 of not being defective as it's chosen from a set where 33 sockets are functionally sound. The next socket has a proportion of 32/37, and this continues onward.

The overall probability calculates to (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%.

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7 days ago