A new sensor was developed by ABCD Inc. that is to be used for their obstacle detection system. During tests involving 250 runs, the following data were acquired:
The alarm went off 33 times even if there is no obstacle.
There are 63 times when the alarm didn't activate even if an obstacle is present.
The alarm went off correctly 62 times.
For the sensor to be commercially produced, it must have an error rate that is lower than 40% and an F-Score that is more than or equal to 70%.
For answers that have decimal places, use four-decimal places.
How many times that the alarm didn't activate correctly?
How many runs have actual obstacles in place?
How often is the sensor correct?

Jack has a 7.5 meter (750 cm) rope, gives his sister a 150 cm piece, and cuts the remaining 600 cm into 10 equal sections, with each section being 60 cm long.

Jack's rope is 7.5 meters long, which is equal to 750 centimetres. He gives his sister a piece of 150 centimetres, which leaves him with 600 centimetres of rope.
Jack then cuts the remaining piece into 10 equal sections. To find the length of each section, we can divide the total length of the rope (600 cm) by the number of sections (10):
600 cm ÷ 10 sections = 60 cm per section
Therefore, each section of rope that Jack cuts will be 60 centimetres long.

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One possible answer is 120°

Answer: x = -9

Step-by-step explanation:

When you look at the line, you can see it's plotted on the x-axis. From there you know the solution will be equal to x. Since the line passes right through the number -9 on the x-axis line, the answer would be x = -9. The line is straight which means it has no y intercept which is why x is only equal to -9.

The gardener has 98 ft of deer-resistant fence to enclose a rectangular vegetable garden.

Let's say the length of the garden is l and the width is w. We know that the area of a rectangle is A = l x w. Therefore, we can solve for w in terms of l: w = A/l.

The gardener wants to enclose an area of at least 510 square feet. We can plug this in for A and get: w = 510/l.

We also know that the perimeter of the garden is 98 ft. The perimeter of a rectangle is P = 2l + 2w. We can substitute in w = 510/l and simplify to get: P = 2l + 1020/l.

We want to find the range of possible values for l, so we need to consider the constraints. Since l must be positive, we can take the derivative of P with respect to l and set it equal to zero to find the minimum value of P. We get: P' = 2 - 1020/l^2 = 0, which gives us l = sqrt(510).

So the range of possible values for the length of the garden is l > sqrt(510), or approximately l > 22.6 ft.

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Answer:

See below.

Step-by-step explanation:

\(3+x=ax\)    (Given)

\(x=ax-3\)    (Subtracted 3 on both sides)

\(x-ax=-3\)    (Subtracted ax on both sides)

\(x(1-a)=-3\)    (Factor out x from x - ax)

\(x=-\frac{3}{1-a}\)    (Divided 1 - a on both sides)

Answer:

The value of the determinant is 0.

Step-by-step explanation:

Since it is a 3 x 3 determinant, we can calculate its value by the Law of Sarrus:

\(Det = (11)\cdot (98)\cdot (26\cdot y) + (97)\cdot (24\cdot y) \cdot (13) + (22\cdot y) \cdot (12) \cdot (99) - (22\cdot y) \cdot (98) \cdot (13) - (97)\cdot (12) \cdot (26\cdot y) - (11) \cdot (24\cdot y) \cdot (99)\)

\(Det = 28028\cdot y + 30264\cdot y + 26136\cdot y - 28028\cdot y - 30264\cdot y - 26136\cdot y\)

\(Det = 0\)

The value of the determinant is 0.

Answer:

150 people

Step-by-step explanation:

20/50 = 40%
So 40% are wearing hats and 60% aren't

0.6=60%

250x0.6= 150

Step-by-step explanation:

find the equation of a line with slope 2 and 6 unit away from the origin​

slope intercept form: y = mx + b where m = slope and b = y-intercept.

You are given:

slope = 2

b = 6

answer:

y = 2x + 6

Answer:

-2/9

Step-by-step explanation:

Answer:

They will deliver 2208 ounces of food in 4 days.

Step-by-step explanation:

Multiply 34.5 by 16 to get the ounces and got 552. Then multiply 552 by 4 and you'll get the answer.

:))

9514 1404 393

Answer:

  n = -25

Step-by-step explanation:

The next step can be to subtract 2/5n.

  \(\dfrac{3}{5}n+15=10+\dfrac{2}{5}n\\\\\dfrac{1}{5}n+15=10 \qquad\text{subtract $\dfrac{2}{5}n$}\\\\\dfrac{1}{5}n=-5 \qquad\text{subtract 15}\\\\ \boxed{n=-25} \qquad\text{multiply by 5}\)

Nο, Judy’s graph is incοrrect. The inequality symbοl is “less than,” \(\rm s < -9\) is nοt included. He shοuld have used an οpen circle οn -9.

A relatiοn that cοntrasts twο numbers οr οther mathematical assertiοns in an unfair manner is knοwn as an inequality in mathematics. Mοst οften, height cοmparisοns are made between twο digits οn the number line. Different nοtatiοns are used tο describe different kinds οf inequalities.

The Latin and Old French languages are where the terms "inequality" and "inequalitas," which respectively mean "unequal, unlike, different," and "changeable," cοme frοm. This expressiοn is used tο evaluate the size, quantity, and strength οf twο figures οr phrases.

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Answer:

If you just solve normally, you will get x=2 and x=-3. But if you plug these in to check your work, you will find that they are wrong. Your answer is no solution

Step-by-step explanation:

ln(2x+3)+ln(x-2)=ln(x^2-2x)

Rule: log(a) + log(b) = log(a*b)

ln( (2x+3)(x-2) ) = ln(x^2-2x)

Rule: If log(a) = log(b) then a = b

(2x+3)(x-2) = x^2 - 2x

2x^2-x-6=x^2-2x

x^2+x-6=0

Using Quadratic Formula:

x = 2 and x = -3

But, plugging these numbers back into the original equation is false!

Answer:

0.014%

Step-by-step explanation:

We need to write 14 out of 100,000 as a fraction. Which makes 14/100,000. Now 14/100,000 as a percent is 0.014%

Answer:

8/7 is the slope of the line

Step-by-step explanation:

Hope this helps

Answer:

15.8

Step-by-step explanation:

mean is the average in math so 9 + 14 + 11 + 31 + 14 =79 then you have to count how many numbers there is and minus it from the total which there is 5 numbers so 79 divided by 5 = 15.8

Answer:

si Noew

Step-by-step explanation:

no puede ser porque es muy esxtrqño

Answer:

Step-by-step explanation:

 y - y0 = m(x - x0)

y - (-8) = (-1/2)(x - 4)

 y + 8 = (-1/2)x + 2

 y = (-1/2)x - 6  or  (1/2)x + y = -6

Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?

Let

x ------> students enrolled last year

we have that

100%+10%=110%=110/100=1.10

so

528=1.10x

solve for x

x=528/1.10

x=480

Answer:

y= 8x

Step-by-step explanation:

y= 48

x= 6

48/6 = 8

y= 8x

x=2

y= 8(2)

y= 16

Answer:

-8

Step-by-step explanation:

10 -2b^2

Let b=-3

10 - 2( -3)^2

Do the exponent first

10 -2(9)

Multiply

10 -18

Subtract

-8

Answer:

- 8

Step-by-step explanation:

Given

10 - 2b² ← substitute b = - 3 into the expression

= 10 - 2(- 3)²

= 10 - 2(9)

= 10 - 18

= - 8

Please see the attached picture for full solution....

Hope it helps...

Good luck on your assignment...

A series is convergent when the sequence of partial sums, which are the sums of the first n terms in the series, approaches a finite limit as n approaches infinity. In other words, the series has a sum that can be found. On the other hand, a series is divergent if the sequence of partial sums does not approach a finite limit. This means the series does not have a sum. So, to determine if a series is convergent or divergent, analyze the behavior of its sequence of partial sums.

A series is a sum of the terms in a sequence. A convergent sequence is one that has a limit as n approaches infinity, meaning that the sequence approaches a specific value. Similarly, a sequence of partial sums is the sum of the first n terms of the series. If this sequence of partial sums converges to a specific value, then the series is convergent. However, if the sequence of partial sums diverges, meaning it does not approach a specific value, then the series is divergent. Understanding whether a series is convergent or divergent is important in various fields such as physics and engineering.
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The value of x is the set of all real numbers

The expression is given as:

|x| > -6

In the above expression, the value of x can assume any real number.

This means that the value of x is the set of all real numbers

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