A home security system is designed to have a 99% reliability rate. Suppose that nine homes equipped with this system experience an attempted burglary. Find the probability that eight or fewer alarms are triggered.

Answer:

New base area = 8 x 25/16 = 25/2 = 12•5 cm²

New height = 7•5 cm²

V = 7•5 x 12•5 cm³

V = 93•75 cm³

Step-by-step explanation:

Answer:

you must flip a coin 25 times and record it on a table for experimental. Theoretical would be 50% chance ( showing working)

The theoretical probability of landing on heads or tails is always 0.5 or 50%. The experimental probability of landing on tails is determined by dividing the number of times you land tails by the total number of flips. Over the long term, thanks to the Law of Large Numbers, these values tend to converge.

The subject of the question is the probability of landing on heads or tails when flipping a coin 25 times. The experimental probability of landing on tails can only be determined empirically by actually performing the experiment. After flipping the coin 25 times, you would calculate the experimental probability of landing on tails by dividing the number of times you landed on tails by the total number of flips (25).

On the other hand, the theoretical probability of landing on heads or tails on a single flip of a fair coin is always 0.5, or 50%, due to the nature of the coin having two equally likely outcomes. This is known as the Law of Large Numbers, which states that as the number of trials of a random experiment increases, the experimental probability approaches the theoretical probability.

For example, if we talk about Karl Pearson's experiment, after flipping a coin 24,000 times, he obtained heads 12,012 times. The relative frequency of heads is 12,012/24,000 = 0.5005, which is very close to the theoretical probability (0.5).

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Answer:

a represents the Number of Minutes Late, (a=15 in this case)

Step-by-step explanation:

If the daycare charges a base fee of $3 plus $0.50 per minute late for late pickups(after closing time).

Albin on arrival for pickup had to pay $10.50;

She uses the equation

10.50=0.50a+3

0.50a=10.50-3

0.50a=7.50

a=7.50/0.5

a= 15

It means Albin was 15 minutes late to a pickup.

Answer:

3.8% chance

Step-by-step explanation:

Answer: the ladder should be 25 feet

Step-by-step explanation:

The ladder forms a right angle triangle with the building and the river. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.

The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.

To determine the length of the required ladder h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

h² = 24² + 7² = 576 + 49

h² = 625

h = √625 = 25 feet

Answer:

The appropriate z multiplier for 66% confidence interval is 0.95

Step-by-step explanation:

We are given the following in the question:

Confidence interval:

[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

We have to make a 66% confidence interval for the proportion of voters.

Confidence level = 66%

Significance level =

[tex]\alpha = 1 - 0.66 = 0.34[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.34} = \pm 0.95[/tex]

Thus, the appropriate z multiplier for 66% confidence interval is 0.95

Step-by-step explanation:

5)

3x³y + x²y² + x²y

x²y (3x + y + 1)

6)

8r³ − 64s⁶

8 (r³ − 8s⁶)

8 (r − 2s²) (r² + 2rs² + 4s⁴)

The answer is no, Chloe did not fill out her math journal correctly.

To determine if Chloe completed all 100 math problems correctly, we need to calculate the total number of problems she completed over the weekend.

On Friday, Chloe completed [tex]\( \frac{39}{100} \)[/tex] of the problems. This fraction represents the portion of the total problems she completed on Friday. To find out how many problems this corresponds to, we multiply the total number of problems by this fraction:

[tex]\[ \text{Problems on Friday} = \frac{39}{100} \times 100 = 39 \text{ problems} \][/tex]

On Saturday, Chloe completed [tex]\( \frac{5}{10} \)[/tex] of the problems. Again, we multiply the total number of problems by this fraction to find out the number of problems completed on Saturday:

[tex]\[ \text{Problems on Saturday} = \frac{5}{10} \times 100 = 50 \text{ problems} \][/tex]

On Sunday, Chloe completed another 15 problems.

Now, we add up the problems completed each day to find the total number of problems completed over the weekend:

[tex]\[ \text{Total problems completed} = \text{Problems on Friday} + \text{Problems on Saturday} + \text{Problems on Sunday} \][/tex]

[tex]\[ \text{Total problems completed} = 39 + 50 + 15 \][/tex]

[tex]\[ \text{Total problems completed} = 104 \][/tex]

Chloe completed a total of 104 problems, which is more than the 100 problems she was supposed to complete. Therefore, she did not fill out her math journal correctly, as she recorded more problems than were assigned.

Chloé's math journal is not filled out correctly.

Let's calculate how many problems Chloé completed each day:

Adding these up: 39 (Friday) + 50 (Saturday) + 15 (Sunday) = 104 problems.

This must be incorrect since she only had 100 problems to start with. Therefore, Chloé's math journal is not filled out correctly.

Answer:

1/3

Step-by-step explanation:

In order for the disc to be entirely contained in a rectangular tile, its center must be at least 1 unit from the nearest edge.  Which means there's a 2 by 4 region that the center can lie in.

So the probability is (2×4) / (4×6) = 8/24 = 1/3.

Answer: he bought 5 green pencils

Step-by-step explanation:

Let x represent the number of green pencils that Dustin bought.

Dustin bought 9 pencils. The remainder of the pencils were purple. This means that the number of purple pencils that he bought is 9 - x

Some of the pencils were green and cost $0.90 each. The remainder of the pencils were purple and cost $0.65 each. If Dustin paid $7.10 for all of the pencils, it means that

0.9x + 0.65(9 - x) = 7.1

0.9x + 5.85 - 0.65x = 7.1

0.9x - 0.65x = 7.1 - 5.85

0.25x = 1.25

x = 1.25/0.25

x = 5

Answer:

f(1) = 4

Step-by-step explanation:

f(1) = 3(1)^2 -(1) + 2 = 4

Just replace all the x's with 1.

Answer: the first option is correct.

Step-by-step explanation:

In a geometric sequence, each consecutive term differ by a common ratio, r.

The formula for determining the nth term of a geometric progression is expressed as

an = a1r^(n - 1)

Where

a1 represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = - 5

r = - 2

n = 3

Therefore, the 3rd term, T3 is

T3 = - 5 × - 2^(3 - 1)

T3 = - 5 × - 2^2

T3 = - 5 × 4

T3 = - 20

Answer:

  60

Step-by-step explanation:

There are 2+5 = 7 ratio units of students. If we multiply the numbers by 5, we can have a total of 35 ratio units of students: 10 : 25.

Now, we can substitute this into the ratio of teachers to students:

  teachers : students = 3 : 35

  teachers : (male students : female students) = 3 : (10 : 25)

Then the number of teachers is seen to be 3/25 of the number of female students:

  (3/25)(500) = 60 . . . teachers

Answer: 20 pounds of walnuts should be mixed with 40 pounds of peanuts.

Step-by-step explanation:

Let x represent the number of pounds of walnuts that should be in the mixture.

Let y represent the number of pounds of peanuts that should be in the mixture.

The number of pounds of the mixture to be made is 60. This means that

x + y = 60

Walnuts cost $3.60 per pound and peanuts cost $2.70 per pound. The mixture will sell for $3.00 per pound. It means that the total cost of the mixture is 3 × 60 = $180. The expression would be

3.6x + 2.7y = 180- - - - - - - - - - - - -1

Substituting x = 60 - y into equation 1, it becomes

3.6(60 - y) + 2.7y = 180

216 - 3.6y + 2.7y = 180

- 3.6y + 2.7y = 180 - 216

- 0.9y = - 36

y = - 36/ - 0.9

y = 40

x = 60 - y = 60 - 40

x = 20

Answer:

Trampolinist will land on the trampoline after 0.9 seconds.

Step-by-step explanation:

The function h(t) = -16t² + 15 represents the relation between height 'h' above the ground and the time 't' of the trampolinist.

We have to find the time when trampolinist lands on the ground.

That means we have to find the value of 't' when h(t) = 15 - 13 = 2

[Since trampoline is 2 feet above the ground]

When we plug in the value h(t) = 2

2 = -16t² + 15

2 + 16t² = -16t² + 16t² + 15

16t² + 2 = 15

16t² + 2 - 2 = 15 - 2

16t² = 13

[tex]\frac{16t^{2}}{16}=\frac{13}{16}[/tex]

[tex]t^{2}=\frac{13}{16}[/tex]

t = [tex]\sqrt{\frac{13}{16}}[/tex]

t ≈ 0.9 seconds

Therefore, trampolinist will land on the trampoline at 0.9 seconds.

Answer:

C < 22

Step-by-step explanation:

Answer: show A had 8394 performances.

Show B had 6010 performances.

Step-by-step explanation:

Let x represent the number of performances of show A.

Let y represent the number of performances of show B.

As of a certain​ date, there had been a total of 14,404 performances of two shows on​ Broadway. This means that

x + y = 14404 - - - - - - - - - -1

There was 2384 more performances of Show A than Show B. It means that

x = y + 2384

Substituting x = y + 2384 into equation 1, it becomes

y + 2384 + y = 14404

2y = 14404 - 2384

2y = 12020

y = 12020/2

y = 6010

x = y + 2384 = 6010 + 2384

x = 8394

Answer:

show A had 8394 performances.

Show B had 6010 performances.

Step-by-step explanation:

Let x represent the number of performances of show A.

Let y represent the number of performances of show B.

As of a certain​ date, there had been a total of 14,404 performances of two shows on​ Broadway. This means that

x + y = 14404 - - - - - - - - - -1

There was 2384 more performances of Show A than Show B. It means that

x = y + 2384

Substituting x = y + 2384 into equation 1, it becomes

y + 2384 + y = 14404

2y = 14404 - 2384

2y = 12020

y = 12020/2

y = 6010

x = y + 2384 = 6010 + 2384

x = 8394

Step-by-step explanation:

Answer: 3) k = 22.5; xy = 22.5

Step-by-step explanation:

If two variables are inversely proportional, it means that an increase in the value of one variable would cause a corresponding decrease in the other variable. Also, a decrease in the value of one variable would cause a corresponding increase in the other variable.

Given that y varies directly with x, if we introduce a constant of proportionality, k, the expression becomes

y = k/x

If y = 2.5 when x = 9, then

2.5 = k/9

k = 9 × 2.5 = 22.5

Therefore, an equation for the inverse variation is

y = 22.5/x

xy = 22.5

Answer: (3)

k = 22.5; xy = 22.5

Step-by-step explanation:

Answer:

The first ranger is approximately 54.88 miles away from the fire.

Step-by-step explanation:

We have drawn the diagram for your reference.

Given:

Distance between first ranger and second ranger (AB)= 99 miles

Angle between fire and second ranger [tex]\angle B[/tex] = [tex]29\°[/tex]

We need to find the distance between the first ranger from the​ fire.

Solution:

Let the distance between the first ranger from the​ fire (AC) be 'x'.

So we can say that;

We know that;

tan of angle B is equal to opposite side divided by adjacent side.

[tex]tan 29\°= \frac{AC}{AB}\\\\tan 29\° = \frac{x}{99}\\\\x= 99\times tan29\°\\\\x \approx 54.88\ mi[/tex]

Hence the first ranger is approximately 54.88 miles away from the fire.

Answer:

The answer to the question is

Its other zero (x-intercept) will be located at x = -5

Step-by-step explanation:

To solve the question, we note that a parabolic function is of the form

ax² + bx +c = 0

Therefore we have the vertex occurring at the extremum  where the slope = 0

or dy/dx =2a+b = 0 also the x intercept occurs at x = 7, therefore when

ax² + bx +c = 0, x = 7 which is one of the solution

when x = 5, y = -4

That is a*25 +5*b + c = -4 also

49*a + 7*b + c = 0

2*a + b = 0

Solving the system of equations we get

a = 0.2, b = -0.4 and c = -7

That is 0.2x² -0.4x -7 = 0 which gives

(x+5)(x-7)×0.2 = 0

Therefore the x intercepts are 7 and -5

the second intercept will be located at x = -5

Final answer:

The other zero of the parabolic function with a vertex at (5, -4), and one zero at x = 7, will be located at x = 3, since it will be symmetrically placed with respect to the vertex.

Explanation:

The vertex of a parabolic function represents the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards. The fact that the vertex of the function is given as (5, -4) and one zero is at x = 7 leads to the conclusion that the other zero must be equidistant from the vertex on the x-axis because a parabola is symmetric about its vertex. Since the distance from the vertex (5) to the given zero (7) is 2 units to the right, the other zero must be 2 units to the left of the vertex. Therefore, the other zero will be at x = 5 - 2, which is x = 3.

The expression 1.18p can be used to find the total cost of the meal with gratuity.

Step-by-step explanation:

Step 1:

If there are more than 6 people, the restaurant charges an automatic gratuity of 18%.

Since there are 8 people this charge will also be applied here.

If the bill amount is p and 18% of p is added, the options 0.18p and 0.82p cannot be the total cost of the meal.

Step 2:

We need to determine how much 18% is in terms of p.

18% of p [tex]= \frac{18}{100} (p) = 0.18p.[/tex]

So the total cost of the meal = Cost of the meal + Gratuity charges [tex]=p + 0.18p = 1.18p.[/tex]

So the total cost is the third option 1.18p.

Answer:

1.18

Step-by-step explanation:

Answer:

Please see attached picture for full solution.

Final answer:

The math and science club scored points by solving problems in a competition, with a total of 8 math problems solved on the first day and 5 science problems on the second day.

Explanation:

The situation from Madison Middle School's math and science club competition can be represented and solved with mathematical equations. Let's break down each part of the problem.

Part A: Equation Representation

Let m be the number of problems solved in the morning, and a the number in the afternoon. The equation representing the total points for the day is: 2m + 3a = Total Points.

Part B: Solving for the Afternoon Session

The team scored 4 points in the morning, meaning they solved 2 problems (as each is worth 2 points). This gives us the equation 2*2 + 3a = 28. Solving this, we find a = 8. Thus, the team solved 8 problems in the afternoon session to finish the day with 28 points.

Part C: Science Portion on the Second Day

On the second day, the team starts with 28 points and ends with 53 points, all from solving science problems worth 5 points each. The equation is 5s + 28 = 53, where s is the number of science problems solved. This simplifies to s = 5, indicating the team solved 5 science problems.

Answer:

The first one: 3.2 units

Answer: 3.2 units

Step-by-step explanation:

The formula for determining the distance between two points on a straight line is expressed as

Distance = √(x2 - x1)² + (y2 - y1)²

Where

x2 represents final value of x on the horizontal axis

x1 represents initial value of x on the horizontal axis.

y2 represents final value of y on the vertical axis.

y1 represents initial value of y on the vertical axis.

From the graph given,

x2 = -2

x1 = - 3

y2 = - 4

y1 = - 1

Therefore,

Distance = √(- 2 - - 3)² + (-4 - - 1)²

Distance = √1² + - 3² = √1 + 9 = √10

Distance = 3.2

Answer:

you will add -√7

Step-by-step explanation:

the only reason you would do that is so that the equation could equal 0

Answer:

the bottom of the ladder from the bottom of the slide is 15 feet far from

the bottom of the slide

Step-by-step explanation:

Given that Mitchel climbs 8 feet up the vertical ladder of a slide and zips down the 17-foot slide.

The slide the vertical ladder and the floor together form a right triangle if we can vizualise.

The hypotenuse would be the slide , and one leg is ladder and other the  bottom of the ladder from the bottom of the slide

We have hypotenuse = 17 feet and one leg = 8 feet

So use Pythagorean theorem to find other leg

Other leg = [tex]\sqrt{17^2-8^2} \\=\sqrt{(17+8)(17-8)} \\= 15[/tex]

the bottom of the ladder from the bottom of the slide is 15 feet far from

the bottom of the slide

Answer:

  -$0.07846 per belt

Step-by-step explanation:

The average cost per belt is ...

  [tex]c(x)=\dfrac{C(x)}{x}=\dfrac{751+12x-0.067x^2}{x}=751x^{-1}+12-0.067x[/tex]

Then the rate of change of average cost is ...

  [tex]c'(x)=-751x^{-2}-0.134\\\\c'(256)=\dfrac{-751}{256^2}-0.067\approx -0.07846[/tex]

The rate at which average cost is changing is about -0.078 dollars per belt.

_____

Note that the cost of producing 256 belts is -$567.91, so their average cost is about -$2.22 per belt.

The student is asked to calculate the rate of change of average cost for producing belts when 256 belts are produced, by finding and evaluating the derivative of the average cost function.

The question asks about the rate at which the average cost is changing for the production of belts given a certain cost function C(x) = 751 + 12x - 0.067x2. To find this rate when 256 belts are produced, we need to first calculate the average cost, which is C(x) divided by x, and then take the derivative of the average cost to find its rate of change. The derivative of the average cost function gives us the rate at which the average cost is changing with respect to the number of belts produced. We evaluate this derivative at x = 256 to find the specific rate of change at the production of 256 belts.

Answer:

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in one variable will cause a corresponding increase in the other variable.

If two variables are inversely proportional, it means that an increase in one variable will cause a corresponding decrease in the other variable.

The variable z is directly proportional to x, and inversely proportional to y. If we introduce a constant k, the equation would be

z = kx/y

When x is 14 and y is 10, z has the value 26.6. It means that

26.6 = 14k/10

Cross multiplying, it becomes

26.6 × 10 = 14k

266 = 14k

k = 266/14

k = 19

The equation becomes

z = 19x/y

When x = 24, and y = 15, the value of z would be

z = 19 × 24/15

z = 30.4

Answer:

The independent variable in this experiment was the attention students gets from the teacher

Step-by-step explanation:

An independent variables are variables in maths, statistics and experimental sciences that stands alone and isn't affected by the other variables you are trying to measure.

Final answer:

The independent variable was the teacher's response to the student behavior of either ignoring or attending to students when they talked without raising their hands.

Explanation:

The independent variable in this experiment was the strategy used by the teacher regarding whether or not to ignore the students when they talked without raising their hands.

In experimental design, the independent variable is the condition that is manipulated by the researcher to observe its effects on the dependent variable.

In this case, students in one group were ignored when they spoke without raising their hands, making them the experimental group.

The other group, which the teacher attended to in their usual manner, acted as the control group.

Since the independent variable is the only factor that is intentionally changed to test its impact on outcomes, observing changes in the students' behavior helped determine the effects of this teaching strategy.

Answer:

a=6 b=4

Step-by-step explanation:

they can't both equal 5 so you need to find 2 numbers that add up to equal 10 but when you subtract one from the other it equals 2

Option C: [tex](4 j+3)^{2}[/tex] is the correct answer.

Explanation:

The given expression is [tex]16 j^{2}+24 j+9[/tex]

We need to factor the expression.

Let us rewrite the expression as

[tex](4j)^{2}+24 j+(3)^2[/tex]

Also, we can rewrite the term [tex]24j[/tex] as [tex]2(4)(3)j[/tex]

Thus, we have,

[tex](4j)^{2}+2(4j)(3)+(3)^2[/tex]

Hence, the equation is of the form,

[tex](a+b)^{2}=a^{2}+2 a b+b^{2}[/tex]

where [tex]a=4 j[/tex] and [tex]b=3[/tex]

Hence, the factor of the expression can be written as [tex](4 j+3)^{2}[/tex]

Thus, the factored expression is [tex](4 j+3)^{2}[/tex]

Therefore, Option C is the correct answer.

Final answer:

The factored form of the expression 16j^2 + 24j + 9 is (4j + 3)².

Explanation:

To factor the expression 16j2 + 24j + 9, we look for two binomials ((aj + b)(cj + d)) that when multiplied together, give us the original quadratic expression. The factors of 16j2 are 4j imes 4j, and the factors of 9 are 3 imes 3. Our binomial factors will have the format (4j + 3).

Expanding the binomial (4j + 3)², we have:

(4j + 3) imes (4j + 3)

= 16j2 + 12j + 12j + 9

= 16j2 + 24j + 9

This matches the original expression exactly, so the factored form of the expression is (4j + 3)².