A gecko is in a room that is 12 feet long, 10 feet wide and 8 feet tall. The gecko is currently on a side wall ($10^{\prime}$ by $8^{\prime}$), one foot from the ceiling and one foot from the back wall ($12^{\prime}$ by $8^{\prime}$). The gecko spots a fly on the opposite side wall, one foot from the floor and one foot from the front wall. What is the length of the shortest path the gecko can take to reach the fly assuming that it does not jump and can only walk across the ceiling and the walls?

Answer: [tex](0.0228\ ,0.0706)[/tex]

Step-by-step explanation:

Given : Sample size : n= 300

The sample proportion of defectives : [tex]\hat{p}=\dfrac{14}{300}=0.0467[/tex]

Significance level for 95% confidence level =[tex]\alpha=1-0.95=0.05[/tex]

Critical z-value:[tex]z_{\alpha/2}=\pm1.96[/tex]

Confidence interval for population proportion :

[tex]\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]= 0.0467\pm (1.96)\sqrt{\dfrac{0.0467(1-0.0467)}{300}}[/tex]

[tex]\approx\ 0.0467\pm 0.0239\\\\=(0.0467-0.0239\ , \ 0.0467-0.0239)\\\\=(0.0228\ ,0.0706)[/tex]

Hence, a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool= [tex](0.0228\ ,0.0706)[/tex]

Answer:

1.38 pm.

Step-by-step explanation:

After 1.05 PM the rate at which he decorates the cakes is 10 - 5 = 5 cakes per 3 minutes = 5/3 cakes per minute. At 1.08 pm he has made 10 cupcakes.

At 1.08 he has to decorate another 50 cakes so the time he will take to do these is  50 / 5/3  = 50 * 3/5 =   30 minutes.

So the time when he finishes 60 cupcakes is  1.08 + 30

= 1.38 pm.

The 60 cupcakes will be decorated at 1.38 pm.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

After 1.05 PM the rate at which he decorates the cakes is 10 - 5 = 5 cakes per 3 minutes = 5/3 cakes per minute. At 1.08 pm he made 10 cupcakes.

At 1.08 he has to decorate another 50 cakes so the time he will take to do these is  50 / 5/3  = 50 * 3/5 =   30 minutes.

The time when he finishes 60 cupcakes is:-

1.08 + 30 = 1.38 pm.

Therefore, 60 cupcakes will be decorated at 1.38 pm.

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Answer:

B) μD = 0.60 ± 0.10(1.397)

Step-by-step explanation:

The confidence interval is given by:

[tex]MD±t_{\alpha/2, n-1} \frac{s}{\sqrt{n} }[/tex]

Where

MD=60

n=9

df=n-1=8

[tex]t_{\alpha/2, n-1}=1.397[/tex]

[tex]s=\sqrt{0.09} =0.3[/tex]

Then the confidence interval is

μD=0.60±1.397*(0.3/√9)

μD=0.60±0.10*(1.397)

Answer:

[tex]39\ parking\ attendants[/tex]

Step-by-step explanation:

Let

x -----> the number of blue lots

y-----> the number of red lots

we know that

[tex]x+y=15[/tex] ------> equation A

we have that

[tex]x=0.60(15)=9\ blue\ lots[/tex]

[tex]y=0.40(15)=6\ red\ lots[/tex]

The total parking attendants required for tonight's event is equal to the product of the number of blue lots by three plus the product of the number of red lots by two

so

[tex]9(3)+6(2)=39\ parking\ attendants[/tex]

Answer:

39

Step-by-step explanation:

Answer:

8320

Step-by-step explanation:

(100%+4%)8000=8320

The balance at the end of the first year of the investment will be $8320, which includes the initial investment of $8000 and the interest earned, calculated as 4% of the initial investment.

This is a basic interest problem in mathematics. To calculate the balance at the end of the first year, we need to add the initial investment to the amount earned through interest. The interest earned is the product of the initial investment and the interest rate.

In this case, the initial investment is $8000 and the interest rate is 4% per year or 0.04 in decimal form. So, the interest earned would be the product of $8000 and 0.04, which equals $320.

Therefore, the balance at the end of the first year would be the initial investment plus the interest earned, which is $8000 + $320 = $8320.

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Answer:

210, 150

Step-by-step explanation:

Answer:

-510, 210 and 570.

Step-by-step explanation:

I'm on the same assignment right now! If you draw them you will see that those are the answers.

Answer:

the probability is 0.1879

Step-by-step explanation:

If a procedure yields a binomial distribution, the probability of having k successes is given by:

[tex]P(k)=nCk*p^{k} *(1-p)^{n-k}[/tex]

Where nCk is calculated as:

[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]

Additionally, n is the number of trials and p is the probability of success in every trial.

Replacing, k by 14, n by 20 and p by 0.72 we get:

[tex]20C14=\frac{20!}{14!(20-14)!}=38,760[/tex]

[tex]P(k)=20C14*0.72^{14} *(1-0.72)^{20-14}[/tex]

[tex]P(k)=38,760*0.72^{14} *(1-0.72)^{20-14}\\P(k)=0.1879[/tex]

So, the probability is 0.1879

To find the probability of 14 successes given a binomial distribution with a trial repeated 20 times and a probability of success of 0.72 on a single trial, use the binomial probability formula.

To find the probability of 14 successes given a binomial distribution with a trial repeated 20 times and a probability of success of 0.72 on a single trial, we can use the binomial probability formula. The formula is:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Plugging in the values, we get:

P(X = 14) = C(20, 14) * 0.72^14 * (1 - 0.72)^(20 - 14)

Calculating this expression will give you the probability of 14 successes out of 20 trials.

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Answer:

  ∛(2b)

Step-by-step explanation:

[tex]\displaystyle\frac{\sqrt[3]{4b^2}}{\sqrt[3]{2b}}=\sqrt[3]{\frac{4b^2}{2b}}=\sqrt[3]{2b}[/tex]

Answer:

The answer to your question is: it's a rectangle

perimeter = 30 u

Step-by-step explanation:

d = √((x2.x1)² + (y2-y1)²)

Now, calculate the distances AB, BC, CD, AD

dAB = √((11-6)² + (-4+4)² = √5² = 5

dBC = √((11-11)² + (-4-6)² =√10 = 10

dCD = √((6-11)² + (6-6)² = √5² = 5

dAD = √((6-6)² + (6+4)² = √10² = 10

From the results we conclude that is a rectangle because two sides have the same length and the other two also measure the same. We can draw it to confirm this.

Perimeter = dAB + dBC + dCD + dAD

                 = 5 + 10+ 5 + 10 = 30 units

To determine the shape of the quadrilateral, calculate the distances between the vertices and check for equal side lengths and 90-degree angles. The given quadrilateral is a parallelogram since the opposite sides are parallel and equal. The perimeter of the quadrilateral is 30 units.

To determine whether the given quadrilateral is a square, a rectangle, or a parallelogram, we can use the properties of each shape. A square is a quadrilateral with all sides equal in length and all angles equal to 90 degrees. A rectangle is a quadrilateral with opposite sides equal in length and all angles equal to 90 degrees. A parallelogram is a quadrilateral with opposite sides parallel and equal in length. To find the perimeter of the quadrilateral, we can calculate the sum of the lengths of all four sides.

Calculating the distances between each pair of given points:

The distances between the vertices are: AB = 5, BC = 10, CD = 5, and DA = 10. Therefore, the perimeter of the quadrilateral is 5 + 10 + 5 + 10 = 30 units.

Answer:

300 Burgers

Step-by-step explanation:

Since the question gives us an approximation of 250 burgers, we can round the number to 300. This is only because they had a estimation of 250 and would like to be prepared for the weekend. Being prepared would consist of ordering more than expected to make sure the burgers do not run out.

Answer:

The answer to your question is: (5/2, -6)

Step-by-step explanation:

Given    f(x) = (6x - 36) / (2x² - 17x + 30)

Factorize both, numerator and denominator

Numerator = 6(x - 6)

Denominator =    2x² - 12x - 5x + 30

                      =   2x(x - 6) - 5(x - 6)

                      = (x - 6) (2x - 5)

Now     f(x) = 6(x - 6) / (x - 6) (2x - 5)     Cancel (x - 6)

            f(x) = 6 / 2x - 5

Find the hole           2x - 5 = 0

                                2x = 5

                                x = 5/2

In 5/2 there is a hole, in y is approximately -6

Answer:

$185,000

Step-by-step explanation:

We have been been given that during the​ year, Fast Dry Corporation has $ 340,000 in​ revenues, $ 155,000 in​ expenses, and $ 12,000 in dividend declarations and payments.

We will use following formula to solve our given problem.

[tex]\text{Net income}=\text{Revenues}-\text{Expenses}[/tex]

[tex]\text{Net income}=\$340,000-\$155,000[/tex]

[tex]\text{Net income}=\$185,000[/tex]

Therefore, the net income for the year was $185,000.

To make the function differentiable at x = 2, we must ensure continuity by matching function values and differentiability by equating derivatives from both sides at x = 2. Solving the system of equations obtained from these conditions will give the values of a and b.

To find the values of a and b that make the function f(x) = { x² if x ≤ 2, ax³ + bx if x > 2 } differentiable at x = 2, we need to ensure both continuity and differentiability of f(x) at this point. First, continuity at x = 2 requires that the limits from the left and the right are the same, meaning f(2) = 2² = 4 should equal a(2)³ + b(2). Second, for differentiability, the derivatives from the left and right at x = 2 must also be equal. The derivative of x² is 2x, so f'(2) = 4. Differentiating ax³ + bx gives 3ax² + b, so f'(2) = 12a + b must also equal 4. Solving these equations:

gives us a system of equations that when solved, will provide the exact values of a and b required.

Answer:

Hello My Friend! The correct answer its double root.

Step-by-step explanation:

In this equation, if we applie the a, b and c coefficients (a=1, b=4, c=4) ind the Bhaskara, the final result will be 4 for both cases. x'=4 and x''=4. It happens because the number of theta is equal to 0. So, both roots will be the same number.

Hey!

-------------------------------------

Formula's:

x_v = -b/2a

y_v = ax² + bx + c

-------------------------------------

Parabola Params:

a = -1

b = 12

c = 4

-------------------------------------

Solve for [tex]x_{v}[/tex]

[tex]x_{v} = \frac{-b}{2a}[/tex]

[tex]x_{v} = \frac{-12}{2(-1)}[/tex]

[tex]x_{v} = -6[/tex]

-------------------------------------

Solve for [tex]y_{v}[/tex]

Use -6 for [tex]x_{v}[/tex]

[tex]y_{v} = -6^2 + 12(6) - 4\\[/tex]

[tex]y_{v} = -36 + 72 - 4[/tex]

[tex]y_{v} = 32[/tex]

-------------------------------------

Answer:

(6, 32)

-------------------------------------

Hope This Helped! Good Luck!

To solve the equation -5(2+x)=53, we need to use the order of operations and follow the steps mentioned in the detailed answer. The solution to the equation is x=-12.6.

In order to solve the equation -5(2+x)=53, we need to use the order of operations. Let's break it down step by step:

So, the solution to the equation -5(2+x)=53 is x=-12.6.

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The final marble left in the bag will be red.

Let, analyze the process step by step:

Initially, the bag contains 99 red marbles and 99 blue marbles.

When you take two marbles out of the bag, there are two possibilities: either you get two red marbles or two blue marbles, or you get one red and one blue marble.

a. If you get two marbles of the same color (both red or both blue), you put a red marble in the bag.

b. If you get one red and one blue marble, you put a blue marble in the bag.

After putting a marble back in the bag, you have one less marble in the bag.

You repeat this process, reducing the number of marbles in the bag by one each time, until only one marble is left in the bag.

Now, let's think about the outcomes at each step:

If the bag contains an odd number of marbles (99 red + 99 blue = 198), the final marble will be red because at each step, you are adding a red marble back to the bag.

If the bag contains an even number of marbles (e.g., 100 red + 100 blue = 200), the final marble will be blue because at each step, you are adding a blue marble back to the bag.

In this case, the bag contains 99 red marbles and 99 blue marbles, which is an odd number (198 marbles).

Therefore, the final marble left in the bag will be red.

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The problem is about finding a length on a blueprint using scale factor. A ratio is established between blueprint measurements and real-life measurements. However, information about Fence B's actual size is needed to calculate its blueprint length.

The subject of this question is mathematics, more specifically proportionality and scale factor. To solve this problem, you need to establish the ratio or scale represented by the blueprint to the actual size. In the given problem, 1 4/5 inches on the blueprint represents 1 1/2 feet in real life. First, convert the measures to improper fractions to easily manage the computations. Hence, 1 4/5 becomes 9/5 inches and 1 1/2 feet becomes 3/2 feet. The scale becomes 9/5 inches:3/2 feet on blueprint:real life. Now, we need additional information about the actual size of Fence B to calculate its length on the blueprint.

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Answer:

The correct answer is 90

Step-by-step explanation:

Answer:

C. The vectors u, minusv, and uminusv form a parallelogram whose other vertex is at 0.

Step-by-step explanation:

We draw the vector u=A at the origin of a Cartesian plane. then at the same point, we draw -v = -B. To find the vector that represents u-v = A-B, straight lines are drawn parallel to each vector, forming a parallelogram. The resulting vector will be the diagonal of the parallelogram that begins at the origin of the plane.

Answer:

x = -9

y = 35/7

Step-by-step explanation:

Given equations :-

-7y - 4x = 1 ....... ( i )

7y - 2x = 53 ........ ( ii )

From ( i )

-7y = 1 + 4x

[tex]y = \frac{ - (1 + 4x)}{7} [/tex]

..........( iii )

From ( ii )

7y - 2x = 53

7y = 53 + 2x

[tex]y = \frac{53 + 2x}{7} [/tex]

.......( iv )

Equating both ( iii ) & ( iv )

y = y

[tex] \frac{ - (1 + 4x)}{7} = \frac{53 + 2x}{7} [/tex]

-(1 + 4x ) = 53 + 2x

-1 -4x = 53 + 2x

-1 - 53 = 2x + 4x

-54 = 6x

-54/6 = x

-9 = x

Also,

[tex]y = \frac{ - (1 + 4x)}{7 } \\ \\ y = - \frac{(1 + 4( - 9))}{7} [/tex]

[tex]y = - \frac{ (1 - 36)}{7} \\ \\ y = - \frac{( - 35)}{7} \\ \\ y = \frac{35}{7} [/tex]

Answer:

option (c) 475

Step-by-step explanation:

let the automobile installment credit be 'C'

Given:.

Automobile installment credit accounted for 36 percent of all outstanding consumer installment credit

Now,

57 billion is [tex]\frac{1}{3}[/tex] of automobile installment credit

or

57 billion = [tex]\frac{1}{3}[/tex] × C

or

C = 57 × 3

or

C = 171 billion

now,

installment credit accounted = 36% of all outstanding consumer installment credit

or

171 billion = 0.36 × all outstanding consumer installment credit

or

All outstanding consumer installment credit = $475 billion

Hence, the correct answer is option (c) 475

Answer:

A real number is a number that is somewhere on a number line, so any number on a number line that isn't a rational number is irrational. The square root of 2 is an irrational number because it can't be written as a ratio of two integers

hope it helps!!

Step-by-step explanation:

Answer:

x= 5 fam trust

Step-by-step explanation:

plug it in brainliest plzzzzzzzzzzzzzzzzz

Answer:

5x-2y=-4

Step-by-step explanation:

2x-5y=0

eq. of line perpendicular to ax+by=c is bx-ay=d,d is calculated by the given condition.

line perpendicular to 2x-5y=0 is 5x+2y=c

if it passes through (-2,3) ,then

5*-2+2*3=c

c=-10+6=-4

reqd. eq. is 5x+2y=-4

Answer:

Step-by-step explanation:

Given that the professor Z has a class of 50 students is corrupt.   However five students already have a special deal (they are professor Z's nephews and nieces) and will get A's for sure.

Thus out of 10 students 5A's are reserved

Remaining 5 can be distributed in

I 5 to any one of the 45, II to any one of the 44....

i.e. 45P5 ways

no of ways = 45P5 == 146611080

Answer:

You have completed 25% of your work.

Step-by-step explanation:

Consider the provided information.

You estimate that you have completed 1/4 of the work.

To find the percentage of work complete simplify the fraction and multiply it with 100.

[tex]\frac{1}{4}=0.25[/tex]

Now multiply it by 100.

[tex]0.25\times 100=25\%[/tex]

Hence, you have completed 25% of your work.

Graphing y = 4 and the focus, we clearly see that the equation we need has the form (x - h)^2 = 4a(y - k).

We need to find a, h and k.

The focus is half way between the vertex and directrix.

You know that y = 4 is 2 units away from the focus and the focus is 2 units down from the focus. So, our vertex is (-3, 0).

From the vertex to the directrix, there are 4 units. Half that distance is the value of a. So, a = 2.

We have all that is needed to form our equation.

(x - (-3))^2 = 4(2)(y - 0)

(x + 3)^2 = 8y

Done.

Answer:

i think this will help (x - (-3))^2 = 4(2)(y - 0)

(x + 3)^2 = 8y

Step-by-step explanation: