Jordan has seven blocks of ice.
The total weight of all seven blocks of ice is 5 kilograms.
6 of the blocks of ice each have a weight of 750 grams.
Work out the weight, in grams, of the other block of ice.

The set S is composed of the integers that are between -5 and -1; with -5 being included. Rewriting this set by using the Roster Method gives us an answer of,

S = {-5, -4, -3, -2}

The term "roster method" refers to a method of displaying a set's components by listing them in bracketed lists. The set can be modeled most easily using the roster form. The components of a set are listed in row format in roster form, with commas between them.

The components of a set are listed in row format in roster form, with commas between them.

A set in mathematical form is simply represented mathematically using the roster notation. The elements (or members) in this approach are listed in a row between curly brackets. When there are multiple elements in a set, there is a comma between every pair of elements.

Based on the given above, the set T is composed of the integers that are between -5 and -1; with -5 being included. Rewriting this set by using the Roster Method gives us an answer of,

S = {-5, -4, -3, -2}

The complete question is:

Rewrite the set S by listing its elements. Make sure to use the appropriate set notation. S = {[ z| z is an integer and -5 ≤ x < -1}

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A: p not equal to the value will be  [tex]$$N=\left(\frac{n / 2}{x}\right)^x\left(\frac{n / 2}{n-x}\right)^{n-9} .$$[/tex]

B.Using the null distribution of X, show how the significance level corresponding to a rejection region |X - n/2| > k can be determined.

C. If n = 10 and k = 2, the significance level of the test = 0.11

D. Use the normal approximation to the binomial distribution of the significance level if n = 100 and k = 10 the value will be N(0.1).

1. The value of the generalized likelihood ratio test statistic will be

[tex]A=\frac{\left(\begin{array}{l}n \\x\end{array}\right)(1 / 2)^n}{m_0 x_{0 < p < 1}\left(\begin{array}{l}n \\x\end{array}\right) p^n(1-p)^{n-x}}[/tex]

As we know, the denominate will be maximized when [tex]$p=x / n$[/tex], the P under [tex]\Omega[/tex]

Hence [tex]$$N=\left(\frac{n / 2}{x}\right)^x\left(\frac{n / 2}{n-x}\right)^{n-9} .$$[/tex]

b)

[tex]$$\begin{aligned}\Lambda & =\left(\frac{n / 2}{x}\right)^x\left(\frac{n / 2}{n-x}\right)^{n-x} \\& =\left[\left(\begin{array}{c}2 x \\n\end{array}\right)^{-2 x / n}\left(2-\frac{2 x}{n}\right)^{-2+2 x / n}\right]^{n / 2} \\& =\left[y^{-y}(2-y)^{-(2-y)}\right]^{n / 2} \\& =\left[(1+v)^{-(1+v)}(1-v)-(1-v)\right]^{n / 2}\end{aligned}$$[/tex]

where [tex]y=2 x / n=1+0[/tex]

The last expression is symmetric about [tex]\theta=0+[/tex] is a maximum [tex]$\rightarrow t v=0$[/tex].

since the test rejects [tex]H_0[/tex] when [tex]$\wedge$[/tex] it is small.

If the only if [tex]$|0|=|1,2 \pi| n \mid$[/tex] is large.

This is equivalent to |x-n/2| is large

c) The significance level [tex]$\alpha$[/tex] of the test that rejects H_0 when [tex]$|x-n| 2 \mid > *$[/tex] is given by [tex]$$P\left(|x-n / 2| > k \mid H_0\right) \text {. }$$[/tex]

This probability can be determined using the pmf of the B(n, 0.5) distribution.

d) If n=10+k=2,

[tex]$$\begin{aligned}& P\left(|x-n|=| > k| H_0\right) \\= & P\left(|x-5| > 2 \mid H_0\right) \\= & P\left(x=0 \mid H_0\right)+P\left(x=1 / H_0\right)+P\left(x=2 \mid H_0\right)+P\left(x=8 / H_0\right) \\& +P\left(x=9 \mid H_0\right)+P\left(x=10\left(H_0\right)\right. \\= & 0.11 .\end{aligned}$$[/tex]

e) Using the normal approximation to the binomial distribution B(100,0.5), x is approximately n amply distributed with mean 50 * variance n p(1-p)=25.

Thus, the significant level of the test is

[tex]$$\begin{aligned}& P(|x-50| > 10) \approx P(|z| > 2)=0.046 . \\& \text { where } z \sim N(0,1) \text {. } \\&\end{aligned}$$[/tex]

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The probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

Given that, at a wedding each guest asked the 80 guests whether they were a friend of the bride or of the groom.

What is the probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Total Number of Guests which forms the Sample Space, n(S)=80

Let the event (a friend of the bride) =A

Let the event (a friend of the groom) =B

n(A) =59

n(B)=50

Friends of both bride and groom,

So,

n(A∪B)=n(A)+n(B)-n(A∩B)

n(A∪B)=59+50-30

n(A∪B)=79

The number of Guests who was a friend of the bride OR of the groom = 79

Thus,

P(A∪B)=n(A∩B)/n(S)

= 79/80

= 0.9875

Hence, the probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

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The ratio of the length of the altitude to the length of one side of the triangle is equal to the ratio of the length of the hypotenuse to the length of the other side.1) AD/AB = BC/AC is true

In the accompanying diagram of right triangle ABC, altitude BD is drawn to hypotenuse AC. This means that the length of BD is equal to the length of the altitude from the vertex of the right angle to the hypotenuse. This also means that the length of BD is a right triangle's altitude. In a right triangle, the altitude of a right triangle is the line segment connecting one vertex of the right angle to the hypotenuse, and is perpendicular to the hypotenuse. This also means that the ratio of the length of the altitude to the length of one side of the triangle (AD/AB) is equal to the ratio of the length of the hypotenuse to the length of the other side (BC/AC). This statement must always be true, regardless of the size of the triangle or its specific shape. This is because the ratio of the length of the altitude to the length of one side of the triangle is always equal to the ratio of the length of the hypotenuse to the length of the other side.

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Answer:

(6, 0.5)

Step-by-step explanation:

midpoint = x1+x2/2 , y1+y2/2

midpoint = 2+10/2 , 9+(-8)/2

midpoint = 12/2, 1/2

midpoint = 6, 0.5

7h25min to min= 445min

3h25min to min= 205min

35600sec to hminsec= 9h53min20sec

Extra Explanation:

To convert hours to minutes, we can multiply the number of hours by the number of minutes in an hour. For example, 7 hours is equal to 7 * 60 = 420 minutes. Similarly, 3 hours is equal to 3 * 60 = 180 minutes.

To convert seconds to hours, minutes, and seconds, we can first convert the total number of seconds to minutes by dividing by the number of seconds in a minute (60). For example, 35600 seconds is equal to 35600 / 60 = 600 minutes. We can then convert the total number of minutes to hours by dividing by the number of minutes in an hour (60). For example, 600 minutes is equal to 600 / 60 = 10 hours. Finally, we can find the remaining minutes and seconds by taking the remainder when the total number of minutes is divided by 60. For example, the remainder when 600 is divided by 60 is 53 minutes. The remaining seconds can be found in a similar manner.

Answer:

7h25mins =445 mins

3h25mins = 205 mins

35600s =9 h 53mins and 20 sec

Step-by-step explanation:

a min equals 60 sec

an hour equals 60 mins

for example 7h equals 60mins ×7

so 420 then add 25 min which then becomes 445 mins

The interest that Marsha will earn is $2000.

Simply multiplying the daily interest rate by the principal and the number of days between payments yields simple interest. Consumers who pay their loans on time or early each month benefit from simple interest. Auto loans and short-term personal loans are typically interest-only loans.

In this case, Marsha deposited $10,000 into a savings account five years ago. The simple interest rate is 4%.

The interest will be:

= PRT

P = Principal = $10000

R = Rate = 4%

T = Time = 5

Interest = PRT

= $10000 × 4% × 5

= $2000

The interest is $2000.

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Answer:

Your Polynomial: [tex]x^3-13x^2+36x=0[/tex]

Step-by-step explanation:

Given information: 0 , 4 , 9

0 -> x = 0 -> (x - 0) = 0

4 -> x = 4 -> (x - 4) = 0

9 -> x = 9 -> (x - 9) = 0

(x - 0)(x - 4)(x - 9) = 0

x * (x - 4) * (x - 9) = 0

(x^2 - 4x) * (x - 9) = 0

x^3 - 9x^2 - 4x^2 + 36x = 0

B) The mean air pressure of all the basketballs produced in Week I was 0.5 psi more than the mean air pressure of all the basketballs produced in Week 2

What is manufacturer?

A manufacturer is a person or business that turns raw materials into completed products using a variety of tools, machinery, and procedures, and then sells those products to customers, wholesalers, distributors, retailers, or other manufacturers who can use them to make more complicated products.

A basketball manufacturer selects a random sample of its basketballs each week to ensure a consistent air pressure within them is maintained. In Week 1, the sample had a mean air pressure of 8.2 psi (pounds per square inch) and a margin of error of 0.1 psi. In Week 2, the sample had a mean air pressure of 7.7 psi and a margin of error of 0.3 psi. Based on these results, Option B, which states that the average air pressure of all basketballs created during week one was 0.5 psi higher than that of all basketballs produced during week two, is the right response.

Option C is not discussed in any detail.

Factually, Option D is inaccurate.

Because the margin of error would have been 0, Option A is wrong.

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1) Using the common factors of the new area of 12,000 m², the new dimensions of the larger rectangle (lot) are:

2) The percent increase for the length and width are:

The new dimensions of the larger lot are determined as follows:

Length of smaller lot = 80 m

Width of smaller lot = 100 m

Area of smaller lot = 8,000 m² (80 x 100)

The increase in the area of the larger lot = 4,000 m²

The total area of the larger lot = 12,000 m² (8,000 + 4,000)

Remember that area is length x width.

The factors that can result in 12,000 m² when multiplied are 100 m and 120 m, they also meet the requirement for increasing the dimensions by the same amount (20 m).

Length of larger lot = 100 m (80 + 20)

Width of larger lot = 120 m (100 + 20)

Length = 25% (100 - 80)/80 x 100)

Width = 20% (120 - 100)/100 x 100)

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Probability provides information about the likelihood that something will happen.

The calculated probabilities are

0.5455

0.5909

0.4615

0.5556

a. The probability of the people that prefer sprite is

Probability = 60/110

= 0.5455

B. The probability that a person is between 21 and 40

probability = 65/110

= 0.5909

C. Probability of drinking lemonade given that age is between 21 and 40

Probability = 30/65

= 0.4615

d. Probability of sprite when under 21

25/45

= 0.5556

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The remainder when the polynomial is divided by x - 5 is given as follows:

B. 24.

The remainder when the polynomial is divided by x - 8 is given as follows:

B. 87.

The Remainder Theorem states that when a polynomial y = f(x) is divided by a binomial given by x - a, the remainder is given by f(a).

The polynomial for this problem is given as follows:

f(x) = 2x² - 5x - 1.

Hence the remainder when the polynomial is divided by x - 5 is calculated as follows:

f(5) = 2(5)² - 5(5) - 1 = 24. (option B).

(x - 5 = 0 -> x = 5 is the value at which the numeric value has to be calculated to obtain the remainder).

Hence the remainder when the polynomial is divided by x - 8 is calculated as follows:

f(8) = 2(8)² - 5(8) - 1 = 87. (option B).

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The Coordinates of the centroid of a triangle with the given vertices are (0, 4), (8, 10) and (6, 1) is (14/3, 5) and Centroid of triangle with vertices (1,5),(3,8),(0,2) is (4/3, 5).

The centroid of a triangle is one of the point where all three medians of the triangle intersect. The median is a line segment drawn from one vertex to the midpoint on the opposite side. Triangle centroid divides each median into individual words in a 2:1 ratio. The centroid is usually at 2/3 of the median.

If the three vertices of a triangle are A(x₁,y₁) B(x₂,y₂), C(x₃,y₃), the centroid of the triangle is given by the formula :

G(x₁+x₂+x₃/3, y₁+y₂+y₃/3 ).

We have , two triangles with vertices,

a) triangle whose vertices are A(0, 4), B(8, 10) and C(6, 0). So, the coordinates of the centroid of a triangle whose vertices are (0, 4), (8, 10) and (6 , 1) are ( (0+8+6)/3 , (4+10+1)/3 ) or (14/3, 5).

b) triangle whose vertices are P(1, 5), Q(3,8) and R(0, 2). So, the coordinates of the centroid of a ∆PQR are ( (1+3+0)/3 , (5+8+2)/3 ) or (4/3, 5).

Hence, the required coordinates of Centroid are (14/3, 5), (4/3, 5).

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Complete question:

Coordinate geometry find the coodinates of the centroid of each triangle with the given vertices are a) (0, 4), (8, 10) and (6, 1)

b) (1,5),(3,8),(0,2)

Congruent triangles are two triangles with the exact same shape and size.

This means that all of their angles and side lengths are congruent, or equal. In order to determine if two triangles are congruent, we must first make sure that the angles of both triangles are the same.

We can do this by using the Angle-Angle (AA) theorem, which states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are congruent. The next step is to check that all three side lengths of both triangles are equal.

We can use the Side-Side-Side (SSS) theorem to do this, which states that if all three side lengths of one triangle are equal to the three side lengths of another triangle, then the two triangles are congruent.

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Answer:

  $114

Step-by-step explanation:

You want to know the interest due on student loans of $5000 (subsidized) and $4500 (unsubsidized) with an APR of 5.05% when Maria starts making payments 6 months after graduation.

The government pays the interest for the first 6 months after graduation, so Maria owes no interest on her subsidized loan.

The interest is figured beginning at graduation. The formula is ...

  I = Prt . . . . . . P is the principal amount, r is the interest rate, and t is years

  I = $4500(0.0505)(1/2) = $113.625 ≈ $114

Maria will owe $114 in interest on her loans 6 months after graduation.

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Answer: 14 degrees F.

Step-by-step explanation:

        To see how many degrees it much rise to reach 0F, we will subtract -14 from 0 to find our answer.

o - - 14 = 0 + 14 = 14 degrees F

Option A is correct that is the results comparing each box size and comparing flashy vs simple graphics.

Given this, a marketing firm tested several package variations, including size, complexity, and simplicity, to determine which would encourage customers to buy more cereal.

Which of the following would be the key conclusions of the study?

We are aware of this since we are comparing various box and graphic sizes.

When contrasting the sizes of each box and the flashy vs. simple images, the influence of the research can be noticed.

The comparison of the sizes of each box and the effectiveness of flashy vs. straightforward images shows that Option A is the best choice.

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The given inequality is y > x^2 + 1. To represent this inequality in a system of equations, we can subtract x^2 + 1 from both sides to get y - x^2 - 1 > 0. The inequality is nonstrict (i.e., it includes the equal sign), so we can represent it using an equation by setting y - x^2 - 1 = 0.

The additional constraints are y < x + 7 and x > 1. The first constraint can be represented by the inequality y - x - 7 < 0, which can be represented by the equation y - x - 7 = 0. The second constraint can be represented by the inequality x - 1 > 0, which can be represented by the equation x - 1 = 0.

Thus, the system of equations representing the situation is:

y - x^2 - 1 = 0

y - x - 7 = 0

x - 1 = 0

We can represent this system graphically by graphing each equation on a coordinate grid. The first equation, y - x^2 - 1 = 0, represents a parabola. The second equation, y - x - 7 = 0, represents a line with a slope of -1. The third equation, x - 1 = 0, represents a vertical line at x = 1.

One example of a height and side length that the obstacle course can use is a height of 6 feet and a side length of 2 feet. This satisfies all of the given constraints, and it can be seen in the graph as a point of intersection between the three lines.

a) The standard error of the mean is equal to the standard deviation divided by the square root of the sample size. In this case, the standard error of the mean would be equal to 23.65/sqrt(8) = 6.61.

b) Using the central limit theorem, we can say that the probability that the mean of the eight plots would be within 1 standard error of the mean is approximately equal to 68%. This is because, under the central limit theorem, the distribution of the sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, in this case, we would expect that 68% of the sample means would be within 1 standard deviation of the population mean.

c) The probability that we calculated in (b) might not be very accurate because the central limit theorem assumes that the underlying population is normally distributed. However, it is not clear from the histogram whether the number of live maples per plot is normally distributed. If the distribution of the number of live maples per plot is not normal, then the central limit theorem would not be applicable and the probability we calculated might not be accurate.

Hence we get the required answer.

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The total time taken by Amy to complete her assignments is 19/20 hours.

Addition is one of the four basic operations of arithmetic, Addition in maths is a process of combining two or more numbers.

Given that, Amy finished her chemistry assignment in 1/5 hours. Then she completed her history assignment in 3/4 hours.

Total time taken by Amy = Time taken for chemistry assignment + Time taken for history assignment

= 1/5+3/4 = (15+4)/20

= 19/20

Hence, The total time taken by Amy to complete her assignments is 19/20 hours.

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If v1,...,vp is linearly dependent in V, then there exist scalars c1,...,cp such that c1v1 + ... + cpvp = 0.

Applying the linear transformation T to both sides of this equation, we get T(c1v1 + ... + cpvp) = T(0). Since T is a linear transformation, T(c1v1 + ... + cpvp) = c1T(v1) + ... + cpT(vp).

Therefore, Tv1,...,Tvp is linearly dependent in W. This shows that if a linear transformation maps a set v1,...,vp onto a linearly independent set Tv1,...,Tvp, then the original set v1,...,vp must be linearly independent as well, because if it were linearly dependent, then Tv1,...,Tvp would also be linearly dependent.

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If a ball is thrown in the air with a velocity of 52 ft/s, its height in feet t seconds later is given by y = 52t − 16t2.

Then the average velocity for the time period beginning when t = 2 and lasting for 0.5s,0.1s,0.05s,0.01s will be -20,-13.6,-12.8,-12.16 respectively

y=y(t)=52t-16t²

At t=2, y=52(2)-16(2)² =40

The average velocity between time 2 and 2+h is Vav. = [tex]\frac{y(2+h)-y(2)}{(2+h)-2}[/tex]

                                                                                      =[tex]\frac{-12h-16h^2}{h}[/tex]

                                                                                      = -12-16h

Now finding the average velocity for the period beginning when t = 3 and lasting-

(i)0.5 s is (2,2.5) , Vav. = -20.0 ft/s

(ii)0.1 s is (2,2.1), Vav = -13.6 ft/s

(iii) 0.05s is (2,2.05), Vav. = -12.8ft/s

(iv) 0.01s is (2,2.01) Vav.=-12.16ft/s

And at t=2 , h will approaches to zero so Vav= -12ft/s

Therefore, If a ball is thrown in the air with a velocity of 52 ft/s, its height in feet t seconds later is given by y = 52t − 16t2.

Then the average velocity for the time period beginning when t = 2 and lasting for 0.5s,0.1s,0.05s,0.01s will be -20,-13.6,-12.8,-12.16 respectively.

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On solving the provided question, we can say that  - h1: μ < $600 and mean - 1/35 X 20307 = 580.2

According to a well-known statistical theory known as the null hypothesis, there is no statistically significant association between any two sets of observable data and measurable events.

By putting X = sales change in $

Null hypothesis -

h0= μ ≥ $600

alternative hypothesis is

h1: μ < $600

where μ  is population mean change in sales per week

point estimate of mean change in sales  is

mean - 1/35 X 20307 = 580.2

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When the area is 24 cm², the height of the triangle is 4 cm.

The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.

Here,

area=1/2(bh)

h=b-8

24=1/2(b(b-8))

48=b²-8b

b²-8b-48=0

b²-12b+4b-48=0

b(b-12)+4(b-12)=0

b=-4,12

b=12 cm

h=12-8

h=4 cm

The height of triangle is 4 cm when area is 24 cm².

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Answer:the simplified form of the expression (10x-5/6)-x+4/3 is 9x - 1.

Step-by-step explanation: To simplify the expression (10x-5/6)-x+4/3, you can start by applying the order of operations, which dictates that you should perform operations within parentheses or brackets first.

The expression (10x-5/6) can be simplified as follows:

(10x-5/6) = 10x - (5/6)

= 10x - (5*6)/6

= 10x - 5

= 10x - 5

Next, you can simplify the remaining terms of the expression:

(10x-5) - x + 4/3

= (10x-5) - (x3)/3 + 4/3

= (10x-5) - x + (43)/3

= (10x-5) - x + 4

= 10x - 5 - x + 4

= 10x - x - 5 + 4

= 9x - 1

Therefore, the simplified form of the expression (10x-5/6)-x+4/3 is 9x - 1.

it's either S or R according to me

Is Shaylee able to invest in all of these projects simultaneously is no. Since the company has limited excess of money i.e. 2 Million to invest.

What is probability index?

The present value of benefits for each dollar of investment is calculated using the profitability index approach. In other words, it involves the ratio that is produced by comparing the ratio of the initial investment to the present value of future cash flows from a project.

A solid investment is one with a profitability index of greater than 1.0, with higher values indicating more alluring enterprises.

The ratio between the initial investment and the present value of future cash flows is measured by the profitability index (PI). The index can be used to rate investment projects and display the value produced per investment dollar.

Profitability Index = Present Value of Cash INflows / Present Value of Cash Outflows

Project : Profitability Index

A : 1.8434 (765,000 / 415,000)

B : 1.8043 (415,000 / 230,000)

C : 1.6667 (1200,000 / 720,000)

D : 1.6508 (1560,000 / 945,000)

Order of Preference

Project - Order of Preference

A - First Preference

B - Second Preference

C - Third Preference

D - Fourth Preference

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No , the carpeted rooms does not have more bacteria than uncarpeted rooms .

Given ,

α=0.05

n1=8

n2 = 8

mean = ∑x / n

x1 = 11.8+10.8+7.1+14.6+8.2+10.1+13.0+14.0 / 8 = 11.2

and

x2 =12.1+12.0+3.8+10.1+8.3+11.1+7.2+13.7 /8 = 9.78

Variance ,

s1  =2.6

s2 = 3.2

HYPOTHESES

H0 : μ 1 =μ 2

H1 : μ 1  ≠μ 2

​Either the alternative hypothesis or the null hypothesis applies to the claim. The equality must be present in the null hypothesis. The alternative hypothesis declares the opposite of the null hypothesis if the claim is the null hypothesis.

On calculating we get the test statistic t as,

t = 1.771

The null hypothesis is rejected if the test statistic's value falls within the rejection zone.

0.956<1.771,

therefore , fail to reject H .

Therefore , there is no support for the null hypothesis , so we accept the alternate hypothesis as true.

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​

The given series is convergent and the first term is 4 and the common ratio is -0.5 and the sum of the series is 8/3 .

The given series is 4 - 4/2+ 4/4 - 4/8 +...

We can see that the first term of the geometric series is 4

Hence a = 4

The second term is  -4/2 and the third term is 4/4

Hence r = 4 ÷ (-4/2) = -4/2 ÷ 4/4 = - 1/2 or -0.5

Since the common ratio is less than 1 we can say that the series is convergent.

Now for a convergent series we know that the sum of the terms of the series is equal to

S = a / (1-r)

or, S = 4 / (1-(-0.5))

or, S = 4 / 1.5

or, S = 8/3

Hence the sum of the convergent series is 8/3 .

Both the ratio test and the root test are based on a comparison with a geometric series and hence function in comparable scenarios.

In fact, if the ratio test works (that is, if the limit exists and is not equal to 1), then so does the root test; the contrary is not true. The root test is thus more broad, although in practise, determining the limit for regularly encountered kinds of series is frequently challenging.

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