1+1 = ??????????????????

Answer: 16 students

Step-by-step explanation:

2x + (2•4) = 4x

2x + 8 = 4x

-2x -2x

8 = 2x
(Divide by 2 on both sides)

vvv

2x/2= x

8/2 = 4

x = 4

(substitute 4 in for x)

2(4) + 8 = 4(4)

8+8 = 16

16 = 16

The slope value of the linear relationship tells us how much Austin pays to his friend weekly, which is: $8.

A linear relationship between two variables, x and y, can be defined by the equation, y = mx + b, where the value of m is the slope and b is the y-intercept or starting value.

If we have a table that represents a linear relationship between two variables, x and y, what we need to do is to use two pairs of values from the table to find the change in y / change in x.

In this context, L = amount Austin owes his friend for t weeks, so the slope will be the amount Austin pays to his friend every week = change in L / change in t.

Using two pair of values from the table, (1, 32) and (4, 8):

Slope (m) = change in L / change in t = (32 - 8) / (1 - 4)

Slope (m) = 24/-3

m = -8

Therefore, the amount Austin will be paying to his friend weekly would be $8.

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The measure of the long -run average value of a random variable used to represent the central location of a probability distribution is called an expected value E(x).

As given in the question,

Reason with explanation :

Therefore, the measure of the long run average value of a random variable representing central location of the probability distribution is called the expected value.

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The probability that marksman will hits the target at most 13 times is  27.92%.

The number of successes ("x") is the probability mass function for such binomial distribution.

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

We are interested in the likelihood that the target will be struck exactly five times, therefore the desired number of successes is five (i.e., x = 13).

P(X = 13) =  ¹⁵C₁₃. (0.89)¹³ (0.11)²

P(X = 13) = 0.2792

P(X = 13) = 27.92%

Thus, the probability that marksman will hits the target at most 13 times is  27.92%.

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To be more certain that it captures the true value of the population proportion, a 95 % confidence interval must be larger than an 80 % confidence interval.

An area created using fixed-size samples of data from a population (sample space) that follows a certain probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% chance of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval.

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If geometric sequence has a1= 5 and r = 3 then the A(n) will be; 5 × 3^(n-1)

There are three parameters which differentiate between which geometric sequence we're talking about. The first parameter is the initial value of the sequence. The second parameter is the quantity by which we multiply previous term to get the next term.

The General form of a geometric sequence:

[tex]A(n) = A_1 \times r^{(n-1)}[/tex]

If a1= 5 and r = 3 then

A(n) = 5 × 3^(n-1)

Therefore, If geometric sequence has a1= 5 and r = 3 then the A(n) will be; 5 × 3^(n-1)

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The number of times the point R ( 120° , P ) needs to be rotated so that the figure is mapped to itself is 3 times

What is Rotation?

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the number of rotation be = n

Let the point be R

Now , the coordinates of the point R is

R ( 120° , P )

Now , to map the figure onto itself it needs to rotate 360°

So ,the number of times 120° needs to rotate to reach 360° is calculated as

n x 120° = 360°

Divide by 120 on both sides , we get

n = 360 / 3

n = 3 times

Therefore , the value of n is 3

Hence ,  The number of times the point R ( 120° , P ) needs to be rotated so that the figure is mapped to itself is 3 times

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Answer:

One or more of the mean differences are statistically significant, but not the precise location of the group differences.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess. Age, for instance, might be an independent variable.

Dependent variables are so-called because, during an experiment, their values are examined on the assumption or presumption that they are governed by the values of other variables.

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Answer:

Its the second one

Step-by-step explanation:

.

The best prediction the price will do next is keep increasing.

What is stock price?

The price at which one share of a company would be purchased is known as the share price or stock price. A share's price is not constant; rather, it changes over time in response to market factors. It is likely to rise if the business is thought to be doing well or fall if it isn't living up to expectations.

A company's price rising more quickly indicates that investors are supporting the rally and that the stock will rise further.

On the other hand, a declining price trend with high volume suggests a possible downward trajectory. A high trade volume could also indicate a change in trend.

Hence, the best prediction the price will do next is keep increasing.

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The approximate distance from the sun to Earth is miles greater than the approximate distance from Earth to the moon by 9.276 × 10^7.

Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper. Furthermore, the numbers in the millions place after the decimal required to be represented in a simpler format.

In this case, the approximate distance from Earth to the moon is 240 thousand miles. This will be 2.4 × 10^5

The approximate distance from Earth to the sun is 93 million miles. This will be:

= 9.3 × 10^7

The difference will be:

= (9.3 × 10^7) - (2.4 × 10^5)

= 9.276 × 10^7

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Answer:

Step-by-step explanation:

2+2+4

Marko needs the amount of money which would be $20 to go to a concert.

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

We have been given that Marko has $22. He needs at least $42 to go to a concert.

We have to determine the required amount of money Marko

the required amount of money = cost of the concert - he has the amount

the required amount of money = $42 - $22

Apply the subtraction operation, and we get

the required amount of money = $20

Therefore, Marko needs the amount of money that would be $20.

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Answer:

Step-by-step explanation:

(3x-2)(3x+1)

Answer:

(3x - 2)(3x + 1)

Step-by-step explanation:

9x^2 - 3x - 2 = 9x^ 2 - 6x  + 3x - 2 =

=3x(3x - 2) + (3x - 2) = (3x - 2)(3x + 1)

Answer: a

Step-by-step explanation:

Answer:

c. -24

Step-by-step explanation:

f(3) means the y value where x = 3, therefore f(3) = -24

Mia will pay a total of $4.5 for the shipping and handling of the t-shirt

From the question, we have the following parameters that can be used in our computation:

Cost of the shirt = $15

shipping and handling = 30%

The amount paid for the shipping and handling of the t-shirt can be calculated using the following equation

Amount paid = original price * + shipping and handling

Substitute the known values in the above equation, so, we have the following representation

Amount paid = 15 * 30%

Evaluate the products

Amount paid = 4.5

Hence, the amount paid is $4.5

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The Central Limit Theorem establishes that the sampling distribution of the sample means with size n can be roughly equivalent to a normal distribution with mean and standard deviation for a normally distributed random variable X, with mean and standard deviation.

The Central Limit Theorem can also be used with skewed variables if n is at least 30.The mean of the sampling distribution of sample means is p for a proportion p in a sapling of size n, and the standard deviation is s=root of p(1-p)/n.This issue involves that:(A) Determine the sample proportion's sampling distribution's mean.The Central Limit Theorem states that 0.85

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98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.

What does a statistical random sampling entail?

P = x/n

= 89/168

= 0.53

α= 0.02

∴Zc = Zi - α/2

= 2.326

Now, C.I = P ± Zc * √[P(1-P)/n]

= 0.5 ± 2.326 * √[(0.53(1-0.53)) / 168

= (0.440, 0.619)

∴98% C.I. = 0.440 < P < 0.619

Hence, 98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.

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Answer:

the answer is $6

Step-by-step explanation:

This is because there are 1000g in 1kg, so 500g is half of that and half of 12 is 6.

The dimensions of the box that minimize the total cost of materials used are:

L = W = 16 cm

H =  32 cm

What is the rectangular dimension?

Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth. A triangle's or an oval's interior likewise has two dimensions.

We have,

volume L* W * H = 512 cm³

sides of the box cost = 1 cent/cm²

top and bottom cost 2 cent/cm²

to find out

dimensions of the box that minimize the total cost of material use

we know here,

L* W * H = 512 cm³

where,

L is length and W is width and H is the height

so when we minimize the cost function

C( L, W, H ) = (1) 1 H ( L + W ) + (2) 1 L W

so put here H

substitute  [tex]H = \frac{512}{LW}[/tex] we get,

C(L, W) = 512([tex]\frac{1}{l}, \frac{1}{W}[/tex]) + 2LW

so

minimum cost will be when the two partial derivatives is 0

dC/dL = 2W - 512/L² = 0

so

dC/dW = 2L - 512/W² = 0

L =  256/W²

so

by solving the above equation we get

L = W = (256)⁻³ = 16cm

and

H = 512/16 = 32

H =  32 cm

Hence, the dimensions of the box that minimize the total cost of materials used are:

L = W = 16 cm

H =  32 cm

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The margin of error for the population proportion is ± 3.39%

Error is the difference between a genuine value and an estimate, or approximate, representation of that value in practical mathematics. The discrepancy between the mean of the complete population and the mean of a sample taken from that population is a frequent example in statistics.

Given that A survey of factories in five northeastern states found that 10% of the 300 workers surveyed were satisfied with the benefits offered by their employers

i.e. sample size n =300

Sample proportion p = 0.10

q=1-p=0.9

[tex]\sqrt{} \frac{pq}{n}[/tex] = [tex]\sqrt{\frac{0.1*0.9}{300} }[/tex]

Standard error ≈ 0.01732

Margin of error at 95% would be

1.96*std error

= 0.0339=3.39%

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There are 4 lattice points on the line segment whose endpoints (3,17) &(48,281)

What is a Lattice point?

In a Cartesian coordinate system, a lattice point is a point whose x-coordinates and y-coordinates are both integers. A point in a regularly spaced array of points, known as a point lattice, that is at the intersection of two or more grid lines is referred to as a lattice point. Point lattices with unit cells that are square, rectangular, hexagonal, and other forms can be built in a plane. An unspecified point in a square array constitutes a point in a point lattice.

The difference in the y-coordinates is 281 - 17 = 264

the difference in the x-coordinates is 48 - 3 = 45.

The gcd of 264 and 45 is 3,

so the line segment joining (3,17) and (48,281) has a slope [tex]\[\frac{88}{15}\][/tex]

The points on the line have coordinates[tex]\[\left(3+t,17+\frac{88}{15}t\right).\][/tex]

If t is an integer, the y-coordinate of this point is an integer if and only if t is a multiple of 15.

The points where t is a multiple of 15 on the segment [tex]3\leq x\leq 48[/tex] are 3, 3+15, 3+30, and 3+45.

There are 4 lattice points on this line. Hence the answer is B

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By using the volume of sphere, it can be calculated that

Volume of the sphere after the hole is drilled = [tex]352\sqrt{33} \pi[/tex]

What is volume of sphere?

Volume of sphere is the total space taken by the sphere.

If r is the radius of the sphere, then volume of the sphere is

[tex]v = \frac{4}{3} \pi r^3[/tex]

Radius of the ball = 14

Radius of the ball after the hole is drilled = 8

By Pythagoras Theorem,

Height of the ball after the hole is drilled =[tex]\sqrt{14^2 - 8^2}[/tex] = [tex]\sqrt{132}[/tex]

Volume of the ball after the hole is drilled = [tex]\frac{4}{3} \pi (\sqrt{132})^3[/tex]

                                                                           = [tex]\frac{4\pi \times 132 \times 2\sqrt{33}}{3}\\352\sqrt{33} \pi[/tex]

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Using system of linear inequality, the number of tacos and burrito he sold was 56 and 54 respectively

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

To solve this problem, we have to write two system of inequality and then graph the inequalities to show the solution.

Let;

x + y = 110 ...eq(i)

7x + 3.25y ≥ 560 ..eq(ii)

From eq(i)

x + y  110

x = 110 - y ..eq(iii)

Put eq(iii) into eq(ii)

7(110 - y) + 3.25y ≥ 560

770 - 7y + 3.25y ≥ 560

770 - 3.75y ≥ 560

-3.75y ≥ 560 - 770

-3.75y ≥ -210

y ≤ 56

Assuming y is less than or equal to 56, x will be

x + 56 = 110

x = 54

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Answer:

Step-by-step explanation:

First, Amelia thinks of a number that is a factor of both 18 and 12. This number is odd, so it can't be a whole number. Next, Amelia has to find the largest number that is a factor of both 18 and her chosen number. This number is 36.

Answer:

  3

Step-by-step explanation:

You want the largest odd factor of both 18 and 12.

The greatest common divisor of both 18 and 12 is 6:

  18 = 3·6

  12 = 2·6

This is an even factor, which has two factors: 2 and 3. Only 3 is an odd factor of both 18 and 12.

The largest odd factor of both 18 and 12 is 3.

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The best way of writing a prolog rule that gives you all the possible coin combinations adding to a dollar is using membership rules and arithmetic condition.

The Prolog interpreter warns that it can only find one occurrence of one or more variables, which is strange, since typically variables are used to perform unification, pass values from one predicate to another, etc.

Arithmetic in Prolog

In arithmetic expression, + - * / symbols are special type of infix operator, and these operators are also known as arithmetic operators. In Prolog, operators are used as predicates but here operators are functions and these operators return a numerical value.

Arithmetic expressions can include variables, numbers, operators, and arithmetic functions. These will be written in parentheses with their arguments. These will return numerical values just like the arithmetic operators.

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Answer:

84

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let, the dimension of cuboid are l=5x,b=4x and h=2x

Now, the surface area of cuboid =2(5x×4x+4x×2x+2x×5x)=76x2

Now,

76x2=1216

x2=16

x=4

Dimensions of cuboid are,

l=5x=5×4=20cm,b=4x=4×4=16cm

h=2x=2×4=8cm

Volume of cuboid=l×b×h=20×16×8=2560cm3

Hence, this is the answer.