help please. this doesn't make sense ​

Answer:

15/2r - 40; Distributive Property

Step-by-step explanation:

You can use the Distributive Property to multiply the 5 across the expression in the parentheses.

5(3/2r - 8)

5 × 3/2r = 15/2r

5 × -8 = -40

Combine.

15/2r - 40

Hope this helps!

Answer:

i think the answer may be acute and isosceles

Dilation by a scale factor of 5 does not preserve congruence, hence the correct answer is option c.

1. Rotation transformation: A rotation is a transformation in which the object is rotated about a fixed point. The direction of rotation can be clockwise or anticlockwise.

2. Reflection transformation: In a reflection transformation, all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection.

3. Translation transformation: Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.

4. Dilation transformation: Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape. A dilation should either stretch or shrink the original shape.

Congruence is preserved by reflection, translation & rotation, as the image & pre-image have the same side lengths & angle measurements. But in case of dilation transformation, the side lengths change, hence this transformation does not preserve congruence.

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Answer:

\(A=339.42\ cm^2\)

Step-by-step explanation:

The diameter of the roll of paper, d = 4.5 cm

Radius, r = 2.25 cm

Height of the roll of papaer, h = 24 cm

We need to find how much is needed to make the inner tube for a roll of paper. The surface area of a cylinder for inner tube is given by :

\(A=2\pi r h\\\\=2\times \dfrac{22}{7}\times 2.25\times 24\\\\=339.42\ cm^2\)

So, the required area is \(339.42\ cm^2\).

The largest value less than 500 that both sets have common is 479.

We have given two arithmetic progression such that,

{2,5,8,11,...} and {3,10,17,24,...}

and we have to find the largest value less than 500 that they have in common.

We know the formula for the nth term of the arithmetic progression,

i.e, an = a + (n - 1)d

for the arithmetic progression {2,5,8,11,...} the formula become

am = 2 + (m - 1)3 ----------- (1)

and for the arithmetic progression {3,10,17,24,...} the formula become

an = 3 + (n - 1)7 ------------- (2)

by solving for m and n we get,

m = 160 and n = 69

so equation (1) implies that,

a(160) = 2 + (159)3 = 479

this is the 160th term in the 1st arithmetic progression

and equation (2) implies that,

a(69) = 3 + (68)7 = 479

this is the 69th term in the 2nd arithmetic expression.

Therefore, the value which less than 500 that both the progressions have in common is 479.

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The following data sets represents the required properties:

a. . Same mean but different standard deviation :

3   3   3  3   3                

1    2   3   4  5              

2    2  3   4  4    

b.  Same mean but different medians

1    2   3   4  5            

1    1   4   4   5            

1    2   2   5  5  

c. Same median but different median:

1      2    3    5   5        

1      2   3    4    5          

2     2   3    5    5  

As given in the question,

Three data sets with 5 numbers representing :

a. Same mean but different standard deviation :

                                       Mean                  Standard deviation

3   3   3  3   3                  15/5 = 3                 0

1    2   3   4  5                 15/5 = 3                  2.5      

2    2  3   4  4                 15/5 = 3                  1    

Mean of the data set = 3

Standard deviation = \(\frac{\sum (x - \bar{x} )^{2} }{n -1}\)

b. Same mean but different medians :

                                   Mean                     Median

1    2   3   4  5             3                                3

1    1   4   4   5             3                                4

1    2   2   5  5            3                                 2

c. Same median but different median:

                                    Mean          Median

1      2    3    5   5          3.2                3

1      2   3    4    5            3                 3

2     2   3    5    5          3.4                3

Therefore, above are the following data set to represent same mean different standard deviation, same mean different median and same median different mean.

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All initial value problems for second-order linear homogeneous ODEs with constant coefficients are solvable and have a unique solution. The given statement is true.

The statement is true, and it is a consequence of the fact that second-order linear homogeneous ODEs with constant coefficients have a general solution of the form:

y(t) = c1e^(r1t) + c2e^(r2t)

where r1 and r2 are the roots of the characteristic equation:

ar^2 + br + c = 0

where a, b, and c are constants, and c1 and c2 are arbitrary constants determined by the initial conditions.

Since the characteristic equation has two roots, it is always possible to find the general solution for any initial value problem of the form:

ay'' + by' + cy = 0

y(0) = y0, y'(0) = y1

by plugging the initial conditions into the general solution and solving for c1 and c2.

Moreover, the solution is unique because the general solution is a linear combination of two functions, and the coefficients c1 and c2 are uniquely determined by the initial conditions.

Therefore, all initial value problems for second-order linear homogeneous ODEs with constant coefficients are solvable and have a unique solution.

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Answer:

\(y=3x+5\)

Step-by-step explanation:

Parallel lines have the same slope.

This means that we would only have to change the y-intercept to get our new line.

We are asked to write an equation of a parallel line with the y-intercept of five.

Rewrite the infomation to create the new equation. Note that parrarell lines have the same slope.

\(y = 3x + 2\rightarrow\boxed{y=3x+5}\)

Hope this helps.

The value of this expression {-1.5(-3.5)}{1/4 - 1/2} is -21/8.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided above, we have the following mathematical expression:

Expression = {-1.5(-3.5)}{1/4 - 1/2}

Expression = {-1.5(-3.5)}{(1 - 3)/4}

Expression = {-1.5(-3.5)}{-2/4}

Expression = {5.25}{-1/2}

Expression = {21/4}{-1/2}

Expression = -21/8.

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The possible dimensions (length and width) of the field are:(10 m × 13 m) or (13 m × 10 m) and (11 m × 12 m) or (12 m × 11 m).

Given that Aaron has 47m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. The fourth side of the enclosure would be the river.

The area of the land is 266 square meters.To find the possible dimensions (length and width) of the field, we can use the given information.The length of fencing required = 47 m.

Since the fence needs to be built on three sides of the rectangular plot, the total length of the sides would be 2l + w = 47.1. When l = 10 and w = 13, we have:

Length of the field, l = 10 m Width of the field, w = 13 mArea of the field = l × w = 10 × 13 = 130 sq. m2. When l = 11 and w = 12,

we have:Length of the field, l = 11 m

Width of the field, w = 12 m

Area of the field = l × w = 11 × 12 = 132 sq. m

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Answer:  The slope-intercept form is y = -2x + 10

Step-by-step explanation:

Step 1: The y-intercept is the point where x=0, so that is (0,10)

Step 2: Use the points (-2,14) and (-1,12) to find the slope

Slope (m) = ΔY/ΔX = -2/1 = -2

Step 3: The slope-intercept form is:

y = mx+b

y = (step 2 value) x + (step 1 value)

y = -2x+10

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The question is not complete, so i have attached it.

Answer:

Options A, B & E are correct

Step-by-step explanation:

In the synthetic division attached, we see that:

: 2 , -2 & -12 are the coefficient of the dividend of the function 2x² - 2x - 12

: The divisor is 3

Thus;

x = 3 is a root of f(x) = 2x² - 2x - 12

Thus, (x - 3) is a factor of the dividend which is the function f(x) = 2x² - 2x - 12

- Now, from the attached image, the coefficients of the quotient are 2 , 4

- The quotient will be 1 degree less than the dividend since it was divided by the factor (x - 3)

The degree of the dividend will be 2 since it contains x²

Thus, the degree of the quotient will be 1

Therefore, the quotient in factor form is (2x + 4)

Looking at the given statements in the options;

- Option A is true, because we have established earlier that 3 is a root of f(x) = 2x² - 2x - 12

- Option B is true because we have established that (x - 3) is a factor of 2x² - 2x - 12

- Option C is not true because the factor is (x + 3) and not (x - 3)

-Option D is not true because the root is 3 and not -3

- Option E is true because we have established that quotient as a factor is: (2x + 4)

Thus, the correct options are A , B , E

Answer:

interior = 3600° , exterior = 360°

Step-by-step explanation:

use the formula : ( n - 2 ) * 180 ..........where n is the number of sides

here the number of sides is 22

so if fall under the formula:

( 22 - 2 ) * 180

3600° is the total sum of the interior angles.

The exterior angle formula:

360° is the sum of the exterior angles.

The lines which are parallel are none.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.

Given;

Coordinates of three lines

a;(1,5) and (-2,-4)

b;(3,2) and (1,-4)

c;(6,1) and (-4,2)

Now, slopes of the lines

a= -4-5/-2-1

=10/3

b=-4-2/1-3

=-3

c=2-1/-4-6

=1/-10

Therefore, by slopes of the line none of them are parallel.

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Answer:

Step-by-step explanation:

Measure the corresponding sides and verify if the ratios are same or not.

Corresponding sides:

The measures, using coorinates and the distance formula:

We can see the ratios of the two pairs are not same:

We can state that Kyle is correct

The value of x and y is y= 3/4 and x= -1/2

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

Given equations:

2x+8y=5........(1)

24x-4y=-15...........(2)

Multiply equation (1) by 12, we get

24x + 96y = 60.....(3)

From (2) and (3), we get

-4y-96y= -15-60

-100 y= -75

y= -75/-100

y= 3/4

and 2x+8y=5

2x + 8 (3/4) =5

2x + 6 = 5

2x= -1

x= -1/2

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The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Answer:

The age of the youngest child = x = 6 years

The age of middle child = y = 8 years

The age of the oldest child = z = 12 years

Step-by-step explanation:

Let us represent:

The age of the youngest child = x

The age of middle child = y

The age of the oldest child = z

The sum of the ages of the children is 26.

Hence: x + y + z = 26...... Equation 1

The oldest is 4 years older than the middle

z = 4 + y

The youngest child is 2 years younger than the middle child

x = y - 2

Hence, we substitute 4 + y for z and y - 2 for x in Equation 1

x + y + z = 26...... Equation 1

y - 2 + y + 4 + y = 26

y + y + y -2 +4 = 26

3y + 2 = 26

Subtract 2 from both sides

3y + 2 - 2 = 26 - 2

3y = 26 - 2

3y = 24

y = 24/3

y = 8

Solving for x

x = y - 2

x = 8 - 2

x = 6

Solving for z

z = 4 + y

z = 4 + 8

z = 12

Therefore:

The age of the youngest child = x = 6 years

The age of middle child = y = 8 years

The age of the oldest child = z = 12 years

Answer:

3 of 9 is expected

since 7 of 21 (7+14) is 1/3 are coconut cupcake

7/21 = 1/3

1/3 x 9 = 3 coconut cupcakes

Answer:

-1 7/8

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

Answer:

3 hrs. 30 mins.

Step-by-step explanation:

7:00 - 3:30

Using probability of independent events, it is found that the probability that it will purchase the mineral rights to exactly one of the two mountains is given by:

c. 0.51

If two events, A and B, are independent, the probability of both happening is the multiplication of the probability of each happening, that is:

\(P(A \cap B) = P(A)P(B)\)

In this problem, these following two events result in the rights of exactly one of the two mountains being bought:

Hence:

\(p = 0.55(0.6) + 0.45(0.4) = 0.51\)

Thus, option c is correct.

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Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

Answer:

Step-by-step explanation:

Step one:

given that the orientation of the garden is a triangular shape(it has three sides)

the perimeter is given as=46ft

one side y=11ft

the second side z= 13ft

let the third side be xft

Step two:

the expression for the perimeter = z+y+x

46=11+13+x

46=24+x

solve for x

x=46-24

x=22ft

Therefore the third side is 22ft long

Answer:

12.25

Step-by-step explanation:

B = 15.25 -0.06x

B = 15.25 -0.06(50)

B = 12.25

Answer:

x=6.6

Step-by-step explanation:

13:5=x:3

33=5x

33/5=x

6.6=x

Answer:

15.16047 cm

Step-by-step explanation:

notice that the smaller triangles ratio is 3 : 5

so the bigger triangle's bottom side has length 13 cm

so lets multiply 13 by (3/5)

we get 7.8

we can just use pythagorean theorem to find AB

\(\sqrt{x} = 7.8^{2} + 13^{2}\)

15.16047 cm

Answer:

Lower quartile = 6

Uppwr quartile = 10

Step-by-step explanation:

Coefficient of quartile deviation = 0.25

Quartile deviation = 2

Coefficient of quartile deviation = (Q3 - Q1) / (Q3 + Q1)

Quartile deviation = (Q3 - Q1) / 2

Hence;

Quartile deviation = (Q3 - Q1) / 2 = 2

Q3 - Q1 = 2 * 2

Q3 - Q1 = 4 - - - - (1)

Q3 = 4 + Q1 - - - - (2)

(Q3 - Q1) / (Q3 + Q1) = 0.25

Q3 - Q1 = 4

4 = 0.25(Q3 + Q1)

Q3 + Q1 = 4 / 0.25

Q3 + Q1 = 16 - - - - (3)

Put Q3 = 4 + Q1 in (3)

4 + Q1 + Q1 = 16

4 + 2Q1 = 16

2Q1 = 16 - 4

Q1 = 12 / 2

Q1 = 6

Q3 = 4 + Q1

Q3 = 4 + 6

Q3 = 10