1l) HAO WENT TO A HOBBY SHOP AND SAW A DISPLAY OF TOY TRAINS. THE SIGN IN FRONT OF
THE DISPLAY SAID THAT THE TOY TRAINS WERE A REPLICA OF THE LONG ISLAND RAILROAD
TRAINS. HAO ESTIMATED THAT ONE OF THE RAILROAD CARS WAS APPROXIMATELY 15
INCHES LONG AND 4 INCHES WIDE. THE SIGN IN FRONT OF THE DISPLAY STATED
"SCALE- 2 /9".
WHAT IS THE LENGTH OF THE RAILROAD CAR ON HE LONG ISLAND RAILROAD?
WHAT IS THE WIDTH OF THE LONG ISLAND RAILROAD CAR?

Answer:

0.9156

Step-by-step explanation:

In the picture attached, the data is plotted (I made it using MS Excel, you can use similar programmes or a calculator).

The line that best correlates the data has the following equation:

y = 0.1037x + 50.922

and its correlation coefficient is:

R² = 0.9156

Answer:

Correlation coefficient, r = 0.957

Step-by-step explanation:

Let y represent the weight

Let x represent the height

y                        x                       x²                 y²                     xy

99                     61                      3721            9801               6039

104                    61                      3721            10816              6344

110                     62                     3844           12100              6820

133                     64                     4096           17689             8512

130                     65                     4225           16900            8550

142                     68                     4629           20169            9656

146                     66                     4356           21316              9636

153                     67                     4489           23409            10251

184                     69                     4761            33856            12696

185                     70                     4900           34225            12950

\(\sum y = 1386\), \(\sum x = 653\), \(\sum x^2 = 42737\), \(\sum y^2 = 200276\), \(\sum xy = 91454\)

Correlation coefficient formula,

\(r = \frac{n \sum xy - \sum x \sum y}{\sqrt{(n \sum x^2 - (\sum x)^2) (n \sum y^2 - (\sum y)^2)} } \\r = \frac{10* 91454 - 653*1386}{\sqrt{(10* 42737 - (653)^2) (10* 200276 - (1386)^2)} }\)        

Correlation coefficient, r = 0.957

Answer:

-139.4

Step-by-step explanation:

36.6 - 528 ÷ 3 = 36.6 - 176

= -139.4

Answer:

48

Step-by-step explanation:

The amount of time needed and the amount of wall to paint are directly proportional. So, when we multiply the amount of wall to paint by 8/5 (going from 5000 square feet to 8000 square feet), we multiply the time needed by 8/5. Therefore, we need 30 * 8/5 = 48  minutes to paint the 8000 square foot wall.

We need 48 minutes to paint 8000 square football . The minute is a measure of time that is typically equal to 60 seconds, or 1/60 of an hour.

Given,

8 team members paint 5000square football in 30 min

So,

30*8/5

= 48 minutes

Therefore We need 48 minutes to paint 8000 square football.

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The constant of proportionality between y and x is the same as the ratio of any corresponding y and x values in the table. Therefore, we need to check each table to see if the ratio of any corresponding y and x values is equal to 8/5.

Table 1:

x y

1 2

2 4

3 6

4 8

Ratio of y to x:

When x=1, y=2, so y/x = 2/1 ≠ 8/5

When x=2, y=4, so y/x = 4/2 = 2/1 ≠ 8/5

When x=3, y=6, so y/x = 6/3 = 2/1 ≠ 8/5

When x=4, y=8, so y/x = 8/4 = 2/1 ≠ 8/5

Table 2:

x y

1 1.6

2 3.2

3 4.8

4 6.4

Ratio of y to x:

When x=1, y=1.6, so y/x = 1.6/1 = 1.6 ≠ 8/5

When x=2, y=3.2, so y/x = 3.2/2 = 1.6 ≠ 8/5

When x=3, y=4.8, so y/x = 4.8/3 = 1.6 ≠ 8/5

When x=4, y=6.4, so y/x = 6.4/4 = 1.6 ≠ 8/5

Table 3:

x y

5 8

10 16

15 24

20 32

Ratio of y to x:

When x=5, y=8, so y/x = 8/5 = 1.6 = 8/5

When x=10, y=16, so y/x = 16/10 = 1.6 = 8/5

When x=15, y=24, so y/x = 24/15 = 1.6 = 8/5

When x=20, y=32, so y/x = 32/20 = 1.6 = 8/5

Therefore, Table 3 has a constant of proportionality between y and x of 8/5.

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The equation of the line passing through the given coordinate with the given slope is; y = 2x + 11

The formula for equation of line in point slope form is;

(y - y1) = m(x - x1)

We are given the slope is 2

Now, if the line passes through the coordinate (-4, 3), then the equation of the line is;

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

y - 3 = 2x + 8

y = 2x + 11

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The uppercase letter H has reflectional symmetry and does not have rotational symmetry or point symmetry.

The uppercase letter H has reflectional symmetry. Reflectional symmetry, also known as mirror symmetry, means that there is a line (axis) along which the shape can be divided into two equal halves that are mirror images of each other. In the case of the letter H, a vertical line passing through the center of the letter can be drawn as the axis of symmetry. When the letter H is folded along this line, the two halves perfectly match.

The letter H does not have rotational symmetry. Rotational symmetry refers to the property of a shape that remains unchanged when rotated by a certain angle around a central point. The letter H cannot be rotated by any angle and still retain its original form.

The letter H also does not have point symmetry, which is also known as radial symmetry or rotational-reflectional symmetry. Point symmetry occurs when a shape can be rotated by 180 degrees around a central point and still appear the same. The letter H does not exhibit this property as it does not have a central point around which it can be rotated and remain unchanged.

In summary, the uppercase letter H exhibits reflectional symmetry but does not possess rotational symmetry or point symmetry.

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Answer:

the last one (-14)+(-8)

Step-by-step explanation:

-14 - -8 any time you have minus a negative it's a + sign

so

-14+8 therefore it's the first one.

Answer:

(a) The probability that the average of the draws will be in the range 80 to 120 is 1.

(b) The probability that the average of the draws will be in the range 99 to 101 is 0.6827.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sample means is given by,

\(\mu_{\bar x}=\mu\)

And the standard deviation of the sample means is given by,

\(\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}\)

As the sample selected is quite large, i.e. n = 400 > 30, then the sampling distribution of sample means will be approximately normally distributed.

Compute the mean and standard deviation of sample mean as follows:

\(\mu_{\bar x}=\mu=100\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{400}}=1\)

So, \(\bar X\sim N(100, 1)\)

(a)

Compute the probability that the average of the draws will be in the range 80 to 120 as follows:

\(P(80<\bar X<120)=P(\frac{80-100}{1}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{120-100}{1})\)

                            \(=P(-20<Z<20)\\\\=P(Z<20)-P(Z<-20)\\\\=(\approx1)-(\approx0)\\\\=1\)

Thus, the probability that the average of the draws will be in the range 80 to 120 is 1.

(b)

Compute the probability that the average of the draws will be in the range 99 to 101 as follows:

\(P(99<\bar X<101)=P(\frac{99-100}{1}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{101-100}{1})\)

                            \(=P(-1<Z<1)\\\\=P(Z<1)-P(Z<-1)\\\\=0.6827\)

Thus, the probability that the average of the draws will be in the range 99 to 101 is 0.6827.

Answer:

a) 5x-1

b) 9x+2

c) 5x+6

Step-by-step explanation:

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

2x+1+3x-2=

5x-1

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

b) (-3+5x)-(-4x-5)=

5x+4x-3+5=

9x+2

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

c) (x+1)-(-4x-5)=

x+1+4x+5=

5x+6

Answer:

B

Step-by-step explanation:

Answer:

number 2

Step-by-step explanation:

because i did the same exersise and this is the solution

The value of  \(log_b(\frac{1}{b^3})\) is -3.

Option B is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

\(log_b(\frac{1}{b^3})\)

This can be written as,

= \(log_b1 - log_bb^3\)

= 0 - 3 \(log_bb\)

= 0 - 3 x 1

= 0 - 3

= -3

Thus,

The value is -3.

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The component form of vector AB minus vector CD is (1, -15, 7).

To find the component form of the vector AB minus vector CD, we subtract the corresponding components of the two vectors.

Given:

Vector AB: Initial point (-4, 4, 0) and terminal point (-4, -8, 1)

Vector CD: Initial point (-5, 7, -2) and terminal point (1, -5, -6)

To find the component form of AB minus CD, we subtract the x-components, y-components, and z-components separately:

Component form of AB minus CD:

(x-coordinate) = (-4) - (-5) = 1

(y-coordinate) = (-8) - 7 = -15

(z-coordinate) = 1 - (-6) = 7

Therefore, the component form of vector AB minus vector CD is (1, -15, 7).

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Step-by-step explanation:

\((6 + 5 + 5) \times 7 = 112\)

The names of 0 employees are written on 0 cards. the cards are placed in a​ bag, and three names are picked from the bag - here simple random sampling technique was used.

Basic irregular testing can provide you with an extremely precise image of how your motto performs with the typical individual, yet it won't give you nitty gritty data about unambiguous gatherings. Utilizing straightforward irregular testing permits scientists to make speculations about a particular populace and leave out any inclination. This can assist with deciding how to settle on future choices. It has been expressed that "the rationale behind straightforward arbitrary examining is that it eliminates predisposition from the choice method and ought to bring about delegate tests".

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Answer:

Each country will have a representative of 565 people in that political gathering.

Step-by-step explanation:

The area of the given trapezoidal site is 250,000 sq. ft.

The area of the trapezoidal with the dimensions of both bases and the height is given by the formula,

Area = 1/2 × height × (base1 + base2)

Units: square units

The given trapezoidal site has a base of 150 feet, i.e., base1 = 150 ft; a height of 2000 ft, i.e., height = 2000 ft and a parallel base of 100 feet, i.e., base2 = 100 ft.

Then, the area of the trapezoidal is

= 1/2 × 2000 × (150 + 100)

= 1/2 × 2000 × 250

= 250,000 sq. ft

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The sum of the three integers is 57.

The term integer in math is known as the collection of whole numbers and negative numbers.

Here we have given that the product of three different positive integers is equal to 7³.

Here let us consider that x,y,z be three positive number.

Then based on the given is written as

=> xyz = 7³

When we expand the equation, then we get,

=> xyz = 343

Here we have expand the equation as,

=> xyz = 1 × 7 × 49

Then the equation written as

=> x + y + z = (1 + 7 + 49)

Then the sum equation is calculated as

=> x + y + z = 57

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Answer:

32

Step-by-step explanation:

x+102=4x+6

102=3x+6

96=3x

32=x

Hope this helps!!!

Answer:

2 cos (x + pi/2)

Step-by-step explanation:

Of the choices given, this looks like a cos curve that is shifted to the Left by pi / 2  and   multiplied to give an amplitude of 2

Answer:

the answer is-

Step-by-step explanation:

42.5% and the estimation is 43%

Answer:

42.5%

Step-by-step explanation:

17/40 = 0.425

Move decimal to the tenths place.

0.425 --> 42.5

Answer:

1

Step-by-step explanation:

\(\frac{3-7}{2-6}\) = \(\frac{-4}{-4}\) = 1

The average change of the function is given by 3.5 over the interval [4,8]

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here : The corresponding values of the functions to input x

now F(4)=-4 & F(8)=11

Thus the average rate of change of the function of the interval is given by

A= F(4)+F(8) / 2

  =-4+11 /2

  = 3.5

Hence,  The average change of the function is given by 3.5 over the interval [4,8]

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Answer:

29/12=2.41666667

..................=2.33333333

.......................=2.58

second

Step-by-step explanation:

Answer:

in the picture

Step-by-step explanation:

in the picture

Using the formula of area of a circle, about 226.08in² has been eaten

The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:

Area = π * r²

where π is approximately 3.14 and r is the radius of the circle.

Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.

Let's calculate the area of the entire pizza first:

Area = 3.14 * 12²

Area = 3.14 * 144

Area ≈ 452.16 square inches

Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:

Area of half of the pizza = 452.16 / 2

Area of half of the pizza ≈ 226.08 square inches

Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.

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For the angle of elevation to the top of a building is 5 degrees from the ground, the height of building is equals to 0.1 miles.

A buliding in New York. The angle of elevation to the top of a building from ground = 5°

Distance from ground point to base of building = 1 mile

We have to determine the height of the building. Now, if we consider all scenario geometrically, then we see the right angled triangle present in above figure. The height of buliding = h

Using the Trigonometric Ratio \( tan(\theta) = \frac{height}{base} \)

Substitute all known values in above formula, \(tan(5°) = \frac{h}{1 \: miles} \)

From the trigonometric table, tan(5°) = 0.087

=> h = 1 × 0.087 miles

=> h = 0.087 miles ~ 0.1 miles

Hence, required height value is 0.1 miles

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Answer:

60

Step-by-step explanation:

asked google

Answer:

60

Step-by-step explanation:

5: 5 10 15 20 25 30 35 40 45 50 55 60 65 70

12: 12 24 36 48 60 72 84

Answer:

$3864

Step-by-step explanation: