The function f(x) = –1∕3x2 is shifted down one unit. Which of the following function equations represents this translation? Question 6 options:
A) f(x) = –1∕3(x – 1)2
B) f(x) = –1∕3x2 + 1
C) f(x) = –1∕3x2 – 1
D) f(x) = –1∕3(x + 1)2

the ratio of the area of the triangle to the area of the rectangle is 1: 2

The formula for calculating the area of a triangle is;

Area of triangle = 1/ 2 base × height

The formula for area of a rectangle is;

Area of a rectangle = length ×  width

From the information given, we have;

Now, let's substitute the values;

Area of a triangle = 1/ 2 × 11 × 4

Area of a triangle = 44/ 2 = 22m²

Area of a rectangle = 11 × 4

Area of a rectangle = 44m²

The ratio of the area of the triangle to the area of the rectangle is

= 22: 44

= 1 : 2

Thus, the ratio of the area of the triangle to the area of the rectangle is 1: 2

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If the ratio of model train to real train is 1:3 and the real train is 12 feet then the model train is 3 feet long.

Given that the model train has a scale of 1:3 and the real train is 12 feet tall.

We are required to find the height of the model train.

Ratio shows how many times one number contains another number. A ratio is the relationship in quantity  between two things. It expresses quantity of one thing in terms of another.

Ratio of model train to real train is 1 inches :3 inches.

Height of model train=12*1/4

=3 inches

Hence if the ratio of model train to real train is 1:3 and the real train is 12 feet then the model train is 3 feet long.

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After 16 days, the total homework questions that have been assigned would be 80 questions.

Ratio expresses the equivalent relationship between two numbers. It shows the frequency of the number of times that one value is contained within other value(s).

A ratio table can be described as table that shows equivalent values between two numbers.

The first step is to determine the ratio between the number of days and the total number of questions.

Ratio = money saved / money earned

8/10 =  total number of questions / number of days

55 / 11 = 5

Now, multiply the ratio gotten in the previous step by the number of days

Total number of homework questions = number of x ratio

5 x 16 = 80 questions

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The base side of the isosceles triangle in discuss as described in the task content is; 10cm.

According to the task content, the area of the isosceles triangle is 60 square cm.

Since, the length of its longest sides is 13 cm and since it follows from convention that the bisection of an isosceles triangle results in the formation of two right-triangles.

Consequently, it follows from Pythagoras triples that the height of each right triangle is 12 and its base is; 5.

Consequently, the base of the whole isosceles triangle is; 2 × 5 = 10cm.

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Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.

At the null hypothesis, it is tested if the average cost is still of $50,000, that is:

[tex]H_0: \mu = 50000[/tex]

At the alternative hypothesis, it is tested if the average cost is decreasing, that is:

[tex]H_1: \mu < 50000[/tex]

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are:

[tex]\overline{x} = 49450, \mu = 50000, \sigma = 2500, n = 100[/tex]

Hence:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{49450 - 50000}{\frac{2500}{\sqrt{100}}}[/tex]

z = -2.2.

Using a z-distribution calculator, for a left-tailed test, as we are testing if the mean is less than a value, with z = -2.2, the p-value is of 0.0139.

Since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.

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The length of the rectangle is 77cm.

According to the statement

we have given that the area of a painting is 4081 c m squared. and width of the painting is 53 cm.

And we have to find the Length of the painting.

So, For this purpose

Area of rectangle is the region occupied by a rectangle within its sides. It depends on its sides.

So, the formula to find the area of rectangle is

Area = Length*Breadth

4081 = L*53

L = 4081/53

L = 77 cm.

So, The length of the rectangle is 77cm.

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There were 204 participants from the three schools

The given parameters are:

X = 12 + Y

X = Z - 18

Girls = Boys + 50

The ratios of the number of boys to girls in the schools are:

1 : 2

1 : 5

2 : 1

This means that:

So, we have:

Boys = 1/3X + 1/6Y + 2/3Z

Girls = 2/3X + 5/6Y + 1/3Z

Substitute the above equations in Girls = Boys + 50

2/3X + 5/6Y + 1/3Z = 1/3X + 1/6Y + 2/3Z + 50

Evaluate the like terms

1/3X + 2/3Y - 1/3Z = 50

Multiply through by 3

X + 2Y - Z = 150

So, we have:

X = 12 + Y

X = Z - 18

X + 2Y - Z = 150

Substitute X = 12 + Y in X = Z - 18 and X + 2Y - Z = 150

12 + Y = Z - 18 ⇒ Y - Z = 30

12 + Y + 2Y - Z = 150 ⇒ 3Y - Z = 138

Subtract Y - Z = 30 from the equation 3Y - Z = 138 to eliminate Z

2Y = 108

Divide by 2

Y = 54

Substitute Y = 54 in X = 12 + Y

X = 12 + 54

X = 66

Substitute X = 66 in X = Z - 18

66 = Z - 18

Solve for Z

Z = 66 + 18

Z = 84

So, the total number of participants from the 3 schools is

Total = X + Y + Z

This gives

Total = 66 + 54 + 84

Evaluate the sum

Total = 204

Hence, there were 204 participants from the three schools

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Answer:

36

Step-by-step explanation:

Honestly, I'd work this out visually (see image) by drawing a rectangle and dividing it up. But if you need to show the math, here's how to do it:

Let x = the number of students in the homeroom

1/3 x have drama

1/4 (x - 1/3x) have band, and we are told 6 students have band, so

1/4 (x - 1/3 x) = 6

1/4 (2/3 x) = 6    

2/12 x = 6          

1/6 x = 6            

6 × 1/6 x = 6 × 6

1 x = 6 × 6            

x = 36

Answer:

36

Step-by-step explanation:

Let n be the total number of students in Mr. Short's homeroom. Then, working backward, we see that 

6 = 1/4(1 - 1/3)n = 1/4(2/3)n = 1/6n,$

so n = 6 x 6 = 36 students.

The 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

Let the random variable & parameters be;

x1 : Number of successes from group 1

x2 : Number of successes from group 2

p1: Proportion of successes in group 1

p2: Proportion of successes in group 2

n1 : number of trial in group 1

n2: number of trial in group 2

We are given;

x1 = 260

n1 =985

x2 = 194

n2 = 842

Thus;

p1 = 260/985

p1 =0.2640

p2 = 194/842

p2 = 0.2304

Constructing a (1 - α)100% confidence interval for proportion from the formula;

(p₁ - p₂) - z√[((p₁(1 - p₁)/n₁) + p₂(1 - p₂)/n₂)]

plugging in z = 2.576 and the values of p₁, p₂, n₁ and n₂, we have the confidence interval as;

(-0.0184631, 0.0855743)

Therefore the 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

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The area of the circle A and B is 86.54 inches and 124.62 mm

According to the statement

we have given that the radius of the circle A and b and we have to find the area of the given circle.

So, we know that the

The area enclosed by a circle of radius r is πr².

So, For area of the circle

For condition A :

diameter = 10.5 inches

then radius = 5.25

Area = πr²

Area = 3.14*27.56

Area = 86.54 inches

Now, For condition B :

radius = 6.3 mm

Area = πr²

Area = 3.14*39.69

Area = 124.62mm

So, The area of the circle A and B is 86.54 inches and 124.62 mm

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Answer:

Option D is correct.

No solution

Step-by-step explanation:

2(x+7)=8

Apply 2 into bracket:

2x+14=8

2x=8-14

2x=-6

Divide both sides by 2:

x=-3

hence here is no option for x=-3, so answer is no solution.

Step-by-step explanation:

let's name the variables for the age of the people as the people themselves :

orlando = omar + 12

carl = 3×orlando

carl + orlando + omar = 68

using the first equation in the second equation, and then that result and the first equation in the third equation :

carl = 3×(omar + 12)

3×(omar + 12) + (omar + 12) + omar = 68

3×omar + 36 + omar + 12 + omar = 68

5×omar + 48 = 68

5×omar = 20

omar = 4

orlando = omar + 12 = 4 + 12 = 16

carl = 3×orlando = 3×16 = 48

the ratio omar : carl : orlando

4 : 48 : 16 = 1 : 12 : 4

The solutions to the questions are given below

a)

sample(n) word length sample mean

1                    5,4,4,2    3.75

2                    3,2,3,6     3.5

3                         5,6,3,3    4.25

b)R =0.75

c)

The table below shows sample means in the table.

sample(n) word length sample mean

1                    5,4,4,2    3.75

2                    3,2,3,6     3.5

3                         5,6,3,3    4.25

b)

Generally, the equation for is  mathematically given as

variation in the sample means

R =maximum -minimum

R=4.25-3.5

R =0.75

c)

In conclusion, In most cases, the mean of many samples will provide a more accurate estimate than the mean of a single sample.

They may have a higher level of confidence in their estimate if the range of the sample means is closer to 0 than it is now.

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Answer:

204

Step-by-step explanation:

6*10=60

6*6=36

6*8=48

2((10*6)/2)=60

60+60+36+48=204

Answer:

..........................................

Answer:

C.  They most likely used an observational study asking students to keep track of their TV habits and weight.

A.  This is an experiment because a treatment was applied to a group.

Step-by-step explanation:

According to our question:

1. The study concluded that there is a relation between watching TV and the weight gain in college freshmen.

Now, this is possible when a group of college students were asked to participate to watch TV for more than 1 hour for a specific amount of time and have a record of their weights.

So, the study is an observational study where the habits and weights of college students were observed.

Hence, option C is correct.

2. The students were divided onto two groups where one group used the computer program and the other did not to check the improvement in the reading levels.

This means that the students were given a procedure to follow during the study in order to see the results..

So, the study is an experiment where a treatment is applied to the group of students.

Hence, option A is correct.

Answer: C

For the people who want only one answer and not 2 for the question if you can only submit one answer :)

The solution to the inequalities 3x + 5 < 6x + 8 and 4x + 3 < 7x + 5 is x > -1 and x > -2/3 respectively

Inequality signs are;

3x + 5 < 6x + 8

3x - 6x < 8 - 5

-3x < 3

x > 3/-3

The inequality sign is flipped from < to greater than because of the division with negative value.

x > -1

2. 4x + 3 < 7x + 5

4x - 7x < 5 - 3

-3x < 2

The inequality sign is flipped from < to greater than because of the division with negative value.

x > -2/3

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Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.

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The number of decorative pillows did the realtor arrange on each twin bed and queen bed is 6 and 9 respectively.

let

x + y = 15

2x + y = 21

From equation (1)

x = 15 - y

2x + y = 21

2(15 - y) + y = 21

30 - 2y + y = 21

- 2y + y = 21 - 30

-y = -9

y = 9

Substitute y = 9 into

x + y = 15

x + 9 = 15

x = 15 - 9

x = 6

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Answer:

6 children passes

Step-by-step explanation:

a = adult and c = children

25a + 15c = 440           and          a + c = 20

                                                     c = 20 - a

25a + 15(20-a) = 440

25a + 300 - 15a = 440

25a - 15a = 440 - 300

10a = 140

a = 140/10

a = 14 and this is 14 adult tickets

Now we plug the a value into the equation to find the c value

14 + c = 20

c = 20 - 14

c = 6

Verify answer:

25(14) = 15(6) = 440

350 + 90 = 440

440 = 440

April's work in checking for the function, [tex]f(x) = x^3 - 1[/tex], to be even, odd, or neither, is incorrect. She did a mistake in step 2, where she took [tex]f(-x) = - f(x)[/tex], which was not true, since [tex]f(-x) = -x^3 - 1[/tex], whereas [tex]- f(x) = -x^3 + 1[/tex].

A function f(x) is said to be odd or even when it completes the condition:

In the question, we are given that April was asked to determine whether  [tex]f(x) = x^3 - 1[/tex], is even, odd, or neither, and are shown her work.

We are asked whether April's work is correct, and if not, what is the first step where April made a mistake.

To check for a function is even or odd, we first calculate f(-x).

April's first step was also finding f(-x), which she found accurately as  [tex]f(-x) = -x^3 - 1[/tex].

Next, we need to check whether f(-x) is equal to f(x), -f(x), or neither, to check if the function is even, odd, or neither, respectively.

April, also choose the right step of checking, but did a mistake in checking, since f(-x) ≠ f(x), and also, f(-x) ≠ - f(x), since, [tex]- f(x) = -(x^3 - 1)[/tex] = [tex]-x^3 + 1[/tex], which is not equal to f(-x).

Thus, April's work in checking for the function, [tex]f(x) = x^3 - 1[/tex], to be even, odd, or neither, is incorrect. She did a mistake in step 2, where she took f(-x) = - f(x), which was not true, since [tex]f(-x) = -x^3 - 1[/tex], whereas [tex]- f(x) = -x^3 + 1[/tex].

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Based on the calculations, the depth of tent is equal to 12 feet.

Based on the diagram (see attachment) and information provided, we can logically deduce the following parameters (points):

Next, we would determine the height of the right-angled triangle (ADC) by applying Pythagorean theorem:

AC² = AD² + DC²

AD² = AC² - DC²

AD² = 5² - 3²

AD² = 25 - 9

AD² = 16

AD = √16

AD = 4 feet.

Also, we would determine the area of the triangle (ABC):

Area = 1/2 × b × h

Where:

Substituting the given parameters into the formula, we have;

Area = 1/2 × 6 × 4

Area = 12 feet².

Depth of tent = 3 × height of ADC

Depth of tent = 3 × 4

Depth of tent = 12 feet.

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The discount to be increased so that he can gain only 15% is 8%.

How much is the discount to be increased so that he can gain only 15%:

The cost price of the goods - y.

The selling price of the goods - x.

The selling price is

1.2y (100% + 20% = 120%).

The refrigerator was sold at 13% VAT at Rs. 10848:

=> 1.2y + 13%(1.2y) = 10848

=> 1.2y + 0.156y = 10848

=> 1.356y = 10848

=> y = 8000

Thus, the cp is Rs 8000.

The selling price is:

=> 0.96x = 1.2y

=> 0.96x = 1.2(8000)

=> x = 10000

The selling price is Rs. 10000

For a profit of 15%, that is 1.15(8000) = 9200, the discount is:

(1 - discount)10000 = 9200

1 - discount = 0.92

Discount = 1 - 0.92 = 0.08 or 8%

How much is the discount to be increased so that he can gain only 15%: Discount=8%

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Answer:

30°

Step-by-step explanation:

To make sure it's complete

Using a quadratic regression equation, it is found that the prediction of volunteers in year 10 is of:

A. 47.

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, we have that the function initially increases, then it decreases, which means that it is a quadratic function. The points (x,y) to  be inserted into the calculator are given as follows:

(1, 20), (2,17), (3, 16), (4,16), (5,18), (6,21), (7,25), (8,31)

Inserting these points into the calculator, the prediction of y for a value of x is given as follows:

y = 0.702x^2 - 4.726x + 23.857

Hence, when x = 10, the prediction is:

y = 0.702 x 10² - 4.726 x 10 + 23.857

y = 47.

Hence option A is correct.

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Anais bought 2 1/2 yards of ribbon. She had 2 feet 8 inches of ribbon left after trimming some curtains. Anais uses 58 inches of ribbon to trim the curtains.

What is Unit Conversion?

Anais bought 2 1/2 yards of ribbon.

And she had 2 feet 8 inches left after trimming some curtains.

The first thing to do is to convert all units to inches;

From standard conversion rate.

1 yard  = 36 inches

As such  2 1/2 yards of ribbon in inches will be:

= 2 1/2 × 36 inches

= 5/2 × 36 inches

= 5 × 18 inches

= 90 inches of ribbon bought.

Similarly, since 1 foot  = 12 inches.

The amount of curtains left after trimming is:

= ( ( 2 × 12 ) + 8 )inches

= (24 + 8) inches

= 32 inches

If Anais bought 90 inches of ribbon and she had 32 inches of ribbon left after trimming some curtains.

It implies that the number of inches of ribbon that Anais used is:

= 90 inches - 32 inches

= 58 inches

Therefore, we can conclude that Anais used 58 inches of ribbon.

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The complete question is-

Anais bought 2 1/2 yards of ribbon. She had 2 feet 8 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains?

Anais used _____ inches of ribbon.

The maximum area of the enclosure is 562500 square feet

The function is give as:

V(x) = 1500x - x^2

Differentiate

V'(x) = 1500 -2x

Set to 0

2x = 1500

Divide by 2

x = 750

Substitute x = 750 in V(x) = 1500x - x^2

V(x) = 1500*750 - 750^2

Evaluate

V(x) = 562500

Hence, the maximum area of the enclosure is 562500 square feet

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The mean of the data set A is 4.58 while the mean of data set B is 5.

An equation is an expression that shows the relationship between two or more numbers and variables.

The mean of a set of numbers is the average of that group of number. It is the ratio of the sum of the data to the total number of data.

Mean of data set A = [(3 * 1) + (4 * 3) + (5 * 2) + (6 * 2) + (7 * 3) + (8 * 1)] / (1 + 3 + 2 + 2 + 3 + 1) = 4.58

Mean of data set B = [(4 * 2) + (5 * 2) + (6 * 2)] / ( 2 + 2 + 2) = 5

The mean of the data set A is 4.58 while the mean of data set B is 5.

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