the number defects per part from an aging machine is shown below. number of defects (x) per part 0 1 2 3 4 5 probability p(x) 0.15 0.20 0.30 0.10 0.20 0.05 what is the mean of the data?

Answer:

turning point = (- 2, - 7 )

Step-by-step explanation:

the vertex form of a parabola is

y = a(x - h)² + k

where (h, k ) are the coordinates of the turning point ( vertex) and a is a multiplier.

given

y = x² + 4x - 3

to complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 4x

y = x² + 2(2)x + 4 - 4 - 3

y = (x + 2)² - 7 ← in vertex form

with turning point (- 2, - 7 )

Answer:

B. [tex](x-3)^2+(y-1)^2=4[/tex]

Step-by-step explanation:

Standard equation of a circle with a center at C=(3,1) and radius 2 is:

[tex](x-3)^2+(y-1)^2=4[/tex]

The equation of a circle with center at (h,k) and a radius of r is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

In this example h=3, k=1 and r=2, so after substituting into above formula we have:

[tex](x-3)^2+(y-1)^2=2^2\\(x-3)^2+(y-1)^2=4[/tex]

Thanks.

Answer:

Equation: 3x - 4 = 6 - 2x

Solution: x = 2

Step-by-step explanation:

Look at the key.

Left side of the equal sign:

A grey rectangle means x.

There are 3 grey rectangles on the left side, so that is 3x.

A white square means -1.

There are 4 white squares on the left side, so that means -4.

Altogether, the left side is 3x - 4.

Right side of the equal sign:

A black square means 1.

There are 6 black squares, so that means 6.

A white rectangle means -x.

There are 2 white rectangles, so that means -2x.

Altogether, the right side is 6 - 2x.

Put both sides together, and you have

3x - 4 = 6 - 2x

Solve the equation:

Add 2x to both sides.

5x - 4 = 6

Add 4 to both sides.

5x = 10

Divide both sides by 5.

x = 2

Answer:

Equation: 3x - 4 = 6 - 2x

Solution: x = 2

If the rate of change is constant, the volume of the water in the pond by the year 2030 will be 147 gallons.

Define volume.

Any three-dimensional solid's volume is just the amount of space it takes up. It can be any shape like a cube, cuboid, cone, cylinder, etc. Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. The SI unit of volume is cubic units.

Solution Explained:

Based on the conditions given in the question, we formulate as follows

(612 X (2024 - 2020) + (612 - 798) X (2030 - 2020) / (2024-2020)

= (612 X 4 - 186 X 10) / 4
= (2448 - 1860) / 4
= 588 / 4
= 147

Therefore, by 2030 the volume of the water in the pond will be 147 gallons.

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The equation that represents the altitude h of the balloon over time.

h = 1500t.

Option B is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 5 is an equation.

3x + 5x = 5 is an equation.

We have,

A hot air balloon rises 1,500 feet in 25 minutes.

This means,

25 minutes = 1,500 feet

h = altitude

The equation that represents the altitude h of the balloon over time.

h = 1500t.

Thus,

The equation that represents the altitude h of the balloon over time.

h = 1500t.

Option B is the correct answer.

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The absolute value of 4 by 3 would be 3.33

What is the absolute value?

The absolute value or modulus of a real number x denoted |x| in mathematics, is the non-negative value of x regardless of its sign.

We have to find the absolute value of 4/3.

So |4/3| = |3.33|

             = 3.33

Hence, the absolute value of 4 by 3 would be 3.33

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The slope of the line from the equation is 2/3.

The line:

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.

The formula of a line:

y = mx + c

m = slope

c = y-intercept

Here we are provided with the equation:

8x - 12y = 108

12y = 8x - 108

y = 2/3x - 9

So by equating we get the slope:

m = 2/3

Therefore the slope is 2/3.

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Answer:thhe one on top good

Step-by-step explanation:

Answer:

f(x) = 1/2x + 3

Answer:

3/2

Step-by-step explanation:

(y2-y1)/(x2-x1)

(-1-2)/(-4+2)

-3/-2

the slope of the line is 3/2

The image is then dilated by a scale factor of half with a center of dilation of (1, 2); Preimage (8, 4), (4, -4), and (1, 2) → Image (1, 2), (2.5, -1), and (4.5, 3).

A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. In a rigid transformation the pre-image and image are congruent (have the same shape and sizes).

The coordinates of the vertices of the preimage will be;

(5, 10), (2, 4), (9, 2)

The coordinates of the vertices of the image will be;

(-9, -2), (-2, -4), (-5, -10)

This is equivalent to a reflection about the origin, and a rotation of 180° clockwise or anticlockwise about the origin.

Part B: Figure 2 to Figure 5

The coordinate points of figure 2 will be;

(-9, 2), (-5, 10), and (-2, 4)

The coordinate points of figure 5 will be;

(1, 2), (2.5, -1), and (4.5, 3)

The lengths of the sides of figure 2 will be;

√((10 - 2)² + ((-5) - (-9))²) = 4·√5

√((10 - 4)² + ((-5) - (-2))²) = 3·√5

√((2 - 4)² + ((-9) - (-2))²) = √53

The lengths of the sides of figure 5 will be;

√(((-1) - 2)² + (2.5 - 1)²) = (3·√5)/2

√((4.5 - 2.5)² + (3 - (-1))²) = 2·√5

√((4.5 - 1)² + (3 - 2)²) = (√53)/2

Thus, Figure 5 is Figure 2 dilated by a scale factor of 1/2(half )

Therefore, the given sides of Figure 2 and Figure 5 are rotated by 180°

1) The rotation of figure 2 by 180° about the origin to get;

(-9, 2), (-5, 10), and (-2, 4) →   (9, -2), (5, -10), and (2, -4)

2) The image is translated left by 1 blocks and up by 6 blocks as;  

(9, -2), (5, -10), and (2, -4)  →   (8, 4), (4, -4), and (1, 2)

3) The image is then dilated by a scale factor of half with a center of dilation of (1, 2);

Preimage (8, 4), (4, -4), and (1, 2) → Image (1, 2), (2.5, -1), and (4.5, 3).

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Answer:

[tex]6\frac{3}{8}[/tex]

Step-by-step explanation:

to multiply fractions turn them into improper fractions and then multiply numerator by numerator and denominator by denominator

-4 1/4*-1 2/4

-17/4*-6/4

102/16

51/8

6 3/8

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

Domain is the input

Range is the output

Function is the equation that is set up by the given information

1)

Domain   2 to 8

Range   1 to 6

Yes, this is a function

2)

Domain  2 to 3

Range  7 to 13

No, this is not a function , b/c functions need a 1 to 1 correspondence

3)

Domain  0 to 4

Range   -1 to 5

No, this is not a function , b/c functions need a 1 to 1 correspondence

The cost for Enrique's ad which he wants to run for 3 weeks is $207

Given,

Number of lines in Enrique's ad = 6 lines

Charge for first two lines of ad = $42

Charge for extra lines after 2 lines = $6.75 each

The above given charges are for one week.

We have to find the cost for Enrique's ad which he wants to run for 3 weeks;

Here,

Total charge for Enrique's ad = 42 + (4 x 6.75) = 42 + 27 = 69

Enrique's 6 line ad charges $69 for a week

Now,

Charge of ad for 3 weeks = 69 x 3 = 207

That is,

The cost for Enrique's ad which he wants to run for 3 weeks is $207

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The value of the blocks he used is 80 blocks.

The difference is that expressions, which are essentially mathematical "phrases," do not contain an equal sign. Equations have an equal sign and demonstrate that two mathematical expressions are equivalent. An algebraic equation is 2x + b = 14, but 2x + b is an algebraic expression.

Arithmetic operations are the most fundamental type of mathematical expression. Any combination of numbers and a mathematical operation, such as multiplication, addition, subtraction, or division, are considered arithmetic operations.

Given ,

A)How many blocks has he used?

150-70

= 80

B) 35 - 20

= 15

70/15

= 4

Therefore the value of the blocks he used is 80 blocks

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Answer:

red grapes cost the most

Step-by-step explanation:

7 bags of red grape cost $24.50 4 bags of green grapes cost $15 what type of grapes is more expensive?

24.5/7 = $3.50 per bag

15/4 = $3.75 per bag

So, the red grapes cost more per bag.

The multiplication of the quotient and the fraction is 1 (2/5).

A fraction is a part of the whole represented by a/b, where a and b are any integers.

The given expression is (1/5) × 7.

Perform the multiplication:

(1/5) × 7

= 7/5

= 1 (2/5)

Hence, the multiplication of the quotient and the fraction is 1 (2/5).

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0.68 is the variable is normally distributed when standard deviation is r29. 44.

What is standard deviation in math?

μ = 146.21   σ = 23.44         x ~ n

P{ x < 160 } = ρ{ x - μ/σ < 160 - 146.21/29.44 }

                  = ρ{ z < 0.47 }

                   = 0.6808

                  ≈ 0.68

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The equation to represent the total amount paid for the book is p=6c.

An equation is a combination of two or more variables in which the two mathematics expressions are equal.

Given that,

Book bought by Agustin = c,

Price for the book = 6 $

The total amount paid by Agustin = Number of books × price of books

Amount  =c×6,

p=6c $.

The amount paid by Agustin is p=6c $.

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Degree of freedom for chi-square test for 10 categories will be 9.

What is chi- square test?

A test that evaluates how well a model matches real observed data is that the chi-square (χ²) statistic. A chi-square statistic can only be calculated with data that's random, unprocessed, mutually exclusive, obtained from independent variables, and drawn from a large enough sample.

The Formula for Chi-Square Is

χ(c)=²∑(Oₐ-Eₐ)₂/Eₐ²

where:

c=Degrees of freedom

O=Observed value(s)

E=Expected value(s)

​

Main Body:

Degree of freedom = total categories -1

so no. of categories= 10

Degree of freedom = 10 - 1

Hence degree of freedom = 9

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Based on the box plot, the number of students that gained more than 48 marks is 80 students.

In Mathematics, the five-number summary of any box and whisker plot include the following:

By critically observing the box and whisker plots which represent the scores of students in a test, we can reasonably and logically deduce that the third quartile (75%) is 70 and the median score is 48. Therefore, we would calculate the total number of students as follows:

Total number of students = 75/100 × T

120 = 0.75T

T = 120/0.75

T = 160 students.

From the median score of 48, the number of students that gained more than 48 marks is given by:

Students = 50/100 × 160

Students = 50/100 × 160

Students = 80 students.

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If we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, then 56 sample size should be used and if we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, then 22 sample size should be used.

In the given question,

A preliminary sample conducted by the wall street journal showed that the standard deviation of the amount of time devoted to previews was 4 minutes.

(a) We have to estimate the population mean time for previews at movie theaters with a margin of error of seconds, what sample size should be used.

Assuming the confidence interval 98% and margin error of 75 seconds.

We can write 98% as 0.98.

So the value of z at 98% confidence interval using the standard table of z is 2.326.

Standard Deviation= 4 minutes

Converting minutes in seconds so,

Standard Deviation= 4*60

Standard Deviation= 240

Margin of error is 75 seconds.

So the sample size = (Value of z * Standard Deviation)/Margin Error

Sample Size = ((2.326*240)/75)^2

Sample Size = (558.24/75)^2

Sample Size = (7.4432)^2

Sample Size = 55.401

Approx value of Sample Size = 56

Hence, if we want to estimate the population mean time for previews at movie theaters with a margin of error of 75 seconds, then 56 sample size should be used.

(b) We have to estimate if we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, what sample size should be used.

The given margin of error is 75 seconds.

Now converting the error in minute by dividing 60.

Now the margin of error = 75/60=5/6 minute

Standard Deviation= 4 minutes

The confidence interval 98% and margin error of 75 seconds.

We can write 98% as 0.98.

So the sample size = (Value of z * Standard Deviation)/Margin Error

sample size = {(0.98*4)/(5/6)}^2

sample size = {6(0.98*4)/5}^2

sample size = (6*3.92/5)^2

sample size = (23.52/5)^2

sample size = (4.704)^2

sample size = 22.13

Approx value of Sample Size = 22

Hence, if we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, then 22 sample size should be used.

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0.86 of the exam scores are between 68 and 77.99 points

Since the set of computer science exam scores are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x-μ)/σ

Where

X = computer science exam scores.

μ = mean score

σ = standard deviation

From the information given,

μ = 71.33 points

σ = 333 points

We want to find the proportion of the exam scores are between 68 and 77.99 points. It is expressed as

P(68 < x ≤ 77.99)

For x = 68,

z = (68 - 71.331)/333 = - 0.01

Looking at the normal distribution table, the probability corresponding to the z score is -0.01

For x = 68,

z = (77.99 - 71.33)/333 = 0.25

Looking at the normal distribution table, the probability corresponding to the z score is 0.25

P(68 < x ≤ 77.99) = 0.25 + 0.01 = 0.26

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The formula to find the length l of a baking sheet that has an area of 117 square units is l = 117/w.

According to the question,

We have the following information:

Formula to find area = lw

Now, l is the length of a baking sheet.

Area of a baking sheet = 117 square units

So, we have the following expression:

lw = 117

Now, in order to find the value of l, we will divide both sides by w:

l = 117/w units

Hence, the formula to find the length l of a baking sheet that has an area of 117 square units is l = 117/w.

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The primary tool for determining whether the assumptions made about the regression model are appropriate is residual analysis.

Regression analysis is a collection of statistical techniques used in statistical modelling to estimate the associations between a dependent variable and one or more independent variables. Regression analysis is a mathematical method for determining which of those factors has an effect.

Regression analysis is an effective statistical tool for examining the connection between two or more variables of interest. When the dependent and independent variables are connected in a linear or nonlinear form and the goal variable has a set of continuous values, it is extensively employed. As a result, regression analysis methodologies aid in the establishment of causal links between variables, as well as in the modelling of time series and forecasting.

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Answer:Consumidores primarios: comen a los productores. Consumidores secundarios: comen a los primarios. Consumidores terciarios: comen a los carnívoros. Descomponedores: se alimentan de restos de seres vivos.

Step-by-step explanation:Consumidores primarios: comen a los productores. Consumidores secundarios: comen a los primarios. Consumidores terciarios: comen a los carnívoros. Descomponedores: se alimentan de restos de seres vivos.

Hello..!

¿What is consumidores primarios?

They are the ones that eat plants. They are herbivores or are parasites of these.

The fraction of the container that is empty, based on the capacity of the container and the water added, is 12 / 25

The fraction of the container that is empty can be found by the formula:

= (Capacity of container - Amount of water added ) / Capacity of container

Capacity of container = 2.5 liters

Amount of water added = 1 . 3 liters

The fraction of the container which is empty is:

= (2 . 5 - 1.3) / 2.5

= 1.2 / 2.5

= (1 . 2 x 10) / ( 2 . 5 x 10)

= 12 / 25

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The standard deviation is 70 %.

acc to our question=

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Andre made a mistake after getting 14x=8x. He divided each side by x, but this is not valid since x may be 0 and dividing by 0 gives an undefined result.

Andre should have collected the like terms in order to have all the variables x on one side before taking the difference.

Inequality expression

Given the inequality expression solved by andre expressed as:

14x + 3 ≤ 8x + 3

Simplify to have:

14x - 8x ≤ 3-3

6x ≤ 0

x ≤ 0

Hence andre should have collected the like terms in order to have all the variables x on one side before taking the difference.

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The sides of the triangle are 17, 19 and 21 and 19 is middle of the three side lengths.

What are triangles?

Let the side of triangle = x

x-2, x, x+2 are the three sides and their sum is 3x.  

3x = 57

 x = 57/3

 x = 19.

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