please help measuring !

Answer:

12-4i

Step-by-step explanation:

i means √-1

(3 - i)(3 + 1) =

3*3=9

3*1=3

-i*3= -3i

-i*1 = -i

9+3-3i-i=

12-4i <--- answer

(3 - i)(3 + i) =

3*3=9

3*i=3i

-i*3= -3i

-i*i = -(√-1)*(√-1) = -(-1) = 1

9+3i-3i+1 =

10 <--- answer

The baker would need 47. 25 cups of floor

We need to know that proportion is a form of mathematical comparison with two equations made equal to each other.

From the information given, we have that;

baker used 33 3/4 cups of flour to make 15 batches of cookies

This is represented as;

Convert to improper fractions

135/4 cups = 15 batches of cookies

Then, x cups = 21 batches of cookies

cross multiply the values

15x = 708. 75

Divide both sides by the coefficient of x, we have ;

x = 708. 75/15

x = 47. 25 cups of floor

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Answer:

B and C

Step-by-step explanation:

Minimum and Maximum points occur when the gradient of the function is equal to 0. Graphically this looks like a bend such that the function dips from decreasing to increasing (the gradient goes form being negative to positive) and vice versa.

A minimum point occurs where all the nearby values are higher than that of the point in question.

A maximum point occurs where all the nearby points are lower than the point in question.

By looking at the graph, there is a maximum point around (4.5, 1.5) which is consistent with B but not A (since A talks about a minimum point)

By looking at the graph, there is a minimum point around (0.5, 1.5) which is consistent with C.

I've highlighted areas of interest below so hopefully that's helpful :>

The solution to the equation is x = 7.

What is the linear equation in one variable?

A linear equation in one variable is an equation of the form ax + b = 0, where a and b are constants and x is the variable. The general form of a linear equation in one variable is ax + b = 0, where a and b are constants and x is the variable. The graph of a linear equation in one variable is a straight line.

The first step in solving the equation 2x - 4 = 10 using algebra tiles would be to add 4 to both sides of the equation to get 2x = 14. The next step would be to divide both sides of the equation by 2 to get x = 7.

Hence, the solution to the equation is x = 7.

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The equation of p(x) in vertex form is p(x) = 3(x - 1)² - 2.

Option C is the correct answer.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

From the table,

From p(x) = 10 to p(x) = -2 the value of p(x) is decreasing and from p(x) = -2 to p(x) = 46 it is increasing.

So,

The vertex is (1, -2).

The vertex form of p(x).

p(x) = a ( x - h)² + k

Where (h, k) is the vertex.

Now,

(1, -2) = (h, k)

Make (0, 1) = (x, p(x))

1 = a (0 - 1)² + (-2)

1 = a - 2

a = 1 + 2

a = 3

Thus,

The vertex equation of p(x).

p(x) = 3(x - 1)² - 2

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The number of students who participated in the survey, based on the histogram showing the number of hours students watch television on the weekend, is 125.

A histogram is a pictorial or graphical representation of categorical data, proportional to the frequency of a variable and whose width is equal to the class interval.

The number of students who watched between 0 - 4 hours = 20

The number of students who watched between 5 - 9 hours = 40

The number of students who watched between 10 - 14 hours = 30

The number of students who watched between 15 - 19 hours = 20

The number of students who watched between 20 - 24 hours = 15

The total number of students who participated = 125

Thus, using the histogram, the total number of students who participated in the survey was 125.

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Answer:

95% of confidence interval of the proportion of all people who pick their noses at red lights

(0.3342 , 0.5258)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 100

Given data  43 out of a random sample of 100 people said they pick their noses at red lights.

sample proportion

                           $p^{-}=\frac{x}{n}=\frac{43}{100}=0.43$

Level of significance = 0.05

Z₀.₀₅ = 1.96

Step(ii):-

95% of confidence interval of the proportion of all people who pick their noses at red lights

$(p^{-}-Z_{\alpha }\sqrt{\frac{p(1-p)}{n}},p^{-}+Z_{\alpha }\sqrt{\frac{p(1-p)}{n}})$

$(0.43-1.96\sqrt{\frac{0.43(1-0.43)}{100}},0.43+1.96\sqrt{\frac{0.43(1-0.43)}{100}})$

( 0.43 -  0.0958 , 0.43 + 0.0958)

(0.3342 , 0.5258)

Conclusion:-

95% of confidence interval of the proportion of all people who pick their noses at red lights

(0.3342 , 0.5258)

The answer of the given question based on the equation is , the unknown number is 6.

An equation is the  mathematical statement that asserts equality of the two expressions. It typically consists of the two expressions separated by equal sign " = ". The expressions can include variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation. Solving an equation involves finding the value(s) of the variable(s) that make the equation true.

The statement can be translated into an equation as follows:

2(y - 2) = 8

Simplifying the equation, we can distribute the 2 on the left-hand side:

2y - 4 = 8

Then, we can add 4 to both sides to isolate the variable:

2y = 12

Finally, we divide both sides by 2 to solve for y:

y = 6

Therefore, the unknown number is 6.

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According to the image, the missing angle is 100°.

When we want to calculate an angle of a triangle we must take into account the following information:

If we know the value of two angles (angles 2 and 3) of the triangle we must add the measure of the two angles we know.

Now we must subtract the sum total of the two known angles from 180°.

So the value of angle 1 would be 100°. Additionally, 180° is a rule that we must follow, because the angles of a triangle must always add up to 180°.

Note: This question is incomplete. Here is the complete information:

Image attached

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The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

A) horizontal asymptote: y = 7 B) vertical asymptote: x = -4, 5 is the required answers for horizontal and vertical asymptotes of the curve.

The horizontal asymptote of a curve is a horizontal line that the curve approaches as x approaches infinity or negative infinity. The vertical asymptote of a curve is a vertical line that the curve approaches but never crosses as x approaches a certain value. In this case, the horizontal asymptote is found by letting x approach infinity in the fraction and observing what the value of y approaches. In the limit as x approaches infinity, the x^2 term dominates and thus y approaches 7, which is the horizontal asymptote. To find the vertical asymptote, we find the values of x where the denominator equals 0 and the numerator is not equal to 0. In this case, the denominator x^2 + x - 20 = 0 has roots of -4 and 5. Thus, the vertical asymptotes are x = -4 and x = 5. To find the vertical asymptotes, we look for the values of x where the denominator of the function equals 0 and the numerator does not equal 0. In this case, the denominator x^2 + x - 20 = 0 has roots of -4 and 5, which means that x = -4 and x = 5 are the vertical asymptotes of the function. These values of x represent the values at which the function is undefined, and as x approaches these values from either side, the value of the function approaches positive or negative infinity.

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The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

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

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Answer:

9%

Step-by-step explanation:

Count the squares side which is 10

Then Count the bootom side of the square which is 10

10 x 10 =100

Now count how many squares are filled. 9

9/100=9%

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

Total value = b

Percentage = a/b x 100

The percent modeled is 9%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

Total value = b

Percentage = a/b x 100

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of cells in the box = 100

Number of shaded cells = 9

The percentage of the shaded cells.

= (Number of shaded cells / Total number of cells) x 100

= 9/100 x 100

= 9%

Thus,

The percentage of shaded cells is  9%

The percent modeled is 9%.

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The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The figures are congruent by the transformation rule: Rotation and Reflection that is option B.

In mathematics, a transformation refers to a function that maps elements from one set to another set. The term is commonly used to describe a change in the position, shape, or size of a geometric figure, often in the context of coordinate geometry or linear algebra. In coordinate geometry, a transformation can be thought of as a change in the position or orientation of a figure on the coordinate plane. For example, a translation is a transformation that shifts a figure a certain distance horizontally and/or vertically, while a rotation is a transformation that turns a figure by a certain angle around a given point.

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Answer:

(-3,-13)

Step-by-step explanation:

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

The equation of the transformed graph will be y = -3(2ˣ) + 2.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

Suppose the equation of the given graph is y = A 2ˣ + k.

Substitute,(0,-1)

-1 = A 2⁰ + k

A + k = -1                (1)

Substitute, (1,-4)

-4 = A 2¹ + k

2A + k = -4            

A + k/2 = -2            (2)

Subtract 1 - 2 as

k - k/2 = -1 + 2

k/2 = 1

k = 2

And, A = -2 - 2/2

A = -3

Thus y = -3(2ˣ) + 2

Hence "The equation of the transformed graph will be y = -3(2ˣ) + 2 ".

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Answer: so the answer is -9 + 23*7 =  152  

Step-by-step explanation:  a24  = a1 + (24-1)d    where a1 = -9 and d = common difference ( 12-5 = 7)  

Hope this helped :D

Answer:

I) ∠2 and ∠5

Step-by-step explanation:

According to the given information the Minimize equation is

Z = 110X11 + 120X12 + 120X21 + 130X22.

What is Statistics ?

Statistics is a branch of mathematics that deals with collecting, analyzing, interpreting, presenting, and organizing data. It provides methods and techniques to make sense of complex data sets, to draw conclusions and make decisions based on the data. Statistics can be applied to a wide range of fields, including business, economics, social sciences, medicine, and many others. Some key topics in statistics include probability theory, hypothesis testing, regression analysis, and data visualization.

Minimize:

Z = 110X11 + 120X12 + 120X21 + 130X22

Subject to:

X11 + X12 ≤ 1500 (capacity constraint for Amarillo)

X21 + X22 ≤ 3300 (capacity constraint for Charlotte)

X11 + X21 ≥ 2100 (demand constraint for Detroit)

X12 + X22 ≥ 1000 (demand constraint for Atlanta)

where:

X11 = number of components produced in Amarillo and supplied to Detroit

X12 = number of components produced in Amarillo and supplied to Atlanta

X21 = number of components produced in Charlotte and supplied to Detroit

X22 = number of components produced in Charlotte and supplied to Atlanta

Therefore, according to the given information the Minimize equation is

Z = 110X11 + 120X12 + 120X21 + 130X22

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Answer:

"a Sample Statistic"

Step-by-step explanation:

A sampling distribution is defined as the probability distribution of "a statistic" drawn from a large number of samples gotten from a specific population. In order words, it is a sample statistic.

Thus, the correct answer is "a Sample Statistic"

The sampling distribution is the probability of a particular report based on random sampling; it displays the most likely values of various sample means

It is a probability distribution of data mining, which is the process of analyzing larger samples gathered from a given population.  

In this, a particular population is the distribution of frequencies of a variety of possible outcomes for a population statistic.

It is the distribution of the probability for a statistic is generated from a large number of samples gathered from a certain population.

Therefore, "The sampling distribution is the probability of a particular report based on random sampling; it displays the most likely values of various sample means".

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Answer:

41.93 degrees

Step-by-step explanation:

The forklift operator can move at most 8 palettes at one time.

A forklift operator is a person who operates a forklift, which is a type of powered industrial truck used to lift and move heavy materials over short distances. Forklift operators are commonly employed in warehouses, manufacturing plants, and other industrial settings where materials need to be moved and stored. They are responsible for loading and unloading trucks, transporting materials to and from storage areas, and positioning materials for storage or processing. Forklift operators must be trained and certified to operate the equipment safely and efficiently.

In the given question,

To move all 43 palettes, the operator needs to make at least 43/8 = 5.375 trips.

Since the operator cannot make a fraction of a trip, he will need to make at least 6 trips in order to move all 43 palettes.

On the first five trips, the operator will move 8 palettes each time, and on the final trip, he will move the remaining 3 palettes.

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Answer: Answer below

Step-by-step explanation: So you would simply have to divide 8 into 72 which would be 9.

we can verify our answer by doing 9x8 which equals 72.

Answer: 9

Step-by-step explanation:

bears divided by shelves = number of bears per shelf

72 bears divided by 8 shelves= 9 bears per shelf

Given:

The universal set is given as U={b, d, g, m, o, r, u, y}.

The elements of set A is given as A= {b, u, y}.

Required:

The complement of set A.

Explanation:

The universal set is given as,

The complement of any set which is a subset of a universal set is obtained by eliminating those elements from the universal set which is present is set A.

Therefore the complement of A is calculated as,

Answer:

Thus the complement of set A is A' = { d, g, m, o, r }.

Answer:

-Twice means muliply by 2

-The difference of a number and 7 means subtract a number/variable and 7.

-Is equal to 9 means =9

2(X - 7) = 9

The length of b and angle B and C are 3cm, 45  degrees and 79 degrees respectively.

To determine the angles and length of sides, we use the sine rule

The sine rule is thus:

$\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}$

Given;

Let's find angle C

$\frac{sin43}{2.5}=\frac{sinC}{3.6}$

cross multiply

0. 682 × 3. 6 = sin C × 2. 5

sin C = 2. 4552/ 2. 5

C = $\text{Double exponent: use braces to clarify}$

C = 79°

To find length of b

$b=\sqrt{c^2-a^2}$

substitute the values

$b=\sqrt{{3.6}^2-2.5^2}$

$b=\sqrt{6.71}$

b = 2. 59 cm

b = 3cm

To find angle B, we have

$\frac{sin43}{2.5}=\frac{sinB}{2.59}$

cross multiply

0. 682 × 2. 59= sin B × 2. 5

sin B = 0. 7065

$\text{Double exponent: use braces to clarify}$

B = 45°

Hence, the length of b and angle B and C are 3cm, 45  degrees and 79 degrees respectively.

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Statement III is not accurate, as the increase in the total number of stuffed toys sold is approximately 0.15%, which is significantly lower than about 2%.

a. I and II

To assess the trends displayed in the given circle graphs for September and October, let's analyze each statement:

I. The market share held by cats increased by about 6.5 percentage points.

In September, the percentage for cats is 199 / 1312 ≈ 15.2%. In October, the percentage for cats is 285 / 1314 ≈ 21.7%.

The difference between these two percentages is approximately 21.7% - 15.2% ≈ 6.5 percentage points.

Therefore, Statement I is accurate, as the market share held by cats increased by about 6.5 percentage points.

II. Roughly 22.2% more stuffed toys in the "other" category were sold in October than in September.

In September, the number of toys in the "other" category is 225. In October, it is 275.

The difference between these two quantities is 275 - 225 = 50.

To assess whether this represents roughly 22.2% more, we calculate 50 / 225 ≈ 0.222, which is approximately 0.222 * 100% ≈ 22.2%.

Therefore, Statement II is accurate, as roughly 22.2% more stuffed toys in the "other" category were sold in October than in September.

III. The total number of stuffed toys sold increased by about 2%.

To calculate the total number of toys sold, we sum the quantities for each category in September (1312) and October (1314).

The difference between these two totals is 1314 - 1312 = 2.

To assess whether this represents an increase of about 2%, we calculate 2 / 1312 ≈ 0.0015, which is approximately 0.0015 * 100% ≈ 0.15%.

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Answer:

Answer is A.) I and II