Mike and Emily are brother and sister. Mike has as many brothers as sisters, and Emily has three times as many brothers as sisters. How many boys and girls are there in this family?

Answer:

I think it is 4.5 length
area= 20.25

Step-by-step explanation:

Step 1: I square rooted 324 to get 18

Step 2: I divided that number by 2 twice to get 4.5
18/2 = 9/2 = 4.5
multiply 4.5 by 4.5 to get 20.25!


Hope this is correct!

The arc lengths of the given circles are 8π/3, 14π/3 and 4π

Arc length is the distance between two points along a section of a curve.

Given are circles, with radii 4, 3 and 3 units, we need to find the arc length of each,

Since, angles are in radian, convert them into degree by multiply them by π/180°

1) radius = 2π/3 × 180°/π

= 120°

2) radius = 7π/6 × 180°/π

= 210°

3) radius = 4π/3 × 180°/π

= 240°

Arc length = θ/360° × 2π × radius, where θ is the central angle,

1) Arc length = 120°/360° × 2π × 4

= 8π/3

2) Arc length = 210°/360° × 2π × 3

= 14π/3

3) Arc length = 240°/360° × 2π × 3

= 4π

Hence, the arc lengths of the given circles are 8π/3, 14π/3 and 4π

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The polynomial function for the cars manufactured in thousands since 1990, where x represents the number of years since 1990 the fourth option

P(x) = 0.2·x³ + 0.5·x² + 0.4·x + 0.3

A polynomial consists of an expression that has two or more terms of (the same) variables with different powers or index.

The possible table in the question, obtained from a similar question on the internet is presented as follows;

Year;              [tex]{}[/tex]                1991     1993       1995        1997         1999

Cars Manufactured; [tex]{}[/tex]      1.4       11.4         39.8         96.2         190.2

(thousands)

The details in the table indicates that we get;

When x = 1991 - 1990 = 1, P(x) = 1.4

Which, based on the coefficients of x³, x², and x, corresponds with the first and the fourth polynomial.

p(x) = 0.5·x³ + 0.2·x² + 0.3·x + 0.4...(1)

p(1) = 0.5 × 1³ + 0.2 × 1² + 0.3 × 1 + 0.4 = 1.4

P(x) = 0.2·x³ + 0.5·x² + 0.4·x + 0.3...(4)

p(1) = 0.2 × 1³ + 0.5 × 1² + 0.4 × 1 + 0.3 = 1.4

When x = 1993 - 1990 = 3, we get in equation (1);

p(3) = 0.5 × 3³ + 0.2 × 3² + 0.3 × 3 + 0.4 = 16.6

The polynomial in equation (4) indicates that we get;

p(3) = 0.2 × 3³ + 0.5 × 3² + 0.4 × 3 + 0.3 = 11.4

Therefore, the polynomial in the fourth equation best represents the polynomial function for the cars manufactured in thousands where x represents the years since 1990

Verifying, we get;

When x = 5; p(5) = 0.2 × 5³ + 0.5 × 5² + 0.4 × 5 + 0.3 = 39.8

When x = 7; p(7) = 0.2 × 7³ + 0.5 × 7² + 0.4 × 7 + 0.3 = 96.2

When x = 9; p(9) = 0.2 × 9³ + 0.5 × 9² + 0.4 × 9 + 0.3 = 190.2

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Answer:

4.5t - 12.5

Step-by-step explanation:

12.5(0.2t − 1) + 21t

12.5(0.2t) + 12.5(-1) + 2t

2.5t - 12.5 + 2t

4.5t - 12.5

A dynamic array is an array with a big improvement: automatic resizing.

How does dynamic array works?

A random access, variable-size list data structure called a dynamic array, growable array, resizable array, dynamic table, or array list allows elements to be added or removed. It comes with standard libraries for many current, widely used programming languages.

A value of type array is stored in a static array variable. A pointer to an array value is stored in a dynamic array variable. The code you write to use either type of array differs very little because of automatic pointer dereferencing and automatic index padding.

Resizable dynamic arrays offer random access to its elements. They can have variable size initializations, and the software can change their size at a later time.

Initial Values:

n = 2

arr[0] = [ ]

arr[1] = [ ]

Query 0: Append 5 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]

last answer = 0

arr[0] = [5]

arr[1] = [ ]

Query 1: Append 7 to arr[( 1 ⊕ 0 ) % 2 )] = arr[1]

arr[0] = [5]

arr[1] = [7 ]

Query 2: Append 3 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]

last answer = 0

arr[0] = [5, 3]

arr[1] = [7 ]

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The number of hours spent walking dogs is 3 hours and 5 hours was spent landscaping.

The first step is to form a system of equations using the information provided in the question:

x + y = 8 equation 1

6x + 13y = 83 equation 2

Where:

The elimination method would be used to solve the equations.

Multiply equation 1 by 6

6x + 6y = 48 equation 3

Subtract equation 3 from equation 2:

7y = 35

Divide both sides of the equation by 7:

y = 35 / 7

y = 5

Substitute for y in equation 1:

x + 5 = 8

8 - 5 = x

x = 3

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Approximately 524 calories are contained in each of the eight slices of a 16-inch pizza (note: this makes good sense since it has a little less than the area as a complete 6-inch pizza).

The diameter of a circle is equal to the number of inches in a pizza's size.

The area of a circle is calculated using the formula: [tex]\pi r^{2} = \pi (d/2)^{2}[/tex].

Assume that a pizza's calories are evenly distributed over its surface (even though we know there is a crust ring around the outsize). C calories per square inch, as an illustration.

The number of calories in a 6-inch pizza is

[tex]CA_{6} = C\pi (6/2)^{2} =9C\pi =590[/tex]      [eq1]

Calories in a 16-inch pizza are calculated as follows:

[tex]CA_{16}=C\pi (6/2)^{2} =64C\pi[/tex]

The number of calories in one of those pizza's eight slices is:

[tex]X=CA_{16} /8=8C\pi[/tex]   [eq2]

math:

[tex]C\pi =590/9[/tex]   [from eq1]

[tex]X=8(C\pi )[/tex]    [from eq2]

[tex]X=8(590/9)[/tex]

[tex]X=524[/tex]        [estimated]

Approximately 524 calories are contained in each of the eight slices of a 16-inch pizza (note: this makes good sense since it has a little less than the area as a complete 6-inch pizza).

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Deandre invested $22,000 in the 10% account and $30,000 - $22,000 = $8,000 in the 5% account.

percentage, a relative value indicating hundredth parts of any quantity.

Let's call the amount Deandre invested in the 10% account x.

The amount he invested in the 5% account is $30,000 - x.

The interest he received from the 10% account is 0.10x and the interest he received from the 5% account is 0.05($30,000 - x).

The total interest received is $2600, so we can set up the equation:

0.10x + 0.05($30,000 - x) = $2600

0.10x + 0.05 * $30,000 - 0.05x = $2600

0.10x - 0.05x + 0.05 * $30,000 = $2600

0.05x = $2600 - 0.05 * $30,000

0.05x = $2600 - $1,500

0.05x = $1100

x = $1100 / 0.05

x = $22,000

Hence, Deandre invested $22,000 in the 10% account and $30,000 - $22,000 = $8,000 in the 5% account.

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The equation of the relation between x and y is y= 2x

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

The table of values

On the table of values, we can see that

y is twice of x

When represented as an equation, we have

y = 2x

Hence, the equation is y = 2x

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Complete question

Without performing any algebraic manipulations, can you define the relation between x and y?

X (input) 7 8 9 10

y (output) 14 16 18 20

Answer:

224 millimeters

or

2.24 cm

Step-by-step explanation:

Scale is 8 millimeters = 1 meter

So 28 meters = 28 x 8 millimeters = 224 millimeters

224 millimeters = 224/10 cm = 22.4 cm

The improved high-speed mixer that allows bakers to produce cookies in less time will result in an increase in production, a decrease in cost, an increase in demand, and an increase in price of chocolate chip cookies.

Point A to Point B illustrates an increase in the production of chocolate chip cookies. This can be calculated using the formula: Change in Output = Output at Point B - Output at Point A. For example, if the output of chocolate chip cookies at Point A is 25 cookies per hour, and the output at Point B is 40 cookies per hour, then the change in output is 40-25=15 cookies per hour.

Point C to Point B illustrates a decrease in the cost of production of chocolate chip cookies. This can be calculated using the formula: Change in Cost = Cost at Point C - Cost at Point B. For example, if the cost of production at Point C is $2 per cookie, and the cost at Point B is $1 per cookie, then the change in cost is $2 - $1 = $1 per cookie.

Point C to Point D illustrates an increase in the demand for chocolate chip cookies. This can be calculated using the formula: Change in Demand = Demand at Point D - Demand at Point C. For example, if the demand for chocolate chip cookies at Point C is 100 cookies per hour, and the demand at Point D is 150 cookies per hour, then the change in demand is 150 - 100 = 50 cookies per hour.

Point A to Point D illustrates an increase in the price of chocolate chip cookies. This can be calculated using the formula: Change in Price = Price at Point D - Price at Point A. For example, if the price of chocolate chip cookies at Point A is $1 per cookie, and the price at Point D is $2 per cookie, then the change in price is $2 - $1 = $1 per cookie.

The improved high-speed mixer that allows bakers to produce cookies in less time will result in an increase in production, a decrease in cost, an increase in demand, and an increase in price of chocolate chip cookies.

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The set is {0, 1, 2, 3, 5, 6, 8}. and the truth set is {0, 1, 2, 3, 5}

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

ID = 01238586

So, the roster notation for the set is

{0, 1, 2, 3, 5, 6, 8}.

We have:

The statement is x ∈ S, (x prime) ∨ (x + 1 ∈ S)

This means that

Using the above as a guide, we have the following:

So, the truth set is {0, 1, 2, 3, 5}

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Answer: 155

Step-by-step explanation: 0.18x=28 divide each side by 0.18.

The claim of Carly is correct that the sum of the deviations for a data set will always be 0.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Sum of the deviations of a data set is always 0.

This is because that the sum of the positive deviations is equal to the sum of the negative deviations.

Let a data set be 3, 2, 4, 5, 1

Mean = (3 + 2 + 4 + 5 + 1) / 5 = 3

Values     Deviations

3               3 - 3 = 0

2               2 - 3 = -1

4               4 - 3 = 1

5               5 - 3 = 2

1                1 - 3 = -2

Sum of the deviations = 0 - 1 + 1 + 2 - 2 = 0

Hence the sum of the deviations for a data set will always be 0.

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a. Inverse of 100B is [tex]100B^{-1}[/tex]

b. To obtain the inverse of B', double the corresponding entries in the first row of [tex]B^{-1}[/tex].

c. To obtain the inverse of B', divide the corresponding entries in the first column of [tex]B^{-1}[/tex] by 2.

a. Inverse of 100B is [tex]100B^{-1}[/tex] by simply taking the mathematical Inverse.

b) To find the inverse of B', we can first write B' in terms of B as follows:

c) To find the inverse of B', we can first write B' in terms of B as follows:

In summary, the inverse of a matrix can change when the original matrix is altered by scalar multiplication or the addition of a multiple of a row or column. However, if we know the inverse of the original matrix, we can use it to find the inverse of the modified matrix.

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The exact values of trigonometric functions cosine and tangent are 4 / 5 and 3 / 4, respectively.

In this question we must determine the exact value of two trigonometric functions on the basis a given value of another trigonometric function, whose quadrant is also known. According to the statement, sine is in the first quadrant, then both cosine and tangent are also positive. The value of cosine can be found by means of following trigonometric formula:

cos θ = √(1 - sin² θ)

cos θ = √[1 - (3 / 5)²]

cos θ = 4 / 5

And the exact value of tangent can be found by this formula:

tan θ = sin θ / cos θ

tan θ = (3 / 5) / (4 / 5)

tan θ = 3 / 4

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The trigonometry ratios are tan(∅) = 2/3√10 and

csc(∅) = 7√10/20

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

0°≤ ∅ ≤ 180°

Also, we have

cos(∅) = -3/7

The tangent is calculated as

tan(∅) = √[1/cos²(∅) - 1]

Substitute the known values in the above equation, so, we have the following representation

tan(∅) = √[1/(-3/7)² - 1]

So, we have

tan(∅) = √[49/9 - 1]

This gives

tan(∅) = √40/9

So, we have

tan(∅) = 2/3√10

Also, we have

cos²(∅) + sin²(∅) = 1

So, we have

(-3/7)² + sin²(∅) = 1

Evaluate

sin²(∅) = 1 - (-3/7)²

sin²(∅) = 1 - (9/49)

sin²(∅) = 40/49

Take the inverse of both sides

csc²(∅) = 49/40

So, we have

csc(∅) = 7/(2√10)

Rationalize

csc(∅) = 7√10/20

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The graph of the function is added as an attachment

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

2x−y=−8​

Make y the subject

y = 2x + 8

The above equation is a linear equation

A linear equation is represented as

y = mx + c

Where

slope = m

y-intercept = c

This means that the slope is 2 and the y-intercept is 8

Next, we plot the graph of the equation

See attachment for the graph

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Answer:

1.D

2.D

3.D

4.A

5.A

6.B

7.A

8.B

hope those are right

Step-by-step explanation:

1.D

2.D

3.B

4.A

5.A

6.B

7.A

8.B

Applying the corresponding angles theorem, m<DEG = 33°.

The Corresponding Angles Theorem states that if two lines are cut by a transversal, then corresponding angles are equal. This means that if two lines intersected by a transversal form a pair of corresponding angles, then those angles are congruent (have the same measure).

Given that:

m<HBC = 33 degrees

m<ABE = m<HBC [vertical angles are congruent]

m<ABE = 33° [substitution property]

Therefore, based on the corresponding angles theorem, we have:

m<DEG = m<ABE

Substitute:

m<DEG = 33°

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 9000\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]9000 = P\left(1+\frac{0.04}{4}\right)^{4\cdot 4} \implies 9000=P(1.01)^{16} \\\\\\ \cfrac{9000}{(1.01)^{16}}=P\implies \boxed{7675.39\approx P}[/tex]

Answer:

hi !!

Step-by-step explanation:

34.70 - 34.70/100*10 = 34.70 - 3.47 = $31.23

Using Factorization, The solution of the algebraic fraction is [tex]\frac{10}{p-4}[/tex].

Due to the fact that they have polynomials on both sides of the equality sign, algebraic equations are also known as polynomials. Variables, coefficients, constants, and algebraic operations like addition, subtraction, multiplication, division, and exponentiation are all components of algebraic equations.

Numbers are factored using formulas for factorization. Decomposing an entity into the result of another entity or factors that, when multiplied together, produce the original number is known as factorization. Simple factorization formulas are used in factorization procedures to simplify algebraic or quadratic equations. Instead of expanding parentheses, expressions are expressed as the sum of their constituent parts. Each equation may have factors that are algebraic expressions, variables, or .

[tex]\frac{p - 8}{8 p²-12p+32} \div \frac{1}{10}[/tex]

first we factorize the denominator and using invert Endo to the other fraction.

[tex]\frac{p - 8}{8 p²-12p+32} \times \frac{10}{1}\\\frac{p - 8}{(p - 8)(p - 4)} \times 10[/tex]

= [tex]\frac{10}{p-4}[/tex]

Hence the simplified fraction is [tex]\frac{10}{p-4}[/tex]

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The format of the equation that shown below:

We know that the standard form of the parabola is y=ax²+bx+c. Thus, the vertex form of a parabola is y = a(x-h)² + k.

Given:

The General form of Vertex form is

y = a(x - h)² + k

where (h, k) are the vertex.

For Example, Pick a point on the graph other than the vertex.  Let's say you see the line pass through (1,5) and the vertex is at (3,4)

First the vertex gives

y = a (x - 3)² + 4

Put the values (1,5) into this equation.

5 = a (1 - 3)² + 4

Solve for a

5 = a x (-2)2 + 4

5 = 4a + 4

1 = 4a

1/4 = a

and, the vertex form of parabola is y = 1/4(x - 3)² + 4.

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Answer:

Step-by-step explanation:

y = mx +c

1 = m0 + c

1=0+c

c=1

5-1=4

3-1=2

4/2=2

m=2

y=2x+1

The equation for the horizontal asymptote will be y = -2.

Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:

y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)

=> y = -2/1

=> y = -2

The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0

=> x + 3 = 0

=> x = -3

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Answer: 0.17193742185

Step-by-step explanation:

Answer:

0.171937422

Step-by-step explanation:

Answer: w=-7/4, x = 3 , z = 8.
You were only incorrect on one which I will provide an image on how I solved that one so you can maybe see what you did wrong. hope it helps !

The square is shown in the complex plane, where each vertex can be represented as a complex number.

If we let the first vertex be 0, then the next vertex [tex]$a$[/tex] is at a distance of 1 unit along the real axis. The complex number representing [tex]$a$[/tex] is [tex]$1 + 0i$[/tex]. The vertex [tex]$b$[/tex] is at a distance of 1 unit along the imaginary axis, so its complex representation is [tex]$0 + 1i$[/tex]. Finally, the vertex [tex]$c$[/tex] is at a distance of 1 unit along the negative real axis, so its complex representation is [tex]$-1 + 0i$[/tex].

To find [tex]$b/a$[/tex], we divide the complex number representing [tex]$b$[/tex] by the complex number representing [tex]$a$[/tex]. We get [tex]$b/a = (0 + 1i) / (1 + 0i) = 0 + 1i$[/tex].

Similarly, to find [tex]$c/a$[/tex], we divide the complex number representing [tex]$c$[/tex] by the complex number representing [tex]$a$[/tex]. We get [tex]$c/a = (-1 + 0i) / (1 + 0i) = -1 + 0i$[/tex].

So, the values of [tex]$b/a$[/tex] and [tex]$c/a$[/tex] in rectangular form are [tex]0 + 1i[/tex] and [tex]-1 + 0i[/tex], respectively.

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