Evaluate each algebraic expression for 46 + (-2k) for k = 3, 23, -2

The lengths of side [tex]\overline{AB}[/tex] and [tex]\overline{AC}[/tex], found using the angle bisector theorem are;

AB = 28, AC = 42

The angle bisector theorem states that the bisector of an angle in a triangle, intersects the opposite side at a point such that the opposite side are divided into proportions that is equivalent to the ratio or proportion of the other two sides.

AB = x - 7

AC = x + 7

According to the angle bisector theorem, we get;

8/12 = (x - 7)/(x + 7)

8·(x + 7) = 12·(x - 7)

8·x + 8 × 7 = 12·x - 12 × 7

8·x + 56 = 12·x - 84

12·x - 8·x = 56 + 84 = 140

4·x  = 140

x = 140 ÷ 4 = 35

x = 35

Therefore;

AB = 35 - 7 = 28

AC = 35 + 7 = 42

The correct option is therefore;

AB = 28, AC = 42

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To compare the two birdbaths, we can compare the equations for their respective cross sections.

Cross sections are a two-dimensional representation of a three-dimensional shape or object. Cross sections can be used to help visualize the internal and external structure of an object, such as a building, machine, or living organism. They are also used to understand the physics and math of a certain area, such as the flow of air or the interactions of particles.

To compare the two birdbaths, we can compare the equations for their respective cross sections. The equation for the first birdbath is y=(x-18)² – 4, while the equation for the second birdbath is y=75. We can compare the two equations by looking at how the x-values affect the y-values. In the first equation, as x increases, y increases. In the second equation, y remains constant. This indicates that the second birdbath is a shallower bowl than the first birdbath.

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a) The area of the floor A = 247 feet² volume of the pod is V = 1,235 feet³

b) The surface area of the lap pool is S = 1,574 yards²  and the volume of the pool is V = 2,760 yards³

c) The area of the bed soil is A = 200 feet² and the volume of the bed soil is V = 360 feet³

A cuboid is defined as a three-dimensional shape, that has six rectangular faces, eight vertices and twelve edges

The volume of a cuboid is the product of its length , width and height

The volume of the cuboid is given by

Volume of Cuboid = Length x Width x Height

Given data ,

a)

Let the length of the pod be L = 19 feet

Let the width of the pod be W = 13 feet

Let the height of the pod be H = 5 feet

Now , the area of the floor = L x W

Substituting the values in the equation , we get

The area of the floor = 247 feet²

Now , the volume of the floor V = L x W x H

Volume of the pod = 247 x 5

Volume of the pod = 1235 feet³

b)

Let the length of the pool be L = 24 yards

Let the width of the pool be W = 23 yards

Let the height of the pool be H = 5 yards

Now , the surface area of the pool = 2 ( LH + LW + HW )

Substituting the values in the equation , we get

The surface area of the floor S = 2 ( 24x5 + 24x23 + 23x5 )

The surface area of the floor S = 2 ( 120 + 552 + 115 )

The surface area of the floor S = 1574 yards²

Now , the volume of the pool V = L x W x H

Volume of the pool = 24 x 23 x 5

Volume of the pool V = 2,760 yards³

c)

Let the length of the bed be L = 40 feet

Let the width of the bed be W = 5 feet

Let the height of the bed be H = 1.5 feet

Now , the area of the bed = L x W

Substituting the values in the equation , we get

The area of the bed = 200 feet²

Now , the volume of the soil V = L x W x H

Volume of the bed soil = 200 x 1.8

Volume of the bed V = 360 feet³

Hence , the volume is solved

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Step-by-step explanation:

oh, come on. this can be easily answered by all the formulas and information from the other question.

again the area of a circle is

pi×r²

so, for the given area of 9pi this means the radius is

r = sqrt(9) = 3 cm

the slant height is 4 times the radius

L = 3×4 = 12 cm

the total surface area of a cone is again

pi×r(r + L) = pi×r² + pi×r×L

the lateral area alone (without the base area) is then

pi×r² + pi×r×L - pi×r² = pi×r×L

in our case

3.14×3×12 = 113.04 ≈ 113 cm²

Applying the exterior angles theorem, the measure of angle JKL is: 22°.

Exterior Angle Theorem states: "The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it."

Applying the exterior angles theorem, we would create the following equation:

m<JKL = m<KIJ + m<IJK

Substitute:

5x - 3 = 2x + 8 + x - 1

Solve for x

5x - 3 = 3x + 7

5x - 3x = 3 + 7

2x = 10

x = 5

m<JKL = 5x - 3 = 5(5) - 3

m<JKL = 22°

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The mean change score is 2.00, the standard deviation is 3.91, the median change score is 2.5, and the change score is 2.2 standard deviations below the mean is -6.602.

(a) To find the mean change score, we sum up the change scores and divide by the number of change scores. The mean change score is:

(3 + 9 + -1 + 2 + 0 + 4 + -3 + 1 + -1 + 5 + 4 + -2) / 12 = (24) / 12 = 2

So the mean change score is 2.00.

(b) To find the standard deviation for this sample, we first need to find the variance. The variance is calculated as follows:

Find the difference between each change score and the mean change score.

Square each of these differences.

Find the mean of these squared differences.

Take the square root of the mean squared difference to get the standard deviation.

The variance is:

( (3 - 2)² + (9 - 2)² + (-1 - 2)² + (2 - 2)² + (0 - 2)² + (4 - 2)² + (-3 - 2)² + (1 - 2)² + (-1 - 2)² + (5 - 2)² + (4 - 2)² + (-2 - 2)² ) / 12 = 15.33

The standard deviation is:

√15.33 = 3.91

So the standard deviation is 3.91.

(c) To find the median change score, we need to sort the change scores in ascending order. The median is the middle value of this sorted list. Since there are an even number of change scores, the median is the mean of the two middle values. The sorted list of change scores is as follows:

-3; -2; -1; -1; 0; 1; 2; 3; 4; 4; 5; 9

The median is the mean of the two middle values, 2 and 3, which is:

(2 + 3) / 2 = 2.5

So the median change score is 2.5.

(d) To find the change score that is 2.2 standard deviations below the mean, we need to subtract 2.2 times the standard deviation from the mean change score:

2 - 2.2 × 3.91 = 2 - 8.52 = -6.602

So the change score that is 2.2 standard deviations below the mean is -6.602.

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The third quartile of the data set is 20, and option C  is correct.

A data set is a structured group of data. As we are all aware, data is a grouping of information that has been gathered by observations, measurements, research, or analysis. Facts, figures, names, and even simple descriptions of objects could be included in it. Data can be arranged for our study in the form of graphs, charts, or tables.

Given a chart for the number of rabbits, a farmer observed on his farm over a period of nine weeks.

week         1     2    3     4       5     6     7      8      9

rabbits       2    3     5     7     11    15     18    22    27

the formula of quartiles is

Lower Quartile (Q1) = (N+1) * 1 / 4

Middle Quartile (Q2) = (N+1) * 2 / 4

Upper Quartile (Q3 )= (N+1) * 3 / 4

here N = 9

third quartile(Q3) = (N+1) * 3 / 4

third quartile(Q3) = (9 + 1)3/4

third quartile(Q3) = 7.5 term

third quartile(Q3) is the term between 7th and 8th week

third quartile(Q3) = (7th term + 8th term)/2

7th term = 18

8th term = 22

third quartile(Q3) = (18 + 22)/2

third quartile(Q3) = 20

Hence option C is correct.

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Answer:

1. 184-x

2. 90

3. y=4x/3-23/3

Step-by-step explanation:

1. 180-(x-4)=184-x (supplementary angles)

2. 180/2=90 (supplementary angles)

3. y=-3x/4+2

y+5=(4/3)(x-2)

y=4x/3-23/3

Answer:

[tex]\frac{4}{3}[/tex] or 1.333333333 euro

Step-by-step explanation:

Answer:

1 euro = £0.75

£1= 4/3 or 1.33333 repeating

Hope this helped!

Step-by-step explanation:

Answer:

42 in^2    <=====not in your answer choices

Step-by-step explanation:

Area of a right triangle = 1/2 base * height = 1/2 (7)(12) = 42 in^2

For given trigonometric function csc^2x(1-cos^2x)=1 to established option D is a key step.

What are trigonometric functions?

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trigonometric functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.

The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant and cosecant can be derived from the primary functions.

Now,

given function is csc^2x(1-cos^2x)=1

=csc^2x(sin^2x)

=1/sin^2x*sin^2x

=1

Hence,

            For given trigonometric function csc^2x(1-cos^2x)=1 to established option D is a key step.

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Answer:

The dimensions of the sand volleyball court are 17 meters by 8 meters.

Answer:

1296

Step-by-step explanation:

2 | 36

3 | 216

the pattern is 6^x

so 6^4 is 1296

Answer:

s + 2.5v ≥ 25

Step-by-step explanation:

           Cost of 1 song = $1

        Cost of 's' songs = s * 1 = s

  Cost of 1 video = $2.50

Cost of 'v' videos = 2.50 * v = 2.5v

As he wants to spend at least $ 25, he wants to buy for an amount equal to $ 25 or more than $ 25.

        Total amount to spend ≥ $ 25

          s + 2.5v ≥ 25

To find an interpolating polynomial, we need to fit a polynomial to the given data points. The simplest way to do this is by using the Lagrange Interpolating Polynomial formula:

p(t) = ∑ (y_i * l_i(t))

where y_i = the y-value of the data point

           l_i(t) = Lagrange basis polynomial for data point i, defined as:

            l_i(t) = (∏ (t-t_j)) / (t_i-t_j) for all j ≠ i

Using this formula, we can find the interpolating polynomial for the given data points:

p(t) = 0.0006t^5 - 0.0222t^4 + 0.2436t^3 - 1.0528t^2 + 2.2080t + 2.0400

So the interpolating polynomial for this data is a 5th degree polynomial, which means that it is necessary to use a polynomial of at least degree 5 in order to accurately fit the data.

If we try to use a polynomial of degree less than 5, the polynomial will not fit the data points accurately, and the difference between the polynomial and the actual data points will be significant. This means that the results of the wind tunnel experiment would be inaccurate if we use a polynomial of lower degree.

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Answer:

D

Step-by-step explanation:

product AB

= (x - 3)(x³ + 2x² + x - 2)

each term in the second factor is multiplied by each term in the first factor, that is

x(x³ + 2x² + x - 2) - 3(x³ + 2x² + x - 2) ← distribute both parenthesis

= [tex]x^{4}[/tex] + 2x³ + x² - 2x - 3x³ - 6x² - 3x + 6 ← collect like terms

= [tex]x^{4}[/tex] - x³ - 5x² - 5x + 6

The worth of the homework is 55% and worth of final exam is 15%. The worth of each three projects is 10%

a) Finding the student's grade, If a student has an 82 homework average and a 96 on the first project.

Students grade = 82(55%) + 96(15%)

= 45.1 + 14.4

Students grade= 59.5

(b) Finding the lowest grade the student If a student gets a 78 on the second project and a 76 on the third project.

Let G be the lowest grade in the final exam.

It was stated that the lowest grade the student can get on the final exam to get an 80 overall in the course:

82(55%) + (96 +74 + 71)(25%)  +G (15%)= 82

45.1 +60.25 + G0.15 = 82

Making G the subject of the relation we have

G0.15 = 82 -105.35

G0.15 = --23.35

G= 155-100

Therefore the lowest grade is 55

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Answer: 6f-6g

Step-by-step explanation:

The sample space for the acceptance outcomes of the three friends is S={G, B, R, G', B', R'}. Therefore, option A is the correct answer.

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.

Given that, Ghanem, Bilal and Rashed, applied for admission at ZU. Define G for "Ghanem is accepted" and G' for "Ghanem is not accepted". Similarly, you can define B & B' for Bilal and R & R' for Rashed.

Sample space of accepted ={G, B, R, G', B', R'}

Therefore, option A is the correct answer.

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Answer:

t ^3

Step-by-step explanation:

t^2.t

= t × t^2+1

= t^3

In the given position-versus-time graph, the object moving the slowest without being at rest is at point B.

A position-versus-time graph illustrates how far an object has travelled from its starting position at any given time since it started moving. The vertical axis describes the position of the object, and the horizontal axis describes the time.

The slope of the graph indicates the speed of the moving object. Hence, the value of the slope at a particular time indicates the speed of the object at that instant. Hence, the steeper the line is, the greater the slope of the line and the faster the object's motion is changing.

In the given graph, at points A, C and E, the slope is zero; the object is not moving, hence at rest. At the point, D slope is steeper as compared to the slope at point B. Hence, the object is moving slower at point B as compared to point D.

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--The given question is incomplete; the complete question is

"The figure shows the position-versus-time graph for a moving object. At which point or points is the object moving the slowest without being at rest?"--

Answer:

$102

Step-by-step explanation:

It cost $25.50 per inch.  They want to buy 4 inches.

Inch 1    Inch 2   Inch 3    Inch 4

    v            v           v             v

25.50 + 25.50 + 25.50 + 25.50 is the same as 25.50 · 4 which equals 102

It depends on the purpose of dividing 30. There is no specific answer for dividing 30 into a certain number of parts. It can be divided into any number of parts, as long as it is a whole number.

Answer:

it depends upon ur requirement that  hw many parts is needed by u

Step-by-step explanation:

like if u need 2 parts it can happen by having 15 on  one side and 15 on the other similarly it,s the way to divide it to many parts required by u

Answer:

0.0625 mL/hr.

Step-by-step explanation:

To calculate the flow rate in mL/hr, we need to know the total volume of the solution, the concentration of the solution, and the desired infusion rate.

Given:

   Volume: 500 mL

   Concentration: 0.45% (or 0.0045 g/mL)

   Infusion rate: 500 units/hr

We know that:

   Infusion rate = Volume x Concentration / Time

We can rearrange the formula to solve for time:

Time = Volume x Concentration / Infusion rate

Now we can plug in the given values:

Time = 500 mL x 0.0045 g/mL / 500 units/hr

To convert the time to hours, we will divide the time by 3600 seconds/hour

Time = 500 mL x 0.0045 g/mL / 500 units/hr / (1 hr/3600 s)

Now we have the flow rate in mL/hr

Time = 0.0625 mL/hr

So the flow rate should be set at 0.0625 mL/hr.

It's important to note that the heparin added is 25000 U, this is not related to the flow rate calculation.

Answer:

2.31m

Step-by-step explanation:

Trigonometry:

cosθ = adjacent/hypotenuse

cos(74) = adjacent/(8.39)

adjacent = 8.39 × cos(74)

adjacent = 2.3125974152

2.31 (to 2 d.p.)

Step-by-step explanation:

=> The simplest form of

56

:

98

56:98 is

4

:

7.

4:7.

Step-by-step explanation:

Given ratio -

56

:

98

56:98

We have to reduce it to its simplest form,

For that, we have to find the GCD of the numerator as well as the denominator:

So, the GCD for

56

56 and

98

98 is

14.

14.

Now, divide both the numerator and denominator by the GCD:

=

>

56

÷

14

98

÷

14

=>

98÷14

56÷14

=

>

4

7

=>

7

4

Hence, the simplest form is

4

:

7.

4:7.

The function of the line passing through the points (0,0) and  (-6,-18) is y = 3x.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

Points are (0,0) and  (-6,-18)

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

m = -18/-6

m = 3

The equation of the line is given as

y - y₁ = 3 (x - x₁)

y + 0 = 3(x - 0)

y = 3x

Thus, the function of the line passing through the points (0,0) and  (-6,-18) is y = 3x.

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The area of the given shape which is a sector of the circle is 3.14 sq.units.

What is a sector of a circle?

An area of a circle that is contained within its two radii and the arc that connects them is called a sector. A semicircle, which represents one-half of a circle, is the most typical sector of a circle.

Given a sector of a circle.

The radius of the circle  = 2

Given π = 3.14

Area of circle = πr²

Area of sector  = ( θ / 360° ) *  πr²

where θ =  sector angle

For the given shape, sector angle = 90°

Area of sector = (90°/360°) × 3.14 × 2² = (1/4) × 3.14 × 4 = 3.14

Therefore the area of the given sector of the circle is 3.14 sq.units.

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