Show that the triangles are similar and write a similarity statement.

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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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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Answer:

36,900

Step-by-step explanation:

it's right I just do not know how to explain lol

The amounts of each solution that he should use are given as follows:

The amounts of each solution are obtained by a system of equations, for which the variables are given as follows:

The total solution is of 18 liters, hence:

x + y = 18.

x = 18 - y.

The final concentration is of 80%, hence:

0.3x + 0.9y = 0.8 x 18

0.3x + 0.9y = 14.4.

As x = 18 - y, the value of y is obtained as follows:

0.3(18 - y) + 0.9y = 14.4

0.6y = 9

y = 9/0.6

y = 15.

Hence the value of x is obtained as follows:

x = 18 - y

x = 18 - 15

x = 3.

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Answer:

the correct answer is A

Step-by-step explanation:

A correspond to Note La

Since 1014 is at median which tells us that 50% of the values are equal. the total number is 11014.

1014 * 11 = 11014.

Since 1014 is at median which tells us that 50% of the values are equal. the total number is 11014.

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The confidence interval for the slope of the regression line relating performance score is 0.71
                   
sample size (n) = 20

slope (b1) = 3.92 and SE of slope = 0.71

Degrees of freedom = 20 - 2 = 18          

Using t-table we get, t-critical value at significance level of 0.10 with 18 degrees of freedom is,

tα/2=1.734

The 90% confidence interval for the slope of the regression line relating performance score and time to fatigue is,

B1±Tα/2*SE

3.92±1.734(0.71) (c)

Regression analysis is a statistical measure that is used in many different fields, including investing, finance, sales, marketing, science, mathematics, and others. It tries to figure out how closely one dependent variable is related to a set of other changing variables. They are commonly referred to as independent variables.

For example, how commodity prices relate to the shares of companies that trade in those commodities.


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Answer:

t ^3

Step-by-step explanation:

t^2.t

= t × t^2+1

= t^3

Step-by-step explanation:

you don't show us all possible answer options.

none of the visible graphs are correct.

just look at x=0. g(0) = -0/2 + 2 = 2

so, the correct graph has to go through (0, 2). and the 3 segments connect at the interval end points

(-2, 3) and (2, 1).

so, please pick the correct answer option based on this information.

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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Answer:

Step-by-step explanation:

Given two segment measures in a right triangle diagram, you want the values of the other measures.

The Pythagorean theorem can be used to find y:

  BC² = BD² +CD²

  65² = y² +25²

  y² = 65² -25² = 3600

  y = √3600 = 60

The proportionality of corresponding sides in similar triangles can be used to find the remaining measures.

  short side/hypotenuse = 25/65 = 65/(25+x)

  25 +x = 65²/25 = 169

  x = 144

And for z, we can use ...

  long side/hypotenuse = AB/AC = BD/BC

  z/169 = 60/65

  z = 169(12/13) = 156

The triangle measures are ...

The inequality is solved to x < -5/4

An inequality can be defined as a mathematical relation that makes a non-equal comparison between two numbers, mathematical expressions or equations.

Inequalities are used  to compare two numbers on the number line on the basis of  their size.

The different inequality signs are;

From the information given, we have that;

|x| < 3x - 5

Note that the signs, "| |" represents modulus which explains that the number must be a positive number.

collect like terms

x -3x< 5

substract the like terms

-4x< 5

Make 'x' the subject

x < -5/4

Hence, the value is x < -5/4

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The complete solution is:

solve the inequality |x| < 3x - 5

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 vertices of quadrilateral B'C'D'E' are obtained exchanging the x and y-coordinates of the vertices of Quadrilateral BCDE.

Then the quadrilateral is drawn connecting the four vertices of quadrilateral B'C'D'E'.

The rule for a reflection over the line y = x is given as follows:

(x,y) -> (y,x).

Meaning that a reflection over the line y = x will exchange the coordinates of the figure.

Then we apply this procedure to obtain the vertices of quadrilateral B'C'D'E', and in the drawing connect the consecutive vertices.

The problem is incomplete, hence the answer was given in general terms.

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Answer:

To solve the proportion, X/2 = 9/27, you can cross multiply to get 2x = 9*27, which simplifies to 2x = 243. Then divide both sides by 2 to get x = 243/2, which simplifies to x = 121. Therefore, the solution to the proportion is x = 121.

No. The determinant doesn't show that the matrix will reduce to an identity matrix.

The determinant of a matrix is a scalar value that can be used to determine whether a matrix is invertible or not. If the determinant is non-zero, the matrix is invertible and can be reduced to an identity matrix through row operations. If the determinant is zero, the matrix is not invertible and cannot be reduced to an identity matrix.

In this case, the determinant of the matrix [3 0 5 1] is equal to 3 * 1 - 0 * 5 = 3, which is non-zero. Therefore, this matrix can be reduced to an identity matrix through row operations, but the determinant does not indicate this directly.

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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

Answer:

Step-by-step explanation:

2x + y = 17 in slope intercept form? Put the y on one side by itself. -2 is the slope and 17 is the y-intercept. Slope / gradient of a line is obtained by making an equation in the form of: where ' m ' gives the slope/gradient of the line and ' c ' gives y-intercept.

The slope of a linear equation will always be the coefficient of the "x" variable when the equation is equalled to "y", this form is called "slope-intercept form" and the reason for that name is because it easily shows both the slope and the y-intercept of the line.

Check attached image 1 to better understand this concept.

As you may see in the picture, the slope is just the number that multiplies variable "x". Hence, the coefficient of this line is 2.

Answer: the line will cross the y-axis at (0, 40).

Step-by-step explanation:

the line of a function crosses the y-axis at the y intercept. to find the y-intercept, equal x to 0 in the slope intercept equation.

because we know that it is 35 per student and 40 processing fee per group, we know that the slope intercept equation is y = 35x + 40.

with the equation, we plug x in as 0 and solve for y.

y = 35(0) + 40

y = 0 + 40

y = 40

because we know the x-coordinate is 0, we now have the y-coordinate, which is 40.

therefore, the line crosses the y-axis at (0, 40)

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.

A possible hypothesis for this study is: "The organic pesticide Z will reduce the number of grasshoppers in cornfields compared to water treatment alone."

The purpose of conducting this experiment is to determine if the new organic pesticide Z is effective at killing grasshoppers that typically invade cornfields and to study its effect on reducing the number of grasshoppers.

The independent variable in the experiment is the treatment with organic pesticide Z.

The dependent variable in the experiment is the number of grasshoppers in the cornfield.

The west field treated only with water is the control group.

It is important to have a control group in the experimental design because it provides a baseline comparison for evaluating the effect of the treatment.

The most accurate conclusion is: "If a cornfield is sprayed with pesticide Z, it will have fewer grasshoppers 10 weeks later."

Based on the results, my recommendation to the farmer would be to spray the cornfield with pesticide Z to decrease the number of grasshoppers in the cornfield.

The stages of the scientific method in order from first to last are: Make observations about nature, formulate hypothesis, conduct experiments, analyze data, reject or accept hypothesis.

This is an example of making observations about nature.

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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 total number of hours that Carly studied for 9 days is; 7¹/₂ hours

She wants to study 5/6 of an hour per day for 9 days.

Thus;

Number of hours studied per day = 5/6 * 1 hour = 5/6 hours

Therefore for 9 days, the total number of hours she will study is;

5/6 * 9

= 45/6

= 15/2

= 7¹/₂ hours

That value denotes the total number of hours that she studied for 9 days

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Complete question is;

Carly needed to study for 5/6 of an hour for 9 days. How many hours did she study?

Therefore, in the previous equation, 6x + 75 = 10x -9, the value of x is 4.  It's really common to contrast expressions and phrases.

It is necessary to duplicate, divide, add, or subtract in mathematics. The following is how an expression are put together: Number, expression, and mathematical operator The components of a numerical method include numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It's really common to contrast expressions and phrases. An language, often known as an algebraic expression, is any mathematical statement that rating systems, numbers, and then an arithmetic function between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the expression 4m + 5.

given

6x + 75 = 10x -9

Because 6x + 75 = 10x -9

6x -10 x = -9 - 75

-4x = -84

x = 21; the value of x is 4.

Therefore, in the previous equation, 6x + 75 = 10x -9, the value of x is 4.

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Answer:

1296

Step-by-step explanation:

2 | 36

3 | 216

the pattern is 6^x

so 6^4 is 1296

Using the relationships between the angles of a parallelogram, the value of x is 12.55°.

A parallelogram has opposite angles that are equal, and adjacent angles that add up to 180°.

We can start with angles a and c. Since they are both equal to 90°, that means that angle b must also be 90°.

We can now use this information to find the value of x.

We can use the fact that angles a, b, and c add up to 270° to find x.

Since angles a and c are both 90°, that means that angle b must be 90°.

We can then solve for x by subtracting 190° (90° + 100°) from 270° and dividing by 7.

In order to solve for the value of x, we must use the properties of a parallelogram.

Since a parallelogram has four sides and four angles, the sum of the interior angles must equal 360°.

Therefore, we can set up an equation using the given angles and the unknown angle of x to solve for the value.

95° + (7x - 4)° + 90° + (3x + 23)° + (9x - 6)° = 360°

20x + 109° = 360°

20x = 251°

x=12.55°

Therefore,  the value of x is 12.55°.

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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 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:

316 street lights.

25 weeks.

Step-by-step explanation:

We can set up a linear equation with the information provided expressed in slope intercept form: [tex]y=mx+b[/tex], where "m" is the slope, and "b" is the initial value.

We're given the initial amount, or what the city already has is 132 street lights, that's our "b" value and they will install 4 each additional week which is our slope. So we have the equation: [tex]y=4x+132[/tex]

To find how many streetlights the city will have at the end of 46 weeks, we can plug in 46 as "x" to give us:

[tex]y=4(46)+132\\y=316[/tex]

To find when the city will have 232 streetlights we can set the equation equal to 232 and solve for "x" the number of weeks.

[tex]232=4x+132[/tex]

Subtract 132 from both sides

[tex]100=4x[/tex]

Divide both sides by 4

[tex]25=x[/tex]

So this will occur after 25 weeks.