PLS HELP ASAP 50 POINTS!!!
Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by AAS

The p-value of the test statistic is calculated as follows:

0.6386.

At the null hypothesis, it is tested if the mean is actually of 48.3 miles per gallon, that is:

[tex]H_0: \mu = 48.3[/tex]

At the alternative hypothesis, it is tested if the mean is different of that, hence:

[tex]H_1: \mu \neq 48.3[/tex]

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 48.2, \mu = 48.3, \sigma = \sqrt{6.76} = 2.6, n = 150[/tex]

Hence the test statistic is obtained as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{48.2 - 48.3}{\frac{2.6}{\sqrt{150}}}[/tex]

z = -0.47.

The p-value is found using a z-distribution calculator, with a two-tailed test, as we are testing if the mean is different of a value, with z = -0.47, hence it is of:

0.6386.

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Answer:

(-9,0)  and (1,0)

Step-by-step explanation:

There is no single answer to this question. It depends on what values are chosen for x and y , equation has an infinite

The equation 5x + 2y = -7 is an indeterminate equation with two unknowns, x and y. This means that the equation has an infinite number of solutions, depending on the values of x and y. For example, if x = 3 and y = -2, then the equation would be satisfied. If x = 2 and y = -3, then the equation would also be satisfied. Therefore, the number of solutions for this equation is infinite.There is no single answer to this question. It depends on what values are chosen for x and y.

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The speed of car moving towards south exists 15 mph and, speed of (as moving towards East = 25 mph.

They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.

Let speed of Car 1 = x mph

Speed of car 2 = (x + 10) mph

Hence,

OA = Distance travelled by car2 in 2 hours

⇒ OA = (x + 10) × 2 = 2x + 20

And, OB = Distance travelled by Car 1 in 2 hours

⇒ OB = x × 2 = 2 x

Now, In ΔOAB, OA² + OB² = AB²

substitute the values in the above equation

⇒  (2 x+20)² + (2 x)² = [tex](10 \sqrt{34})^2 \\[/tex]

⇒  4x² + 400 + 80x + 4x² = 3400

simplifying the equation

⇒ 8x² + 20x - 3000 = 0

⇒ x² + 10x - 375 = 0

⇒ x² + 25x - 15x - 375 = 0

simplifying the above equation, we get

⇒ x(x + 25) - 15(x + 25) = 0

⇒ (x + 25)(x - 15) = 0

⇒ x + 25 = 0, x - 15 = 0

⇒ x = -25, x = 15

Since speed can not be negative.

Hence, x = 15 mph

⇒ x + 10 = 15 + 10 = 25 mph.

Hence, speed of car moving towards south =15 mph.

And, speed of (as moving towards East = 25 mph.

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The speed of car moving towards south exists 15 mph and, speed of (as moving towards East = 25 mph.

When two or more lines in a plane cross one another, they are referred to as intersecting lines. The common point shared by all intersecting lines is the point of intersection, which can be found on all of them.

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Let speed of Car 1 = x mph

Speed of car 2 = (x + 10) mph

Hence,

OA = Distance travelled by car2 in 2 hours

⇒ OA = (x + 10) × 2 = 2x + 20

And, OB = Distance travelled by Car 1 in 2 hours

⇒ OB = x × 2 = 2 x

Now, In ΔOAB, OA² + OB² = AB²

substitute the values in the above equation

⇒  (2 x+20)² + (2 x)² =

⇒  4x² + 400 + 80x + 4x² = 3400

simplifying the equation

⇒ 8x² + 20x - 3000 = 0

⇒ x² + 10x - 375 = 0

⇒ x² + 25x - 15x - 375 = 0

simplifying the above equation, we get

⇒ x(x + 25) - 15(x + 25) = 0

⇒ (x + 25)(x - 15) = 0

⇒ x + 25 = 0, x - 15 = 0

⇒ x = -25, x = 15

Since speed can not be negative.

Hence, x = 15 mph

⇒ x + 10 = 15 + 10 = 25 mph.

Hence, speed of car moving towards south =15 mph.

And, speed of (as moving towards East = 25 mph.

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The area of one base of the triangular prism is given as 16√3 square cm, and since the base is equilateral, the sides of the triangle are of equal length.

The formula to calculate the area of an equilateral triangle is (sqrt(3)/4) * s^2 where s is the length of a side of the triangle.

So, plugging in the given area of base, 16√3, we can find the length of a side of the equilateral triangle, s.

16√3 = (sqrt(3)/4) * s^2

s = (4*16√3)/sqrt(3) = 16√3 cm

Now we can use the height of the prism, which is given as 30 cm, to find the area of the rectangular surface.

Area of the rectangular surface = 2 * base area * height = 2 * 16√3 * 30 cm²

This simplifies to:

960√3 cm²

So the total area of the rectangular surface of the prism is 960√3 square cm.

Hassan can paint maximum 11 bookcases with 10 gallons of paint.

A fraction represents a numerical value, which defines the parts of a whole.

Generally, the fraction can be a portion of any quantity out of the whole thing and the whole can be any specific things or value.

The basics of fractions explain the top and bottom numbers of a fraction.

Suppose a number has to be divided into four parts, then it is represented as x/4. So the fraction here, x/4, defines 1/4th of the number x. Hence, 1/4 is the fraction here.

Given,

Hassan has 10 gallons of paints.

1 bookcase requires 7/8 gallons of paint

Let Hassan paints x bookcases.

According to the question

7/8x = 10

7x = 80

x = 80/7

x = 11.43

But no. of bookcases should be in whole.

Number of bookcases painted with 10 gallons of paint = 11.

Hence, Maximum 11 bookcases can be painted by Hassan with 10 gallons of paint

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If point P(2k, k) is equidistant from A(-2, 4) and B (7,-5), the numerical value of k is 3.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

The distance between P(2k, k) and A(-2, 4) is:

d = √((2k - (-2))² + (k - 4)²)

d = √((2k +2)² + (k - 4)²)

The distance between P(2k, k) and B(7, -5) is:

d = √((2k - 7)² + (k - (-5))²)

d = √((2k - 7)² + (k + 5)² )

Since the distances are equal, we can set the two equations for d equal to each other and solve for k.

√((2k +2)² + (k - 4)²) = √((2k - 7)² + (k + 5)² )

Square both sides

(2k +2)² + (k - 4)² = (2k - 7)² + (k + 5)²

(2k +2)² + (k - 4)² = 5k² - 18k + 74

5k² + 20 = 5k² - 18k + 74

Collect like terms

5k² - 5k² + 18k = 74 - 20

18k = 74 - 20

18k = 54

k = 54/18

k = 3

Therefore, the value of k is 3.

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The length of y using sine rule is 6664.2 inches

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

in this case w/sinW = y/sinY

Y = 180-(55+42)

Y = 180-(97)

Y = 83°

Therefore 470/sin55 = y/sin83

470× sin83 = y sin55

= 466.50 = 0.707y

divide both sides by 0.707

y = 466.50/0.707

y = 6664.2 inches

therefore the length of y is 6664.2 inches

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For acceptable x values of √12(x-1)+√√2(x-1)², the option is equivalent to the quotient given here (x-1) ² is [tex]$2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$\\[/tex] .

The equivalent of the quotient displayed above for allowable x values is

[tex]$\sqrt{1} \cdot 2(x-1)+\sqrt{\sqrt{2}}(x-1)^2$[/tex]

[tex]$2(x-1)+\sqrt[2 \cdot 2]{2}(x-1)^2$\\[/tex]

[tex]\$2(x-1)+\sqrt[4]{2}(x-1)^2$\\$(2 x-2)+\sqrt[4]{2}\left(x^2+2 x(-1)+(-1)^2\right)$\\$(2 x-2)+\sqrt[4]{2}\left(x^2-2 x+1\right)$\\$2 x-2+\sqrt[4]{2}\left(x^2-2 x+1\right)$\\$2 x+\sqrt[4]{2}\left(x^2-2 x+1\right)-2$\\$2 x+\left(\sqrt[4]{2} \cdot x^2-\sqrt[4]{2} \cdot 2 x+\sqrt[4]{2}\right)-2$\\$2 x+\left(\sqrt[4]{2} \cdot x^2-2 \cdot \sqrt[4]{2} \cdot x+\sqrt[4]{2}\right)-2$\\$2 x+\sqrt[4]{2} \cdot x^2-2 \cdot \sqrt[4]{2} \cdot x+\sqrt[4]{2}-2$[/tex]

[tex]$f(x)=\sqrt{12(x-1)}-\sqrt{2(x-1)^2}$[/tex]

[tex]$\frac{d}{d x}\left(\sqrt{12(x-1)}-\sqrt{2(x-1)^2}\right)$[/tex]

[tex]$\sqrt{12(x-1)}-\sqrt{2(x-1)^2}=2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$[/tex]

[tex]$\sqrt{12(x-1)}-\sqrt{2(x-1)^2}$[/tex]

[tex]$\sqrt{12(x-1)}=2 \sqrt{3} \sqrt{x-1}$[/tex]

[tex]$\sqrt{2(x-1)^2}=\sqrt{2}(x-1)$\\$=2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$\\[/tex]

Values that might result in a fraction's denominator being equal to zero are excluded. Finding these omitted values is crucial for resolving a rational statement because you cannot divide by 0.

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The function y = -2x + 9 have ordered pairs (-4, 17), (-2, 13), (0, 9), (2, 5) and (4, 1)

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Given that:

y = -2x + 9

When x = -2; y = -2(-2) + 9 = 13

When x = 0; y = -2(0) + 9 = 9

When x = 2; y = -2(2) + 9 = 5

When x = 4; y = -2(4) + 9 = 1

The function y = -2x + 9 is a linear equation

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The required transformations of the original image are the first translation of 7 units to the right side, then a reflection across the x-axis.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The triangle is given in the represented graph, which vertices are as follows :

(-5, -1)

(-2, -1)

(-5, -3)

The image after a translation of 7 units to the right side will be given a triangle the vertices are as follows :

(-5 + 7, -1) → (2, -1)

(-2 + 7, -1) → (5, -1)

(-5 + 7, -3) →(2, -3)

Then the image after a reflection across the x-axis will be a triangle the vertices are as follows :

(2, -1) → (2, 1)

(5, -1) → (5, 1)

(2, -3) → (2, 3)

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Answer: x= 1/7y + 19/7 (Standard form will be:7x−y=19)

Step-by-step explanation:

Step 1: Add -y to both sides.

−7x+y+−y=−19+−y

−7x=−y−19

Step 2: Divide both sides by -7.

−7x/−7

= −y−19/−7

x= 1/7y + 19/7

Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

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The correct option is (a) 48.

In algebra, an equation is a statement of equality between two expressions. These expressions can be numbers, variables, or a combination of both.

In the equation:

b/4 = 12, the variable b is on one side of the equation and the value 12 is on the other side.

To find the value of b that makes the equation true, we need to isolate the variable b on one side of the equation.

In this case, we can do this by multiplying both sides of the equation by 4.

This cancels out the denominator of the fraction on the left side, and we get,

b = 12*4= 48.

This means that when b is equal to 48, the equation b/4 = 12 is true.

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True statement is number C.

The method of sampling where a portion of population are given priority over the rest of the population is called biased sample.

In the unbiased sampling method almost, each population is valued, and they are given chance to be selected in the data list.

flawed sampling means the method of sampling is inappropriate such as survey works that taken in non-random way. As example, researchers start to ask people walking in the street.

The survey was taken at a playground on 20 families.

the survey estimated that mean number of children per household in the community was 2.4.

The main purpose of the survey was to determine the mean number of children per household in the community.

but the survey study was held at the playground and the sample size is too small.

The above data could not give the true estimation.

So, the sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.

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The Trigonometric inequality Sec (x)< cot(x) will hold true in π/2 < x < π.

How can a trigonometric inequality be expressed?

The intervals where the trigonometric inequality sec (x) cot (x) always holds true are what we are looking for.

This can also be expressed as: 1/cos (x) < 1/tan (x)

Now, this is only possible in the fourth quadrant, where cos x is positive and tan (x) is negative, where: π/2 < x < π.

The values for sin, cos, and tan are all positive in the first quadrant.

Only positive values for sin are present in the second quadrant.

The tan values in the third quadrant are all positive.

Only positive values for cos are present in the fourth quadrant.

Therefore the inequality Sec(x) < cot(x) will hold true in π/2 < x < π.

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Answer:

x < -20

Step-by-step explanation:

To solve x/5 + 6 < 2,

First subtract 6 from both sides of the equation.

This makes x/5 < -4.

Then multiply both sides of the equation by 5.

This makes x < -20.

Therefore, the solution to the equation is x < -20.

Answer:

the answer is (3,4) and (2,3)

Step-by-step explanation:

that's my answer

The length of jump by Pythagoras = 25 units

The length of jump by Newton = 29 units

The length of jump by Fermat = 20 units

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the length of the jump by Pythagoras be P

Let the length of the jump by Newton be N

Let the length of the jump by Fermat be F

Now , the equation will be

The total number of steps = 120 steps

The number of jumps by Pythagoras = 5 jumps

The number of steps overshoot by Pythagoras = 5 steps

So , P ( 5 ) - 5 = 120   be equation (1)

On simplifying the equation , we get

Adding 5 on both sides of the equation , we get

5P = 125

Divide by 5 on both sides of the equation , we get

P = 25 units

The number of jumps by Newton = 4 jumps

The number of steps fell short by Newton = 4 steps

So , N ( 4 ) + 4 = 120   be equation (2)

On simplifying the equation , we get

Subtracting 4 on both sides of the equation , we get

4N = 116

Divide by 4 on both sides of the equation , we get

N = 29 units

The number of jumps by Fermat = 6 jumps

So , F ( 6 ) = 120   be equation (2)

On simplifying the equation , we get

Divide by 6 on both sides of the equation , we get

F = 20 units

Therefore , the value of P , N and F are 25 , 29 and 20 units respectively

Hence , the length of each jump is 25 , 29 and 20 units

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Answer:

[tex]y=\sqrt{10}[/tex]

Step-by-step explanation:

Using the geometric mean theorem, [tex]y=\sqrt{(2)(5)}=\sqrt{10}[/tex].

Answer:

x ≈ 10.6

Step-by-step explanation:

using the cosine ratio in the right triangle

cos35°= [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{13}[/tex] ( multiply both sides by 13 )

13 × cos35° = x , then

x ≈ 10.6 ( to the nearest tenth )

The figure also has a line symmetry for the vertical line x is  5, and a line symmetry for the horizontal line y is 5 .Therefore the figure has both symmetry

A form or item is divided into two equal and symmetrical portions by a line of symmetry. Because it creates a symmetrical split in the figure and the separated pieces look like mirror reflections of one another, we also refer to this line as the axis of symmetry or the mirror line.

An imaginary line that splits a line or shape into two identical parts is called the axis or line of symmetry. The symmetry axis of a parabola will be required of you at higher level mathematics. This u-shaped line on the graph is a parabola.

B) The transformation that maps the figure unto itself are therefore;

1) Rotating the figure 180° about the point (5, 5) which is the center of the figure

2) The figure reflected across the line x = 5 and the figure reflected across the line y = 5

The complete question is : Determine if the figure below has rotational symmetry, line symmetry or both and

describe the transformation that mas the figure onto itself. BE SPECIFIC. You must

name the center of rotation and degree of rotation if it has rotational symmetry or lines of reflection if it has line symmetry

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Answer:

p = -7/4 or -1 3/4

Step-by-step explanation:

-1 23/40 = 9/10p

-1 23/40 = -63/40

So, our equation is

-63/40 = 9/10p

Divided both sides by 9/10

p = -7/4

So, the answer is

p = -7/4

or

-1 3/4

35-55-90 is a right-angle triangle because one of the angles is 90 degrees.

The explanation for a right triangle says that if one of the angles of a triangle is a right angle - 90º, the triangle is called a right-angled triangle or simply, a right triangle.

The right triangle formula can be presented in the following way: The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.

In a right triangle we have: (Hypotenuse)² = (Base)² + (Altitude)²

Properties of Right Triangle:

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The data of the rainfall amount in inches to the locations are used to plot the attached line plot created with MS Excel.

A line plot is a graph is the graphical display of data as check marks or points above a number line.

A line plot shows the frequency of the values in the data on the number line, using dots or check marks. The frequency of the data is shown above the specified locations on the graph of a line plot.

The line plot is therefore, indicative of how frequent particular values in the dataset are.

The possible data in the question are presented as follows;

Rainfall Amount; 1/8,[tex]{}[/tex] 3/8,  3/4,  3/4,     1/4,    1 1/4, 1/8,     1/4,    1,     1/8

Location;     [tex]{}[/tex]          1,    2,     3,      4,        5,       6,     7,       8,      9,    10

The frequency of the data in a tabular form are;

Rainfall        [tex]{}[/tex]  Frequency

1/8        [tex]{}[/tex]          3 locations

3/8        [tex]{}[/tex]         1 location

3/4        [tex]{}[/tex]         2 locations

1/4       [tex]{}[/tex]           2 locations

1 1/4       [tex]{}[/tex]         1 location

1        [tex]{}[/tex]              1 location

The above frequency values can be used to create the attached line plot created with MS Excel

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Answer:

[tex]t = \dfrac{I}{Pr}[/tex]

Step-by-step explanation:

Given the equation [tex]I = Prt[/tex]:

To solve for [tex]t[/tex], all we have to do is divide both sides by [tex]Pr[/tex].

[tex]\textrm{} \ \, I = Prt\\\overline{Pr} \ \ \ \overline{\: Pr \: }[/tex]

[tex]t = \dfrac{I}{Pr}[/tex]

Text form:

t = I / Pr

Answer:

[tex]t= \frac{I}{Pt}[/tex]

Step-by-step explanation:

Given the equation,[tex]I=Prt[/tex], solve for the value, t.

[tex]I=Prt[/tex], divide both sides of the equation by [tex]Pr[/tex]. We get,

[tex]t= \frac{I}{Pr}[/tex], final answer.

By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.

Expressions are polynomials, but expressions that equal zero are polynomial equations.

A polynomial may be written as the sum of a finite number of terms, where each term is the product of one or more variables raised to a positive integer exponent and a constant coefficient (or power).

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

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The ratio of the green houses to the the total number of houses is 17:103

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here, The number of green houses as 17 and total number of houses altogether 103

Therefore the required ratio is 17:103

Hence, The ratio of the green houses to the the total number of houses is 17:103

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Answer: It's a homozygous dominant genotype.

Step-by-step explanation: Two capital letters or two lowercase letters are homozygous.