The angle measurements in the diagram are represented by the following expressions.
∠A=5x−12 ∠B=2x+24
Solve for X

In a test of significance, if the test z-value is in the tail region or the low probability region, it does not necessarily mean that we have strong evidence against the null hypothesis.

This statement is false.

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Answer:

let the cost price be x

then the profit is 1/5x

profit percent -profit *100/cp

or,1/5x*100/x

or,20x/x

here x cuts x

and profit % is 20

Step-by-step explanation:

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Answer:

6\(x^{8}\)\(y^{5}\)

Step-by-step explanation:

Using the rule of exponents

\(a^{m}\) × \(a^{n}\) ⇔ \(a^{(m+n)}\)

Given

3x²\(y^{4}\) × 2\(x^{6}\)y, then

3 × 2 × x² × \(x^{6}\) × \(y^{4}\) × \(y^{1}\)

= 6 × \(x^{(2+6)}\) × \(y^{(4+1)}\)

= 6\(x^{8}\)\(y^{5}\)

Answer:

≈$.12 average price of gallon per year increase

Step-by-step explanation:

Given:

$1.58 in the year 1997

$3.11 in the year 2010

Conclude:

In (2010 -1997=)13 years the prices increased by (3.11-1.58 =)1.53 dollars.

The average rate of change in the price of a gallon of gasoline per year

1.53price per gallon /13 years ≈$.12/year

Interpret the result:

Each year since 1997, an increase of about $.12 will result in a price of about $3.11 in the year 2010.

To find the standard form of the equation of an ellipse, we need to know the center, the lengths of the major and minor axes, and the orientation of the ellipse.

Given that the center is (1, 8) and the vertices are (1, 0) and (1, 16), we can see that the major axis is vertical and has a length of 16 (since the distance between the vertices is the length of the major axis). Therefore, the length of the minor axis is 2c = 8 (where c is the distance from the center to one of the foci).

To find c, we can use the relationship a^2 = b^2 + c^2, where a is half the length of the major axis (8 in this case) and b is half the length of the minor axis (4 in this case).

a^2 = b^2 + c^2
8^2 = 4^2 + c^2
c^2 = 48
c = sqrt(48) = 4sqrt(3)

Now we have all the information we need to write the standard form of the equation of the ellipse. Since the major axis is vertical, we have the equation:

(x - h)^2 / b^2 + (y - k)^2 / a^2 = 1

where (h, k) is the center of the ellipse, a is half the length of the major axis (8 in this case), and b is half the length of the minor axis (4 in this case).

Plugging in the values, we get:

(x - 1)^2 / (4^2) + (y - 8)^2 / (8^2) = 1

Simplifying, we get:

(x - 1)^2 / 16 + (y - 8)^2 / 64 = 1

Therefore, the standard form of the equation of the ellipse is:

(x - 1)^2 / 16 + (y - 8)^2 / 64 = 1.
Given the center (h, k) = (1, 8), vertices (1, 0) and (1, 16), and the relation a = 2c, we can determine the standard form of the ellipse equation.

From the vertices, we can see that the ellipse is vertically oriented. The distance between the center and a vertex is the major radius "a." Therefore, a = 8 (half of the distance between the vertices).

Since a = 2c, we can solve for c:
c = a / 2 = 8 / 2 = 4.

Now, we can find the minor radius "b" using the relationship a² = b² + c²:
64 = b² + 16
b² = 48

Finally, the standard form of the ellipse equation is:

((x - h)² / b²) + ((y - k)² / a²) = 1

Substitute the values of h, k, a, and b:

((x - 1)² / 48) + ((y - 8)² / 64) = 1

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To find h′(−1), we first need to find h(x) by multiplying f(x) and g(x) together. Then, we differentiate h(x) with respect to x to find h′(x). Finally, we substitute x=−1 into the derivative function to find the value of h′(−1). The value of h′(−1) is -64.

Given that \(f(x)=4x^2+3x+1\) and g(x)=3x^2−3x−4, we can find h(x) by multiplying f(x) and g(x) together:
h(x) = f(x)g(x) = \((4x^2+3x+1)(3x^2−3x−4)\)
To find h′(x), we differentiate h(x) with respect to x using the product rule and simplifying the expression:
\(h′(x) = (4x^2+3x+1)(6x) + (4x^2+3x+1)(6x^2−6)\)
Simplifying further, we get:
\(h′(x) = 24x^3 + 6x^2 + 6x + 18x^2 − 18 − 6x^2 + 6x − 6\)
Combining like terms, we have:
\(h′(x) = 24x^3 + 24x − 24\)
Finally, substituting x=−1 into the derivative function, we find:
\(h′(−1) = 24(-1)^3 + 24(-1) − 24 = -64\)
Therefore, h′(−1) is equal to -64.

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Answer:

(-2.5,-2.5)

Step-by-step explanation:

(-4+-1)÷2=-2.5

(-3+-2)÷2=-2.5

Answer:

(-7, -4)

Step-by-step explanation:

Equating A and B to the Midpoint (M) :

Equations formed :

    2. -2 + y / 2 = -3

Coordinates of B :

Using the triangle inequality theorem, the largest possible whole-number length for the third side is 4.

The third side of a triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides.

So, for a triangle with sides of length 1, 4, and x (where x is the length of the third side), we have:

1 + 4 > x

4 + x > 1

1 + x > 4

Simplifying these inequalities, we get:

5 > x

x > 3

x > -3 (this inequality is always true)

The largest possible whole-number length for the third side is 4, since it is the largest integer that satisfies the above inequalities.

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Answer:

7

Step-by-step explanation:

Answer:

19.50 pounds for the $2.10 per pound and 3.50 for the $0.90 per pound

Step-by-step explanation:

Answer:

Hope It Help

Brainliest please

Answer:

3

Step-by-step explanation:

The unit rate is a rate with 1 in the denominator. The unit rate for this equation would be how much money he makes in one hour. So, to find the unit rate plugin 1 for r and solve for g. One times three (1*3) is equal to 3; therefore, that is the unit rate.

well since its this its its its 27

On a circle with center O, points P and A are marked such that the arc PA is a 46º arc. This implies that angle POA is half the measure of the intercepted arc PA, which is 23º. When segment PO is extended to meet the circle again at point T, the size of angle PTA is also 23º

In a circle, the measure of an inscribed angle is half the measure of its intercepted arc. Since arc PA is a 46º arc, angle POA, which intercepts arc PA, will have half that measure, which is 23º.

When segment PO is extended to meet the circle again at point T, we can observe that angle PTA is an inscribed angle. As a result, angle PTA will also have the same measure as its intercepted arc PT. Since point P lies on arc PT, which has a measure of 46º, angle PTA will also measure 46º.

This relationship between the intercepted arc and the inscribed angle is a fundamental property of circles. It allows us to determine the measure of an inscribed angle if we know the measure of its intercepted arc, and vice versa. In this case, the measures of both angle POA and angle PTA are determined by the 46º arc PA.

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The radius is approximately 3.78 inches.

We can solve the question using the formula for the surface area of a sphere:

S=4πr^2

We are given that the surface area is 225 square inches, so we can substitute this value into the formula and solve for r:

\(225=4\pi r^2\frac{225}{4\pi}\)

      = r^2

r={{225}{4π}}

approx  3.78

A sphere does not have any edges or vertices, like other 3D shapes. The points on the surface of the sphere are equidistant from the center.

Hence, the distance between the center and the surface of the sphere are equal at any point. This distance is called the radius of the sphere.

The Radius of a circle or sphere is equal to the Diameter divided by 2.

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The decibel value of the noise is 50 db.

What is meaning of intensity of sound?

The quantity of energy going across a unit area in a unit time in a direction that is opposite to the direction of the sound waves.

The unit that used to calculate intensity of sound is decibel.

Given equation that represents the relation between intensity of sound and the ratio of the sound to the human hearing threshold is

db = 10 log i

Where i = the ratio of the sound to the human hearing threshold.

Putting i = 100,000 in the given equation:

db = 10 log 100,000

Replace 100,000 by 10⁵ :

db = 10 log 10⁵

Applying the formula of logarithm log 10^{a} = a:

db = 10 × 5

db = 50

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Therefore, the equation of the line tangent to the graph of f(x) = x^4 + 2x^2 at the point where f'(x) = 1 is:y = -3x + 13/16 or y = 3x + 1/16.

The given function is f(x) = x^4 + 2x^2. We are to find the equation of the tangent line to this function at the point where f'(x) = 1. Let's first find the derivative of f(x) as follows:f(x) = x^4 + 2x^2f'(x) = 4x^3 + 4xAt the point where f'(x) = 1, we have:1 = 4x^3 + 4x4x^3 + 4x - 1 = 0Solving for x using the Rational Root Theorem gives:x = (-1/2) or x = (1/2) or x = (√5)/2 or x = -(√5)/2Substituting each of these values of x back into the original function gives the corresponding y-coordinates:f(-1/2) = (-1/16) + 1/2 = 7/16f(1/2) = (-1/16) + 1/2 = 7/16f(√5/2) ≈ 4.84f(-√5/2) ≈ 4.84Thus, there are two points where f'(x) = 1: (-1/2, 7/16) and (1/2, 7/16). We can now use the point-slope form of the equation of a line to find the tangent line at each of these points. For example, at the point (-1/2, 7/16), the slope of the tangent line is:f'(-1/2) = 4(-1/2)^3 + 4(-1/2) = -3Thus, the equation of the tangent line is:y - (7/16) = -3(x + 1/2)Simplifying:y = -3x + 13/16Similarly, at the point (1/2, 7/16), the slope of the tangent line is:f'(1/2) = 4(1/2)^3 + 4(1/2) = 3Thus, the equation of the tangent line is:y - (7/16) = 3(x - 1/2)Simplifying:y = 3x + 1/16

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An equation of the line tangent to the graph of,

\(f(x) = x^4 + 2x^2\)

The required equation is \(y = 3x - \frac{3}{16}\)

We know that if the line tangent to the graph of the function f(x) at the point (a,f(a)) exists, then it passes through the point (a,f(a)) and has the slope f'(a).

The slope of the function is f'(x) = 4x³ + 4x.

We want to find an equation of the line tangent to the graph of the function f(x) = x⁴ + 2x² at the point

where f'(x) = 1.

So, we have, f'(x) = 1 = 4x³ + 4x

Thus, solving this equation,

\(x(x^2+1) = \frac{1}{4}\)

\(x^3+x-\frac{1}{4} = 0\)

Thus, the roots of the polynomial,

\(x^3 + x - \frac{1}{4} = 0\)

are

\(x = \frac{1}{2},-1,-\frac{1}{2}\)

Now, we have to find the point of the function

\((\frac{1}{2}, f(\frac{1}{2}))\)

where the slope is 1.

We have,

\(f(x) = x^4 + 2x^2\)

\(f(\frac{1}{2}) = (\frac{1}{2})^4 + 2(\frac{1}{2})^2 = \frac{9}{16}\)

So, the point is ,

\((\frac{1}{2}, \frac{9}{16})\)

Therefore, an equation of the line tangent to the graph of

\(f(x) = x^4 + 2x^2\)

at the point

\((\frac{1}{2},\frac{9}{16})\)

where f'(x) = 1 is:

\(y - \frac{9}{16} = (4(\frac{1}{2})^3 + 4(\frac{1}{2}))(x - \frac{1}{2})\)

\(y - \frac{9}{16} = 3(x - \frac{1}{2})\)

Therefore,

is the required equation.

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A supermarket sells cornflakes for $3 the selling price the supermarket pay for each box is $2.

The markup is the percentage added to the cost price to determine the selling price. We can use the formula:

selling price = cost price + markup

We know that the selling price of the cornflakes is $3.60 per box and the markup is 80%, so we can write:

3.60 = cost price + 0.80(cost price)

Simplifying this equation, we get:

3.60 = 1.80(cost price)

Dividing both sides by 1.80, we get:

cost price = 2

Therefore, the supermarket paid $2 for each box of cornflakes.

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Answer:

\(\sqrt{(6w)^2+(10w)^2} \)

Step-by-step explanation:

You need to use Pythagoras' theorem:

\(c=\sqrt{a^2+b^2} \) where a and b are the sides of the field.

So the distance from one corner to the opposite corner = \(\sqrt{(6w)^2+(10w)^2} \)

Answer:

21.15 $

Step-by-step explanation:

Answer:

$21.15

Step-by-step explanation:

$2.35 x 9= $21.15

Hope this helps

The process of counting the number of observations is knowns as Tabulation.

The logical representation of the numerical data written in rows and columns is known as tabulation. It helps in to facilitate the statistical analysis. The data that can be organized in the form of table is termed as tabulation. The data in the table can be represented in a systematic manner. The main objective of tabulation is to present the systematic data in a brief manner.

There are two types of tabulation. They are:

1.Simple tabulation

2.Complex tabulation

A simple example for the tabulation is, The population of the people is divided into religion, caste, gender, age etc.

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The equation that best represents this solution is:

40t + 1,280 = 2,680

What is the algebraic equations?

An algebraic expression is when we use numbers and words in solving a particular mathematical question.

Each time Sophia shops at the grocery store, she earns 40 points. If she needs a total of 2,680 points to receive a free prize and she has already earned 1,280 points, then she needs to earn an additional 2,680 - 1,280 = 1,400 points. Let t represent the number of times Sophia visits the store.

Since Sophia earns 40 points every time she shops at the grocery store, the total number of points she will earn after t visits is 40t. Therefore, we can set up the following equation:

40t = 1,400

Solving for t, we can divide both sides of the equation by 40:

t = 1,400/40

t = 35

Hence, Sophia will need to shop at the grocery store 35 more times in order to earn the additional points she needs for a free prize.

The equation that best represents this solution is:

40t + 1,280 = 2,680

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Plot two points of each equation

Equation 1 Equation 2

3x - 2y = 10 9x + 4y = - 50

x y x y

0 -5 0 12.5

10/3 0 -50/9 0

Graph

The equation of the line in point-slope form is y + 3 = (1/2)(x - 6), and in slope-intercept form is y = (1/2)x - 6.

To write the equation of a line in point-slope form and slope-intercept form given a point (6, -3) and a slope of 1/2:

1. Point-Slope Form:

The point-slope form of a linear equation is given by: \(y - y_1 = m(x - x_1)\), where (\(x_1, y_1\)) is a point on the line and m is the slope.

Substituting the values into the equation:

y - (-3) = 1/2(x - 6)

y + 3 = 1/2(x - 6)

2. Slope-Intercept Form:

The slope-intercept form of a linear equation is given by: y = mx + b, where m is the slope and b is the y-intercept.

Using the given slope (1/2) and the point (6, -3), we can solve for the y-intercept (b).

-3 = (1/2)(6) + b

-3 = 3 + b

b = -6

The equation in slope-intercept form is:

y = 1/2x - 6

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Answer:

D.480 Ft/S

Step-by-step explanation:

um, Just ask your teacher if you don't understand:P

The next 3 terms of 1/2, 1/4, 1/8 are 1/16, 1/32 and 1/64.

Number is a concept used in mathematics to represent a quantity or an amount. It can be used to describe anything from the exact number of objects in a collection to the amount of money in a bank account. Numbers can be used to measure, count, or compare different items or amounts. They can also be used to describe relationships between objects or values. For example, the number 2 can be used to represent a relationship between two objects, such as a pair of shoes.

These terms are obtained by dividing each of the previous terms by 2. This is called a geometric sequence, and each term is obtained by multiplying the previous term by 1/2.

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Complete questions as follows-
List the next 3 terms of 1/2, 1/4, 1/8

Answer:

3ab(c+2a)

Step-by-step explanation:

Given data

3abc+6a²b

we can see that 3, a, and b are common between the two terms

so let us factor them out

3ab(c+2a)

Hence the factored form is

3ab(c+2a)

Aymptotes exist when a function gets very close to a value but never reaches it, for vertical asymptotes we draw vertical lines, in this case, at x equals 2, for horizontal asymptotes draw a horizontal line, in this case at y equals 1.

The coordinates of point F are (15/4 , -5/2)

From the image attached:

AB divided into 4 similar parts, hence

Note that the rule of the mid-point states that:

When M (x , y) is the mid-point of the segment of AB, where A (x1 , y1)  and B (x2 , y2), Then  x = (x1 + x2)/2 and that of  y = (y1 + y2)/2

Then lets solve for points E, F, D

Since A (-3 , -1) and B (6 , -3),

E is the mid-point of AB

Then  E =[(-3 + 6)/2, (-1 + -3)/2]

         = (3/2 , -2)

Since  F is the mid-point of EB,

         E (3/2 , -2) , B (6 , -3)

Then F = [(3/2 + 6)/2 , (-2 + -3)/2]

       = (15/4 , -5/2)

Since D is the mid-point of AE, A (-3 , -1), E (3/2 , -2)

Then  D = [(-3 + 3/2)/2 , (-1 + -2)/2]

           = (-3/4 , -3/2)

Note also that:

 BC is said to be an  horizontal segment due to the fact that B and C have similar y - coordinate and G can be found on BC.

Since the y-coordinate of G is similar to y-coordinate of B and C

Then  y-coordinate of G is =  -3

Since DG ⊥ BC

Then DG =  vertical segment

So  G has similar x-coordinate of D

Then  The x-coordinate of G = -3/4

The  G = (-3/4 , -3)

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