A. 66

B. 53

C. 87

D. 73

Answer:

The exact answer to this inequality is x < 3.

Step-by-step explanation:

4x - 7 < 5

    +7   + 7

4x < 12

/4     /4

x < 3

Hope this helps and I hope u have an Amazing day!!

The statement that must be true is (c) If a quadrilateral has opposite sides that are both congruent and parallel, then it is a parallelogram.

A parallelogram has parallel and congruent opposite sides.

However, the following are true about parallelograms at:

Hence, the true statement is (c)

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Answer:

2 15/26

Step-by-step explanation:

Make them both fractions and find a common demoninator. 8 1/13 = 105/13 and 5 1/2 = 11/2. A common denominator is 26, so 105/13 * 2 = 210/26 and 11/2 * 13 = 143/26. You then subtract the fractions to find out how much is left to walk, 210-143 = 67/26, or 2 15/26.

1. Solution of the rational equation \(\frac{x}{3} -6=\frac{9}{3}\)   is x = 27

How is the equation solved?

\(\frac{x}{3} -6=\frac{9}{3}\\\\\frac{x- 18}{3} =\frac{9}{3}\\\\x= 18+9\\\\x= 27\)

2.The two numbers = 2, 6

How to find the two numbers?

Let the two whole numbers = x, y

Given:

x+ y =8 --- (1)

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

Considering (2),

\(\frac{1}{x} +\frac{1}{y} =\frac{2}{3}\\\\\frac{x+ y}{x y} =\frac{2}{3}\\\\\text{Applying } (1),\\\\\frac{8}{x(8-x)} =\frac{2}{3}\\\\(8x-x^{2} )2 =24\\\\(8x-x^{2} ) =12\\\\x^{2} -8x+12 =0\\\\(x-6) (x-2)= 0\\\\x= 2, 6\)

Substituting  x in (1)

We have,

When x = 2 ; y= 6

When x = 6 ; y = 2

So, the two numbers = 2, 6

3. The two numbers = 3, 9

How to find the two numbers?

Let the two whole numbers = x, y

Given:

x- y =6 --- (1)

1/y -1/x = 2/9 ---(2)

Considering (2),

\(\frac{x-y}{xy} =\frac{2}{9} \\\\\text{Applying } (1)\\\\\frac{6}{x y} =\frac{2}{9} \\\\x y = 27\\\\(6+y)y = 27\\\\y^{2} +6y-27=0\\\\(y+9) (y-3) = 0\\\\y= 3, -9\)

Since x and y are whole numbers we will have y = 3

When y = 3 ; x=9 (substituting in (1))

So, the two numbers = 9,3

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Answer:

The cost of that car in 2012 dollars is $20,755

Step-by-step explanation:

We take a look at inflation values of the dollar to solve this question.

100 dollars in 1976 are equivalent to 469.48 dollars in 2021.

100 dollars in 2012 are worth 113 dollars today.

So, to find the 2012 equivalent, we divide 469.48 by 113/100 = 1.13. So

469.48/1.13 = 415.5.

That is, 100 dollars in 1976 are equivalent to 415.5 dollars in 2012, that is, 1 dollar in 1976 was worth 4.155 dollars in 2012.

In 1976, a certain model of car cost $5,000. What would be the cost of that car in 2012 dollars?

Multiplying by 4.155

5000*4.155 = 20,755

The cost of that car in 2012 dollars is $20,755

Answer:

∠EGF= 65

∠CGF= 115

Step-by-step explanation:

Answer:

the answer is $521.10 per hour

Step-by-step explanat

if you want the unrounded answer its  $521.103333

Answer:

It would be a diagnol line.

On solving the provided question we can say that median from the vertex in an isosceles triangle is perpendicular to the base.

ƒ(x)=sin(x)

consider Asin(Bx + C) = y +D changes the amplitude of the function (how high or low it is).

if you want to

Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.

Let O be the circle's centre and P be the midpoint of BC. After that, OP LBC.

Let AP =x and PB = CP -y.

Applying Pythagoras theorem in As AP B and OP B, we have

AB2 = BP2 + AP2 and OB2 = OP2 +BP2

Y2 +x2 ... (i) and, 81 = (9 —x)2 + Y2

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Let's assume x gallons of milk containing 8% butterfat and y gallons of milk containing 2% butterfat are used.

The total amount of milk is x + y gallons, and we want it to be equal to 258 gallons.

To determine the amount of butterfat in the mixture, we can multiply the volume of each type of milk by its respective butterfat percentage and sum them up.

For milk containing 8% butterfat, the amount of butterfat is 0.08x (8% is equivalent to 0.08 as a decimal).

For milk containing 2% butterfat, the amount of butterfat is 0.02y (2% is equivalent to 0.02 as a decimal).

Since we want the final mixture to contain 7% butterfat, we can set up the following equation:

0.08x + 0.02y = 0.07(258)

Simplifying the equation, we have:

0.08x + 0.02y = 18.06

To solve for x and y, we need another equation. Since the total amount of milk is x + y = 258, we can rearrange it to y = 258 - x.

Substituting this value into the equation above, we get:

0.08x + 0.02(258 - x) = 18.06

Solving this equation will give us the values of x and y, which represent the gallons of milk containing 8% butterfat and 2% butterfat, respectively, needed to obtain the desired 258 gallons.

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Answer:

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Step-by-step explanation:

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line G

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 8 } \implies {\Large \begin{array}{llll} - \cfrac{3 }{ 8 } \end{array}}\)

The volume of blocks is 8n³ cm³ and volume of box is 216 n⁹ cm³.

According to the question we have been given that the

  side length of the cube shaped box = 6n³ cm

  side length of the cube shaped blocks = 2n cm

We need to find the volume of the box and the blocks.

The formula for the volume of cube is

                      V = (s)³ cubic units.

     where, s = side length of the cube

Now putting the required values in the above formula we get

  volume of box = (6n³)³ cm³

                         = 216 n⁹ cm³  

 volume of the blocks = (2n)³ cm³

                                   = 8n³ cm³

Hence the volume of blocks is 8n³ cm³ and volume of box is

216 n⁹ cm³.

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(m + n) has a magnitude of approximately 25.8.

We have,

Consider the two vectors as m and n.

To find (m + n), we need to add the two vectors.

To do this, we first need to determine the components of each vector.

Let's call the angle between vector m and the x-axis α, and the angle between vector n and the x-axis β.

Then we have:

|m| = 10, so the x-component of vector m is m_x = 10 cos α and the

y-component is m_y = 10 sin α.

|n| = 15, so the x-component of vector n is n_x = 15 cos β and the

y-component is n_y = 15 sin β.

We also know that the angle between vectors m and n is 75 degrees. Using the dot product, we can find the cosine of this angle:

m · n = |m| |n| cos 75

m · n = 10 * 15 * cos 75

m · n = 37.32

We also know that the dot product is equal to the sum of the products of the corresponding components:

m · n = (m_x) x (n_x) + (m_y) x (n_y)

37.32 = 10 cos α x 15 cos β + 10 sin α * 15 sin β

Now we have two equations with two unknowns:

m_x + n_x = (10 cos α) + (15 cos β)

m_y + n_y = (10 sin α) + (15 sin β)

We can solve for α and β using the equations we just derived:

m_x + n_x = (10 cos α) + (15 cos β)

10 cos α = (m_x + n_x - 15 cos β)

cos α = (m_x + n_x - 15 cos β) / 10

α = arccos[(m_x + n_x - 15 cos β) / 10]

m_y + n_y = (10 sin α) + (15 sin β)

10 sin α = (m_y + n_y - 15 sin β)

sin α = (m_y + n_y - 15 sin β) / 10

α = arcsin[(m_y + n_y - 15 sin β) / 10]

Now we can substitute these values into the equations for m_x + n_x and m_y + n_y to find (m + n):

m_x + n_x = 10 cos α + 15 cos β

m_y + n_y = 10 sin α + 15 sin β

We can use a graphical method to estimate the values of α and β. Start by drawing vector m with length 10 and angle α with respect to the x-axis. Then draw vector n with length 15 and angle β with respect to the x-axis, starting the tail of n at the head of m.

The parallelogram formed by the two vectors will have a diagonal that represents (m + n). Use a ruler to measure the length of this diagonal to the nearest hundredth.

We can use the law of cosines to find the magnitude of (m + n):

|(m + n)|² = |m|² + |n|² + 2|m||n| cos 75

|(m + n)|² = 10² + 15² + 2(10)(15) cos 75

|(m + n)|² = 665.19

|(m + n)| = 25.8 (to the nearest hundredth)

Therefore,

(m + n) has a magnitude of approximately 25.8.

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The degree of the polynomial is a f(x)=x^3-2x^2+16x-32.

According to the statement

We have to find that the degree of the polynomial.

So, For this purpose, we know that the

The degree of a polynomial is the highest power of the variable in a polynomial expression.

From the given information:

with real coefficients having zeros 2 and 4 i and a lead coefficient of 1.

Then

We know that the complex zeros always occur in pairs.

zeros are 2,4i,-4i

f(x)=(x-2)(x-4i)(x+4i)

f(x)=(x-2)((x)^2-(4i)^2)

f(x)=(x-2)(x^2-16i^2)

f(x)=(x-2)(x^2+16)

f(x)=x^3-2x^2+16x-32.

So, The degree of the polynomial is a f(x)=x^3-2x^2+16x-32.

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Answer:

90ft x 90ft. 8100ft^2

Step-by-step explanation:

Perimeter(P) = 180 = length + width

Length(L) = 180 - width

Width(W) = 180 - length

Area = length*width = length*(180-length) = 180*length - length^2

Because the sum of length and width must always be 180, when one increases, the other decreases.

The largest area will happen when the derivative of the area is equal to 0. The derivative can be found with the power rule.

Derivative of Area (slope of Area) = 180 - 2*length

180 - 2*length = 0

180 = 2*length

length = 180/2 = 90ft

When the length is 90ft and width is 90ft, the area is 8100ft^2.

Based on the given information, the type of data set created using this survey is Univariate categorical.  So the answer is option D.

In this survey, the data collected represents a single variable, which is the mode of transportation to school. The variable has discrete categories such as walking, car, bus, and bike.

Each student is assigned to one of these categories, and the count of students in each category is provided. Since there is only one variable being considered (mode of transportation), it falls under the category of univariate data.

Additionally, the data is categorical in nature as it represents different transportation options, rather than numerical values.

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Complete question:

A survey of middle school students asked participants how they get to school each morning. The results of the survey are summarized

21 students walk to school

127 students ride in a car to school

105 students take the bus to school

76 students ride their bikes to school

What type of data set was created using this survey?

A. Bivariate numerical

B. Bivariate categorical

C. Univariate numerical

D. Univariate categorical

Answer:

OA. (1,6), (2, 7), (4,9), (0,5).

Step-by-step explanation:

To determine whether a list of ordered pairs is a function, you need to check whether each element in the domain (the set of input values) is associated with exactly one element in the range (the set of output values).

In this case, the list OA. (1,6), (2, 7), (4,9), (0,5) is a function because each element in the domain (1, 2, 4, 0) is associated with exactly one element in the range (6, 7, 9, 5).

List OB. (2, 4), (0, 2), (2, -4), (5, 3) is not a function because the element 2 appears twice in the domain and is associated with two different elements in the range (4 and -4).

List OC. (0, 2), (2, 3), (0, -2), (4, 1) is not a function because the element 0 appears twice in the domain and is associated with two different elements in the range (2 and -2).

List OD. (1, 2), (1, -2), (3, 2), (3, 4) is not a function because the element 1 and 3 appear twice in the domain and are associated with two different elements in the range (2 and -2, and 2 and 4, respectively).

Therefore, the correct answer is OA. (1,6), (2, 7), (4,9), (0,5).

An exponential equation in the form \(y=a(b)^x\) that can model the amount of caffeine, y, in Kendall's body x hours after drinking the coffee is

The amount of caffeine that will be in Kendall's body after 12 hours is 18 milligrams.

In Mathematics, an exponential function can be modeled by using the following mathematical equation:

f(x) = a(b)^x

Where:

Since Kendall drank a cup of coffee that had 95 milligrams of caffeine which is decreasing at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:

Rate of change (decay rate) = 100 - 13 = 87% = 0.87.

By substituting the parameters into the exponential equation, we have the following;

\(f(x) = 95(0.87)^x\)

When x = 12, we have;

\(f(12) = 95(0.87)^{12}\)

f(12) = 17.86 ≈ 18 milligrams.

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Answer: The answer is -4.37u-11

Step-by-step explanation: Just do math.

Answer:

C, (-2,1).

Step-by-step explanation:

y = -2x - 3 ---1

y = 1/2x + 2 ---2

Substitute 1 into 2.

-2x - 3 = 1/2x + 2

Simplify the equation.

5/2x = -5

Multiply 2 to get rid of fraction.

5x = -10

x = -2

Substitute x into either equation to find y. I will substitute x into 1.

y = -2(-2) - 3

= 4 - 3

= 1

x = -2, y = 1

Hence, (-2,1).

Answer:

16  is ur answer

Step-by-step explanation:

1. open calculator

2. write 1232/77

3. get 16

Answer:

224

Step-by-step explanation:

360.-136.

A formula is a fact or rule that uses mathematical symbols. It will usually have: an equals sign (=) two or more variables (x, y, etc) that stand in for values we don't know yet.

Example: The formula for finding the volume of a box is:

x = 2y - 7 Formula (relating x and y)

a2 + b2 = c2 Formula (relating a, b and c)

The annual interest is $22.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

Given;

Amount invested= $550

Annual interest= 4%

SI= 550*4*1/100

=5.5*4

=22

Therefore, the simple interest will be $22.

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Answer:

6

Step-by-step explanation:

Answer:

x<2

Step-by-step explanation:

2x+6<10

2x<10-6

2x<4

x<4/2

x<2

Answer: Just look it up on goo gle

Step-by-step explanation:

The rate per annum compound interest is approximately 11.5%.

To find the rate per annum compound interest, we can use the formula for compound interest:

\(A = P(1 + r/n)^{nt}\)

Where:

A = the final amount (N5353 in this case)

P = the principal amount (N4000 in this case)

r = the annual interest rate (what we want to find)

n = the number of times interest is compounded per year (assuming once per year)

t = the number of years (5 years in this case)

Now, we can plug in the values:

\(N5353 = N4000(1 + r/1)^{1*5}\)

Divide both sides by N4000:

\(1.33825 = (1 + r)^5\)

Now, isolate (1 + r) by taking the fifth root of both sides:

\(1 + r = (1.33825)^{1/3}\\1 + r \approx 1.115\)

Now, subtract 1 from both sides to find the interest rate (r):

r ≈ 1.115 - 1

r ≈ 0.115

Finally, convert the interest rate to a percentage:

r ≈ 0.115 * 100

r ≈ 11.5%

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In the quadratic equation y = a\(x^{2}\) + c ,the value of x = ± \(\sqrt \frac{y-c}{a}\)

A quadratic equation is any equation containing one term wherein the unknown is squared and no term wherein it's far raised to a higher power.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, in which a and b are the coefficients, x is the variable, and c is the constant term.

To find the value of x

Assuming \(a\neq o\)

First, subtract c from both the sides to get:

\(y-c=ax^{2}\)

then, divide both sides by \(a\) and transpose to get:

\(x^{2} =\frac{y-c}{a}\)

So, \(x\) must be a square root of \(\frac{y-c}{a}\)  and we can deduce:

\(x=\) ± \(\sqrt \frac{y-c}{a}\)

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We're given:

If the shop sold " \(9\dfrac{9}{10}\)  times as much milk chocolate as white chocolate", we must multiply \(9\dfrac{9}{10}\) by the amount of white chocolate sold to find the amount of milk chocolate sold.

Multiply \(9\dfrac{9}{10}\) by 9 ounces:

\(9\dfrac{9}{10}\times9\)

Convert the fraction into an improper fraction:

\(=\dfrac{99}{10}\times9\)

Multiply:

\(=\dfrac{891}{10}\)

The shop sold \(\dfrac{891}{10}\) ounces of milk chocolate.