Which number should be added to the data so that the range of the data is 63?

78, 61, 95, 77, 85, 97

The factorized form of the quadratic equation is:

4(x - 3)*(x + 0.25) = 0

The quadratic equation is 4x² - 11x -3 = 0

To do that, we need to find the zeros, so let's use the quadratic formula:

[tex]x = \frac{11 \pm \sqrt{(-11)^2 - 4*4*-3} }{2*4} \\\\x = \frac{11 \pm 13 }{8}[/tex]

Then the two roots are:

x = (11 + 13)/8 = 3

x = (11 - 13)/8 = -2/8 = -0.25

Then the factorized form is:

4(x - 3)*(x + 0.25) = 0

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Answer:

36cm

Step-by-step explanation:

The lightning bolt on the right is 3 times bigger than the one on the left. You can tell this because that leftside, vertical-ish piece (on both of them) is labelled. The small one is 25cm and the big one is 75cm.

25 × 3 = 75

The bottom right side is 12cm, so times by 3 to find the bigger one that matches.

12 × 3 = 36

In 58 seconds after starting its descent, the aircraft will touch down.

The plane will land when its altitude y is zero.

So we can set y = 0 in the equation:

0 = 464 - 8x

Solving for x:

8x = 464

x = 58

Therefore, the plane will land 58 seconds after it begins its descent.

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The ordered pairs to a solution for the given linear equation are (-1, 3.5) and (4, -4).

To find the ordered pair that is a solution to the equation 6x + 4y = 8, we can substitute the given value of x or y and solve for the other variable.

For the first option, substituting x = -1, we get:

6(-1) + 4y = 8

-6 + 4y = 8

4y = 14

y = 3.5

So, the ordered pair (-1, 3.5) is a solution to the equation.

For the second option, substituting y = -4, we get:

6x + 4(-4) = 8

6x - 16 = 8

6x = 24

x = 4

So, the ordered pair (4, -4) is a solution to the equation.

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Answer:

20%  (D)

Step-by-step explanation:

The amount of sand Eloise will put in each sandbox is 7.5 pounds (30 divided by 4).

Answer:

The function f(x,y) = x^2 + y^2 represents the equation of a paraboloid with its vertex at the origin. Since the function increases as we move away from the origin, there are no maximum points, but there is a minimum point at the origin.

To find this minimum point, we can take the partial derivatives of f(x,y) with respect to x and y, and set them equal to zero:

df/dx = 2x = 0

df/dy = 2y = 0

Solving these equations simultaneously gives us x = 0 and y = 0, which is the only critical point of the function. To determine whether this point is a minimum or maximum, we can use the second partial derivative test.

Taking the second partial derivatives, we have:

d^2f/dx^2 = 2

d^2f/dy^2 = 2

d^2f/dxdy = 0

At the point (0,0), both second partial derivatives are positive, which indicates that the point is a minimum. Therefore, the function f(x,y) = x^2 + y^2 has a minimum value of 0 at the point (0,0).

The numbers as an integer or not are:

From the question, we have the following parameters that can be used in our computation:

7/10 - yes or no

-6/1 - yes or no

-30.18 - yes or no

7 - yes or no

-76 - yes or no

integers are numbers without decimal point (including 0)

Using the above as a guide, we have the following:

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Answer:2^4=4x-4 would be the answer

Step-by-step explanation: You would exponentiate both sides

92 more students favor visiting Florida than Colorado

From the question, we have the following parameters that can be used in our computation:

Students = 400

Florida = 38%

Colorado = 15%

The percentage difference is

Difference = 38% - 15%

So, we have

Difference = 23%

This means that

Students = 23% * 400

Evaluate

Students = 92

Hence, the number of students is 92

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The largest interior angle of the triangle is the angle A

The side lengths of the triangles are given as

b = 10 cm

a = 14 cm

The other side length is not given

So, we solve the question using the two side lengths

Having said that:

The general rule is that; the higher the side length, the larger the angle

14 cm is greater than 10 cm

This means that the angle A is greater than the angle B

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The triangles are classified according to their sides as:

1. equilateral 2. Scalene   3. and 4. Isosceles   5. equilateral     6. and 7. scalene triangle.      8. Isosceles   9. and 10. Equilateral

Recall the following:

A triangle is equilateral if all three sides are equal.

It is isosceles if it has two equal sides.

A triangle is scalene if all three sides are of different lengths.

1. The triangle is equilateral because all sides are equal.

2. Scalene

3. and 4. Isosceles (two sides are equal)

5. All sides are equal, so it is an equilateral triangle.

6. and 7. The three sides have different lengths, therefore, it is a scalene triangle.

8. Isosceles

9. and 10. Equilateral

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Answer:

If the shoes are 20% off, then the sale price of the shoes will be:

67 - 0.20 * 67 = 67 - 13.40 = 53.60

So the sale price of the shoes is $53.60.

If the sales tax is 5%, then the tax on the shoes will be:

0.05 * 53.60 = 2.68

So the tax on the shoes is $2.68.

To find the total price of the shoes including tax, we need to add the sale price of the shoes and the tax:

53.60 + 2.68 = 56.28

Therefore, the total price of the shoes, including tax, is $56.28.

Answer:

$56.28

Step-by-step explanation:

1. Find the shoes' sale price.

The shoes are 20% off. We will find the new price by first finding 20% of $67.

An easy way to do it:

10% of 67 = 6.7
20% of 67 = 13.4

to double the percentage of the first equation, double the answer.

Now that we know 20% of 67 we can take away 20% from it:

67 - 13.4 =53.6

Money uses 2 decimal points so we will add a 0 at the end of the result.

The price of the shoes with only the sale is $53.60.

2. Add sales tax

First find out 5% of $53.60.

An easy way to do it:

10% of 53.60 = 5.360

5% of 53.60 = 2.68

to half the percentage of the first equation, half the answer.

Now that we know the price of the tax we can add it to our shoe price. With the sale the shoe costs $53.60 and we will add our tax:

53.60 + 2.68 = 56.28

Add your units:

The equations that can be used to solve for y, the length of the room are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0

From the question, we have the following parameters that can be used in our computation:

Area = 750

Length = y

Width = y - 5

The area is the product of the length and the width

So, we have

y * (y - 5) = 750

When expanded. we have

y^2 - 5y = 750

Lastly, we have

(y + 25)(y – 30) = 0 -- when factored

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Answer:

A parallelogram is a quadrilateral with 2 pairs of parallel sides.

Step-by-step explanation:

Mark brainliest, pls

The graph of the system of inequalities is on the image at the end.

Here we have the system of inequalities:

y > -2x + 9

y < 5x - 6

First we need to graph both of these lines with dashed lines (that is because the values on top of the lines are not solutions for the inequalities).

Then we need to shade the region above the first line, and the region below the second line.

Thenh the graph of the system is the one you can see in the image at the end.

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Answer:

53,352 cm

Step-by-step explanation:

1. The first step is to draw the rectangle draw one rectangle over the other and start labeling the sides.

2. After labeling use the rectangle prism formula: L times W times H in this case it would be 38 times 18 times 13 this is equal to 8,892.

3. From there, we know that there are six sides so we can multiply this value by 6 so it would be 8,892 times 6 = 53,352 cm.

If I made a mistake or if have any questions feel free to tell me!

-Mathematics and Science Major for Middle School Students at Harvard University

Answer: Angle one equals -15, and angle two equals 14, if the +7 equals a positive seven.

Step-by-step explanation:

There are more negatives than positives, so we make the ending answer negative, giving us -15. And the second one is simple multiplication, you double the 7 times two, or vice versa.

Hope this helps!

Answer:

  u = -4

Step-by-step explanation:

You want the solution to the equation 16u -5u +18 = 3u -14.

The equation can be simplified by combining like terms:

  11u +18 = 3u -14

Adding (-18-3u) to both sides, we have ...

  8u = -32

  u = -32/8 = -4 . . . . . . divide by the coefficient of u

The solution is u = -4.

Answer:

452 square centimeters.

Step-by-step explanation:

To find the area of a circle, we use the formula:

A = πr^2

Where A is the area of the circle, r is the radius, and π is a mathematical constant (approx. 3.14).

Given that the radius of the circle is 12 cm, we can substitute r = 12 in the formula:

A = π(12)^2

A = 3.14 x 144

A = 452.16

Therefore, the area of the circle is approximately 452.16 square centimeters. However, we need to round the answer to the nearest whole number.

Since the decimal part of the answer is less than 0.5, we round the answer down to the nearest whole number. Therefore, the area of the circle nearest the whole number is 452 square centimeters.

Using the given information, the cost of Max's electricity bill is R551.10

From the question, we are to calculate the cost of Max's monthly electricity bill

From the given information,

"Max's monthly electricity budget only allows him to use 250.50 kWh"

and

"The cost for 1 kWh is R2.20"

To determine the cost of Max's monthly electricity bill, we will multiply his monthly electricity budget by the cost for 1 KWh

That is,

Max's monthly electricity bill = 250.50 × R2.20

Max's monthly electricity bill = R551.10

Hence,

The cost of Max's monthly electricity bill is R551.10

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The equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.

To find the equation of the line perpendicular to y=1/2x-1, we need to determine its slope. We can recall that the slope of a line in slope-intercept form, y = mx + b, is given by m, the coefficient of x. So in the given equation y=1/2x-1, the slope is 1/2.

The slope of a line perpendicular to this line will be the negative reciprocal of the slope, which means it will be -2. To see why this is true, remember that the product of the slopes of two perpendicular lines is always -1. So if the slope of the original line is m, the slope of the perpendicular line will be -1/m.

Now that we know the slope of the perpendicular line is -2, we can use the point-slope form of the equation of a line to find its equation. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

We are given a point on the perpendicular line, (5, 6), so we can substitute that into the equation and also substitute in the slope, -2:

y - 6 = -2(x - 5)

y - 6 = -2x + 10

y = -2x + 16

Hence, the equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.

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Check the picture below.

Using an equation, the number of children, parents, and grandparents in attendance were:

An equation is an algebraic statement showing the equality or equivalence of two or more mathematical expressions.

Mathematical expressions combine variables, numbers, values, and constants using mathematical operands.

The total number of people in attendance at the family reunion = 400

Let the number of grandparents = x

Let the number of parents = 2x

Let the number of children = 2x + 50

x + 2x + 2x + 50 = 400

5x = 350

x = 70

Grandparents = 70

Parents = 140 (2 x 70)

Children = 190 (2 x 70 + 50)

Total = 400 (70 + 140 + 190)

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Answer:

Step-by-step explanation:

To answer this question, we need to calculate the mean and median of the given data set and then see how the additional earnings affect them.

First, let's calculate the mean of the original data set:

Mean = (50 + 82 + 39 + 50 + 31 + 70) / 6 = 322 / 6 = 53.67

Next, let's calculate the median of the original data set. To do this, we need to arrange the data set in order:

31, 39, 50, 50, 70, 82

The median is the middle value, which is 50.

Now, let's add Becky's earnings of $23 to the data set:

31, 39, 50, 50, 70, 82, 23

The new data set has 7 values. Let's calculate the new mean:

Mean = (50 + 82 + 39 + 50 + 31 + 70 + 23) / 7 = 365 / 7 = 52.14

The new mean is less than the original mean, so we can eliminate options A and C.

Now let's calculate the new median. We need to arrange the data set in order:

23, 31, 39, 50, 50, 70, 82

The median is still 50.

Therefore, the answer is option D: The mean decreases and the median remains the same.

The balance after 5 years, if $1500 is deposited in an account with 6%

interest rate, compounded continuously is calculated as: $2,024.79.

The formula for calculating the balance (F) in a continuously compounded account is:

[tex]F = Pe^{(rt)}[/tex]

where we have:

P is the principal amount,

e is the mathematical constant approximately equal to 2.71828, and

r is the interest rate, and t is the time in years.

In this case, P = $1500, r = 6%, and t = 5 years.

Plug these values into the formula and solve for F:

F = 1500e^(0.065)

F = 1500e^0.3

F = 15001.34985880758

F = $2,024.79 (rounded to the nearest cent)

Therefore, the balance after 5 years is $2,024.79.

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The value of 5cos(tetha) + 4/sin(beta) is 9

Complementary angles are two angles that sum up to 90°. This means that in a right angled triangle sin( beta) is thesame as cos(90-tetha) and cos (beta) is sin(90-tetha).

Examples of complementary angles include: 30 and 60, 50 and 40 e.t.c

Therefore if tan ( tetha ) = 3/4, and tan(tetha) = opp/adj. This means opp is 3 and adj is 4

therefore hyp = √3²+4²

= √9+16 = √25

= 5

therefore cos(tetha) = 4/5

and sin beta = 4/5

therefore 5cos(tetha) + 4/sin(beta) = 5 × 4/5 +(4÷4/5)

= 4+5 = 9

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Part A: Note that the best graphical representation to use for this kind of data is a Histogram.

Part B : Creating the historgram means you have to first chose the intervals for the data.

When it comes to displaying the distribution of a set of continuous data, histograms offer an appropriate visualization method.

This display type divides the data into intervals and plots the number of observations that fall within each interval, hence providing frequency distribution information.

For instance, in creating a histogram for this particular dataset, one can choose intervals or bins with sizes e.g. 5 units covering a range between 0 and 30 before tabulating the count of observed variables in each bin and plotting these counts on the chart's vertical axis.

A histogram illustrates how often students ate breakfast within a 30-day timeframe. This frequency distribution features labeled axes, with the vertical axis representing "Frequency" and the horizontal axis depicting "Number of times students ate breakfast."

Each bar on the horizontal axis corresponds to an interval and shows its frequency on a scaled height basis.

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