Lucy runs 6 miles in 55 minutes. At the same rate, how many miles would she run in 44 minutes

Answer:

x = 40

Step-by-step explanation:

We can set up the following equations to represent the problem:

x = number of quarters

x + 16 = number of dimes

0.25x + 0.1(x + 16) = 12.45

Solving for x, we get:

x = 40

So there are 40 quarters and 56 dimes in the coin bank.

Answer: 38.3 cm

Step-by-step explanation:

To find the size of a rectangular monitor measured diagonally, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Here are the steps to calculate the diagonal size of the monitor:

Therefore, the size of the rectangular monitor that is 30 centimeters wide by 24 centimeters high is approximately 38.3 cm. to the nearest centimeter.

The size of the given mirror as a rectangular diagonal is 38.41 cm which is almost 39 cm.

We know that;

d=√ {(l)^2 + (w)^2}.........(i), where,

d= diagonal of the rectangle,

l= length of the rectangle = 30 cm

w= width of the rectangle = 24 cm.

Therefore, Substituting the values of each in equation (i), we get;

d=√{(30)^2+(24)^2} cm,

or, d = 38.41 cm

So, the size of the rectangular mirror measured diagonally is 38.41 cm which is almost 39 cm.

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Based on the histogram above, we will use median to describe this variable.

Hence, option (b) is correct choice.

A histogram is a graphical depiction of data distribution in statistics. The histogram is represented by a series of neighbouring rectangles, with each bar representing a different type of data. Statistics is a branch of mathematics that is used in a variety of areas.

The frequency distribution is represented graphically by a histogram.

The histogram may be analysed as a representation of frequencies and classes as linked rectangles.

Option B is the correct answer to this question.

Because the median is unaffected by big observations, we use it as a measure of central tendency while analysing the left skewed distribution.

The required image/ histogram is attached below:

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The probability of a random patient being alcoholic with elevated cholesterol levels is 55/80, or 0.6875. The probability of a random patient being nonalcoholic is 320/400, or 0.8. Lastly, the probability of a random patient being nonalcoholic with Non elevated cholesterol levels is 248/400, or 0.62.

To calculate the probability of a random patient being alcoholic with elevated cholesterol levels, we must first determine the total number of patients with elevated cholesterol levels. This can be done by adding the number of alcoholic patients (55) with elevated cholesterol levels to the number of nonalcoholic patients (72) with elevated cholesterol levels.

The result is a total of 127 patients with elevated cholesterol levels. This means that out of 400 patients, 55 of them were alcoholic and had elevated cholesterol levels. Therefore, the probability of a random patient being alcoholic with elevated cholesterol levels is 55/400, or 0.6875.

The probability of a random patient being nonalcoholic is equal to the total number of nonalcoholic patients (320) divided by the total number of patients (400). This yields a probability of 0.8.

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inequalities:  y ≤ −2x + 10 & y > (1/2x) - 2  is a solution to the system of inequalities .

What does co ordinate math entail?

An exact position of a point in the coordinate plane can be demonstrated using a collection of values called coordinates. Definition of a coordinate plane.

                        An intersection of two perpendicular lines known as the x-axis and y-axis results in a 2D plane known as a coordinate plane.

The points which represents a the solution are: A, C, D and K

See the attached figure.

The given inequalities:  y ≤ −2x + 10 & y > 1/(2x − 2)

The given points: A(-5,4), B(4,7), C(-2,7), D(-7,1), E(4,-2),

F(1,-6), G(-3,-10), H(-4,-4), I(9,3), J(7,-4) and K(2,3).

The attached figure represents the graph of the given inequalities.

The shaded area represents the solution of the inequalities.

So, the points lies in the shaded area represents the solution of the inequalities.

So, points A, C, D and K are a solution to the system of inequalities.

If the given inequalities:  y ≤ −2x + 10 & y > (1/2x) - 2

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The equation of the secant line containing the points (-7,g(-7)) and (8,g(8)) is y = (123/15)x + (98 - (123/15) * (-7)).

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. To find the equation of the secant line, we need to find the slope (m) and the point of intersection (x,y) of the line with the y-axis.

To find the slope (m) of the secant line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1,y1) = (-7, g(-7)) and (x2,y2) = (8, g(8)).

So, m = (g(8) - g(-7)) / (8 - (-7)) = (g(8) - g(-7)) / 15

Now, we can substitute the value of g(x) in the above equation and get the value of m

g(x) = 2x^2-7

m = (2(8^2)-7 - 2(-7^2)-7) / 15 = (2(64)-7 - 2(49)-7) / 15 = (128-7-98-7) / 15 = 123/15.

To find the point of intersection (x,y) of the line with the y-axis, we can use one of the given points and the slope. Let's use the point (-7,g(-7))

y = mx + b

g(-7) = m * (-7) + b

b = g(-7) - m * (-7)

We can substitute the value of g(x), m and x = -7 in the above equation and get the value of b.

g(x) = 2x^2-7

b = 2(-7)^2-7 - m * (-7) = 2(49)-7 - 123/15 * (-7) = 98 - 123/15 * (-7)

So, the equation of the secant line containing the points (-7,g(-7)) and (8,g(8)) is y = (123/15)x + (98 - (123/15) * (-7))

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The coordinates of the points A and B, after scaling becomes

A(x, y) → A'(2x, 2y)

B(x₁, y₁) → B'(2x₁, 2y₁)

        {K} = L{final}/L{initial}

Given is that shape is being enlarged using a scale factor of 2 and centre (6, 3).

Assume the coordinates of the point are A(x, y) and B(x₁, y₁). After scaling, the coordinates will become -

A(x, y) → A'(2x, 2y)

B(x₁, y₁) → B'(2x₁, 2y₁)

Therefore, the coordinates of the points A and B, after scaling becomes

A(x, y) → A'(2x, 2y)

B(x₁, y₁) → B'(2x₁, 2y₁)

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Answer:

The 1st one is A and the  2nd one is C

Step-by-step explanation:

Answer:

13.86

Step-by-step explanation:

You have the exact value, just compute it and round the number to get your approximate

Answer:

13.86

Step-by-step explanation:

You'll most likely need the calculator since ✓192 is not a perfect square.

Calculating it

✓192 = 13.856

Rounding it two places would be 13.86

The cubic function whose graph passes through the given points is defined as follows:

y = -2(x³ - 4x² + x + 6).

The cubic function is defined by the Factor Theorem, as a product of it's linear factors.

The x-intercepts of the function are given as follows:

Hence the linear factors of the function are given as follows:

As a product of the linear factors, the function is defined as follows:

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

y = a(x² - x - 2)(x - 3)

y = a(x³ - 4x² + x + 6).

When x = 0, y = -12, hence the leading coefficient a is obtained as follows:

6a = -12

a = -2.

Thus:

y = -2(x³ - 4x² + x + 6).

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The following are the respective values of the angles:

∠5 = 44°

∠3 = 117°

x = 60°

x = 157°

angles (∠5 + ∠6)° and ∠2 are corresponding angles and are equal so;

∠5 + 90° = 134°

∠5 = 134° - 90°

∠5 = 44°

angles (∠5 + ∠6)° and ∠3 are alternate angles and are equal so;

∠3 = ∠5 + ∠6

∠3 = 27° + 90°

∠3 = 117°

(x + 5) + 90° + (180° - 155°) = 180° {sum of interior angles of a triangle}

x + 5 + 90° + 25° = 180°

x + 120° = 180°

x = 180° - 120°

x = 60°

x = 22° + (180° - 45°) {exterior angle of a triangle equals two opposite interior angles}

x = 22° + 135°

x = 157°

Therefore, the following are the values of the angles: ∠5 = 44, ∠3 = 117°, x = 60°, and x = 157° respectively.

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According to the question, the closing balance for quarter 2 is £82,750.

A quarter is one fourth of a year. It is typically a three month period, usually consisting of January, February, and March; April, May, and June; July, August, and September; or October, November, and December. The terms of a quarter can vary depending on the context. For example, in the United States, quarters are commonly referred to as “fiscal quarters,” and begin on the first day of October, January, April, and July. In this case, each quarter covers a three-month period.

Inflows for quarter 2: 540,000 x 1.075 = £581,000

Outflows for quarter 2: 495,000 x 1.05 = £519,250

Closing balance for quarter 2:

Opening balance + Inflows - Outflows =

20,000 + 581,000 - 519,250 = £82,750

Therefore, the closing balance for quarter 2 is £82,750.

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The required Linear function among the following option is D) y=|x|.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

A)  y=3x³

It is cubic function.

B) y=¼x

It is inverse function.

C) Y=x²

It is a quadratic function.

D) y=|x|

It is a modulus function, but after remove the Mode in x, we get

y = x and y = -x

So, Here power on x is one. It is Linear function as well.

Thus,  y=|x| is linear function.

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Answer:

The median is 79.

Step-by-step explanation:

Answer: 7 is the 10% of 70

Step-by-step explanation:

1. write 10% as 10/100 as we convert in this form to find the percentage.

2. 10/100 x 70 = 7

therefore the answer is 7

Answer:

Below

Step-by-step explanation:

You are counting the number of SUBSETS

Example  set  {2,7}

  has subsets { }   {2}  {7}  {2,7}

The number of subsets given a set of 'n'  is   2^n

When you calculate the number of combinations of "r" objects taken from a group of "n" objects, you are counting the number of different ways you can choose "r" items from the "n" items without regard to their order (i.e. their arrangement does not matter).

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. For example, if you have a group of 6 books and you want to know how many different combinations of 3 books you can choose, you would use the formula: C(6,3) = 6!/(3! * (6-3)!). The answer would be 20, meaning there are 20 different combinations of 3 books you can choose from the group of 6.

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Answer:

A. -63 is not a solution, B. 72 is a solution, C. 0 is a solution, D. 18 is not a solution.

Step-by-step explanation:

Therefore , the solution of the given problem of hexagon comes out to be 2700 meters square is the area of hexagon.

It is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles.

Here,

Given :

=> 300 meters

and

2400 meters

So,

=> area = 2400 +300 = 2700 meters square

Therefore , the solution of the given problem of hexagon comes out to be 2700 meters square is the area of hexagon.

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The equation in slope intercept form is : [tex]y = \frac{1}{8} x - 223.05[/tex]

The slope intercept form is a process used to determine the equation of a straight line in the coordinate plane. It can be used to determine the equation of a line when given the slope of the straight line and the y-intercept

The slope-intercept form of a line is:

y = mx+b

where m is the slope of the line and b is an intercept of the y-axis.

[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

[tex]m = \frac{26.7 - 23.2 }{1998- 1970}[/tex]

[tex]m = \frac{1}{8}[/tex]

So,

[tex]y = \frac{1}{8} x + b[/tex]

To find b we get the point (1970, 23.2) and introduce it in the previous equation.

[tex]23.2= \frac{1}{8} (1970)+ b[/tex]

⇒ 23.2 - 246.25 = b

⇒ b = - 223.05

Then, the equation is : [tex]y = \frac{1}{8} x - 223.05[/tex]

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1. The surface area of a triangular pyramid is (P * h) / 2.

So, (12 * 2) / 2 = 12 sq ft

2. The surface area of a square pyramid is B * P / 2.

So, 4 * 16 / 2 = 32 sq in

3. The surface area of a square pyramid is B * P / 2.

So, 12 * 48 / 2 = 288 sq m

4. The surface area of a triangular pyramid is (P * h) / 2.

So, (45 * 12) / 2 = 270 sq yds

5. The surface area of a square pyramid is B * P / 2.

So, 6 * 24 / 2 = 72 sq ft

6. The surface area of a triangular pyramid is (P * h) / 2.

So, (15 * 4) / 2 = 30 sq ft

7. The surface area of a square pyramid is B * P / 2.

So, 4 * 16 / 2 = 32 sq in

8. The surface area of a square pyramid is B * P / 2.

So, 10 * 40 / 2 = 200 sq m

9. The surface area of a triangular pyramid is (P * h) / 2.

So, (45 * 8) / 2 = 180 sq yds

10. The surface area of a square pyramid is B * P / 2.

So, 16 * 64 / 2 = 512 sq ft

11. The surface area of a square pyramid is B * P / 2.

So, 5 * 20 / 2 = 50 sq ft

12. The surface area of a triangular pyramid is (P * h) / 2.

So, (45 * 8) / 2 = 180 sq ft

13. The surface area of a square pyramid is B * P / 2.

So, 13 * 52 / 2 = 338 sq in

14. The surface area of a square pyramid is B * P / 2.

So, 7 * 28 / 2 = 98 sq m

15. The surface area of a triangular pyramid is (P * h) / 2.

So, (27 * 25) / 2 = 675 sq yds

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The complete question goes thus:

Calculate The Surface Area Of Each Pyramid With The Following Values. (P = Perimeter, B = One Side Of The Base, S=Side, H=Height). Number Of Sides Is Given In Each Problem. The First Two Have Hints To Let You Know What The Shape Of The Base Is...

1. P = 12 ft, s = 4 ft, b = 4 ft, h=2 ft, 3

sides (base is a triangle)

2. b = 4 in, P = 16 in, s = 12, 4 sides

(base is a square)

3. P = 48 m, b = 12 m, s=12, 4 sides

4. P = 45 yds, b = 15 yds, s=15, h=12,

3 sides

5. b = 6 ft, P = 24 ft, s=6, 4 sides

6. P = 15 ft, b = 5 ft, s=5 ft, h= 4, 3

sides

7. b = 4 in, P = 16 in, s-11, 4 sides

8. P = 40 m, b = 10 m, s-10, 4 sides

9. P = 45 yds, b = 15 yds, s=10, h=8,

3 sides

10. b = 16 ft, P = 64 ft, s=8, 4 sides

11. b = 5 ft, P = 20 ft, s=7, 4 sides

12. P = 45 ft, b = 15 ft, s=10, h=8, 3

sides

13. b 13 in, P = 52 in, s=11, 4 sides

=

14. P = 28 m, b = 7 m, s=8, 4 sides

15. P = 27 yds, b = 9 yds, s=30, h=25,

3 act

The required end behavior of the graph of y = f(x) is given as, x → ∞, y→-∞ and when x → -∞, y →∞. Option B is correct.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
As we can see in the graph of y =f(x)

As x approaches -∞ y approaches ∞, and as As x approaches ∞ y approaches -∞

Thus, the required end behavior of the graph of y = f(x) is given as, x → ∞, y→-∞ and when x → -∞, y →∞. Option B is correct.

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The arc angle mWX is 9 degrees.

An inscribed angle is the angle that is formed by the intersection of two chords on the circumference of a circle. Therefore, inscribed angles subtended by the same arc are equal.

Hence,

3x - 20 = 15x - 64

3x - 15x = - 64 + 20

- 12x = -44

divide both sides by -12

x = -44 / -12

x = 3.7

Let's find the arc angle

Hence,

mWX = 3(3.7) - 20

mWX = 11 - 20

mWX = 9 degrees

The answer can't be negative.

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y=-1/4x-2 is the  equation of the line that is perpendicular to y = 4x + 6 and passes through the point (8, −4).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The slope of perpendicular line will be -1/m

In the equation  y = 4x + 6  the slope m is 4

The slope of perpendicular line will be -1/4

Now let us find the y intercept

-4=-1/4(8)+b

-4=-2+b

-2=b

y=-1/4x-2 is the equation of perpendicular line.

Hence, y=-1/4x-2 is the  equation of the line that is perpendicular to y = 4x + 6 and passes through the point (8, −4).

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The polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros is a³ - 5a³ - 4(5 - √8)a.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

For the given factors, write the factors in the coefficient form, following form:

a, (a - 5), (a + 5 - √8)

Multiply all the factors:

(a)(a - 5) = a² - 5a

(a² - 5a) (a + 5 - √8) = a³ + (5 - √8)a - 5a² - 5(5 - √8)a

Combine the like terms:

a³ - 5a³ - 4(5 - √8)a

Hence, the polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros is a³ - 5a³ - 4(5 - √8)a.

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Answer:

x=291/X

Step-by-step explanation:

it mean 29=xX-262

xX=29+262

xX=291

x=291/X

Answer:

0.712GB

Step-by-step explanation:

1 day = 24hrs = 24*60 seconds

speed 890KB per 18 seconds

so 24*60/18 = 80 *890KB= 71200KB

1GB = 100000KB

so 0.712GB

The value of x in the isosceles triangles is 169 degrees

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

A series of isosceles triangles are drawn between two red line segments

Also, we have

a = 11°

Because the triangles are isosceles triangles, we have the following equation

x + a = 180

Substitute the known values in the above equation, so, we have the following representation

x + 11 = 180

Evaluate the like terms

x = 169

Hence, the value of x is 169

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Answer:

4

Step-by-step explanation: