Ronald is walking at a rate of 3 miles per hour. If he walks for 2 hours and then runs at a rate of 6 miles per hour for another 1 hour, how far did Ronald travel in total?

Answer:

Step-by-step explanation:

Distance between 2Points XY=Distance between 2 points YZ=7.615

Distance between 2 points ZX=5.6568

Hence it is an isosceles triangle

If the Raj’s bathtub is draining at rate of 1.5 gallons of water per-minute, then the range will be (c) all real numbers such that 0 ≤ y ≤ 40.

The "Range" of function is defined as the set of all possible "output-values'.

The amount of water remaining in the bathtub is decreasing as it drains, so the range of the function is bounded below by 0 (because we cannot have negative water in the bathtub) and above by 40 (the initial amount of water in the bathtub).

Looking at the given values of y, we can see that the value of "y" lies between 0 and 40.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining.

   x          y

   0         40

  0.5     39.25

    1        38.5  

   1.5       37.75

What is the range of this function?

(a) all real numbers such that y ≤ 40

(b) all real numbers such that y ≥ 0

(c) all real numbers such that 0 ≤ y ≤ 40

(d) all real numbers such that 37.75 ≤ y ≤ 40.

a) On a coordinate plane, points are at (1, 48.1), (2, 50.9), (3, 62.4), (4, 67), (5, 76.5), (6, 83.9), (7, 86.8), (8, 88.1), (9, 79.2), (10, 69.9), (11, 59.5), (12, 49.6)  best represents the data.

This is because the data represents a set of paired values, with the months as the independent variable (x) and the average maximum monthly temperature as the dependent variable (y). A scatter plot is the appropriate graph for displaying this type of data.

Option a shows the correct placement of the data points on a scatter plot, with the x-axis representing the months and the y-axis representing the average maximum monthly temperature. The points are clearly organized in a sequence from January to December, with an upward trend in temperature from the winter months to the summer months, followed by a gradual decrease in temperature in the fall and winter months.

Option b has the correct range of temperatures, but the points are not arranged in a logical sequence and are scattered randomly across the graph. Option c also has a similar issue with random placement of points and does not reflect the actual values in the data set. Option d only has three points and does not represent the complete data set.

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2401/16 square inches

Step-by-step explanation:

Given:

The quilt made by Spencer had a 7×7 array of different color square patches such that each patch is  in long.

To find: the area of the whole quilt

Solution:

Side of each quilt =

Quilt is in the form of a square such that area of square is given by

Therefore, area of quilt =   square inches

Answer:

c

Step-by-step explanation:

Answer:

(2,1)

Step-by-step explanation:

The line 4y - 2x = 0 can be written in slope-intercept form as y = 1/2x.

So any point that satisfies this equation will lie on the line. For example, the point (2,1) satisfies the equation:

4(1) - 2(2) = 0

So the point (2,1) is on the line.

Answer:

If the diameter of the circle increases to 60 inches, the new area would be approximately 2700 square inches.

Answer:

Area of shaded region:

12r^2 - (2(2r^2) + 2πr^2) =

12r^2 - 4r^2 - 2πr^2 =

(2r^2)(4 - π)

Probability of point chosen in shaded region:

(2r^2)(4 - π)/(12r^2) = (4 - π)/6 = .143 = 14.3%

Answer:

13 + 8 + 13 + (1/2)(8π) = 34 + 4π feet

= 46.57 feet

For the function f(x) = -2x² + 5x + 7 the slope of the secant line between x = -3 and x = 5 is -4

Consider the function f(x) = -2x² + 5x + 7

We need to find the slope of the secant line between x = -3 and x = 5

We know that the slope of secant line for the function f(x) on the interval [a, b] is given by the formula,

m = [f(b) - f(a)] / (b - a)

Let [a, b] = [-3, 5]

For x = -3 the value of the function would be,

f(-3) = -2(-3)² + 5(-3) + 7

      = -2(9) - 15 + 7

      = -18 - 15 + 7

      = -26

And the value of the function for x = 5 would be,

f(5) = -2(5)² + 5(5) + 7

      = -2(25) - 25 + 7

      = -50 - 15 + 7

      = -58

Using above formula the slope would be,

m = [f(5) - f(-3)] / (5 - (-3))

m = [-58 - (-26)] / 8

m = (-58 + 26) / 8

m = -4

Thus, the required slope is -4

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Answer:

Slope = 1

Step-by-step explanation:

A secant line is a straight line that intersects a curve at two or more points.

Given a curve represented by a function f(x), a secant line is determined by choosing two distinct points on the curve, (x₁, f(x₁)) and (x₂, f(x₂)).

The secant line passes through these two points and can be represented by a linear equation in the form y = mx + b, where m is the slope of the secant line and b is the y-intercept.

The slope of the secant line between the points (x₁, f(x₁)) and (x₂, f(x₂)) is given by the formula:

[tex]m = \dfrac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]

To find the slope of the secant line between x = -3 and x = 5 for the function f(x) = -2x² + 5x + 7, first find f(-3) and f(5).

[tex]\begin{aligned}f(-3)&=-2(-3)^2+5(-3)+7\\&=-2(9)-15+7\\&=-18-15+7\\&=-26\end{aligned}[/tex]

[tex]\begin{aligned}f(5)&=-2(5)^2+5(5)+7\\&=-2(25)+25+7\\&=-50+25+7\\&=-18\end{aligned}[/tex]

Input the values into the slope formula:

[tex]m = \dfrac{f(5) - f(-3)}{5 - (-3)}=\dfrac{-18-(-26)}{5+3}=\dfrac{8}{8}=1[/tex]

Therefore, the slope of the secant line between x = -3 and x = 5 is 1.

Answer:

Step-by-step explanation:

The required probability is simply the (shaded area)/(area of the whole box)

The area of the whole box would be:

6r*2r = 12 r^2

The shaded area is tough to calculate, but you can get the

white area instead.

The left hole (white area) consists of a semi-circle and a rectangle.

The center hole is a circle.

The right hole (white area) consists of a semi-circle and a rectangle.

The 2 semi-circles in the left and right hole combine to be a circle.

The 2 rectangles in the left and right hole combine to be a square.

The total area of holes are:

(area of circle)*2 + (area of square)       ### 2 circles 1 square in total

=r^2*pi*2 + (2r)^2

=r^2*pi*2 +4*r^2

then we can get the shaded area by:

(area of the whole box) - (The total area of holes)

= 12 r^2 - (r^2*pi*2 +4*r^2)

=8*r^2 - r^2*pi*2

Finally:

(shaded area)/(area of the whole box)

=(8*r^2 - r^2*pi*2)/(12 r^2)

=(8-pi*2)/(12)

=0.143067891

=14.3% (corr. to 3 sig. fig.)

Answer:

Quick internet search:

Answer:

G^-1(t)=t/7+4

Step-by-step explanation:

G(t) = 7(t - 4)

y = 7(x - 4)

x = 7(y - 4)

x/7 = y - 4

y = x/7 + 4

G^-1(t) = t/7 + 4

Answer: G^-1(t)=t/7+4

Answer:

Step-by-step explanation:

just do how tall times the diamiter divided by the

Figure O is reflected followed by a translation of 4 units in the left direction.

Given that:

Figure O and Figure P are shown on the graph.

The translation does not change the shape and size of the geometry. But changes the location.

Figure O is translated leftward by 4 units.

The reflection does not change the shape and size of the geometry. But flipped the image. A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersect the line of reflection at a right angle.

The translated figure O is reflected across the x-axis.

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Answer:

  -9 11/12

Step-by-step explanation:

You want the product of 2 5/6 and -3 2/4.

The product of mixed numbers is often most easily computed by rewriting them to improper fractions.

  (2 5/6)(-3 2/4) = (17/6)(-7/2) = -(17·7)/(6·2) = -119/12

  = -(108/12 +11/12)

  = -9 11/12

__

Additional comment

Your calculator can probably help you with this.

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The coordinates of the fourth vortex of the rectangular piece of material drawn by Freddy would be  (4. 6, - 3 ).

Rectangles are quadrilaterals which have two sets of parallel lines. This means that two sets of sides are equal which are the opposite ones. This means that when plotted on a coordinate plane, of the four points, the x - values should repeat twice and the y - values should repeat twice as well.

They would do so by alternating with each other. This means that in a rectangle with (-2, -3), (- 2 . 3, 1 . 6), ( 4 . 6 , 1. 6 ), the fourth vertex would be the two x and y values that are yet to repeat which would be:

( 4. 6, - 3 ).

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The solution to all parts from a to f is shown below.

A) Matrix A:

[ 2  -3 ]

[ 4   3 ]

B) The determinant of matrix A is:

det(A) = (2*3) - (-3*4) = 6 + 12 = 18

C) Matrix X:

[ -8  -3 ]

[ -34  3 ]

D) The determinant of matrix X is:

det(X) = (-8*3) - (-3*-34) = -24 - 102 = -126

E) Matrix Y:

[ 2  -8 ]

[ 4  -34 ]

F) The determinant of matrix Y is:

det(Y) = 2(-34) - (-8) (4) = -68 + 32 = -36

G) Using Cramer's rule, we can solve for x and y as follows:

x = det(X) / det(A) = -126 / 18 = -7

y = det(Y) / det(A) = -36 / 18 = -2

Therefore, the solution to the system is (-7, -2).

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Answer:  -5, 3

Step-by-step explanation:

Equation:

x² + 2x -15 = 0   The equation is already set =0   so you will factor.

To factor, find 2 numbers that multiply to the last term (-15) but add up to the middle term (+2).  Be careful with signs,  signs matter

+5 and -3 multiply to -15 but add up to the +2    so these are your factored numbers

put it in factored form

(x+5)(x-3)=0         set each parenthesis =0 to solve for x

x+5 =  0                    x-3=0

x= -5        and           x=3

Using rules for logarithms we can see that the statement is false.

Here we have the equation:

logₐ(x^3 + y^3) = 3logₐ(x) + 3logₐ(y)

And we want to see if it is true.

First, remember two rules:

logₐ(x^n) = n*logₐ(x)

and:

logₐ(x) + logₐ(y) = logₐ(x*y)

Then, the right side of the statement can be rewritten as:

3logₐ(x) + 3logₐ(y)

3(logₐ(x) + logₐ(y)) = 3*logₐ(x*y) = logₐ((x*y)^3)

And that is different to what we got in the statement, so the statement is false.

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The increase in Fahrenheit temperature  is of 12.6 degrees.

The formula to have a change of units is:

To convert Celsius to Fahrenheit, you can use the formula:

°F = (°C x 1.8) + 32

(So you are correct, the rate is 9/5 = 1.8)

The increase of 7°C wold be given by the difference:

increase = ((°C + 7°) x 1.8) + 32 - (°C x 1.8) + 32

Solving that equation we can see that

increase =  12.6°F

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Answer:

he increase in Fahrenheit temperature  is of 12.6 degrees.

What is the increases in Fahrenheit temperature?

The formula to have a change of units is:

To convert Celsius to Fahrenheit, you can use the formula:

°F = (°C x 1.8) + 32

(So you are correct, the rate is 9/5 = 1.8)

The increase of 7°C wold be given by the difference:

increase = ((°C + 7°) x 1.8) + 32 - (°C x 1.8) + 32

Solving that equation we can see that

increase =  12.6°F

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Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{x}{24}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = 24 ( divide both sides by 2 )

x = 12

The cord will begin to stretch after approximately 1.46 seconds.

h(t) = -16t^2 + V0t + h0

149 = h0 - h(t)

Substituting h0 = 241 and h(t) = -16t^2 + V0t into this equation, we get:

149 = 241 - (-16t^2 + V0t)

we get:

16t^2 - V0t - 92 = 0

4(16)(-92) / (2(16)

t = sqrt(1856) / 32

Using a calculator, we get:

t ≈ 1.46 seconds

Therefore, the cord will begin to stretch after approximately 1.46 seconds.

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Answer:

Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.

Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:

x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)

So the value of x is option B: 8√2 / 2 or simplified, 4√2.

Answer:

6

Step-by-step explanation:

this is if you meant: Jasmine sold 5 cherry pies and 12 lemonade how much more did Jasmine sell of lemonade than cherry pies

The number of weeks that Vanessa ran for the number of miles given would be = 24 weeks

The amount of distance that Vanessa covers for a week = 4 miles

The amount of weeks it will take for her to cover 96 moles would be = ?

That is;

1 week = 4 miles

X weeks = 96 miles

Make X the subject of formula;

X = 96× 1/4

= 24 weeks

Therefore Vanessa will be able to cover 96 miles in only 24 weeks.

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The 99% confidence interval for the population proportion p is (0.776, 0.824).

To find the 99% confidence interval for a proportion, we can use the formula:

CI = p^ ± z*(SE)

where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.

For a 99% confidence interval, the critical value z is 2.576.

Substituting the given values into the formula, we have:

CI = 0.80 ± 2.576*(0.03/√200)

Simplifying this expression, we have:

CI = 0.80 ± 0.024

This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.

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