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A sample was taken of dogs at a local dog park on two random days. The counts are displayed in the table below. If there are estimated to be 50 dogs at the park at any given time, which proportion could be used to find the average number of shepherd mixes at the park at any given time?

Answer:

Step-by-step explanation:

y=−7x+3x intercept when y = 0so-7x + 3 = 0-7x = -3   x = 3/7y intercept when x = 0 so y = 3

answer

x intercept (3/7 , 0)y intercept (0, 3)

It would take the newer pump 4.5 hours to drain the pool working alone.

Given that,

It takes an older pump twice as long to drain a certain pool as it does a newer pump.

Let us assume that,

The time it takes for the newer pump to drain the pool alone is x hours.

Hence, According to the information given, the older pump takes twice as long, so it would take 2x hour to drain the pool alone.

Now, When both pumps work together, their combined rate of draining the pool is additive.

Therefore, the equation is,

[tex]\dfrac{1}{x} + \dfrac{1}{2x} = \dfrac{1}{3}[/tex]

Simplify the equation for x,

[tex]\dfrac{(2 + 1)}{2x} = \dfrac{1}{3}[/tex]

[tex]\dfrac{(3)}{2x} = \dfrac{1}{3}[/tex]

Cross multiplication,

[tex]3 \times 3 = 2x[/tex]

[tex]2x = 9[/tex]

Dividing both sides by 2:

[tex]x = 4.5[/tex]

Therefore, it would take the newer pump 4.5 hours to drain the pool working alone.

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a =16 is the solution of the given equation.

To solve the equation 6 = a/4 + 2, we'll perform two steps to isolate the variable 'a'.

Step 1: Subtract 2 from both sides of the equation:

6 - 2 = a/4 + 2 - 2

4 = a/4

Step 2: Multiply both sides of the equation by 4 to get rid of the fraction:

4 * 4 = (a/4) * 4

16 = a

Therefore, the solution to the equation is a = 16.

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Answer:

A. 55 dimes and 165 quarters

Step-by-step explanation:

Given,

The number of pennies in the Jar = 220,

∵ There are 3 quarters for every 4 pennies,

i.e. 4 pennies = 3 quarters,

⇒ 1 penny = [tex]\frac{3}{4}[/tex] quarter

⇒ 220 pennies = [tex]220\times \frac{3}{4}[/tex]

[tex]=\frac{660}{4}[/tex]

= 165 quarter.

Therefore, there are 165 quarters.

Now, there is 1 dime for every 3 quarters,

i.e.  3 quarters = 1 dime

⇒ 1 quarter = [tex]\frac{1}{3}[/tex] dime,

⇒ 165 quarters = [tex]\frac{165}{3}[/tex] = 55 dimes.

Therefore, there are 55 dimes.

Option 'A' is correct.

perimeter = 2l +2w

length = 22

perimeter = 60

 60 = 2(22) +2w

60 = 44 +2w

 subtract 44 from both sides

16 = 2w

w = 16/2

w = 8

 width is 8 inches

It is found that there are 43,800 minutes in a month.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We knowt that there are 365 days per year, 24 hours per day, 12 months per year, and 60 minutes per hour.

1 day = 24 hour

1 hour = 60 minutes.

1 minutes = 60 seconds

Therefore, 24 hours = 24 x 60 = 1440 minutes

There are 1440 minutes in one day.

Then 30 days = 30 x 1440 = 43,800

Hence, It is found that there are 43,800 minutes in a month.

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Answer: 1. A) 3x−4y=10

2. [tex]y=-\frac{x}{4}+3[/tex]

3. In the attachment.

Explanation:

1. Given equation=[tex]y=\frac{3}{4}x-\frac{5}{2}[/tex]

To reduce it into standard form , multiply both sides by 4,we get

[tex]4y=4(\frac{3}{4}x-\frac{5}{2})\\\Rightarrow4y=3x-10......[distributive\ property]\\\Rightarrow3x-4y=10[/tex] which is option A.

2. Given linear equation : x+4y=12

The standard slope intercept form is given by y=mx+c where m is the slope and c is the constant.

To reduce given linear equation subtract x from both sides, we get

4y=12-x

Divide 4 on both sides.

[tex]\Rightarrow\ y=\frac{12-x}{4}=3-\frac{x}{4}\\\Rightarrow\ y=-\frac{x}{4}+3[/tex] is the slope-intercept form of the linear equation x + 4y = 12.

3. To graph equation [tex]y=\frac{1}{2}x[/tex] on the coordinate plane.

We need to find points to plot the line

Put x=0,we get y=0

Put x=2,we get y=1

Thus we have points (0,0) and (2,1) to plot the line on the graph.

Answer: 1. A) 3x−4y=10

Step-by-step explanation:

Final answer:

The expected number of heads and tails when tossing a coin 10 times is 5 each.

Explanation:

If you toss a coin ten times:

Expected number of heads: 5

Expected number of tails: 5

This is because for each toss, the probability of getting a head is 0.5 (50%) and the same for a tail. Over multiple tosses, the outcomes tend to approach these expected values.

Answer:

the answer is C. -5/7

Answer:

The correct answer is f(-2)= -2

Step-by-step explanation:

the measure of angle ABC (m∠ABC) is 130 degrees. it's essential to recognize that the sum of the angles along a straight line is always 180 degrees.

In this case, we have two angles, 2x and 5x+5, forming a straight line with an unknown angle (m∠ABC). So, we set up the equation:

2x + 5x + 5 = 180

Next, combine the like terms on the left side:

7x + 5 = 180

7x = 180 - 5

7x = 175

x = 175/7

x = 25

Therefore, the measure of angle ABC = 5x + 5

= 5(25) + 5

=130 degree

So, the measure of angle ABC (m∠ABC) is 130 degrees.

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the value of (t) that satisfies the equation is approximately (37.6992).

Let's solve the equation [tex]\(-\frac{t}{4} = -3\pi\) for \(t\).[/tex]

Step 1: Multiply both sides by \(-4\) to isolate \(t\).

[tex]\[-\frac{t}{4} \times (-4) = -3\pi \times (-4)\][/tex]

This simplifies to:

[tex]\[ t = 12\pi \][/tex]

Step 2: Substitute the value of \(\pi\) to get the final answer.

[tex]\[ t = 12 \times 3.14159 \][/tex]

[tex]\[ t = 37.6992 \][/tex]

Therefore, the value of ( t ) is approximately ( 37.6992 ).

To solve the equation [tex]\(-\frac{t}{4} = -3\pi\) for \(t\)[/tex] , we first want to isolate (t) on one side of the equation. To do this, we can multiply both sides of the equation by (-4). This cancels out the fraction and leaves us with (t) on the left side:

[tex]\[-\frac{t}{4} \times (-4) = -3\pi \times (-4) \\t = 12\pi\][/tex]

Now, to get the numerical value of \(t\), we substitute the value of \(\pi\), which is approximately \(3.14159\), into the equation:

[tex]\[ t = 12 \times 3.14159 \][/tex]

[tex]\[ t \approx 37.6992 \][/tex]

Therefore, the value of (t) that satisfies the equation is approximately (37.6992).

complete question

−t/4=−3π

What is the answer to T

Answer:

x ≤ 7

Yuuupeeee

Answer:  The required slope-intercept form is [tex]y\leq 3x+21.[/tex].

Step-by-step explanation:  We are given to write the following inequality in slope-intercept form :

[tex]-6x+2y\leq 42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the slope-intercept form of an inequality of the given form is as follows :

[tex]y\leq mx+c,[/tex] where m is the slope and c is the y-intercept.

From inequality (i), we have

[tex]-6x+2y\leq 42\\\\\Rightarrow 2y\leq6x+42\\\\\Rightarrow y\leq\dfrac{6}{2}x+\dfrac{42}{2}\\\\\Rightarrow y\leq 3x+21.[/tex]

Thus, the required slope-intercept form is [tex]y\leq 3x+21.[/tex].

Answer: The cost of 1 lemon is $1.2 and the cost of 1 lime is $0.4.

Step-by-step explanation:

Let x be the cost of 1 lemon and y be the cost of 1 lime.

Then for Ray, the equation representing total price will be :-

[tex]5x+3y=7.20[/tex]................................(1)

For Lia, the equation representing total price will be :-

[tex]4x+6y=7.20[/tex]..................................(2)

Dividing 2 on the both sides of equation (2), we get

[tex]2x+3y=3.60[/tex]...............................(3)

Subtracting (3) from (1), we get

[tex]3x=3.6\\\\\Rightarrow x=1.2[/tex]

Substitute value of x in (3), we get

[tex]2(1.2)+3y=3.6\\\\\Rightarrow2.4+3y=3.6\\\\\Rightarrow3y=1.2\\\\\Rightarrow y=0.4[/tex]

Thus, the cost of 1 lemon is $1.2 and the cost of 1 lime is $0.4.

Answer:

option 3 aka c

Step-by-step explanation:

In mathematics, specifically geometry, the least angle measure by which a regular, symmetric figure can be rotated to map onto itself is usually 90°. This concept falls under the umbrella of rotational symmetry.

The question is about rotation of objects in geometry. To identify the least angle measure for a figure to map onto itself, we need to know the shape of the figure. However, assuming the figure is regular and symmetric (a square or a rectangle for example), the least angle measure by which it can be rotated to map onto itself is 90°.

It's important to remember the concept of rotational symmetry. A figure has rotational symmetry if it can be rotated less than 360° around a central point and still appear the same. For instance, a regular rectangle or square has a rotational symmetry of 90°, since we can rotate it 90 degrees and it appears the same.

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Answer:

S''(-3/2, 9/2)

Step-by-step explanation:

In a dilation, the coordinates of every ordered pair in the pre-image are multiplied by the scale factor to create the ordered pairs of the image.

The first dilation has a scale factor of 1/2.  This maps:

R(-6, 10)→R'(-6/2, 10/2) = R'(-3, 5)

S(-2, 6)→S'(-2/2, 6/2) = S'(-1, 3)

T(-10, 0)→T'(-10/2, 0/2) = T'(-5, 0)

The second dilation has a scale factor of 3/2:

R'(-3, 5)→R''(-9/2, 15/2)

S'(-1, 3)→S''(-3/2, 9/2)

T'(-5, 0)→T''(-15/2, 0)

This makes S'' have coordinates (-3/2, 9/2).

Answer: a :)

Step-by-step explanation: