mr.james runs a petting zoo. he records the number of visitors each week,v, t weeks, after opening the petting zoo. according to the table what is the average rate of change over the interval [2,5]
a.57 visitors per month
b. 28 visitors per month
c. 36 visitors per month
d 19 visitors per month ​

Two buckets of seawater contain [tex]13\frac{28}{40}[/tex] kg of salt.

Step-by-step explanation:

Amount of salt in 1 kg water = [tex]\frac{1}{40}\ kg[/tex]

It is given that;

1 liter = [tex]1\frac{12}{125} = \frac{137}{125}\ kg[/tex]

500 liters = [tex]500*\frac{137}{125} = \frac{68500}{125}[/tex]

500 liters = 548 kilogram

As,

1 kg of seawater = [tex]\frac{1}{40}\ kg[/tex] of salt

548 kilograms = [tex]\frac{1}{40}*548[/tex]

548 kilograms = [tex]13\frac{28}{40}[/tex] kilograms of salt

Two buckets of seawater contain [tex]13\frac{28}{40}[/tex] kg of salt.

Keywords: unit rate, multiplication

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Answer:

The area would be 111.41 unit² ( approx )

Step-by-step explanation:

Given,

KLMN is a trapezoid,

In which KL=MN, KM=15, m∠MKN=49°,

Suppose O and P are point in the segment LM, ( shown below )

Such that,

KN = OP,

In triangle MKO,

m∠KMO = 49° ( ∵ KM ║ LM, using alternative interior angle theorem ),

KM = 15 unit ( given )

[tex]\sin 49^{\circ} = \frac{KO}{KM}[/tex]

[tex]\implies KO = KM \sin 49^{\circ}=15 \sin 49^{\circ}[/tex]

i.e. height of the trapezoid KLMN is 15 sin 49°,

Again,

[tex]\cos 49^{\circ} = \frac{OM}{KM}[/tex]

[tex]\implies OM = KM \cos 49^{\circ}=15 \cos 49^{\circ}[/tex]

[tex]OP + PM = 15 \cos 49^{\circ}[/tex]

[tex]\implies KN + PM = 15 \cos 49^{\circ}----(1)[/tex]

Now, in right triangles KOL and NPM,

KL = MN,

OK = NP

By HL postulate of congruence,

Δ KOL ≅ Δ NPM

By CPCTC,

LO = PM,

⇒ LM = LO + OP + PM = PM + OP + PM = OP + 2PM = KN + 2PM-----(2),

Thus, the area of the trapezoid KLMN,

= 1/2 × height × sum of opposite parallel sides

[tex]=\frac{1}{2}\times KO\times (KN+LM)[/tex]

[tex]=\frac{1}{2}\times KO\times (KN+KN + 2PM)[/tex]

[tex]=\frac{1}{2}\times KO\times (2KN+2PM)[/tex]

[tex]=KO\times (KN+PM)[/tex]

[tex]=15 \sin 49^{\circ}\times 15 \cos 49^{\circ}[/tex]

[tex]=111.405157734[/tex]

[tex]\approx 111.41\text{ square unit }[/tex]

The area of a triangle can be found using the formula 1/2 x base x height. For a base of 166 mm and height of 930 mm, the area is 77.19 cm². However, for trapezoid KLMN, additional information is needed to calculate its area.

To find the area of a trapezoid, especially when it has special properties like equal non-parallel sides (as trapezoid KLMN does with KL equal to MN), we often need to break it down into simpler shapes such as triangles and rectangles. However, with the information given, it's not straightforward to calculate the area of the trapezoid without additional height or angle information. The area of a triangle can be calculated using the formula ½ × base × height. For example, if you have a triangle with a base of 166 mm and height of 930.0 mm, the area is calculated as ½ × 166 mm × 930.0 mm which equals 77190 mm² or 77.19 cm² when converted to square centimeters, maintaining the proper number of significant figures.

Answer:

The length of A'B' is 15 units

Step-by-step explanation:

As line segment AB has end points

The distance formula to calculate the distance between two points is given by:

[tex]{\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}}[/tex]

[tex]{\displaystyle d={\sqrt {(20-4)^{2}+(4-16)^{2}}}}[/tex]

[tex]d=\sqrt{16^2+(-12)^2}[/tex]

[tex]d=\sqrt{256+144}[/tex]

[tex]d=\sqrt{400}[/tex]

[tex]d=20[/tex]

[tex]d=20[/tex] is also the length of the line segment AB.

As segment will be dilated with a scale factor of 3/4 and a center at the origin to create A'B'.

So,

The length of A'B' can be obtained by multiplying the length of AB by 3/4

Therefore,

The length of A'B' = 3/4 × 20 = 15

So, the length of A'B' is 15 units.

Keywords: dilation, distance formula, length, line segment

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Answer:

(i) [tex]k\in (-\infty,-16)\cup (0,\infty)[/tex]

(ii) [tex]p\in (9,\infty)[/tex]

Step-by-step explanation:

(i) Given equation

[tex]2x^2+4x+2=k(x+3)[/tex]

Rewrite this equation as quadratic equation in the standard form:

[tex]2x^2+4x+2=kx+3k\\ \\2x^2+4x+2-kx-3k=0\\ \\2x^2+(4-k)x+(2-3k)=0[/tex]

If the equation has two distinct real roots, then its discriminant is greater than 0. Find the discriminant:

[tex]D=(4-k)^2-4\cdot 2\cdot (2-3k)=16-8k+k^2-16+24k=k^2+16k[/tex]

Solve the inequality [tex]D>0:[/tex]

[tex]k^2+16k>0\\ \\k(k+16)>0\Rightarrow k\in (-\infty,-16)\cup (0,\infty)[/tex]

(ii) The quadratic expression is always greater than 0 when:

[tex]p>0\\ \\D<0[/tex]

Find the discriminant:

[tex]D=6^2-4\cdot p\cdot 1=36-4p[/tex]

Solve the inequality [tex]D<0:[/tex]

[tex]36-4p<0\\ \\-4p<-36\\ \\4p>36\\ \\p>9[/tex]

Assuming that [tex]p>0[/tex] and [tex]p>9,[/tex] you get

[tex]p>9\Rightarrow p\in (9,\infty)[/tex]

Answer:

The equation [tex]2+\frac{1}{3}n=8[/tex] represents the corresponding statement ' two more than 1/3 of a number is eight'.

Step-by-step explanation:

As the sentence statement is

"Two more than 1/3 of number is eight".

Lets decode this sentence and write the corresponding mathematical expression.

Hence, the equation [tex]2+\frac{1}{3}n=8[/tex] represents the corresponding statement ' two more than 1/3 of a number is eight'.

Keywords: equation, algebraic expression

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Answer:

19.6 gallons.

Step-by-step explanation:

She drives 225/ 10 = 22.5 miles per gallon of gas.

So driving 441 miles she will use 441/22.5

= 19.6 gallons.

Answer: Yes, it does, because each input value has an unique output value.

Step-by-step explanation:

First, you need to know when a relation is considered a function.

By definition, a relation is a function if an only if each input value has one and only one output value.

It is important to remember that the input values are the values of "x" and the output values are the values of "y".

Then, in this case, you can observe in the graph attached ( which shows the data for Camille’s puppy), that each x-value (Weeks) has an unique y-value (Weight in pounds).

Therefore, based on this and keeping on mind the explained before, you can conclude that the data for Camille’s puppy shows a function.

Answer:

Yes it does

Step-by-step explanation:

Because it passes the vertical line test and it only touches 1 unit point in the line no need for big explanations you cant understand

Answer:

5184

Step-by-step explanation:

first of all we sove multiplication of terms then addition

2592+1296+1296

5184 ans

Answer:

67

Step-by-step explanation:

9*7=63

13*5=65

23*3=69

Answer:

67

Step-by-step explanation:

Only number whose factors are 67 and 1

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Answer: 105.26

Step-by-step explanation: 9263/88=105.26

Do you have or own a calculator?

Answer:

The x-coordinate gives the solution of the original equation.

Step-by-step explanation:

Let us assume that the original equation is 2x = x + 5 ........... (1) and the solution that this equation has will be x = 5.

But, if we solve the equation by graphing each side as a separate line i.e. y = 2x and y = x + 5, then solving those two equations we get the solution x = 5 and y = 10.

Therefore, the x-coordinate i.e. x = 5 gives the solution of the original equation (1). (Answer)

Answer:

D

Step-by-step explanation:

edge

Answer:

option C. and D.

Step-by-step explanation:

For two quantities with inverse variation, as one quantity increases, the other quantity decreases. For example, when you travel to a particular location, as your speed increases, the time it takes to arrive at that location decreases.An inverse variation can be represented by the equation xy=k or y=kx .

Answer:

A) [tex]\frac{x+y+z}{3}[/tex]

Step-by-step explanation:

the formula for average is the sum of the digits, then divide that sum by the number of digits.

for example: let x = 1, let y = 2, let z = 3

so 1+2+3 is 6

then divided by the number of digits: 3

6/3=2

the average is 2

Answer:

B or D ( answer = 5 => Two options is one! One of the options should be 5)

Note: The width of a rectangle will never be negative.

Answer:

its d. 5

Step-by-step explanation:

Answer:

[tex]\frac{1}{20}[/tex]

Step-by-step explanation:

First, we need to look at the # of chips. There are a total of 25, 6 of which are blue.

This means that the chance of getting the first blue chip would be [tex]\frac{6}{25}[/tex]

As there is no replacement, the total number of chips is 24 and there are only 5 blue left. This gives us the chance of [tex]\frac{5}{24}[/tex]

Now all we need to do is mulitply these two and then simplify

[tex]\frac{6}{25} *\frac{5}{24} =\frac{30}{600} =\frac{1}{20}[/tex]

Answer:

1/20

Step-by-step explanatio

pick without replacement must mean pick it two times without put back the first chip

6/25 x 5/24 = 1/20

Answer:

11/10

Step-by-step explanation:

4/5-(-3/10)=4/5+3/10=8/10+3/10=11/10

Answer:

$768

Step-by-step explanation:

Let x bet the cost of 124 training session.

Given:

Maria finds a local gym that advertises 101 training sessions for $626.

Find the cost of 124 training sessions.

Solution:

cost for each training sessions [tex]=\frac{626}{101}[/tex]

cost for each training session = $6.19

So, we get cost of 124 training sessions by multiplication of cost of each training sessions and number of training sessions.

[tex]x=cost\ of\ each\ training\ session\times number\ of\ training\ session[/tex]

[tex]x=6.19\times 124[/tex]

[tex]x=767.56[/tex]

round 767.56≅768

[tex]x=768[/tex]

Therefore, the cost of 124 training sessions is $768

Complete Question with table is attached

Answer:

Miguel will save money of $90 if he earns $120.00

Step-by-step explanation:

The figure attached clearly shows the ratio of his earnings and savings. We have to find what would be the savings amount if he earn $120.00. So, first we have to calculate the percentage of ratio of his earnings and savings. As per the data given in the figure,

If he earns $10.00, he saves $7.50, calculate %amount he saves as below,

           [tex]\frac{\$ 7.50}{\$ 10.00} \times 100=0.075 \times 100=75 \%[/tex]

Likewise, calculate for all given data. If he earns $50.00 then he saves $37.50

           [tex]\frac{\$ 37.50}{\$ 50.00} \times 100=0.75 \times 100=75 \%[/tex]

If he earns  $150.00 and save $112.50,

           [tex]\frac{\$ 112.50}{\$ 150.00} \times 100=0.75 \times 100=75 \%[/tex]

So, from all above, it clearly tells that Miguel saves 75% of amount from his earnings. Now, given earnings as $120.00. By finding 75% of $120.00, we can find his savings in that amount. So,

             [tex]\frac{75}{100} \times \$ 120=0.75 \times 120=\$ 90[/tex]

Answer:

D. $90.00

Step-by-step explanation:

The best use of a sign chart when graphing rational functions involves identifying critical points, determining function values within each interval, and using this information to sketch the graph. The sign chart is a valuable tool for analyzing the behavior of a rational function on the x-axis.

The sign chart is a useful tool when graphing rational functions because it helps identify the intervals where the function is positive, negative, or undefined. This information is crucial for accurately sketching the graph of a rational function. Here is how to use a sign chart:

Identify the critical points of the function by setting the numerator and denominator equal to zero and solving for the variables.

Choose a value from each interval determined by the critical points and evaluate whether the function is positive or negative at that value.

Record the signs in a table or chart to visualize the pattern.

Use the sign chart to determine the intervals on the x-axis where the function is positive, negative, or undefined.

Plot any vertical asymptotes, holes, and x-intercepts on the graph.

Sketch the graph by using the information from the sign chart and locating the appropriate points.

Learn more about sign chart when graphing rational functions here:

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s>7

So, all values greater than 7 are included in the number line.

Step-by-step explanation:

We need to use number line to show numbers in the solution set of the inequality 2s+ 36 greater than 50

Solving and finding value of s:

2s+36>50

Adding -36 on both sides

2s+36-36>50-36

2s>14

Divide both sides by 2

s>7

So, all values greater than 7 are included in the number line.

The number line is shown in figure attached below

Keywords: Solving inequalities

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Answer:

A

Step-by-step explanation:

Took the test in edge

Answer:

The next 3 steps are

Step 4: [tex](x+2)=\pm \sqrt{10}[/tex]

Step 5: [tex]x=-2\pm \sqrt{10}[/tex]

Step 6: [tex]x=-2+\sqrt{10}\ or\x=-2-\sqrt{10}[/tex]

Step-by-step explanation:

Given:

Quadratic Equation is

x² + 4x - 6 = 0

To Find:

x = ?

Solution:

Step 1: x2 + 4x = 6

Step 2: x2 + 4x + 4 = 6 + 4

Step 3: (x + 2)2 = 10

Step 4: [tex](x+2)=\pm \sqrt{10}[/tex]

Step 5: [tex]x=-2\pm \sqrt{10}[/tex]

Step 6: [tex]x=-2+\sqrt{10}\ or\x=-2-\sqrt{10}[/tex]

Answer:

The acceleration of the object is 4 [tex]m/s^2[/tex]

Step-by-step explanation:

Given:

The mass of the object is = 2 kg

To Find:

Acceleration of the object = ?

Solution:

From the diagram below we know that

The resultant force is 8N along the east Direction

we know the acceleration is the"Rate of change of Velocity"

And Expressed as

F = ma

Where

F is the Force

m is the mass

Now substituting the known values we get

[tex]8 = 2 \times a[/tex]

[tex]a =\frac{8}{2}[/tex]

a=4 [tex]m/s^2[/tex]

Answer:

b the object is 4 m/s

Step-by-step explanation:

Answer:

m3=43°

Step-by-step explanation:

The total has to add up to 180° so 180-137 = 43°

Final answer:

The resulting solid will have four edges.

Explanation:

To find the number of edges in the resulting solid, let's first determine the dimensions of the solid after the wedges are cut off.

The original wooden block measures 2 inches by 2 inches by 3 inches. After cutting off the wedges, each side will be reduced by 2 inches (1 inch from each corner), resulting in a solid with dimensions of 2 - 2(1) = 0 inches by 2 - 2(1) = 0 inches by 3 - 2(1) = 1 inch.

A solid with dimensions of 0 inches by 0 inches by 1 inch is essentially a rectangular prism with one dimension equal to zero. Such a solid has six faces, eight vertices, and four edges.

Therefore, the resulting solid will have four edges.

I think you mean [tex]\sqrt{68}[/tex] so I will just simplify that.

[tex]\sqrt{68}=\sqrt{4}*\sqrt{17}=2\sqrt{17}[/tex]

answer: [tex]2\sqrt{17}[/tex]

the answer is 2√17

hope this helps :)))

Answer:

Y(n) = 7n + 23

Step-by-step explanation:

Given:

f(0) = 30

f(n+1) = f(n) + 7

For n=0 : f(1) = f(0) + 7

For n=1 :  f(2) = f(1) + 7

For n=2 : f(3) = f(2) + 7 and so on.

Hence the sequence is an arithmetic progression with common difference 7 and first term 30.

We have to find a general equation representing the terms of the sequence.

General term of an arithmetic progression is:

T(n) = a + (n-1)d

Here a = 30 and d = 7

Y(n) = 30 + 7(n-1) = 7n + 23

The question is missing the graph. So, it is attached below.

Answer:

(D) 3.2

Step-by-step explanation:

Given:

A graph of height versus width.

The equation given is:

Height = constant × Width

Rewriting in terms of 'constant'. This gives,

[tex]\textrm{Constant}=\frac{Height}{Width}[/tex]------------- (1)  

The width is plotted on the X-axis and the corresponding height is plotted on the Y-axis.

The four points plotted on the line are:

[tex](x, y) = (0.5, 1.6), (1, 3.2), (2, 6.4)\ and\ (3, 9.6)[/tex].

Now, any point will satisfy equation (1).

Consider the point (0.5, 1.6). So, height = 1.6 and width = 0.5. Therefore,

[tex]\textrm{Constant}=\frac{Height}{Width}\\\\\textrm{Constant}=\frac{1.6}{0.5}=3.2[/tex]

Also, we observe that for all the remaining points,

[tex]\dfrac{3.2}{1}=\dfrac{6.4}{2}=\dfrac{9.6}{3}=3.2[/tex].

Hence, the value of the constant is 3.2.

Option (D) is correct.

Answer:

[tex]f(5)=f(1)+12[/tex]

Step-by-step explanation:

If [tex]f(5) = f(4) + 3,[/tex] then

[tex]f(n)=f(n-1)+3[/tex]

So,

[tex]f(2)=f(2-1)+3=f(1)+3\\ \\f(3)=f(3-1)+3=f(2)+3=f(1)+3+3=f(1)+6\\ \\f(4)=f(4-1)+3=f(3)+3=f(1)+6+3=f(1)+9\\ \\f(5)=f(5-1)+3=f(4)+3=f(1)+9+3=f(1)+12[/tex]

Answer:f(5) = f(1) + 12

Step-by-step explanation:

Answer: 2/3

Step-by-step explanation:

7/9 - 2/8 =x 4/9

= 48/72

However, they are asking for the answer in SIMPLEST FORM.

48/72 in simplest form is 2/3.