Simplifly by using the distributive property 4r+3(r-2)

6 1/2 divided by  1/4

6.5 /0.25 =26 servings

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Answer:  The length of the chord AB is √2 r units.

Step-by-step explanation: Given in the question that Circle P is tangent to the X-axis at the point A and tangent to the Y-axis at the point B.

Also, the co-ordinates of centre of the circle P are C(r, r). See the attached image below.

We are to find the length of the chord AB, with end-points A and B as the points of tangency.

From the figure, we note that

the co-ordinates of the points A and B are  (0, r) and (r, 0) respectively.

As the X-axis and Y-axis are perpendicular to each other, so the lines parallel to them, OB and OA are also perpendicular to each other.

That is, ∠ACB = 90°.

This implies that the triangle ACB is a right-angled triangle.

Now, using Pythagoras theorem in ΔACB, we have

[tex]AB^2=CA^2+CB^2~~~~~~~~~~~~~~~~~~~~~(i).[/tex]

The lengths of the line segments CA and CB are calculated, using distance formula, as follows:

[tex]CA=\sqrt{(0-r)^2+(r-r)^2}=\sqrt{r^2}=r,\\\\CB=\sqrt{(r-r)^2+(0-r)^2}=\sqrt{r^2}=r.[/tex]

From equation (i), we get

[tex]AB^2=r^2+r^2\\\\\Rightrarrow AB^2=2r^2\\\\\Rightarrow AB=\sqrt2r~\textup{units}.[/tex]

Thus, the length of the chord AB is √2 r units.

A circle, tangent to the x-axis and y-axis, forms a square where its radius r is the side length. The chord, which is the diagonal, can be found using the Pythagorean theorem resulting to r√2.

In the given problem, a circle P is tangent to the x-axis and y-axis at two points. This means that the radius of the circle is the distance from the center to either axis, which are both r, as the coordinates of the center are (r,r). We are asked to find the length of the chord whose endpoints are the points of tangency.

The chord is actually the diagonal of a square that has sides of length r. So, its length can be found using the Pythagorean theorem (a^2 + b^2 = c^2), where a and b are the lengths of the sides of the square and c is the diagonal. Hence the length of the chord can be found as √(r^2 + r^2) = √(2r^2) = r√2.

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Final answer:

To determine the number of songs Jose can purchase using his gift card, the inequality 1.19x ≤ 10 is solved, resulting in x ≤ 8.4, meaning Jose can purchase a maximum of 8 songs.

Explanation:

Jose's gift card scenario:

Let's denote the number of songs he can purchase as x.

The inequality to represent this situation is: 1.19x ≤ 10 (the total cost of the songs cannot exceed the value of the gift card).

Solving for x, we get x ≤ 8.4. Since he can't purchase a fraction of a song, Jose can purchase a maximum of 8 songs using the gift card.

The required solution of  the equation of a line is −2x+5y=−20 is x = 10.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

The given equation of a line is

−2x+5y=−20.

According to given question we have

BY the use of x- intercept put y=0 we get

-2x + 5y = -20

-2x + 5(0) = -20

-2x = -20

x = -20/-2

x = 10.

Therefore, the required solution of  the equation of a line is −2x+5y=−20 is x = 10.

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The total volume of diesel that the pair have altogether is equal to 20.8 L.

Measurement is a process through which the size, magnitude, volume or other physical quantities that are associated with an object or chemical substance are taken, especially for the purpose of a scientific research (experiment).

In order to determine the total volume of diesel that they have, we would convert the value in centiliter (cL) to liter (L) and then add them together as follows:

840 cL to L = 840/100 = 8.4 L.

Total = 8.4 + 12.4

Total = 20.8 L.

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To solve such problems we must know about Tangent (Tanθ).

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

The height of the mountain is 1.495 miles.

Given to us

[tex]\rm{ tan(\angle A) = \dfrac{Perpendicular}{Base}[/tex]

[tex]tan(\angle A) = \dfrac{CD}{AD}[/tex]

[tex]tan(3.5^o) = \dfrac{CD}{15+x}[/tex]

[tex]CD=tan(3.5^o) \times(x+15)[/tex]

[tex]\rm{ tan(\angle B) = \dfrac{Perpendicular}{Base}[/tex]

[tex]tan(\angle B) = \dfrac{CD}{BD}[/tex]

[tex]tan(9^o) = \dfrac{CD}{x}[/tex]

[tex]CD=tan(9^o) \times(x)[/tex]

Equating CD,

[tex]tan(3.5^o) \times (x+15) = tan(9^o) \times x\\\\(x+15)= \dfrac{tan(9^o) }{tan(3.5^o) }\times x\\\\x+15=2.59\ x\\15 = 2.59x-x\\15= 1.59x\\x = 9.44[/tex]

Substituting the value of x

[tex]CD=tan(9^o) \times(x)[/tex]

[tex]CD=tan(9^o) \times(9.44)\\CD= 1.495[/tex]

Hence, the height of the mountain is 1.495 miles.

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Let

x-------> the time in minutes

y-----> the function that represent the amount of water in gallons

Step 1

Find the x-intercept

we know that

The x-intercept is the value of x when the value of the function is equal to zero

In this problem (see the graph)

For [tex]y=0[/tex]

the value of x is [tex]15\ min[/tex]

so

the x-intercept is the point [tex](15,0)[/tex]

that means

The number of minutes it takes for the container to empty  is [tex]15\ min[/tex]

Step 2

Find the y-intercept

we know that

The y-intercept is the value of the function y when the value of x is equal to zero

In this problem (see the graph)

For [tex]x=0[/tex]

the value of the function y is [tex]120\ gal[/tex]

so

the y-intercept is the point [tex](0,120)[/tex]

that means

The number of gallons in the container before the drain is open is [tex]120\ gal[/tex]

therefore

the answer in the attached figure

simple first we find the miles per gallon

so 300/15=20 therefor he would only need a extra 3 gallons to go 360 miles so your answer is

B.18

In the subtraction problem 17 - 8, the number 9 is the difference, which is the result obtained after subtracting 8 from 17.

In the problem 17 - 8 = 9, the number 9 is the difference. In subtraction, the difference is the result of subtracting one number from another. Here, when we subtract 8 from 17, we get the difference of 9. This is because 17 is the minuend (the number from which another number is subtracted), 8 is the subtrahend (the number that is to be subtracted), and 9 is the difference (the result of the subtraction).

250/10 = 25 bagels per hour

25*12 = 300 bagels in 12 hours

After the z value is calculated, the probability is obtained by using the corresponding area under the normal curve from the z-table. The z-table shows the area to the left of the calculated z-score and can be used to determine probabilities and critical values for the standard normal distribution.

After the z value is calculated, the probability is obtained from a table of z-scores. The z-table is used to find the area under the normal curve, which represents the probability associated with a z-score. When looking up a z-score in the z-table, you will see the area under the normal curve to the left of the z-score which corresponds to the probability of obtaining a score within that range. The z-table provides critical values for the standardized normal distribution which has a mean of 0 and a standard deviation of 1. To calculate the area between two z-scores, subtract the smaller area from the larger area.

For example, if we need to find the z-score that corresponds to an area of 0.9, we would look up this value in the z-table to discover that the z-score is approximately 1.28. This z-score then can be used with the mean and standard deviation of the distribution to find the original score using the formula μ + (z)(σ) = x. It's important to note that while most z-tables show the area to the left, some may provide the area from the mean to the z-score, so the method used will be indicated on the table itself.

0.955 rounded to the nearest tenth would be 1.0

Answer:

The probability of a positive test result is 0.017919

Option C is correct.

The probability is quite​ low, indicating that further testing of the individual samples will be a rarely necessary event.

Step-by-step explanation:

Probability of finding bacteria in one public swimming pool = 0.009

We now require the probability of finding bacteria in the combined test of two swimming pools. This probability is a sum of probabilities.

Let the two public swimming pools be A and B respectively.

- It is possible for public swimming pool A to have bacteria and public swimming pool B not to have bacteria. We would obtain a positive result from testing a mixed sample of both public swimming pools.

- It is also possible for public swimming pool A to not have bacteria and public swimming pool B to have bacteria. We would also obtain a positive result from testing a mixed sample of both public swimming pools.

- And lastly, it is possible that both swimming pools both have bacteria in them. We will definitely get a positive result from this too.

So, if P(A) is the probability of the event of bacteria existing in public swimming pool A

And P(B) is the probability of the event of bacteria existing in public swimming pool B

P(A') and P(B') represent the probabilities of bacteria being absent in public swimming pool A and public swimming pool B respectively.

P(A) = P(B) = 0.009

P(A') = P(B') = 1 - 0.009 = 0.991

Since the probabilities for each public swimming pool is independent of the other.

P(A or B) = P(A n B') + P(A' n B) + P(A n B)

= P(A)×P(B') + P(A')×P(B) + P(A)×P(B)

= (0.009×0.991) + (0.991×0.009) + (0.009×0.009)

= 0.008919 + 0.008919 + 0.000081

= 0.017919

Evidently, a probability of 0.017919 (1.7919%) indicates an event with a very low likelihood. A positive result is expected only 1.7919% of the time.

Hence, we can conclude that the probability is quite​ low, indicating that further testing of the individual samples will be a rarely necessary event.

Hope this Helps!!!

divide 40 by 4/5 =

40*5/4 = 200/4 =50

 Emma can jump 50 inches