The two-way table shows the number of students in a class who help in an animal shelter and/or library.








Help in Animal Shelter


Do Not Help in Animal Shelter


Total




Help in Library

12

?

15



Do Not Help in Library

11

10

21



Total

23

13

36



What is the missing number in the table?
3
5
25
27

Answer: 2.661

Step-by-step explanation:

A P E X

Answer:

x^2 + 3x – 20

Step-by-step explanation:

I just did the assignment

Answer:

The answer has a positive 5 and 33.

Step-by-step explanation:

I used a calculator.

Answer:

Step-by-step explanation:

First, let's find the equation of the line.

The slope is defined by

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

Where we are gonna use points (2,0) and (9,7).

[tex]m=\frac{7-0}{9-2}=\frac{7}{7}=1[/tex]

Then, we use the point-slope formula to find the equation.

[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-2)\\y=x-2[/tex]

So, if David's bill came to $66 after coupon, it means [tex]y=66[/tex].

Replacing this value in the equation, we have

[tex]y=x-2\\66=x-2\\x=66+2\\x=68[/tex]

Therefore, the price without coupon is $68.

Answer :- Yes the two triangles are similar because there are two pairs of congruent corresponding angles.

Explanation:-

In Δ ABC

∠A=30° , ∠C=65 °

By angle sum property of triangle

∠A + ∠B + ∠C= 180°

⇒∠B= 180°-∠A-∠C=180°-30°-65°=85°

⇒∠B=85°

Now in ΔABC and ΔDEF

∠A=∠D=30° and ∠B=∠E=85°

⇒ there are two pairs of congruent corresponding angles.

So by AA-similarity criteria

ΔABC ≈ ΔDEF

Answer:

Yes, because there are two pairs of congruent corresponding angles.

Step-by-step explanation:

Two triangles ABC and DEF are given .

The measure of angles in triangle ABC are:

m<A=30°,m< C=65°,

m<B= 180-(30+65)=85°(measure of sum of angles in any triangle is 180°)

In triangle DEF the measure of the angles are :

m<D=30°,m<E=85°,m<F=180-(30+85)=65°(sum of angles in a triangle add to 180°)

In triangles ABC and DEF,

< A=<D=30°

<B=<E=85°

<C=<F=65°

The two triangles are similar by AAA property.

The statistic that the coach should study is mean or the average score of the two teams. If the coach wants to know if football players who warm up before a game will score more points than those who don't warm up. He will break the team up into two groups and make sure each player gets equal time on the field. He will then count how many points each player makes during the game. After counting them, add the scores of the group that he divided and then divided it by the number of player in that group to get an average score on teams that warm up or do not warm up before the game. 

Answer:

the value of x= 4.5

Step-by-step explanation:

If x varies directly with y and x = 3.5 when y = 14

x varies directly with y , so equation is x= ky

where k is the constant of proportionality

x = 3.5 when y = 14, use the given values and find out k

Plug in the given values in x=k y

3.5= k * 14

Divide by 14 on both sides

0.25= k

So the value of k = 0.25

Now find out x when y= 18

x= ky

x= 0.25 * 18= 4.5

4 2/3 = 14/3

15 = 15/1

14/3 * 15/1 = 14*15=210, 3*1 = 3

210/3 = 70

answer is 70

Answer:

F( x) = 0.35 x + 55

Her mistake is in the first step, she wrote the equation incorrectly.

A general quadratic equation:

ax^2 + bx + c = 0

has the solutions:

x = (-b ± √(b^2 - 4ac))/(2a)

In this case, the equation is:

y = x^2 - 8x + 7

And what Joyce writes in each step is:

Step 1:

x = (-8 ± √(8^2 - 4*1*7))/(2*1)

Then we can already see the mistake.

Notice that in the given equation, we have:

b = -8

And the general solution has:

x = (-b ± √(b^2 - 4ac))/(2a)

-b would be equal to 8, then what Joyce must have written here is:

x = (8 ± √((-8)^2 - 4*1*7))/(2*1)

If you want to learn more about quadratic equations, you can read:

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The system of equations has exactly one solution, but it is located at (16,15), not (–8, 3), (–4, 3) or any other points. So, none of the provided options are true.

The task is to identify the statement that is correct about the system of equations –3x + 4y = 12 and x – y = 1. To discover this, we must solve the system which consists of these two linear equations. Adjust equation two to be in the same format as equation one by adding y to both sides which gives x = y + 1. Substitute it into the first equation: -3(y + 1) + 4y = 12, which simplifies to -3y - 3 + 4y = 12, giving y = 15. Substitute y = 15 to the second equation, it gives us x = 16. Hence, none of the provided solutions is correct, because the system has exactly one solution at (16,15).

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Answer:

56

Step-by-step explanation:

Brand A's data are probably linear, while brand B's data are probably not.

A graph shows how much a set of data fits into a pattern. This data is defined by the regression line.

Now, when we have the graph for brand A as an increasing curve, and the residuals for brand B form a U-shaped pattern, we can conclude that Brand A's data are probably linear, while brand B's data are probably not.

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An equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]

The correct answer is option (A)

"The standard form of equation of ellipse with center (0, 0) is, [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]

"The vertices of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm a,0)[/tex] "

"The foci of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm c,0)[/tex], where [tex]c^{2} =a^{2}- b^{2}[/tex] "

For given question,

The center of the ellipse is at the origin.

Using the standard form of equation of the ellipse,

[tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]

A vertex at (13, 0)

⇒ (a, 0) = (13, 0)

⇒ a = 13

And a focus at (12, 0).

⇒ (c, 0) = (12, 0)

⇒ c = 12

We know, [tex]c^{2}= a^{2}- b^{2}[/tex]

Now, we find the value of b i.e., minor axis

[tex]\Rightarrow 12^{2} =13^{2}- b^{2}\\\\\Rightarrow b^2=169-144\\\\ \Rightarrow b^2=25\\\\\Rightarrow b=\pm 5[/tex]

Substituting these values in the standard form of equation of ellipse with center (0, 0),

[tex]\Rightarrow \frac{x^2}{a^2} +\frac{y^2}{b^2} =1\\\\\Rightarrow \bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]

Therefore, an equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]

The correct answer is option (A)

Learn more about ellipse here:

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Final answer:

The simplified expression of 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³ is -4m³ + 13p³ - 5p, which is option d).

Explanation:

To simplify the expression 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³, we need to combine like terms.

Like terms have the same variable raised to the same power.

In this case, terms with p raised to the third power can be combined, and terms with m raised to the third power can also be combined, as well as the terms with just p.

Now the expression is simplified to -4m³ + 13p³ - 5p, which corresponds to option d).

Answer:

The correct answer is option B

Step-by-step explanation:

Payment done per week [tex]= 35 dollar\\[/tex]

Total number of weeks in a  year [tex]= 52 weeks\\[/tex]

Total number of weeks in two  year [tex]= 104 weeks\\[/tex]

Total amount paid in two weeks

[tex]= 35 * 104\\=3,640\\[/tex]

The make up rate is basically the amount paid over and above $2400

[tex]=(\frac{3640 - 2400}{2400} ) * 100\\= 51. 7 perecent[/tex]

Final answer:

By adding all the odd numbers from 1 to 11 inclusive (1, 3, 5, 7, 9, 11), the sum is 36.

Explanation:

If you were to add all odd numbers between 1 and 11 (both inclusive), the odd numbers are: 1, 3, 5, 7, 9, and 11. To find the result of adding these numbers together, you simply add each one sequentially:

1 + 3 = 4

4 + 5 = 9

9 + 7 = 16

16 + 9 = 25

25 + 11 = 36

So, the result of adding all the odd numbers from 1 to 11 inclusive is 36.