What is the vertex of the parabola?
y - 3 = 1/2 (x + 5)²
( __ , __ )

Hello,

[tex]Data:\\\\\begin{array}{|c|c|c|c|c|}Year&French&Spanish&German&Total\\----&----&----&----&---\\Y10&-&-&-&54\\Y11&15&20&-&-\\----&----&----&----&---\\&-&29&31&100\\\end{array}\\\\Calculus:\\\\\begin{array}{|c|c|c|c|c|}Year&French&Spanish&German&Total\\----&----&----&----&---\\Y10&25&9&20&54\\Y11&15&20&11&46\\----&----&----&----&---\\&40&29&31&100\\\end{array}\\\\[/tex]

20 Year10's students learn German.

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Explanation:

Make a table that has "Year 10", "Year 11", and "Total" as the three rows.

Then you'll have the columns "French", "Spanish", "German", "Total".

In the bottom right corner is the value 100. This is the grand total of everyone surveyed.

We're told that 54 people are in Year 10, which leaves 100-54 = 46 people in Year 11.

Along the "total" column on the far right side, we'll have 54, 46, and 100 in that order from top to bottom.

--------------------------

The info that "20 of the 29 people who study Spanish in Year 11" tells we have 20 people in year 11 who study Spanish, out of 29 people who study Spanish. That leaves 29-20 = 9 people in Year 10 who study Spanish. In the "Spanish" column, we have the values 9,20,29 in that exact order from top to bottom.

Next, we'll write 31 at the bottom of the "German" column to indicate 31 people study German.

The last bit of info is that "15 Year 11 students study French". So we'll write 15 in the "year 11" row and "french" column.

--------------------------

After all that info is sorted out and entered into the table, you should end up with what is shown in figure 1 (see attached image below). Ignore figure 2 for now as we'll work our way to getting there eventually.

The variables a,b,c,d are placeholders for positive whole numbers.  

There are probably a few approaches to take, but possibly the quickest is to notice that in the second row, we can say

15+20+c = 46

c+35 = 46

c = 46-35

c = 11

We have 11 students who study German in Year 11.

Once you determine c, it helps us find b. Focus on the German column to see that

b+11 = 31

b = 31-11

b = 20

There are 20 students in Year 10 who study German. You could stop here if you want.

--------------------------

Just two more variables to go.

Along the top row, we see that

a+9+20 = 54

a+29 = 54

a = 54-29

a = 25

and along the bottom row we see that

d+29+31 = 100

d+60 = 100

d = 100-60

d = 40

Or you could note along this first column to say

a+15 = d

d = a+15

d = 25+15

d = 40

So there are a few alternative paths to take.

--------------------------

All of the sections mentioned so far only involve filling out the table that is shown below in figure 2.

To answer the question your teacher wants to ask, which is how many Year 10 students study German, well that's simply 20 students. Refer to the conclusion of the previous two sections earlier.

By this point, we just simply copy the value from the completed table. This value being of course in the "Year 10" row and "German" column.

Answer:

Y = - 7/4 X + 31/4

Step-by-step explanation:

M = 14/-8 = - 7/4

6 = - 7/4 + B

24 = -7 + 4B

31 = 4B

B = 31/4

Answer:

[tex]x = 0.143[/tex]

[tex]P(High\ |\ Cancer) = 0.215[/tex]

Not independent

Step-by-step explanation:

Given

See attachment for proper table

Solving (a): The missing probability

First, we add up the given probabilities

[tex]Sum = 0.242+0.047+0.079+0.391+0.098[/tex]

[tex]Sum = 0.857[/tex]

The total probability must add up to 1.

If the missing probability is x, then:

[tex]x + 0.857 = 1[/tex]

Collect like terms

[tex]x = -0.857 + 1[/tex]

[tex]x = 0.143[/tex]

Solving (b): P(High | Cancer)

This is calculated as:

[tex]P(High\ |\ Cancer) = \frac{n(High\ n\ Cancer)}{n(Cancer)}[/tex]

So, we have:

[tex]P(High\ |\ Cancer) = \frac{0.079}{0.242+0.047+0.079}[/tex]

[tex]P(High\ |\ Cancer) = \frac{0.079}{0.368}[/tex]

[tex]P(High\ |\ Cancer) = 0.215[/tex]

Solving (c): P(Leukemia) independent of P(High Wiring)

From the attached table

[tex]P(Leukemia\ n\ High\ Wiring) = 0.242[/tex]

[tex]P(Leukemia) = 0.242 + 0.391 =0.633[/tex]

[tex]P(High\ Wiring) = 0.242+0.047+0.079=0.368[/tex]

If both events are independent, then:

[tex]P(Leukemia\ n\ High\ Wiring) = P(Leukemia) * P(High\ Wiring)[/tex]

[tex]0.242 = 0.633 * 0.368[/tex]

[tex]0.242 \ne 0.232[/tex]

Since the above is an inequality, then the events are not independent

Given:

Consider the given equation is:

[tex](2\cdot 2^2)^x=64[/tex]

To find:

The value of x.

Solution:

We have,

[tex](2\cdot 2^2)^x=64[/tex]

It can be written as:

[tex](2\cdot 4)^x=8\times 8[/tex]

[tex]8^x=8^2[/tex]

On comparing the exponents of both sides, we get

[tex]x=2[/tex]

Therefore, the value of x is 2.

Answer:

strangely worded question....

[tex]361^{1/2} = \sqrt{361}[/tex]

Step-by-step explanation:

=========================================================

Explanation:

Notice how (19)^2 = 19*19 = 361

This shows that 19 is a square root of 361. We can say [tex]\sqrt{361} = \sqrt{19^2} = 19[/tex]

Similarly, (-19)^2 = (-19)*(-19) = 361. The two negatives cancel each other out. So that's why there are two solutions to [tex]x^2 = 361[/tex] which are x = 19 and x = -19.

So far that accounts for answer choices B and D.

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The other two answers are [tex]-361^{1/2}[/tex] and [tex]361^{1/2}[/tex] (choices C and F) because anything to the 1/2 power represents a square root.

[tex]x^{1/2} = \sqrt{x}[/tex]

anything to the 1/3 power is a cube root

[tex]x^{1/3} = \sqrt[3]{x}[/tex]

anything to the 1/4 power is a fourth root

[tex]x^{1/4} = \sqrt[4]{x}[/tex]

and so on.

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Side note: For choice C, the exponent is done first before we apply the negative. So technically we could say [tex]-1*(361)^{1/2}[/tex] for choice C to mean the same exact thing. If your teacher said [tex](-361)^{1/2}[/tex] then this would not be an answer because this results in a non-real number.

Answer:

-4/15

Step-by-step explanation:

Mathematically, we know that;

alpha= -b/a and beta = c/a

a refers to the coefficient of the x^2 which is 2

b is the coefficient of x which is 3

c is the last number which is 5

alpha = -b/a = -3/2

beta = c/a = 5/2

1/alpha = -2/3

1/beta = 2/5

so we have the sum as;

-2/3 + 2/5

= -5(2) + 3(2)/15 = (-10 + 6)/15 = -4/15

Answer:

[tex]s =\frac{25 + 26 + 17}{2} = 34[/tex]

[tex] = \sqrt{34 \times 9 \times 8 \times 17} [/tex]

[tex]17 \times 3 \times 2 \times 2 = 204cm ^{2} [/tex]

area ∆ BEC

[tex] = \frac{1}{2} \times 17 \times h = 204[/tex]

[tex]h = \: \frac{204 \times 2}{17} = 24[/tex]

[tex]area \: trap \: \: abcd \\ = \frac{1}{2}(60 + 77) \times 24 \\ = 137 \times 12 = 1644cm ^{2} [/tex]

Step-by-step explanation:

#keep learning!!

Answer:

The minimum number of different tanks needed to safely house all the fish is:

Step-by-step explanation:

To identify the minimum number of different tanks, we're gonna concentrate in a fish species, in this case can be the A: as you see in the table, the A species can live with all the fish excepting the F and G, by their side, the F and G can't live together , by this reason, this three species must live in a different tank, in the next form:

Now the B species, it can live with A, F and G, but for this example we can put in the tank 1 (the tank of the A species). The C especies can live with A, F and G, but how we have A and B together, we're gonna put the C especies in the tank 3 (the tank of the G especies). The D species can live with A and G, we're gonna put in the tank 1 because can live with B species too. The E species can live with A and F, we're gonna put in the tank 2 (the tank of the F species) because the E species can't live with D that is in the in the tank 1. Al last, the H species just can live with A, E, F, and H species, by this reason, the only tank that can be put is the tank 2. In this form, the order is the next:

And the owner of the pet store must buy three different tanks to display these tropical fish.

Answer:

9.32m is the height of. the tree from the ground.

Answer:

4/3 x 3.14 x 2.25=9.42

Hope This Helps!!!

Answer:

9.4

Step-by-step explanation:

[tex] \sf \frac{ \bold{4 }}{ 3 } × 3.14 × \underline{2.25}[/tex]

Step 1 :- Multiply decimal by the number. So, that the results equals whole number.

[tex] \sf \frac{ \underline{ 4 }}{ 3 } \\ [/tex] × 2.25 × 3.14 .

[tex] \sf \frac{9}{ 3 } \\ [/tex] × 3.14

Step 2 :- Divide the fraction.

Step 3 :- Multiply both .

Round to one decimal place :- 9.4

Answer:

[tex]y_1 = -2[/tex] and [tex]y_2 = 4[/tex]

Step-by-step explanation:

[tex] \sqrt{10y + 24} - 3 = y + 1[/tex]

Move the constant to the right-hand side and change their sign.

[tex] \sqrt{10y + 24} = y + 1 + 3 [/tex]

combine like terms

[tex] \sqrt{10y + 24} - 3 = y + 4[/tex]

Square both side to remove square brackets.

10y + 24 - 3 = y²+ 8y + 16

Move the expression to the left-hand side and change its sign.

10y + 24 - y² - 8y - 16 = 0

Combine like terms

10y - 8y + 24 - 16 - y² = 0

2y + 8 - y² = 0

Use commutative property to reorder the terms.

-y² + 2y + 8 = 0

Change the sign of expression.

y² -2y -8 = 0

split -2y

y² + 2y - 4y - 8 = 0

Factor out y from the first pair and -4 from the second equation.

y ( y + 2 ) - 4 ( y + 2 ) = 0

Factor out y+2 from the expression.

( y + 2 ) ( y - 4)

When the products and factors equals 0, at least one factor is 0.

y + 2 = 0

y - 4 = 0

Solve for y

y = -2

y = 4

When we plug the both solution as y we found that both is true solution of this equation.

This equation has two solutions which are -2 and 4.

Answer:

Solution given:

[tex] \sqrt{10y + 24} - 3 = y + 1[/tex]

keep the constant term in one side

[tex] \sqrt{10y + 24} =y+1+3[/tex]

solve possible one

[tex]\sqrt{10y+24}=y+4[/tex]

now

squaring both side

[tex](\sqrt{10y+24})²=(y+4)²[/tex]

10y+24=y²+8y+16

taking all term on one side

10y+24-y²-8y-16=0

solve like terms

8+2y-y²=0

doing middle term factorisation

8+4y-2y-y²=0

4(2+y)-y(2+y)=0

(2+y)(4-y)=0

either

y=-2

or

y=4

y=-2,4

Answer: C. (0, -3)

Step-by-step explanation:

You don't even need to find the function, just mentally graph every point in the options on the graph.

The line is not dotted, showing that the inequality is probably either ≥ or ≤, so points on the line do count as solution.

Answer:

D is the correct answer.

Please thank me

Step-by-step explanation:

[tex] \frac{3}{8} \div \frac{4}{9} \\ = \frac{3}{8} \times \frac{9}{4} \\ = \frac{27}{32} [/tex]

Hope it helps!!!

Thanks!!!

Answer:

Not really。。

Step-by-step explanation:

this school had remained excellent。students grduating from these school have higher ACT scores

f ( - 2 ) = 5 × 3^( - 2 )

f ( - 2 ) = 5 × 1/9

f ( - 2 ) = 5/9

Answer:      I believe the answer would be 1.3

           HOWEVER, if you do have to round to the nearest tenth then the answer would be 1

Step-by-step explanation:    

2x+7 = 12x - 6

(subtract 2x from both sides)

7 = 10x - 6

(add 6 to both sides)

13 = 10x

(divide 13/10)

1.3 = x

answer is C. 252 ft^2

split the figure into two pieces and first figure out the rectangle (shown in turquoise).

If you multiply the width and length (18*6) you should get 108.

Then figure out the trapezoid (in magenta). the formula is (a+b)/2*h where a and b are the bases and h is the height. the bases are given, 6 and 18. to find the height, subtract the entire figure's height by 6, which is 18-6 and gives us 12. so the formula converted to this problem is (6+18)/2*12. simplify parenthesis and get 24/2*12. 24/2=12, so multiply 12*12. The area of the trapezoid is 144. Add the areas of both figures together and get 252.

Answer:

x+115=180 x=65

90+65+y=180 y=25

Step-by-step explanation:

Answer:

1  4/5

Step-by-step explanation:

3/4 ÷ 5 /12

Copy dot flip

3/4 * 12/5

Rewriting

3/5 * 12/4

3/5 * 3

9/5

1 4/5

answer

4

2

Step-by-step explanation:

4x+3y=19

4x=19-3y

4x=16

x=16/4

x=4

2x+5y=20

5y=20/2x

5y= 10

y=10/5

y=2

Answer:

The more spread out your graph is, the greater the standard deviation.

So the option with the most spread out graph, which I think is A, can't see very clear.

Answer:

O D

Step-by-step explanation:

f+g(x)

3x+10+2x-4

3x +2x+6

Answer:

x = (4,0)

y = (0,-4)

Step-by-step explanation:

x - y = 4

(0) - y = 4

-(-y) = -(4)

y = -4

x - (0) = 4

x = 4

x = (4,0)

y = (0,-4)

Answer:

x = 4 . 0

y = 0 . -4)

Step-by-step explanation:

Answer:

the answer is B, comment if you need explanation

Step-by-step explanation:

Answer:

The slope is 1.5

Step-by-step explanation:

To get the slope of the graph, we proceed to select any two points lying on the given line, and applying the slope formula

The two selected points are as follows;

(x1,y1) = (-4,0)

(x2,y2) = (-2,3)

m = (y2-y1)/(x2-x1)

m = (3-0)/(-2-(-4)

m = 3/2 = 1.5

Answer:

it cost 80 dollars

Step-by-step explanation:

cost per bag for X brand =25 $

cost per bag for y brand = 20$

minimize Z=(25X +20 y)

further formulate the problem

the given constraints are

2x + y equal 12

2x + 9y equal 36

2x + 3y equal 24

well on the graph given plot of the constraints

the corner points are

(0;0)

(6;0)

(0;4)

(9;2.5)

minimum z occurs at (0:4)

value of Z(minimum cost)=80$

Answer:i dont know

Step-by-step explanation:

Answer:

The positive correlation between the number of socks and the number of shoes in home

Step-by-step explanation:

Nah i just get an example so that i can get clue,if my answer is wrong sorry in advanced

Answer:

1866.10604

Step-by-step explanation:

V=3.14(r sqaured)1/3h