At lunch, $60\%$ of the students selected soda while $20\%$ selected milk. If 72 students selected soda, how many students selected milk?

ΔABC and ΔACD are similar. Therefore the sides are in proportion:

[tex]\dfrac{y}{7}=\dfrac{7}{6}[/tex]            multiply both sides by 7

[tex]y=\dfrac{49}{6}\\\\\boxed{y=\dfrac{1}{6}}[/tex]

Answer: x=12, y=30

Step-by-step explanation: 180=40+5x+2y+20, 140=5x+2y+20, 120=5x+2y, 60+60=120, so 5*12=60, and 2*30=60

The value of y is determined by solving the algebraic equation presented, which after simplifying and isolating y, gives us a value of y equal to 3200.

To find the value of y, we can use the given equations and perform the necessary algebraic manipulations. The question appears to contain a regression analysis problem where ŷ, read as 'y hat', represents the estimated value of y. This value is obtained from the regression line, which helps in making predictions about y based on corresponding values of x.

Here are the steps to solve the provided equations:

Answer:

8) Sale price : 45* (100%-22%)= 45* 78/100= 35,1 $

9) 89* ( 100%-33%)= 89*67/100=59,63 $

10) 23,99* (100%-44%)= 13,43 $

11) 279,99*25/100= 69,99 $

12) Sell price= regular price* ( 100%- Markdown)

Step-by-step explanation:

Answer:

C. 97,000

Step-by-step explanation:

9.7x10^4 = 9.7 x 10000 = 97,000

Final answer:

To write 9.7x10^4 in standard form, you multiply 9.7 by 10,000, resulting in 97,000. Therefore, the correct answer is C. 97,000.

Explanation:

To write 9.7x10^4 in standard form, you multiply the coefficient (9.7) by 10 to the power of 4.

Since 10^4 means 10,000, you would perform the calculation 9.7 multiplied by 10,000. Doing this gives you 97,000. Therefore, the correct answer is:

C. 97,000

Here are steps to write numbers in scientific notation or standard form from the examples provided:

To convert the number 4,500 to scientific notation, you move the decimal three places to the left to get 4.5 x 10^3.

The number 2,220,000 would be 2.22 x 10^6 in scientific notation.

A smaller number like 0.0035 would be written as 3.5 x 10^-3.

For 0.7, the scientific notation is 7 x 10^-1.

The number 858.67 would be 8.5867 x 10^2 since the decimal is moved two places to the left.

The length of Line BC is 10

A figure bounded by 3 sides and all the internal angles add up to 180 ° is called a triangle.

Triangles having the same corresponding angles measures and proportional side lengths are called similar triangles.

Considering Δ AXY    and    ΔABC

                      ∠AXY       =      ∠ACB  (corresponding angles are equal)

                       ∠AYX       =      ∠ABC   (corresponding angles are equal)

                       ∠A is common in both the triangles

∴ We can say the triangles are similar .

Now, let H be the height of ΔABC and h be the height of ΔAYX

So, we can say,  [tex]\frac{XY}{BC} = \frac{h}{H}[/tex]

So,   [tex]\frac{AYX}{ABC} = \frac{7.5}{30}[/tex]

⇒    [tex]{\frac{\frac{1}{2} (XY) h }{\frac{1}{2}(BC) H } = \frac{1}{4}[/tex]

Now, substituting XY = 5 and  [tex]\frac{XY}{BC} = \frac{h}{H}[/tex]  in the above equation, we get

[tex]\frac{25}{BC^{2} } = \frac{1}{4}[/tex]

⇒ BC² = 100

⇒ BC = ± 10

Since BC is the length , so it cannot be negative.

So, the negative value is rejected.

∴  BC = 10

Option B is correct.

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Answer:

Step-by-step explanation:

The first four terms of geometric series is:

[tex]a,ar,ar^2,ar^3[/tex]

Since, we have given information that the third number is greater than 44 that means:

[tex]ar^2=a+44[/tex]

Above equation can be rewritten as:

[tex]a(r^2-1)=44[/tex]

Now, using:

[tex]a^2-b^2=(a+b)(a-b)[/tex]

Here, a=r,b=1

[tex]a(r+1)(r-1)=44[/tex]        (1)

The sum of first four terms is:

[tex]a+ar+ar^2+ar^3=220[/tex]

[tex]a(1+r+r^2+r^3)=220[/tex]

[tex]a(1(1+r)+r^2(1+r))=220[/tex]

[tex]a((1+r)(1+r^2))=220[/tex]      (2)

Divide equation (2) by (1) we get:

[tex]\frac{r^2+1}{r-1}=\frac{220}{44}[/tex]

[tex]r^2+1=5r-5[/tex]

[tex]\Rightarrow r^2-5r+6=0[/tex]

[tex]\Rightarrow r^2-3r-2r+6=0[/tex]

[tex]\Rightarrow r(r-3)-2(r-3)=0[/tex]

[tex]\Rightarrow (r-2)(r-3)=0[/tex]

[tex]\Rightarrow r=2,3[/tex]

CASE1: When r=2 in [tex]ar^2=a+44[/tex]

[tex]a(4)=a+44[/tex]

[tex]3a=44[/tex]

[tex]a=\frac{44}{3}[/tex]

CASE2:When r=3 in [tex]ar^2=a+44[/tex]

[tex]a(3)^2=a+44[/tex]

[tex]\Rightarrow 9a=a+44[/tex]

[tex]\Rightarrow 8a=44[/tex]

[tex]\Rightarrow a=\frac{44}{8}=\frac{11}{2}[/tex]

The series becomes:

From CASE1: [tex]\frac{44}{3},\frac{44\cdot 2}{3},\frac{44\cdot 2^2}{3},\frac{44\cdot 2^3}{3}[/tex]

[tex]\Rightarrow \frac{44}{3},\frac{88}{3},\frac{176}{3},\frac{352}{3}[/tex]

From CASE2: [tex]\frac{11}{2},\frac{11\cdot 3}{2},\frac{11\cdot 3^2}{2},\frac{11\cdot 3^3}{2}[/tex]

[tex]\Rightarrow \frac{11}{2},\frac{33}{2},\frac{99}{2},\frac{297}{2}[/tex]

A geometric progression is characterized by a common ratio.

The terms of the progression are: [tex]\mathbf{T_n =5.5, 16.5, 49.5,148.5}[/tex] or [tex]\mathbf{T_n =\frac{44}{3}, \frac{88}{3}, \frac{176}{3},\frac{352}{3}}[/tex]

The given parameters are:

[tex]\mathbf{S_4 = 220}[/tex]

[tex]\mathbf{T_3 = T_1 + 44}[/tex]

The third term is represented as:

[tex]\mathbf{T_3 = ar^2}[/tex]

The first term is:

[tex]\mathbf{T_1 = a}[/tex]

So, we have:

[tex]\mathbf{ar^2 = a + 44}[/tex]

Subtract a from both sides

[tex]\mathbf{ar^2 - a = 44}[/tex]

Factor out a

[tex]\mathbf{a(r^2 - 1) = 44}[/tex]

Express as difference of two squares

[tex]\mathbf{a(r + 1)(r - 1) = 44}[/tex]

Make r + 1 the subject

[tex]\mathbf{r +1 = \frac{44}{a(r -1)}}[/tex]

Recall that:

[tex]\mathbf{S_4 = 220}[/tex]

This gives:

[tex]\mathbf{a + ar + ar^2 + ar^3 = 220}[/tex]

Factor out a

[tex]\mathbf{a(1 + r + r^2 + r^3) = 220}[/tex]

Factor out r^2

[tex]\mathbf{a(1 + r + r^2(1 + r)) = 220}[/tex]

Rewrite as:

[tex]\mathbf{a(1(1 + r) + r^2(1 + r)) = 220}[/tex]

Factor out 1 + r

[tex]\mathbf{a((1 + r^2)(1 + r)) = 220}[/tex]

Substitute [tex]\mathbf{r +1 = \frac{44}{a(r -1)}}[/tex] in [tex]\mathbf{a((1 + r^2)(1 + r)) = 220}[/tex]

[tex]\mathbf{a((1 + r^2)\times \frac{44}{a(r -1)} = 220}[/tex]

[tex]\mathbf{((1 + r^2)\times \frac{44}{(r -1)} = 220}[/tex]

Divide both sides by 44

[tex]\mathbf{(1 + r^2)\times \frac{1}{(r -1)} = 5}[/tex]

Multiply through by r - 1

[tex]\mathbf{1 + r^2 = 5r - 5}[/tex]

Collect like terms

[tex]\mathbf{r^2 - 5r + 5 +1 = 0}[/tex]

[tex]\mathbf{r^2 - 5r + 6 = 0}[/tex]

Expand

[tex]\mathbf{r^2 - 2r - 3r + 6 = 0}[/tex]

Factorize

[tex]\mathbf{r(r - 2) - 3(r - 2) = 0}[/tex]

Factor out r -2

[tex]\mathbf{(r - 3)(r - 2) = 0}[/tex]

So, we have:

[tex]\mathbf{r = 3\ or\ r = 2}[/tex]

Calculate a using: [tex]\mathbf{a(r^2 - 1) = 44}[/tex]

When r = 3

[tex]\mathbf{a(3^2 -1) = 44}[/tex]

[tex]\mathbf{a(9 -1) = 44}[/tex]

[tex]\mathbf{8a = 44}[/tex]

[tex]\mathbf{a = 5.5}[/tex]

When r = 2

[tex]\mathbf{a(2^2 -1) = 44}[/tex]

[tex]\mathbf{a(4 -1) = 44}[/tex]

[tex]\mathbf{3a = 44}[/tex]

[tex]\mathbf{a = \frac{44}{3}}[/tex]

The nth term of a GP is:

[tex]\mathbf{T_ = ar^{n-1}}[/tex]

So, the terms of the progression are:

[tex]\mathbf{T_n =5.5, 16.5, 49.5,148.5}[/tex]

or

[tex]\mathbf{T_n =\frac{44}{3}, \frac{88}{3}, \frac{176}{3},\frac{352}{3}}[/tex]

Read more about geometric progressions at:

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Answer:

1/365 (or 1/366 in the case of a leap year.)

Answer:

x=12

Step-by-step explanation:

16x - (8x  + 6) =90

The first step is to distribute the - sign

16x -8x -6 =90

Now we combine the like terms

8x-6 = 90

Add 6 to each side

8x-6+6 = 90+6

8x = 96

Divide each side by 8

8x/8 = 96/8

x =12

Answer:

f(x) = 3(x + 1)² + 2

Step-by-step explanation:

Use the method of completing the square

3x² + 6x + 5

= 3(x² + 2x) + 5

add/ subtract (half the coefficient of the x-term)² to x² + 2x

= 3(x² + 2(1)x + 1 - 1) + 5

= 3(x + 1)² - 3 + 5

f(x) = 3(x + 1)² + 2 ← in vertex form

Answer:

The graph shifts 3 units left and 15 down. It narrows by a factor of 2 and is right side up.

Step-by-step explanation:

There are two ways of doing this. You can graph it, or you can put it in the vertex form by completing the square.

A quick way of putting this into the vertex form is write the general equation

y = a(x - h)^2 + k

h= - b/2a = - 12/4 = - 3

So the equation in vertex form is

y = 2(x + 3)^2 - 15

Description

y = 2(x + 3)^2 - 15

shifts 3 units to the left and 15 units down. It also narrows by a factor of 2. Finally, it is right side up.

Graph

Since you have seen the graph before, there is not much more to add. It just shows what has been written above.

Answer:

$69.60

Step-by-step explanation:

20% of $58 is $11.60. So you add $11.60 + 58 which equals $69.60, so that is the total cost.

Answer:

$69.60

Step-by-step explanation:

The desired amount (total cost) is equivalent to the sum of the bill and 20% of the bill, or, equivalently, 120% of the bill.

1.20($58) = $69.60

The total cost is $69.60, including a 20% tip.

Answer:

210 miles=3.5 hours×speed

3.5 hours=210 miles/speed

speed=210 miles/3.5 hours

                              I Honestly Juat Guessed

Answer:

210 miles=3.5 hours×speed

3.5 hours=210 miles/speed

speed=210 miles/3.5 hours

Hope this helps =]

Answer:

$1.25

September

$30

Step-by-step explanation:

Let's take this a step a time.

First we need to find how much the price of the flowers were in September.

We know that each flower cost $1.50 on October.

The October price was a 20% increase of the September price.

To calculate for the price of the flowers on September, we can solve it like this:

Let x = Price during September

1.2x = 1.50

We used 1.2 because the price of $1.50 is 120% of the original price.

Now we divide both sides by 1.2 to find x.

[tex]\dfrac{1.2x}{1.2}=\dfrac{1.5}{1.2}[/tex]

x = 1.25

The price of the flowers during September was $1.25 each.

Now the 7th grade class earned 40% of the selling price of each flower.

40% = 0.40

To find how much they made on each month, we simply multiply the percentage to the price and the number of flowers sold.

September = 0.40 x 1.25 x 900

September = 0.5 x 900

September = $450

Now for October.

October = 0.40 x 1.50 x 700

October = 0.6 x 700

October = $420

The 7th Graders earned more on September.

They earned $30 more on September than October.

Answer:

4/3 or D

Step-by-step explanation:

Let's get this equation into y=mx+b form.

m=slope b=y-int

Subtract 5 from both sides to isolate y on a side.

4x-6=3y

Divide both sides by 3 to isolate y on one side.

(4/3)x-2=y

y=(4/3)x-2

m=4/3

b=-2

So our slope is 4/3

Answer:

The set of all points on a plane equidistant to a given point

Step-by-step explanation:

"following"?

Answer:

The collection of all points in a plane that are the same distance from a given point.

Step-by-step explanation:

Answer:

The ascending order is [tex]8.11\times 10^{-3},435, 34\times 10^2, 1.2\times 10^7[/tex]

Step-by-step explanation:

First of all find the exact value of each number.

[tex]34\times 10^2=34\times 100=3400[/tex]

[tex]1.2\times 10^7=1.2\times 10000000=12000000[/tex]

[tex]8.11\times 10^{-3}=\frac{8.11}{1000}=0.00811[/tex]

The fourth number is 435.

Using the above calculation we can easily arrange these numbers form least to greatest.

The ascending order is

[tex]0.00811, 435, 3400, 12000000[/tex]

It can be written as

[tex]8.11\times 10^{-3},435, 34\times 10^2, 1.2\times 10^7[/tex].

Answer:

16. No

18. Yes

20. Yes

Step-by-step explanation:

Because there is a right angle at at least one corner of the triangle.

Answer:

The correct answer is (−4, −8)

Step-by-step explanation:

You have to substitute!!! :)

−3x + 4y = −20                y = x − 4

-3(4) + 4(8) = -20             8 = 4 - 4

-12 + 32 = -20                  8 = 0

20 = 20

−3x + 4y = −20                y = x − 4

-3(0) + 4(-5) = -20           -5 = 0 - 4

0 + 20 = -20                    -5 = -4

20 = -20

−3x + 4y = −20                y = x − 4

-3(-2) + 4(-6) = -20          -6 = -2 - 4

6 - 24 = -20                    -6 = -6

-18 = -20      

−3x + 4y = −20                y = x − 4

-3(-4) + 4(-8) = -20         -8 = -4 - 4

12 - 32 = -20                  -8 = -8

-20 = -20

Answer:

(-4,-8)

Step-by-step explanation:

This a system of equation that have two variables x and y and we have two equations that we have to solve simultaneously

−3x+4y=−20 ....(1)

y=x−4 ....(2)

We can substitute equation (2) and (1)

-3x+4y = −20

-3x+4(x−4) = −20

-3x + 4x -16 = -20

x = -4

Now we need to find the value of y

y=x−4 = -4 - 4 = -8

(-4,-8)

Answer:

x = -3/7

Step-by-step explanation:

We are given the following equation for which we have to solve for x:

[tex]3(3x - 1) + 2(3 - x) = 0[/tex]

So we will start by expanding the equation by multiplying the common factor with the brackets to get:

[tex]9x-3+6-2x=0[/tex]

Arranging the like terms together (variables on one side of the equation and constants on the other side) to get:

[tex]9x-2x=3-6\\\\7x=-3\\\\x=-\frac{3}{7}[/tex]

Therefore, x = -3/7.

Answer:

x - 2y = -15

Step-by-step explanation:

Given: m = 1/2 and (-3, 6)

We are given slope and a point.

The equation of the line y - y1 = m (x  - x1)

y - 6 = 1/2 (x -  (-3))

y - 6 = 1/2 (x + 3)

y - 6 = 1/2x + 3/2

1/2x - y = -6 - 3/2

1/2x - y = -15/2

Taking LCD as 2, we get

x - 2y = -15

Thank you.

Answer:

Option B is correct

the degree of rotation is, [tex]-90^{\circ}[/tex]

Step-by-step explanation:

A rotation matrix is a matrix that is used to perform a rotation in Euclidean space.

To find the degree of rotation using a standard rotation matrix i.e,

[tex]R = \begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex]

Given the matrix: [tex]\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}[/tex]

Now, equate the given matrix with standard matrix we have;

[tex]\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex] =  [tex]\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}[/tex]

On comparing we get;

[tex]\cos \theta = 0[/tex]       and [tex]-\sin \theta =1[/tex]  

As,we know:

[tex]\cos \theta = \cos(90^{\circ}) = \cos( -90^{\circ})[/tex]

we get;

[tex]\theta = -90^{\circ}[/tex]

and

[tex]\sin \theta =- \sin (90^{\circ}) = \sin ( -90^{\circ})[/tex]

we get;

[tex]\theta = -90^{\circ}[/tex]

Therefore, the degree of rotation is, [tex]-90^{\circ}[/tex]

The degree of rotation represented on a matrix is measured in angles, such as degrees or radians.

The degree of rotation represented on a matrix is typically measured in terms of angles, such as degrees or radians. In order to determine the degree of rotation on a matrix, you need to identify the angle of rotation.

If the matrix is rotated clockwise, the angle is considered negative (-). If the matrix is rotated counterclockwise, the angle is considered positive (+).

For example, if a matrix is rotated 90 degrees counterclockwise, the degree of rotation would be +90°.

Answer:

Possible number of outcomes = 24

Number of outcomes have an 'a' and an odd number = 3

Step-by-step explanation:

The total outcomes are as follows:

S = {(a, 1), (a, 2), (a, 3), (a, 4), (a, 5), (a, 6),

      (b, 1), (b, 2), (b, 3), (b, 4), (b, 5), (b, 6),

      (c, 1), (c, 2), (c, 3), (c, 4), (c, 5), (c, 6),

      (d, 1), (d, 2), (d, 3), (d, 4), (d, 5), (d, 6)}

n(S) = 24

Hence, possible number of outcomes = 24

The outcomes have an 'a' and an odd number are:

E = {(a, 1), (a, 3), (a, 5)}

n(E) = 3

Hence, there are 3 outcomes have an 'a' and an odd number.

Answer:  (a) $6,600

                (b) $28,600

Step-by-step explanation:

Interest (I) = Principal (P) x rate (r) x time (t)

I = 22,000(0.06)(5)

 = 6,600

Accrued (A) = Principal (P) + Interest (I)

A = 22,000 + 6,600

  = 28,600

Question

Anna picked 37 apples . She divided the apples equally among 7 baskets. How many apples are in each basket? How many are leftover?

Answer:

Step-by-step explanation:

37 : 7 = 5 (2 left over)

check

(7 * 5) + 2 = 37

better solution in the picture

Answer:

5 apples in each basket with 2 left over

Step-by-step explanation:

37/7 =5 R 2

brainliest pls

Answer:

The answer is 0.2.

Step-by-step explanation:

10-(a+b)

A=4.1 B=5.7

10-(4.1+5.7)

10-4.1-5.7

10-9.8=

0.2

Final answer:

To find the value of p when c = 3.2, substitute c = 3.2 into the expression for p. The value of p is 2. To find the value of c when p = 85, substitute p = 85 into the expression for p and solve for c. The value of c is -30.

Explanation:

To find the value of p when c = 3.2, we substitute c = 3.2 into the expression for p.

Substituting c = 3.2 into p = 10 - 2.5c, we get p = 10 - 2.5 * 3.2 = 10 - 8 = 2.

So, p = 2 when c = 3.2.

To find the value of c when p = 85, we substitute p = 85 into the expression for p.

Substituting p = 85 into p = 10 - 2.5c, we get 85 = 10 - 2.5c.

Then, we solve for c: 2.5c = 10 - 85 = -75.

Dividing both sides by 2.5, we get c = -75/2.5 = -30.

So, c = -30 when p = 85.

Answer:

1/2

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] ÷[tex]\frac{2}{3}[/tex] equals 1/2 so 1 mius that will be 1/2

Answer:

5x+2

Step-by-step explanation:

Ok so the expression 5(x+2) is not 5x+2 because you have to use the distributive property. So with that being said:

5(x+2)=5 times x and 5 times 2

so the realest answer is 5x+10 instead of 5x+2

EXPLANATION: The error in the rewritten expression done by your 'friend' is that he/she did not multiply the five in the parenthesis by ALL terms (meaning numbers and/or variables) as he/she should have done according to the distributive property. In the distributive property, you distribute equally to all numbers and parts in the equation or expression.

Take, For example, 7(x+4). Instead of just multiplying 7 times x in the parenthesis, you would also multiply seven times to four and add that to the end of the expression, making the rewritten expression 7x+28.

So, the correct rewritten expression for this problem is 5x+10.

Answer: 615= 140 + 19x

Step-by-step explanation:

19x represents the price per guess (x) how many people are coming. Good Luck!

To solve for the number of guests Taryn can invite, set up the inequality 140 + 19x < 615 and then solve for x.

To solve for the number of guests Taryn can invite, we need to set up an inequality. Let x represent the number of guests. The total cost, C, can be calculated by adding the cost to rent the space, $140, to the cost per guest, $19, multiplied by the number of guests. So, the inequality can be written as 140 + 19x < 615.

To solve for x, we need to isolate it by subtracting 140 from both sides: 19x < 475. Finally, divide both sides by 19 to get the solution: x < 25.

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Answer:

81

Step-by-step explanation:

45% × 180 = [tex]\frac{45}{100}[/tex] × 180 = 81

Answer:

The answer is  81

Step-by-step explanation:

You can do it following the next steps

1.- Place the the "45" by 100 = 0.45

2.- Multiply 0.45 times 180= 81