Rachel has 30 pounds of a mixture of candy that sells for $1.00/lb. If lollipops sell for $0.95/lb and caramel candies sell for $1.10/lb. How many pounds of lollipops are in the mixture?

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:

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:

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:

y = 10  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

The angles of this triangle should all add up to 180 degrees.

There are 3 angles so 180 ÷ 3 = 60.  Each angle will = 60 degrees.

To find y:

5y + 10 = 60

5y = 60 - 10

5y = 50

y = 50 ÷ 5

y = 10

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:

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:

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:

The answer is 1/square root 2

Step-by-step explanation:

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

Answer:

I think it's rotated 90 degrees clockwise

Step-by-step explanation:

The transformation of circle K to circle K' is a translation, specifically a movement of 4 units to the right and 10 units down, represented by T(4, -10).

The transformation that maps circle K to circle K' is a translation. In a translation, every point of the object moves the same distance in the same direction. For circle K to circle K', this would be a shift 4 units to the right and 10 units down. The coordinates of the center of the circle move from (3,7) to (7,-3). We can calculate this movement by subtracting the initial coordinates from the final ones: (7-3, -3-7) = (4, -10). Therefore, the transformation would be written as T(4, -10).

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Answer: [tex]\frac{27}{125}[/tex]

Step-by-step explanation:

Here the total numbers are 1,  4,  3,  7,  6

Since the total number of possible arrangement = [tex]5\times 5 \times5 \times 5 \times 5=5^5[/tex]

The total number of the odd numbers in the given numbers = 3

Thus the possible arrangement that the first three digits will be odd numbers = [tex]3\times 3\times 3\times 5\times 5=3^3\times 5^2[/tex]

Thus, the probability that the first three digits of Irvings ID number will be odd numbers = the possible arrangement that the first three digits will be odd numbers / total possible arrangement =  [tex]\frac{3^3\times 5^2}{5^5} = \frac{3^2}{5^{5-2}}[/tex]

= [tex]\frac{3^3}{5^3} = \frac{27}{125}[/tex]

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:

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:

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 =]

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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Hello from MrBillDoesMath!

Answer:

 80,100  (which is NONE of the provided answers)

Discussion:

-225 * -356 =

+ (225 * 356)   =            as the product of two negative numbers is positive

 80,100

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

The answer should be D. 9 1/5

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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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:

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)

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:

Yes

Step-by-step explanation:

2 x √3 = 3.46410161514 , which is a rational number, because it is a real nomber

The distance of line AB if A(3, 5) and B(-3,-3) is D.10.

[tex]\sqrt[/tex] (5--3)^2 + (3-(-3))^2 = V100 = 10.

To calculate the distance AB between points A (x1, y1) and B (x2, y2), first draw a right triangle with segment ¯AB in the hypothalamus. AC is a horizontal distance, so it's just a difference in x-coordinates: | (x2-x1) |. Similarly, BC is the vertical distance | (y2-y1) |. ..

The vertical distance of the line (Ax + By + c = 0) from point

is equal to | Ax'+ By' + c√A2 + B2 |. Where (x', y') are the coordinates of the point. Since we need the distance of the line from the origin, the coordinates will be (0,0), which is the vertical distance of the line from the origin.

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This is classic Pythagorean solving:

Side^2 + Side^2 = Hypotenuse^2

The hypotenuse is the longest side of a triangle, and it connects the leg and the base usually. In this triangle, 18 is the hypotenuse -- so since we are solving for the unknown side, the equation is:

a^2 + 5.7^2 = 18^2 -- now solve

a^2 = 18^2 - 5.7^2

a^2 = 291.51

a = sqrt(291.51)

a = 17.07 -- because height is the square root of the difference of the squares of 18 and 5.7

The answer is choice B.

The correct answer is b. 17.07 centimeters, because height = Square root of the difference of the squares of 18 and 5.7.

To find the approximate height of the cone-shaped hat, we need to use the Pythagorean theorem. The height of the cone (h) can be found using the formula:

[tex]\[ h = \sqrt{r^2 - a^2} \][/tex]

 where r is the slant height of the cone and a is the radius of the base of the cone.

Given that r = 18 cm and a = 5.7 cm, we substitute these values into the formula:

[tex]\[ h = \sqrt{18^2 - 5.7^2} \][/tex]

[tex]\[ h = \sqrt{324 - 32.49} \][/tex]

[tex]\[ h = \sqrt{291.51} \][/tex]

 Now, we can approximate the square root of 291.51 to find the height:

[tex]\[ h \approx 17.07 \text{ cm} \[/tex]]

 Therefore, the approximate height of the hat is 17.07 centimeters. The other options are incorrect because they do not correctly apply the Pythagorean theorem:

 a. 3.51 centimeters: This is the square root of the difference of 18 and 5.7, which does not use the correct formula for the height of a cone.

c. 18.88 centimeters: This is the square root of the sum of the squares of 18 and 5.7, which would be the length of the slant height, not the height of the cone.

d. 4.87 centimeters: This is the square root of the sum of 18 and 5.7, which is not a correct application of the Pythagorean theorem for finding the height of a cone."

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:

$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: 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:

Jaimie swims 12 the length of the swimming pool every 14 of a minute. Then in one minute, he will swim = 14/12=1.16  So, he will be able to swim 1.16 length in 1 minute.

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:

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

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.