After a few rides, your friends are ready for some ice cream! You stop into Scoops to You for some ice-cream. Which is the better deal?

3 scoops for $3.69

2 scoops for $2.69

1 scoop for $1.79

Answer:

6a. 13.5m

6b. 12.4m

Step-by-step explanation:

We can use trig identities to solve these problems because each triangle is a right triangle.

6a. Find the measure of the hypotenuse.

Using the angle in the top corner, which is defined as 66 degrees and its adjacent side, we can find the hypotenuse. Remember that the hypotenuse is the longest side, which in this case would be AB. The adjacent side is the side next to the angle that is not the hypotenuse, in this case it would be AC, which is shown to be 5.5m.

The trig identity cos(x) is defined as adjacent/hypotenuse, or the value of the adjacent side divided by the value of the hypotenuse, where x is the degrees of the angle.

So we can set up the equation:

cos(x)=adj/hyp

If we know that x=66 (the degree of the angle) and adj=5.5m, we can substitute this into the equation. Let c represent the hypotenuse.

cos(66)=5.5/c

Then we can multiply by c:

c*cos(66)=5.5

Then divide by cos(66):

c=5.5/cos(66)

Use a calculator to estimate that c approximately equals 13.5m when rounded to the nearest tenth (remember to use degree mode because our angle is measured in degrees).

6b. Find the measure of side a.

Side a is the side opposite to angle A. This can also be known as side CB or the bottom of the triangle.

Method 1: Use trig identity tan(x)tan(x)=opp/adj

Remember x=66 and adj=5.5m. Let a represent the opposite side. Plug in these values into the equation:

tan(66)=a/5.5

Multiply both sides by 5.5:

a=tan(66)*5.5

Use a calculator to estimate that a approximately equals 12.4m when rounded to the nearest tenth (remember to use degree mode because our angle is measured in degrees).

Method 2 (I would recommend method 1, however because you are basing this answer off of the first answer, and in a test or a quiz, you might not be sure if your first answer was correct):

Use Pythagorean Theorem:

a^2+b^2=c^2

c, or the hypotenuse is 13.5m as found in out last problem, and b, the adjacent side is 5.5m which was a given. Substitute these values into the equation:

a^2+5.5^2=13.5^2

a^2+30.25=182.25

a^2=152a=sqrt(152) which rounds to 12.3m, which is almost the same as Method 1, however our answers are different because we used a rounded value of b, rather than the approximate.

Answer:

x = 34

Step-by-step explanation:

complementary angle sum to 90°

sum the 2 angles and equate to 90

x + x + 22 = 90

2x + 22 = 90 ( subtract 22 from both sides )

2x = 68 ( divide both sides by 2 )

x = 34

The factored form of the polynomial is (x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242).

In this question we have an algebraic expression to be expanded by means of algebraic properties, the purpose of this handling is to modify the polynomial until its standard form is finally obtained and later we find its factor form by Cardano's method. Now we proceed to show the procedure in detail:

2 · x · (2 · x + 1)² + (2 · x + 1) · (4 · x² - 3)     Given

2 · x · (4 · x² + 4 · x + 1) + (2 · x + 1) · (4 · x²) + (2 · x + 1) · (- 3)      Perfect square trinomial/Distributive property

8 · x³ + 4 · x² + 2 · x + 8 · x³ + 4 · x² - 6 · x - 3     Distributive property/(- 1) · a = - a

16 · x³ + 8 · x² - 4 · x - 3     Distributive property/Definitions of addition and subtraction

(x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242)      Cardano's method/Result

The factored form of the polynomial is (x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242).

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Answer:

f¯¹(x)=x²+12x+36

Step-by-step explanation:

[tex]f(x) = \sqrt{x} - 6 \\ substitute \: y \: for \: f {}^{ - 1} (x) \\ y = \sqrt{x} - 6 \\ interchange \: x \: and \: y \\ x = \sqrt{y} - 6 \\ swap \: the \: side \: of \: the \: equation \\ \sqrt{y } - 6 = x \\ move \: the \: constant \: to \: the \: right \: hand \: side \\ \sqrt{y} = x + 6 \\ square \: both \: sides \: of \: the \: equation \\ y = x {}^{2} + 12x + 36 \\ substitute \: f \frac{}{ -1} (x) \: for \: y \\ f {}^{ - 1} (x) = x {}^{2} + 12x + 36 \\ domain \: x∈R[/tex]

Remember that an ordered pair is of the form (x, y), then the ordered pairs on the inverse of the relation are (x, -x/5).

Assuming the given relation is:

y + 5x = 0

We can rewrite it to:

y = -5x

Then the inverse will be a function g(x) such that:

y = -5*g(x) = x

Solving for g(x):

g(x) = (-x/5).

Then the inverse of the relation is:

y = -x/5

Remember that an ordered pair is of the form (x, y), then the ordered pairs on the inverse of the relation are (x, -x/5).

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Using the uniform distribution, the standard deviation of the timeout is of 34.64 seconds.

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The standard deviation is:

[tex]S = \sqrt{\frac{(b - a)^2}{12}}[/tex].

For this problem, the bounds are:

a = 0, b = 120.

Hence the standard deviation is found as follows:

[tex]S = \sqrt{\frac{(120 - 0)^2}{12}} = 34.64[/tex].

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Based on the setup costs, the steady annual demand, and the costs to store, the number of cases to produce to minimize cost is 528 units .

This can be found by using the Economic Order Quantity.

= √ ( (2 x Setup costs x annual demand) / holding costs for the year)

Solving gives:

= √ ( ( 2 x 33 x 38,016) / 9)

= √278,784

= 528 units

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Inscribed angles that are formed by segments which extend from one side of the hypotenuse to the other are right angles.

Therefore, angle PRQ is a right angle and is equal to 90 degrees.

53y - 16 = 90

53y = 106

y = 2

Hope this helps!

Answer:

y=2

Step-by-step explanation:

the angle is 90 degrees which is equal to (53y-16).therefore find a number which you can substitute to get 90 which is y=2

Given the total number of students in the university freshman class and the number of students majoring in computer science, the percentage of the class majoring in computer science is 46%.

Percentage is simply number or ratio expressed as a fraction of 100.

It is expressed as;

Percentage = ( Part / Whole ) × 100%

Given the data in the question;

We substitute the given values into the above equation.

Percentage = ( Part / Whole ) × 100%

Percentage = ( 4554 / 9900 ) × 100%

Percentage = ( 0.46 ) × 100%

Percentage = 46%

Given the total number of students in the university freshman class and the number of students majoring in computer science, the percentage of the class majoring in computer science is 46%.

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The volume of the composite figure is 655.44 unit³.

The information is incomplete. An overview will be given. Let's assume that the shape is a cylinder.

The volume of a cylinder is πr²h

Assumed radius = 7

Assumed height = 4

The volume will be:

= πr²h

= 3.14 × 7² × 4

= 615.44 unit³

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The secant in the diagram is [tex]\overline{AD}[/tex]

Segment AD intersect the circle at two points. So it can be a secant.

We have been given that a circle of center O. We have to find the segment that is secant.

Secant : If a line which intersect the circle at two points.Then the line segment  is called  secant.

If the ray lies onto the considered line segment(overlapping), then it can be said belonging to the considered line segment.

(line segment has 2 fixed ends, whereas a ray has one end only, other end is not fixed)

Segment OB intersect the circle at one point B only. so OB cannot be a Secant.

Segment AD intersect the circle at two points. So it can be a secant.

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A correlation coefficient of 0.76 indicates a very strong positive linear relationship between the two variables.

Correlation is a statistical measure used to measure the linear relationship that exists between two variables.

If the sign of the  correlation coefficient is positive, it means that the two variables exhibits a positive correlation. The closer to 1, the  correlation coefficient is, the stronger the linear relationship.

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The geometric center of the graph under the function is 5/3

The equation of the function is given as:

f(x) = 3 - |x - 2|

The interval is given as:

x ∈ [0, 3]

The geometric center (gc) of the graph under the function is calculated using

gc = ∫x f(x) dx/∫f(x) dx

Substitute the known values in the above equation

gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx

Integrate the numerator and the denominator of the above equation

gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]

Recall that the interval is given as x ∈ [0, 3]

Substitute the interval values in the above equation.

The equation is then simplified using a graphing calculator.

So, we have

gc = (65/6)/(13/2)

Express the quotient expression as a product

gc = (65/6) * (2/13)

Divide 65 by 13

gc = 5/6 * 2

Divide 2 by 6

gc = 5/3

Hence, the geometric center of the graph under the function is 5/3

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The probability of inductees who are female will be 0.155.

Question: What proportion of inductees have been female or have included female members?

From the information, 303 groups or individuals and forty-seven of the inductees have been female or have included female members.

Therefore, the proportion will be:

= 47/303

= 0.155

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The list of data points used to generate the histogram is

   x            Frequency

15-20              0

20-25             4

25-30              6

30-35              3

35-40              4

40-45              0

45-50              3

From the question, we are to write the list of data points used to generate the given histogram

The list of data points used to generate the histogram is

   x            Frequency

15-20              0

20-25             4

25-30              6

30-35              3

35-40              4

40-45              0

45-50              3

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[tex] \huge{↬ \boxed{ \sf{ \pink{A\green{n \blue{s \color{yellow}w \red{e \orange{r}}}}}}}}[/tex]

[tex] \leadsto[/tex]According to Angle sum property of a triangle , sum of the interior angles of a triangle is 180°.

➱ ∠SPR + ∠QPR = 180° [Linear pair]

➱ 135° + ∠QPR = 180°

➱ ∠QPR = 180° - 135°

➱ ∠QPR = 45°.....(i)

➱ ∠PQT + ∠PQR = 180° [Linear pair]

➱ 110° + ∠PQR = 180°

➱ ∠PQR = 180° - 110°

➱ ∠PQR = 70°.....(ii)

➛ ∠PQR + ∠QPR + ∠PRQ = 180° [Angle sum property of a triangle]

➱ 70°+ 45° + ∠PRQ = 180° [from (i) and (ii)]

➱ ∠PRQ = 180° - 115°

➥ ∠PRQ = 65°

hope it's help u!! :D

The missing Statement and reason for the transverse line angles is; m∠YXD = 60° and  Supplementary angles sum up to 180°.

Statement 1; AB ║ CD

Reason 1; Given

Statement 2; m∠ZYB = 60°

Reason 2; Given

Statement 3; ∠YXD and ∠DXW form a linear pair

Reason 3; Definition of Linear Pair

Statement 4; m∠YXD = 60°

Reason 4; Corresponding angles have equal measure.

Statement 5; m∠DXW = 120°

Linear pairs usually sum up to 180° because they are supplementary angles. Thus;

m∠YXD = 180° - 60° = 120°

Reason 5; Supplementary angles sum up to 180°.

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Answer: graph c

Hope I was able to help

Answer:

The numbers 1 to 12 must be placed in the circles of the star shown on the right. The sums of the numbers in each row, and the sum of the numbers in the six outer circles of the star, must be equal to 26. Arrange the numbers accordingly.

The function is increasing on the intervals:

(-∞, 3] and [5, ∞)

Then the correct options are a and c.

The function is increasing when, reading from left to right, we can see that the curve goes upwards.

By looking at the graph, we can see that the function increases between -∞ and 3, and also increases between 5 and ∞, then the correct options are a and c-

(-∞, 3] and [5, ∞)

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The quantity reported an equivalent net percentage change of 28 percent.

In this problem we must determine the simple percentage change equivalent to two consecutive percentual changes. The formula that describes the situation is:

1 + r/100 = (1 - 60/100) · (1 + 80/100)

1 + r/100 = 72/100

r/100 = - 28/100

r = - 28

The quantity reported an equivalent net percentage change of 28 percent.

The statement is incomplete. Complete form is presented below:

A quantity is changing. At first it descreased by 60 percent and it increased by 80 percent. What is net change of the quantity in percentage?

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The list price of the house is $260,869.57

What is a list price?

This is the price the property is valued to sell at in an arm's length transaction in a transaction that occurs between independent parties.

In this case, the property was sold for 92% of its list price, which means the sales price is 92% multiplied by the list price.

sales price=92%* list price

sales price=$240,000

list price=unknown(assume it is X)

$240,000=92%*X

X=$240,000/92%

X=$260,869.57

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The side lengths of rectangle is 3 cm and 1.75 cm  and  5.25 cm and  9 cm.

According to the statement

we have given that Rectangle A has side lengths of 6 cm  and 3.5 cm

And The side lengths of rectangle B are proportional to the side lengths of rectangle A.

And we have to Find that the What could be the side lengths of rectangle B?

A  3 cm and 1.75 cm

B  5 cm and  2.5 cm

C  7 cm and  7 cm

D  12 cm and  5 cm

E  5.25 cm  and  9 cm

Here we see that the side B are proportional to side length A of rectangle.

So,

Let say sides of rectangle B are  a  and  b  corresponding to sides  6 and 3.5 cm

=> a/6  = b/3.5

=> a/b = 6/3.5

=> a/b  = 12/7

A  3 cm and 1.75 cm    

3/1.75  = 12/7

Hence this is proportional

B  5 cm and  2.5 cm

5/2.5  = 2  ≠ 12/7

Not Proportional

C  7 cm and  7 cm

7/7 = 1 ≠ 12/7

Not Proportional

D  12 cm and  5 cm

12/5   ≠ 12/7

Not Proportional

E  5.25 cm  and  9 cm

9/5.25  = 36/21  = 12/7

Hence this is proportional

So, 3 cm and 1.75 cm   and   5.25 cm and  9 cm  could be the side lengths of rectangle B.

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The area of the equilateral triangle is 110.9 cm

area of a triangle = 1 / 2 bh

where

Therefore,

tan 60 = opposite / adjacent

tan 60 = 8√3 / x

x =  8√3 / √3

x = 8

hence,

b = 8 + 8 = 16

Therefore,

area of a triangle =  1 / 2 × 16 × 8√3

area of a triangle = 64√3

area of a triangle = 110.851251684

area of a triangle = 110.9 cm

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he instructions to find the LCM of 20, 35 and 40 are the next:

1. Decompose all numbers into prime factors

20 2 10 2 5 5 1

35 5 7 7 1  

40 2 20 2 10 2 5 5 1  

2. Write all numbers as the product of its prime factors

Prime factors of 20 = 22 . 5

Prime factors of 35 = 5 . 7

Prime factors of 40 = 23 . 5

3. Choose the common and uncommon prime factors with the greatest exponent

Common prime factors: 5

Common prime factors with the greatest exponent: 51

Uncommon prime factors: 2 , 7

Uncommon prime factors with the greatest exponent: 23, 71

4. Calculate the Least Common Multiple or LCM

Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.

LCM = 51. 23. 71 = 280

Reflection and dilation is the transformation which will occur to map triangle ABC triangle to A^ * B^ n C^ prime.

This refers to a plane figure which has features such as three angles and three sides.

Reflection and dilation involves flipping and enlargement/reduction respectively which gives rise to the sides being changed.

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Answer:

c. a reflection and a dilation

Step-by-step explanation:

The equation rule for the reflection of the triangle over the line y = -x is given as (x, y) ⇒ (-y, -x)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

The equation rule for the reflection of the triangle over the line y = -x is given as (x, y) ⇒ (-y, -x)

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