Lionel sold at $10.70 each and 15 pens at $2.10 each during a sale. Janet sold the same number of balls at $11.20 each and 15 pens at $1.90each. They collected the same amount of money. How many ball did each of them sell?

a) The triangles are congruent by the AAA criterion.

b) The triangles are congruent by the SAS criterion.

a) In the first triangle the interior angles are 40 degrees and 30 degrees.

The other interior angle would be 180 - (40 + 30) = 110 degrees.

As per the diagram, the triangles have equal proportionate-sized side lengths.

Therefore, the triangles are congruent by the AAA criterion.

b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.

Therefore, the triangles are congruent by the SAS criterion.

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Given that in circle S, a sector is shaded and ZTSU measures 40°. We are to find out what fraction of the interior of the circle is shaded and simplify the answer.The correct answer is 16π/9 cm².

To find out the fraction of the interior of the circle that is shaded, we need to determine the measure of the central angle that intercepts the entire circle.The total measure of a circle is 360 degrees.

To find the fraction of a circle shaded, divide the number of degrees in the sector by

360.4x = (40/360) × πr² = (1/9) × πr².

We simplify the answer: 4x = πr²/9 Fraction of the interior of the circle that is shaded = 40/360 = 1/9.Expression for the area of the shaded sector in square centimeters is:

A = (40/360) × πr² = πr²/9 =  π(4²)/9 = 16π/9 cm²

Therefore, the correct answer is 16π/9 cm².

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Answer:

y = -6x + 8

Step-by-step explanation:

\begin{bmatrix}6x+y=8\\ y=-6x+8\end{bmatrix}

I don't know why it came out like this

Answer: x=15.6

Step-by-step explanation:

An isosceles triangle has two congruent sides. (1 pair). So, the other side (not x) must equal 11.

Using the Pythagorean Theorem; a^2+b^2=c^2, you can substitute the values in as follows

11^1+11^2=x^2

121+121=x^2

242=x^2

15.55634918610405=x

round to the nearest tenth as said in the question...

x=15.6

Angles 1 and 2 are congruent and AB is parallel to DC, so by the Corresponding Angles Theorem, AC is congruent to DB.

Therefore, AC is congruent to DB.

Given: AB is parallel to BC

DC is parallel to BC

Angle 1 is congruent to Angle 2

Prove:

AC is congruent to DB

Proof: AB is parallel to BC and DC is parallel to BC.

Therefore, AB is parallel to DC.

Angle 1 is congruent to Angle 2.

Angles 1 and 2 are alternate interior angles, so they are congruent.

Angles 1 and 2 are congruent and AB is parallel to DC, so by the Corresponding Angles Theorem, AC is congruent to DB.

Therefore, AC is congruent to DB.

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Answer: 30

Step-by-step explanation:

18/5 divided by 3/25 is the same thing as multiplying 18/5 with the reciprocal of 3/25 (25/3).

[tex]\frac{18}{5} *\frac{25}{3} =\frac{450}{15}[/tex]

And when multiplying out you get 450/15.

Simplifying (by dividing 450 by 15) this you will get 30.

The classroom coin box required less than 11.11 Square feet of cardboard (100 square feet divided by 9), then 100 square feet would be sufficient

The 100 square feet of cardboard is enough to build the new coin box with a scale factor of 3 times the classroom coin box, we need to consider the relationship between the areas of the two boxes.

The area of the original classroom coin box is unknown, as it is not given in the problem. However, since we know that the new coin box has a scale factor of 3 times the original, we can infer that its area will be 3^2 = 9 times greater than the original.

Let's assume that the area of the classroom coin box is A square feet. In that case, the area of the new coin box would be 9A square feet.

Now, we are given that 100 square feet of cardboard is available. To determine if it's sufficient, we need to compare this value to the area of the new coin box, which is 9A.

If 100 square feet is greater than or equal to 9A, then it would be enough to build the new coin box. Conversely, if 100 square feet is less than 9A, it would not be enough.

Since we do not have a specific value for A, we cannot determine the exact answer. However, we can provide the argument to defend our solution.the classroom coin box required less than 11.11 square feet of cardboard (100 square feet divided by 9), then 100 square feet would be sufficient.

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Note the question be like :

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn from the bag without replacement, what is the probability that both marbles are red?

The value of the variable x in the right angle triangle is: 9

Pythagoras Theorem is defined as the way in which we can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

The tangent forms a right angle with the circle and as such using Pythagoras theorem, we have:

8 + x = √(15² + 8²)

8 + x = √289

8 + x = 17

x = 17 - 8

x = 9

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Answer:

When the cab travels 0 miles, the total fee will be $10.00.

Step-by-step explanation:

We Know

2 miles = $13.00

5 miles = $17.50

3 miles = 17.50 - 13.00 = $4.50

1 mile = 4.50 / 3 = $1.50

So, for every 1-mile go, the cost is increasing by $1.50; this is the slope.

What does the y-intercept mean in this situation?

It is the total fee that Tyrell pays when the cab goes 0 miles (when he first steps in the cap).

So, the answer is D. When the cab travels 0 miles, the total fee will be $10.00.

Carter would need to invest approximately $76,869.06 to reach a value of $174,000 in 19 years with a 4.3% annual interest rate compounded daily.

The formula accrued amount in a compounded interest is expressed as;

[tex]A = P( 1 + \frac{r}{n})^{(nt)}[/tex]

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

Accrued amount A = $174,000

Compounded daily n = 365

Time t = 19 years

Interest rate r = 4.3%

Principal P = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 4.3/100

r = 0.043

Plug these values into the above formula and solve for principal P.

[tex]A = P( 1 + \frac{r}{n})^{(nt)}\\\\A = 174,000( 1 + \frac{0.043}{365})^{(365\ *\ 19)}\\\\A = \$ 76,869.06[/tex]

Therefore, the principal that needs to invested is $76,869.06.

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Answer:

∆SMK is similar to ∆RMT by AA.

Domain: {-15, 0, 9, 33, 44, 45}

Range: {15, 21, 33, 46, 57, 97}

The domain and range describe the x and y-values of a function.

Domain

The domain of a function shows the x-values covered by a function. Since the function cannot be proved to be continuous, we have to list the domain as a discrete list of values. We cannot say that the values between the listed x-values are a part of the domain. Any x-value included in the function is a part of the domain. As stated in the question, we should list our answer as an ordered list with braces.

Range

The range of a function shows the y-values covered by the function. Similar to the domain, we cannot assume that the y-values between those listed are included in the range. This means that the range will also be a list of values. Range and domain should be listed from least to greatest. So, we can create a list of all the y-values in numerical order.

Answer:

2.

Quarterly:

Monthly:

Continuously:

3.

Twice a year:

Eight times a year:

Continuously:

Step-by-step explanation:

The formula for compound interest is:

A = P(1+r/n)^nt

The formula for compounded continuously is:
A = Pe^rt

Where:

A = the future value of the investment

P = the principal balance

r = the annual interest rate (decimal)

n = number of times interest is compounded per year

t = the time in years

Using that we can plug the formula in for each question:

2.

Quarterly:

Monthly:

Continuously:

3.

Twice a year:

Eight times a year:

Continuously:

Step-by-step explanation:

sin Φ  = 5/6 = .8333

Arcsin ( sin Φ) =  arcsin (.8333)

Φ = 56.4 degrees

Step-by-step explanation:

1) the 1-st prism is cube. Then its surface area can be calculated as:

A=5*5*6=150 [ft²];

2) A=[Perimeter of triange]*height+2*[Area_of_triangle];

according to the formula above height=3; Perimeter of triangle=9+12+15=36; Area of triangle=12*9*0.5=54;

Finally, A=36*3+2*54=108+108=216 [cm²].

The mean score of a random student (YY) is 574.5. the standard deviation of the random student's score (YY) is 8.

Given:

- Each correct question is worth 10 points.

- Every student receives an additional 555 bonus points.

Let's calculate the mean and standard deviation of YY:

Mean of YY:

The mean score, denoted as μY, can be calculated using the mean of XX (μX) and the scoring scheme:

μY = μX * 10 + 555

Substituting the value of μX from the given information:

μY = 1.95 * 10 + 555

μY = 19.5 + 555

μY = 574.5

Therefore, the mean score of a random student (YY) is 574.5.

Standard Deviation of YY:

The standard deviation of YY, denoted as σY, can be calculated using the standard deviation of XX (σX) and the scoring scheme:

σY = σX * 10

Substituting the value of σX from the given information:

σY = 0.8 * 10

σY = 8

Therefore, the standard deviation of the random student's score (YY) is 8.

Complete question: Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions

that a randomly chosen student answered correctly. Here is the probability distribution of X along with

summary statistics:

0

1

2

2.

3

X = # correct

P(X)

0.05

0.20

0.50

0.25

Mean: Hex = 1.95

Standard deviation: Ox 0.8

Mr. Gupta decides to score the tests by giving 10 points for each correct question. He also plans to give

every student 5 additional bonus points. Let Y represent a random student's score.

What are the mean and standard deviation of Y?

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Step-by-step explanation:

This is a quadratic with vertex at (2,1) ....write the equation first in vertex form, then expand to the form requested

  y = ( x -2)^2  + 1

  y = x^2 -4x +4    + 1

 y = x^2 -4x + 5     Done.      a = -4   b = 5

Answer:

24

Step-by-step explanation:

For this problem, substitute the value -3 for x and solve. It would look like this:

[tex]4(-3)^2+2(-3)-6[/tex]

Using the order of operations (PEMDAS) we solve the exponent first.

[tex]-3^2=9[/tex]

Then solve the multiplication parts.

[tex]4(9)+2(-3)-6\\4*9=36[/tex]and        [tex]2*(-3)=-6[/tex]

Finally subtract to get the answer.

[tex]36-6-6=24[/tex]

The rays in Tiffany’s design are EA, FB, GC, GH, ED

From the question, we have the following parameters that can be used in our computation:

Tiffany’s design

By definition, the rays in Tiffany’s design are lines that have one fixed endpoint and the other endpoint extends indefinitely

Using the above as a guide, we have the following:

The rays in Tiffany’s design are EA, FB, GC, GH, ED

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Answer:

  (b)  $3564.54

Step-by-step explanation:

You want the new balance showing on a credit card statement if the APR is 27.99%, the old balance is $3109.87, a payment of $159 was made, and purchases were made totaling $532.42.

Apparently, the new balance is computed by subtracting payments, and adding new charges to the old balance, then computing and adding the finance charge on this sum.

  balance before finance charge: $3109.87 -159.00 +532.42 = $3483.29

The finance charge is 1 month's interest at the annual rate:

  I = Prt = $3483.29×0.2799×(1/12) = $81.25

The new balance is the subtotal above, with the finance charge added:

  new balance = $3483.29 +81.25 = $3564.54

Kyle's new balance will be $3564.54.

__

Additional comment

This is a very expensive credit card. Not only is the interest rate of 27.99% very high, but also finance charges are charged on new purchase in the month they are purchased.

Some cards these days have interest rates of 12.75% or lower, with no finance charge for purchases made during the month. Some cards offer a rebate of up to 1.5% of purchases, so a net "negative" finance charge if you pay off the card every month.

Answer: 127

Step-by-step explanation:

360 - 70 - 36 = 254

254/2 = 127

D = 127

1) sin θ + tan θ is equal to 5/6. 2) sin θ is 5/12. 3) sec θ + cosecc^2 θ = 12/√119 + 144/25 4) cot θ + sin θ is equal to 169/60.

1) To find sin θ + tan θ, we need to find the value of sin θ. Using the identity tan θ = sin θ / cos θ, we can rewrite tan θ as sin θ / cos θ.

tan θ = 5/12 = sin θ / cos θ

Since we are given that 0 < θ < 90, both sin θ and cos θ are positive.

Using the Pythagorean identity[tex]{sin^2}[/tex] θ + [tex]cos^2[/tex] θ = 1, we can solve for cos θ:

[tex]cos^2[/tex] θ = 1 - sin^2 θ

[tex]cos^2[/tex] θ = [tex]1 - (5/12)^2[/tex]

[tex]cos^2[/tex]θ = 1 - 25/144

[tex]cos^2[/tex] θ = 119/144

cos θ = √(119/144)

cos θ = √119/12

Now, we can find sin θ using the relationship [tex]sin^2[/tex] θ + [tex]cos^2[/tex]θ = 1:

[tex]sin^2[/tex] θ = 1 - [tex]cos^2[/tex] θ

[tex]sin^2[/tex]θ = 1 - (119/144)

[tex]sin^2[/tex]θ = 25/144

sin θ = √(25/144)

sin θ = 5/12

Finally, we can substitute the values of sin θ and tan θ into the expression sin θ + tan θ:

sin θ + tan θ = (5/12) + (5/12) = 10/12 = 5/6

Therefore, sin θ + tan θ is equal to 5/6.

2) The value of sin θ is already calculated as 5/12.

3) To find sec θ + [tex]csc^2[/tex] θ, we need to find the values of sec θ and csc θ.

Since sec θ is the reciprocal of cos θ, we can calculate sec θ as:

sec θ = 1/cos θ = 1/(√119/12) = 12/√119

csc θ is the reciprocal of sin θ, so:

csc θ = 1/sin θ = 1/(5/12) = 12/5

Now, we can substitute these values into the expression sec θ + [tex]csc^2[/tex]θ:

sec θ + [tex]csc^2[/tex]θ = (12/√119) + [tex](12/5)^2[/tex]= 12/√119 + 144/25

4) To find cot θ + sin θ, we need to calculate the value of cot θ.

cot θ is the reciprocal of tan θ, so:

cot θ = 1/tan θ = 1/(5/12) = 12/5

Now, we can substitute the values of cot θ and sin θ into the expression cot θ + sin θ:

cot θ + sin θ = 12/5 + 5/12

To add these fractions, we need a common denominator:

cot θ + sin θ = (12/5)(12/12) + (5/12)(5/5)

              = 144/60 + 25/60

              = 169/60

Therefore, cot θ + sin θ is equal to 169/60.

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The area of the given figure is 133 m²

Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,

The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height

Therefore,

The area of the given figure = 9.5 x 14 = 133

Hence, the area of the given figure is 133 m²

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Answer:

6* 2.2lb = 13.2 lb

Step-by-step explanation:

If 1 bag weights 2.2lb than 6 bags will weight 6 times more or:
2.2 lb * 6 = 13.2 lb

We can use the provided conversion factor, which states that 1 kg is equal to 2.2 pounds, to determine the weight of the cat food in pounds.

Since each bag of cat food weighs 6 kg, we can calculate the weight of 5 bags as follows.

5 bags of 6 kg each equal the total weight = 30 kg.

Now, we can convert the total weight from kilograms to pounds using the conversion factor:

Total weight multiplied by the conversion factor equals total weight in pounds.

= 30 kg x 0.2 lb/kg.

= 66 lbs.

Consequently, the cat food has a 66-pound weight when measured in pounds.

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The measure of a length of 10cm on the scale is 1/6 units

From the question, we have the following parameters that can be used in our computation:

Scale = 1 : 60

For a length of 10 cm, we have

Actual length = 10 cm

This means that

Scale ; 10 cm = 1 : 60

Express as fraction

So, we have

Scale/10 cm = 1/60

When evaluated we have

Scale = 1/6 units

Hence, the measure of a length of 10cm on the scale is 1/6 units

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The diagram represents the trajectory of an airplane at take off the angle representing the airplane's trajectory is approximately 147.83 degrees.

To solve this problem, let's denote the angle of the airplane's trajectory as x degrees. According to the given information, the angle representing the trajectory of the jet is 15% greater than the airplane's trajectory.

The angle representing the trajectory of the jet can be calculated as:

x + 0.15x = 1.15x

Therefore, the angle representing the trajectory of the jet is 1.15x degrees.

Given that the airplane's trajectory is at 170 degrees, we can set up the following equation:

1.15x = 170

To solve for x, divide both sides of the equation by 1.15:

x = 170 / 1.15 ≈ 147.83

Thus, the angle representing the airplane's trajectory is approximately 147.83 degrees, and the angle representing the jet's trajectory is approximately 1.15 * 147.83 ≈ 170 degrees.

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The angle formed by the cable between chairs B and J, and then

continue chair G is

75 degrees

The angle is determined with the knowledge of the total angle in a circle which is 360 degrees. Also, intercepted arc = 2 * inscribed angle

Assuming each chair is equal distance apart, then they will subtend equal angle.

The number of chairs for A to L is 12

angle per chair = 360 / 12 = 30 degrees

number of chairs from B to G = 5 and angle intercepted arc = 30 * 5 = 150 degrees

Inscribed angle = 1/2 * intercepted arc

Inscribed angle = 1/2 * 150

Inscribed angle = 75 degrees

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Rhett's house is a rectangular prism

Given data ,

Let the figure be represented as A

Now , the value of A is

Rhett made a simple drawing of his house.

And , It is a three dimensional figure with four faces that are rectangular and two that are square

So , the figure is represented as a rectangular prism

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

Hence , the figure is rectangular prism

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