Help……………………………………..

Answer: 6) 33° , 7) x=3°

Step-by-step explanation:

The sum of the three angles of any triangle is equal to 180 degrees.

6) ∡SUT= 180-102 = 78 Linear Pair

   ∴ ∡UTS=180-(69+78)

            =180-147

            = 33°

7) ∡DBC=180-123=57 Linear Pair

57+25x+2+15x+1=180

60+40x=180

40x=180-60

      =120

x=120/40=3°

∴ ∡D=77

  ∡C=46

The markup is of amount $97.5

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

P = $500

i = 0.5%

n= 1

Using the formula

F = P + P x i x n

F= 500 + 500 x 0.005 x 1

F= 500+ 2.5

F= $502.5

So, the team need to raise

= 600- 502.5

= $97.4

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A. The linear relationship can be expressed by the equation, 3y = 5x + 10

B. For  25 kg, the height is 45 cm

   For  52 kg, the height is 90 cm

C. For 60 cm, the mass is 34

    For 80 cm, the mass is 46

The equation of a straight line is a relationship between x and y coordinates, The two point form of the equation of a straight line is,

y-y₁ =  (y₂-y₁)/(x₂-x₁)*(x-x₁)

Given that,

The scatter plot,

which shows the linear relationship,

And passes through the points,

(10, 20), (40, 70)

the equation of line can be written as,

y - 20 =  (70-20)/(40-10)*(x-10)

y - 20 = 50/30*(x-10)

y - 20 = 5/3*(x-10)

3y - 60 = 5x - 50

3y = 5x + 10

A. The linear relationship,
3y = 5x + 10

B.    If x = 25, we can substitute this value into the equation to find the corresponding value of y:

3y = 5 x 25 + 10

3y = 125 + 10

3y = 135

Dividing both sides of the equation by 3:

y = 45

So, if x = 25, then y = 45.

similarly,  the value of y for x = 25 is, 90

In the same manner,

when,

For y = 60 x will be 34

And for y = 80 x will be 46

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Answer:

16 = 3x

Step-by-step explanation:

We are here given a equilateral triangle in which each side length measure is " x " .

By perimeter we mean the sum of all the side lengths of the figure.

By question , we have each side length as x ,

So its perimeter would be ,

x + x + x = 3x

But it is given that the perimeter is 16in . So they must be equal .

Hence our required equation is ,

16 = 3x

and if we want to solve out for x , divide both the sides by 3 ,

x = 16/3

and we are done!

The price of a child ticket is $4 and the price of a senior citizen ticket is $10

Let's call the price of a senior citizen ticket "x" and the price of a child ticket "y".

On the first day, the school sold 3 senior citizen tickets and 4 child tickets for a total of $46, so we can write the equation:

3x + 4y =46

On the second day, the school took in $48 by selling 4 senior citizen tickets and 2 child tickets, so we can write another equation:

4x + 2y = 48

Now that we have two equations, we can use substitution or elimination to find the value of x and y.

For substitution, we can solve one equation for one variable and then substitute that expression into the other equation. For example, let's solve the first equation for x:

x = (46 - 4y)/3

Then, we can substitute this expression for x into the second equation:

4((46 - 4y)/3) + 2y = 48

Expanding the left side of the equation:

(184 - 16y)/3 + 2y = 48

Multiplying both sides by 3:

184 - 16y + 6y = 144

Combining like terms on the left side:

184 - 10y = 144

Subtracting 184 from both sides:

-10y = -40

Dividing both sides by -10:

y = 4

So the price of a child ticket is $4. To find the price of a senior citizen ticket, we can substitute this value back into the equation we solved for x:

x = (46 - 4y)/3 = (46 - 4 * 4)/3 = (46 - 16)/3 = 30/3 = $10

So the price of a senior citizen ticket is $10.

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According to the area of rhombus and length of one diagonal, the length of other diagonal is 10.5 cm.

The formula for the length of the diagonal is as follows -

Area = product of diagonal 1 and diagonal 2/2

Keep the values in formula to find the length of diagonal

360 = 40 × diagonal 2/2

Rewriting the equation with diagonal 2 on Left Hand Side of the equation

Diagonal 2 = (360 × 2)/40

Performing multiplication on Right Hand Side of the equation

Diagonal 2 = 420/40

Performing division on Right Hand Side of the equation

Diagonal 2 = 10.5 cm

Thus, the diagonal 2 is 10.5 cm.

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Answer:

(x + 11)² + (y - 15)² = 81

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 11, 15 ) and r = 9 , then

(x - (- 11) )² + (y - 15)² = 9² , that is

(x + 11)² + (y - 15)² = 81

Answer: Roots are real and distinct

Step-by-step explanation:

a = +ve  b = -ve  c = -ve

determinant = +ve

if determinant is positive then roots are real and distinct

Answer:

6048 should be multiplied by 98.

Step-by-step explanation:

6048 = 2⁵ * 3³ * 7

To make 6048 a perfect cube, 6048 should be multiplied by 2 * 7 * 7.

2* 7 *7 = 98

Check: 6048 * 98 = 592704

592704 = 2⁶ * 3³ * 7³

[tex]\sqrt[3]{592704}= 2 * 2 * 3 * 7[/tex]

              = 84

The best way is to use the Ratio Test to see that the series = ∑∞ₙ₋₁ n/5ⁿ converges.

In mathematics, convergence definition is the property (some described by myriad series and functions) that it approaches its limit more and more distinctly as the arguments (variables) of the function increase or decrease, or as the number of terms in the series increases.

For example, the function y = 1/x converges to zero as x increases. Even in this case, the final value of x doesn't affect the value of y to actually be zero, and the marginal value of y is zero, since y can be made arbitrarily small by choosing a large enough "x". The line y = 0 (x-axis) is known as the asymptote of the function.

According to the Question:

Let aₙ= n/5ⁿ. If  lim(n→∞)

|an+1|/ |an| <1, the Ratio Test will imply that  

∑∞ₙ₋₁ aₙ = ∑∞ₙ₋₁ n/5ⁿ converges.

Now,

aₙ₊₁ = n + 1/ 5ⁿ⁺¹

    = n + 1 /5.5ⁿ.

Therefore,

since these terms are positive,

    |aₙ₊₁|/|aₙ| = n + 1 /5⋅5ⁿ

⇒ n +1/ 5ⁿ → 1/5 as n→∞

Hence,

∑∞ₙ aₙ = ∑∞ₙ₋₁ n/5ⁿ converges.

Full Question:

How do you test the series (n/5ⁿ ) from n = 1 to infinity for convergence? Determine the values of all positive, for which the series. Determine the values of all positive k for which the series. Express your answer in interval notation will converge. Express your answer in interval notation.

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Answer:

Step-by-step explanation:

Based on the information in the tape diagram and table, we can see that the ratio of oil to vinegar in Iara's salad dressing is 8 to 1. This means that for every 8 spoonfuls of oil, she uses 1 spoonful of vinegar.

To calculate the amount of oil and vinegar in the dressing, we can use the following formula:

amount = original ratio * total amount of dressing ÷ (original ratio + 1)

For the oil, the formula would be:

oil amount = 8 * 33 ÷ (8 + 1) = 8 * 33 ÷ 9 = 88 spoonfuls

And for the vinegar, the formula would be:

vinegar amount = 1 * 33 ÷ (8 + 1) = 1 * 33 ÷ 9 = 11 spoonfuls

So the final answer is:

Oil: 88 spoonfuls

Vinegar: 11 spoonfuls

so your problem is 2x+y=18 and y=4x+6

solution

solve for the first variable in one of the equations then substitute the result into the other equation

point form:

(2,14)

equation form

x=2, y=14

The maximum amount of space that the teacher can reserve on her bulletin board using the 40-inch long roll of string is 400 square inches.

A rectangle is a two-dimensional shape with four sides and four right angles. It is characterized by having two equal sides that are parallel to each other and two equal sides that are perpendicular to the first two sides.

First, let's consider the perimeter of the rectangle. The perimeter is the total length of the four sides of the rectangle.

So, if we use the entire 40-inch long roll of string to form the border, it will equal the perimeter of the rectangle. We can represent the length and width of the rectangle using variables "l" and "w", respectively.

The perimeter of the rectangle can be calculated using the formula: P = 2l + 2w.

Now, we can set the perimeter equal to 40 inches and solve for l and w.

P = 40

2l + 2w = 40

l + w = 20

Next, we want to find the maximum area of the rectangle. The area of a rectangle can be calculated using the formula: A = l * w.

So, to find the maximum area, we need to maximize the product of l and w. This can be done by setting l and w equal to half of the perimeter, or 20 inches each.

l = w = 20

A = l * w

A = 20 * 20

A = 400 square inches

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Answer:

6

Step-by-step explanation:

Let x be the vertical height

area of triangle=1/2×6×6=18

1/2×3×x=18/2

1.5x=9

x=6

Answer:

Step-by-step explanation:

Answer:

a) See attached image

b) AA (or AAA) similarity; either one is correct

c) The statue is 22 meters tall

Step-by-step explanation:

Let's assume the height of the statue is h (to be determined)

a) First let's create a diagram to model this scenario. See attached image
 One of the properties of a mirror reflection is that the angle of incidence i.e. the angle at which light strikes the mirror = angle of reflection i.e. the angle at which the light reflects off the mirror

These angles are shown as α and β in the diagram

The two triangles we choose to solve this problem are
ΔABC and ΔCED

Given that ∠BCA is a complementary angle to angle of reflection and ∠ECD is complementary to the angle of incidence, it follows that

m∠BCA = m∠CED

m∠BAC of ΔABC = m∠ECD of ΔECD = 90°

Therefore the third angles of both triangles are also equal

b) By the AA (or AAA) or Angle-Angle Similarity theorem, the two triangles are similar

Therefore the ratio of the sides must be the same for corresponding sides

Therefore
[tex]\dfrac{AB}{DE} = \dfrac{AC}{CD} \\\\Given AD = 12, CD = 3\\\\\dfrac{AD}{CD} = \dfrac{12}{3}= 4\\\\\therefore \\\\\dfrac{AB}{ED} = 4\\\\[/tex]

Since ED is the height of the girl = 5.5 meters and AB = height of the statue = h

we get
[tex]\dfrac{h}{5.5} = 4\\\\h = 4 \times 5.5\\\\h = 22\\\\[/tex]

Answer (c) height of statue = 22 meters

Answer:

two plus two equals five

Step-by-step explanation:

The triangles ΔABC and ΔDEF are congruent with each other by the SAS postulate. And ∠ABC = ∠DEF, ∠BCA = ∠EFD, ∠CAB = ∠FDE, and AB / DE = BC / EF = CA / FD.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

In triangles ΔABC and ΔDEF, then we have

AB = DE

BC = EF

∠ABC = ∠DEF = 92°

Then the triangles ΔABC and ΔDEF are congruent with each other. Then we have

∠ABC = ∠DEF

∠BCA = ∠EFD

∠CAB = ∠FDE

And the corresponding ratios are given as,

AB / DE = BC / EF = CA / FD

The triangles ΔABC and ΔDEF are congruent with each other by the SAS postulate.

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The odds of an event are calculated by taking the number of positive outcomes and dividing it by the number of negative outcomes.the odds in favor of her teaching both classes are 15:85 or 1:5.5.

a. The probability that she chooses to teach both classes is 15%.

b. The odds in favor of her choosing to teach both classes are 1:5.5.

a. The probability of an event is calculated by taking the number of positive outcomes and dividing it by the total number of outcomes. In this case, the professor has a 50% chance of teaching the first class and a 30% chance of teaching the second class. Therefore, the probability of her teaching both classes is 0.5 x 0.3 = 0.15 or 15%.

b. The odds of an event are calculated by taking the number of positive outcomes and dividing it by the number of negative outcomes. In this case, there is a 15% chance of her teaching both classes and an 85% chance of her not teaching both classes. Therefore, the odds in favor of her teaching both classes are 15:85 or 1:5.5.

The complete question is :

A professor is deciding whether to teach two classes. There is a 50% chance that she will teach the first class and a 30% chance that she will teach the second class.

a. What's the probability that she chooses to teach both classes?

b. What are the odds in favor of her choosing to teach both classes?

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Let's say event A is the selection of four positive numbers, event B the selection of four negative numbers, and event C the selection of two positive and two negative numbers.

Since four numbers are chosen without replacement,  n(A) = 6 × 5 × 4 × 3 = 360  n(B) = 8 × 7 × 6 × 5 = 1680. In event C, four numbers are to be chosen without replacement such that two numbers are positive and two numbers are negative.

This can be done in following ways:  + + – – OR + – + – OR + – – + OR – + – + OR – – + + OR – + + –  ∴ n(C) = 6 × 5 × 8 × 7 + 6 × 8 × 5 × 7 + 6 × 8 × 7 × 5 + 8 × 6 × 7 × 5 + 6 × 5 × 8 × 7 + 8 × 6 × 5 × 7  = 6 × (8 × 7 × 6 × 5)  =10080  Here, total number of numbers = 14  ∴ n(S) = 14 × 13 × 12 × 11 = 24024

Since A, B, C are mutually exclusive events,

Required probability = P(A) + P(B) + P(C)

= n(A)/n(S) + n(B)/n(S)+ n(C)/n(S)

= 360+1680+10080/24024

= 505/1001

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The length of YZ in the triangle is 12.5 units

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

The triangle

On the triangle, we have the following equivalent ratio

YZ : 5 = 10 : 4

Express as fraction

So, we have

YZ/5 = 10/4

This gives

YZ = 5 * 10/4

Evaluate

YZ = 12.5

Hence, the length is 12.5 units

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It's impossible to say Sean should base his decision on the marginal cost and marginal benefit of creating another table. The marginal cost of making a table is not the same as the average cost of making a table. As a result, there is insufficient information to determine what Sean should do.

The opportunity cost of an activity is the value of what must be sacrificed in order to engage in the activity (plus the cost). A cost that cannot be recovered at the time a decision must be made.

The science of decision-making is often used as a crude definition of economics. This stems from the fact that economics is frequently concerned with making the best decision in the most efficient manner. One way to quantify this is to consider total costs and total benefits.

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The given line y = -2x + 3 will cross the y-axis at (0, 3).

A coordinate plane is a two-dimensional plane that consists x-axis and a y-axis. These are perpendicular to each other and will be intersected at the point called the origin.  

The coordinates of the point that lies on the y-axis are (0, y), Similarly, the coordinates of the point that lies on the x-axis are (0, x).    

Here we have

The equation of the line is y = -2x + 3  

To find the required point take x = 0

=> y = -2(0) + 3

=> y = 0 + 3

=> y = 3

Therefore,

The given line y = -2x + 3 will cross the y-axis at (0, 3).

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By using the data from the bar graph, each of the statistical value are as follows;

Median = 6.

Lower quartile = 4.

Upper quartile = 7.5.

Interquartile range = 3.5

From the information provided in the bar graph above, we can logically deduce the following data set:

Data set = {3, 5, 6, 7, 8}

Median = 6.

For Q₁ of the lower half of the data set, we have:

Lower quartile, Q₁ = {3, 5}

Lower quartile, Q₁ = (3 + 5)/2

Lower quartile, Q₁ = 8/4 = 4.

For Q₃ of the upper half of the data set, we have:

Upper quartile, Q₃ = {7, 8}

Upper quartile, Q₃ = (7 + 8)/2

Upper quartile, Q₃ = 15/2 = 7.5.

Mathematically, interquartile range (IQR) is the difference between lower quartile (Q₁) and upper quartile (Q₃):

IQR = Q₃ - Q₁

IQR = 7.5 - 4

IQR = 3.5

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Her average speed for the entire trip, in kilometers per hour, is equal to 2d / (7.1 * 3600) * 3600 km/h

Let's assume that the total distance of the round trip is d kilometers and that she drove at a constant speed of v km/h for the entire trip. The time it takes for her to travel the entire distance at speed v is given by t = d/v.

Since she drove back home using the same path she took out to the university, her average speed for the entire trip must be equal to her speed on the way out and back. Therefore, the total time it took for her to complete the round trip is 2t = 2d/v.

Since the total time it took for her to complete the round trip is 7.1 hours, we can set up an equation:

2d/v = 7.1 hours

Converting hours to seconds and solving for v, we have:

v = 2d / (7.1 * 3600) km/s

Finally, converting to km/h, we get:

v = 2d / (7.1 * 3600) * 3600 km/h

Therefore, her average speed for the entire trip, in kilometers per hour, is equal to 2d / (7.1 * 3600) * 3600 km/h

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The best prediction of the number of tagged salmon in a sample of 2000 is 100.

The best prediction of the number of tagged salmon in a sample of 2000 returning salmon can be estimated using the proportion of tagged salmon in the sample of 400.

The proportion of tagged salmon in the sample of 400 is [tex](\frac{20}{400} )=(\frac{1}{20} )[/tex].

We can use this proportion:

To estimate the number of tagged salmon in a sample of 2000:

Tagged salmon in a sample of 2000 = [tex](\frac{1}{20}) * 2000[/tex] = 100

Therefore, the best prediction of the number of tagged salmon in a sample of 2000 is 100.

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The required form of a parabola in vertex form is y = a(x - h)² + k.

A parabola is a cross-section cut out of the cone and represented by an equation.

Here,

The standard form of a parabola in vertex form is:

y = a(x - h)² + k

where (h, k) is the vertex of the parabola and a determines the direction of opening (a > 0 for an upward-facing parabola and a < 0 for a downward-facing parabola). The coefficient also determines the shape and steepness of the parabola.

Thus, the required form of a parabola in vertex form is y = a(x - h)² + k.

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Answer:

-5

Step-by-step explanation:

−15a = 75

a = 75/-15

a = -5

Answer:

-67

Step-by-step explanation:

- 203 - (-136)

The 2 minuses cancel out each other, turning it into a plus sign.

-203 + 136 = -67

Basic addition

Step-by-step explanation:

Because there is a double negative in between 203 and 136 that would turn into a positive

So

-203+136

Now because 203 is negative you would take 203 and subtract 136 to get 67

Because 136 is less then 203 it would still be negative

So

The answer is -67