For a project in her Geometry class, Morgan uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 13.85 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. She then walks 4.25 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.15 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

The value of cosα is 2/5.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Given that, tanα= -2/5 and α is quadrant IV.

We know that, tan(−θ) = − tan(θ)

α= 2/5

As we know cos(−θ) = cos(θ)

cosα =2/5

Therefore, the value of cosα is 2/5.

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a. The perimeter of the figure is:  61.4 cm

b. The area of the figure is: 160.69 cm²

The figure consists of two semicircles which makes one full circle and a rectangle. Therefore:

a. The perimeter of the given figure = circumference of a circle + 2w.

d = 8.6 cm

Circumference of the circle = 2 * pi * r = 2 * 3.14 * (8.6/2) = 27.00 cm

Perimeter = 27.00 + 2(17.2)

Perimeter = 61.4 cm

b. Area = area of circle + area of rectangle = 2πr + (length * width)

r = 7.9/2 = 3.95 cm

length = w = 17.2 cm

width = d = 7.9 cm

Area = 2*3.14*3.95 + (17.2*7.9) = 160.69 cm²

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After 3 3/5 weeks, they will have the same number of pictures.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, Yuki and Roman are photographers for the yearbook. Yuki starts with 20 photos. She then takes 60 photos each week. Roman starts with 110 photos. He then takes 35 photos each week.

Let "w" the number of weeks they collected the pictures

For Yuki,

The total picture he has after 0 weeks = is 20

The total picture he has after 1 week = 20 + 60

The total picture he has after 2 weeks = 20 + 60*2

The total picture he has after w weeks = 20 + 60*w

For Roman,

The total picture he has after 0 weeks = is 110

The total picture he has after 1 week = 110 + 35

The total picture he has after 2 weeks =110 + 35*2

The total picture he has after w weeks = 110 + 35*w

To calculate the number of weeks when they have equals pictures:

20 + 60*w = 110 + 35*w

25w = 90

w = 3 3/5

Therefore, After 3 3/5 weeks, they will have the same number of pictures.

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Answer:

The range is -11,-4,3,10

Step-by-step explanation:

The measure of the angle K is equal to 12.2° approximately to the nearest tenth, using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

For the triangle KLM, by sine rule;

k/sinK = m/sinM = l/sinL

We first derive the angle K as follows:

5.8/sin28° = 2.6/sinK

sinK = (2.6 × sin28°)/5.8

sin K = 0.2105

K = sin⁻¹(0.2105)

K = 12.1517

Therefore, the measure of the angle K is equal to 12.2° approximately to the nearest tenth, using the sine rule.

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Answer:

The length of the train can be calculated using the formula:

Length of the train = Speed x Time / 2

Where,

Speed = 60 km/hr = 60 x 1000/60 = 1000 m/min

Time = 9 sec = 9 / 60 min = 0.15 min

So,

Length of the train = 1000 x 0.15 / 2 = 75 m

Therefore, the length of the train is 75 meters.

Answer:

Length of the train shold be 75m

Step-by-step explanation:

The graph will be piecewise. Then the graph of the function is given below.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

S(n) = 0.50n + 3.5, if 1 ≤ n ≤ 14

S(n) = 0                 , if n ≥ 15  

The graph will be piecewise. Then the graph of the function is given below.

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Answer:

b

Step-by-step explanation:

:)

Therefore , the solution of the given problem of probability comes out to be likelihood that the full batch will be approved is therefore 0.832.

Probability theory is an area of mathematics that focuses on calculating the probability that a claim is accurate or that a particular occurrence will occur. Chance can be represented by any number range between 0 and 1, where 1 often denotes certainty and 0 typically denotes possibility. A probability diagram shows the possibility that a specific event will occur. The numerals 0 and 1, fractions with a ranging of 0% to 100%, or a few more characters can all be used to indicate probabilities.

Here,

Given that we've done it

Amount of CDs: 2100

50 faulty CDs total.

If every component of the sample is acceptable, the complete batch is accepted.

Therefore, we shall apply the "Binomial Theorem"

If there is no flaw, let p be the likelihood of success.

So, => p = 2100 - 50 / 2100

=> p = 2050/2100

=> p =0.97

q is the likelihood of a failure, or defect.

So,

=> q = 50/2100

=> q = 0.02

hence, the number of CDs chosen is 6.

Consequently, it is => P(X=6) = (0.97)6 = 0.832.

The likelihood that the full batch will be approved is therefore 0.832.

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In Venn diagram All three papers 39,exactly two of the papers 189, exactly one of the papers 251 and  The Guardian alone 142.

A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects. Circles that overlap share certain characteristics, whereas circles that do not overlap do not. Venn diagrams are useful for showing how two concepts are related and different visually.

They frequently serve to visually group objects while highlighting how they differ and how they are similar.

(I) All three papers

(G∪P∪T) = G + P+T+G∩P+G∩T+P∩T-(G∩P∩T)

290=142+181+117+75+60+54-(G∩P∩T)

(G∩P∩T)=39

(ii) exactly two of the papers = 60+75+54=189

(iii) exactly one of the papers =251

(iv) The Guardian alone =142.

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Answer:

Step-by-step explanation:

W(40)x25  

Answer:

YOUR ANDWER MIGHT BE D

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

a=50 because it's cut out of a full circle = 360, and it tells you what's left = 310

so 360-310=50

The equation the line is, y = 3/8 *x - 23/8, equation of the line in POINT-SLOPE form that passes through the given points (5,-1) and (-3,-4).

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have to points (5,-1) and (-3,-4)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

now, solving we get,

3x-8y = 23

equation of the line in POINT-SLOPE form is,

y = 3/8 *x - 23/8

Hence, the required equation is, y = 3/8 *x - 23/8

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The surface area of the square pyramid is given by S = 323.6 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of the square pyramid be S

Now , the equation will be

The base of the square pyramid a = 10 inches

The height of the lateral face h = 10 inches

The base area of the pyramid = a²

The lateral surface area of the pyramid = 2a √ ( ( a²/4 ) + h² )

So , the total surface area of square pyramid S = a² + 2a √ ( ( a²/4 ) + h² )

Substituting the values in the equation , we get

The base area of the pyramid = 100 inches²

The lateral surface area of the pyramid = 2 ( 10 ) √ ( ( 100/4 ) + 100 )

On simplifying the equation , we get

The lateral surface area of the pyramid = 223.6 inches²

The total surface area of square pyramid S = 100 inches² + 223.6 inches²

The total surface area of square pyramid S = 323.6 inches²

Hence , the surface area of the pyramid is 323.6 inches²

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Answer:

1) 9

2) 27

3) Read explanation below!

Step-by-step explanation:

1) Use the Pythagorean theorem to find AD. Show your working

To find '?' we first have to expand the indices...

Now work out '?'

2) Find AC. Show your working

We have found out that AD is 9 and to find AC we have to add 18!

3) Is ΔABC a right triangle? Explain

We can that ΔABC is not a right angle as none of the angles in the triangle are 90°!  If it was a right angled triangle we would see the ∟sign on one of the angles. Even though there are two of those in the middle it does not count as the question is asking about ΔABC!!

Have a lovely day :)

The total amount spent on tickets by Edgar is $15.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Let x be the cost of one game ticket and y be the cost of one ride ticket.

From the table, we can form two linear equations regarding the total amount spent by Erica and Penny.

10x + 5y = 10

15x + 10y = 16.25

Multiplying the first equation throughout with 2,

20x + 10y = 20

Subtracting 15x + 10y = 16.25 from the above equation,

(20x + 10y) - (15x + 10y) = 20 - 16.25

5x = 3.75

x = 0.75

Substituting x = 0.75 in 10x + 5y = 10,

7.5 + 5y = 10

5y = 2.5

y = 0.5

Cost of a game ticket is $0.75 and cost of a ride ticket is $0.50.

Total cost by Edgar = (12 × 0.75) + (12 × 0.5) = $15

Hence the total money spent by Edgar for both game and ride tickets is $15.

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Answer: False.

Step-by-step explanation:

A concave polygon is a polygon that has at least one interior angle greater than 180 degrees. This means that the polygon has a "cave" or indentation on its interior. However, the fact that a polygon is concave does not automatically mean that one of its diagonals will be drawn outside the polygon. Whether a diagonal is drawn inside or outside the polygon depends on the specific arrangement of the vertices, and cannot be determined solely based on the fact that the polygon is concave.

The servings that can be made from two quarts is 24

To convert the recipe's milk measurement from cups to quarts,

We first need to determine how many cups are in a quart.

There are 4 cups in a quart.

So, 3 cups of milk is equivalent to

3 / 4 = 0.75 quarts of milk.

Since the recipe uses 0.75 quarts of milk to make 9 servings,

Then each serving uses 0.75 / 9 = 0.083 quarts of milk.

Now, 2 quarts of milk is equivalent to 2 / 0.083 = 24 servings.

Therefore, from two quarts of milk, 24 servings can be made using this recipe.

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The value of x is approximately 3.875.

Given that angle JKL is inscribed in a circle and the measure of angle JKL is (16x-2)°, we can use the property of inscribed angles to find x. Inscribed angles that subtend the same arc have equal measure.

Let's call the measure of angle JKL "m". Then, the measure of angle JKL = m, the measure of angle KJL = m, and the measure of angle JLK = m.

The sum of the angles in a triangle is 180°, so we have:

m + m + m = 180°

3m = 180°

m = 60°

Substituting the value of m into the equation for the measure of angle JKL:

60° = (16x - 2)°

60 = 16x - 2

62 = 16x

x = 3.875

So, the value of x is approximately 3.875.

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The statements that are true are:

Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.

Clayton could negate both the x and y values in the points to find the points of the image.

C’ will move because all points move in a reflection.

The image and the pre-image will be congruent triangles.

The image and pre-image will not have the same orientation because reflections flip figures.

Options A, B, D, E, and F.

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

Clayton could use the relationship (x, y) → (y, x) to find the points of the image.

This is the y = x reflection rule.

This is true.

Clayton could negate both the x and y values in the points to find the points of the image.

Reflection of (x, y) along the x-axis and y-axis consecutively will give us

(-x, -y).

This is true.

C’ will remain in the same location as C because it is on the line of reflection.

This is not true.

C’ will move because all points move in a reflection.

This is true.

The image and the pre-image will be congruent triangles.

This is true.

The image and pre-image will not have the same orientation because reflections flip figures.

This is true.

Thus,

All statements are true except the statement:

C’ will remain in the same location as C because it is on the line of reflection.

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20(2/5x+3/4y-1/2) = 2(2x+7), 3x-2x+0.5x = 1/2 (16x+30y-20) corresponding expression from column B for each expression in column A

It is necessary to multiply, distribute, add, or take in mathematics. The following is the way an expression is put next to each other: Number, expression, and logical operator The ingredients of a mathematical expression include numerals, variables, and equations (such as addition, subtraction, multiplication or division etc.) It is conceivable to contrast statements with phrases. An phrase, often known as an arithmetic operation, is any logical statement that abstract, numbers, and a mathematical operation between those. For instance, the word m in the formula given is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the phrase 4m + 5.

given

3x-2x+0.5x  =  1/2 (16x+30y-20)

6(x+4)-2(x+5)  =  1.5%

3(x+4)-2(x+4) +0.5(x+4) =  1.5

20(2/5x+3/4y-1/2) = 2(2x+7)

20(2/5x+3/4y-1/2) = 2(2x+7), 3x-2x+0.5x = 1/2 (16x+30y-20) corresponding expression from column B for each expression in column A .

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Lilianna spend d= 7 minutes total to the park. Therefore, option C is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is d(3/4+1)=12 1/4.

Now, d(3/4+1)= 49/4

d(7/4)=49/4

d=49/4 ×4/7

d= 7

Thus, she spent d= 7 minutes total in the park.

Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Lilianna uses 3/4 calories per minute just by sitting. She uses 1 more calorie per minute by walking. Liliana uses a total of 12 1/4 calories walking to the park. Lilianna uses the equation, d(3/4+1)=12 1/4 to represent the situation. What does the variable d represent in the equation?

The arena should be financed by selling $  320   million in bonds and borrowing $  480   million.

==========================================================

Work Shown:

Something like x = 27 means "27 million dollars of bonds were sold".

The variable x has the restriction of [tex]0 \le x \le 480[/tex] since $480 million is the ceiling for the bonds.

The variable y has the restriction of [tex]0 \le y \le 640[/tex] since $640 million is the ceiling for the money borrowed from the insurance company.

The two amounts, x and y, must add to 800 to represent the $800 million total that needs to be raised.

x+y = 800

y = 800-x

-------------------

Let's calculate the interest for each item. Use the simple interest formula.

Bonds at 7% interest rate:

i = P*r*t

i = x*0.07*1

i = 0.07x

Borrowed money at 2% interest rate:

i = P*r*t

i = y*0.02*1

i = 0.02y

Total annual interest = 0.07x+0.02y = 32

The 32 at the end represents the $32 million of interest payout. This amount of money is paid to the bondholders and to the insurance company, and is done so yearly.

-------------------

Apply substitution to solve for x.

0.07x+0.02y = 32

0.07x+0.02(800-x) = 32 ...... plug in y = 800-x

0.07x+16-0.02x = 32

0.05x+16 = 32

0.05x = 32-16

0.05x = 16

x = 16/(0.05)

x = 320

They should sell $320 million in bonds.

320 million = 320,000,000

Note how x = 320 is in the interval [tex]0 \le x \le 480[/tex]

y = 800-x

y = 800-320

y = 480

They should borrow $480 million at an interest rate of 2%

480 million = 480,000,000

Note how y = 480 is in the interval [tex]0 \le y \le 640[/tex]

Answer:

The arena should be financed by selling $320 million in bonds and borrowing $480 million.

Step-by-step explanation:

Simple interest is calculated by multiplying the principal by the interest rate (in decimal form) and the time (in years).

Let x be the amount raised by selling bonds that pay an annual simple interest rate of 7%.

Therefore:

As the total cost of the sports arena is $800 million, the amount raised from borrowing money from the insurance company at an annual simple interest rate of 2% is (800 - x).  Therefore:

To determine whether the arena can be financed so that the annual interest is $32 million, equate the sum of the two expressions for interest to 32 and solve for x:

[tex]\implies 0.07x+0.02(800-x)=32[/tex]

[tex]\implies 0.07x+16-0.02x=32[/tex]

[tex]\implies 0.05x+16=32[/tex]

[tex]\implies 0.05x=16[/tex]

[tex]\implies x=320[/tex]

As x is the amount raised by selling bonds, then the amount in bonds that should be sold is $320 million.

To calculate the amount to borrow, subtract the amount in bonds sold from $800 million:

[tex]\implies 800-320=480[/tex]

Therefore, the amount to be borrowed from an insurance company is $480 million.

As both these amounts are less than the maximum limits set, they are both valid.

This is a problem finding the slope of a line at some point "a"

It accomplishes this by doing an average rate of change formula over an area approaching 0.

We must know the format of this type of equation.

See first image.

The variables in this example don't match up.

Let the function input be x, and the limit being a --> 0

a = 2

f(x) = x^5

Answer:

[tex]\displaystyle{f(x)=x^4 \ \: \text{and} \ \: a =2}[/tex]

Step-by-step explanation:

The first principal of derivative:

[tex]\displaystyle{f'(x) = \lim_{h\to 0} \dfrac{f(x+h)-f(x)}{h}}[/tex]

Since the given problem represents f'(a), meaning:

[tex]\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{f(a+h)-f(a)}{h}}[/tex]

If we compare:

[tex]\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{f(a+h)-f(a)}{h}}[/tex]

and

[tex]\displaystyle{ \lim_{h\to 0} \dfrac{(2+h)^4-16}{h}}[/tex]

which can be rewriten as:
[tex]\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{(2+h)^4-2^4}{h}}[/tex]

We can conclude by comparing that:

This would mean that:

[tex]\displaystyle{f(x)=x^4}[/tex]

Therefore:

[tex]\displaystyle{f(x)=x^4 \ \: \text{and} \ \: a =2}[/tex]

The equity of Company X's is $13,291.

The difference between assets and liabilities is the equity.

The equity is the portion of assets belonging to the owners.

Initial investment = $12,000

Retained Earnings = $1,291

Long-term loan = $9,982 ($12,000 - $2,018)

Land and building = $8,878

Equipment = $4,230

Cash $8,250

Inventory = $1,225

Accounts Receivable = $675

Accounts Payable = $485

Short-term loan = $500

Company X

As of current date

Cash                                 $8,250

Inventory                            1,225

Accounts Receivable          675  $10,150

Long-term investment  $1,000

Land and building          8,878

Equipment                      4,230    $14,108

Total Assets                               $24,258

Accounts Payable         $485

Short-term loan               500       $985

Long-term loan                         $9,982

Total liabilities                         $10,967

Initial capital           $12,000

Retained earnings       1,291  $13,291

Total liabilities and equity   $24,258

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Determine Company X's equity?

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:

0.5874 = 58.74%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953[/tex]

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (18.1 - 17.2)/0.3953

Z = 2.28

Z = 2.28 has a p-value of 0.9887.

Z = (17.1 - 17.2)/0.3953

Z = -0.25

Z = -0.25 has a p-value of 0.4013.

Hence:

0.9887 - 0.4013 = 0.5874 = 58.74%.

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The temperature at noon is equal to -0.1°C.

Mathematically, the standard form or slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Note: Let x represent the time.

Next, we would write an equation that models the situation based on the rate of change (slope) and y-intercept (initial value) as follows;

y = mx + c

y = -0.8x - 2.5

y = -0.8(3) - 2.5

y = -2.4 - 2.5

y = -0.1°C

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Answer:pls brainly award

Step-by-step explanation:

The 330 feet of rope is equivalent to 330/3 = 110 yards.

The cost of the rope at SportsStuff.com is 110 * $5.50 = $605.

The cost of the rope at OutdoorHaven.com is 110 * $5.20 + $12.25 = $604.45.

Therefore, the cheapest price you can pay is $604.45.