Please help me to solve this trigonometry problem!!!

The 95% confidence interval for the mean mass of the population is 24.57 ± 1.06. The upper limit of the 95% confidence interval is 25.63.

Given the masses, in grams, of ten ball bearings taken at random from a batch are: 25.9, 24.7, 23.4, 24.5, 25.0, 26.9, 26.4, 25.8, 23.2, 21.9

We have to calculate a 95% confidence interval for the mean mass of the population, supposed normal, from which these masses were drawn.The formula for the Confidence Interval is given by,

CI = X bar± tα/2 * (s/√n)

Where,

CI = Confidence Interval

Xbar = Sample mean

tα/2 = α level of significance/2 (α is the level of significance)

s = sample s

tandard deviationn = sample size

tα/2 = t-distribution value for α/2 and (n-1) degrees of freedomtα/2 for α = 0.05 and (n-1) degrees of freedom

tα/2 = 2.262

Hence,CI = X bar ± tα/2 * (s/√n)

CI = 24.94 ± 2.306 * (1.618/√10)

CI = 24.94 ± 1.36

Upper limit of 95% confidence interval

x2 = 24.94 + 1.36= 26.30

Rounded off to two decimal places, x2 is 26.30.

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If a company understates its ending balance of inventory in year 1 and states its inventory correctly in year 2, then the correct statement is option (c) Net income is understated in year 2

Understating the ending balance of inventory in year 1 would result in the cost of goods sold (COGS) being overstated and net income being understated in that year. This is because the COGS is calculated as the beginning inventory plus purchases minus ending inventory. By understating the ending inventory balance, the COGS for year 1 would be overstated, which would result in a lower net income for year 1.

In year 2, if the inventory is stated correctly, it would not have an impact on the COGS for that year. However, if the net income for year 1 was understated due to the understated ending inventory balance, the cumulative effect would be an understated net income for both years. This means that the correct answer is c. Net income is understated in year 2.

Therefore, the correct option is (c) Net income is understated in year 2

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The sοlutiοn tο the  radical equatiοn is x = 5.

In mathematics, a radical is the οppοsite οf an expοnent, which is symbοlised by the symbοl "," alsο referred tο as rοοt. A square rοοt οr a cube rοοt can be used, and the number befοre the symbοl οr radical is regarded as an index number οr degree. The expοnent οf this number cancels the radical and is a whοle number.

The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Starting with:

-5√(2x - 1) = -15

Divide bοth sides by -5:

√(2x - 1) = 3

Square bοth sides:

2x - 1 = 9

Add 1 tο bοth sides:

2x = 10

Divide bοth sides by 2:

x = 5

Hence, the solution to the equation is x = 5.

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If the perimeter of the base of the pyramid is 314 centimeters, then radius of the cone is approximately 17.44 centimeters.

Perimeter is a measurement of the distance around the outside of a two-dimensional shape. It is the sum of the lengths of the shape's sides.

Since the pyramid and cone have the same base and slant height, they are similar geometric figures. Therefore, their corresponding dimensions are proportional. Let's denote the radius of the cone as r.

Since the perimeter of the base of the pyramid is 314 centimeters, and the base of the pyramid is a square, we can find the length of one side of the square base by dividing the perimeter by 4:

Length of one side = Perimeter / 4 = 314 cm / 4 = 78.5 cm

Since the pyramid and the cone have the same area of the base, and the base of the pyramid is a square, we can find the area of the base by squaring the length of one side:

Area of the base = (Length of one side)² = (78.5 cm)²= 6,152.25 cm²

Since the pyramid and the cone have the same surface area, we can use the formula for the surface area of a cone to find the radius of the cone:

Surface area of the cone = πr(r + l), where l is the slant height.

The surface area of the cone is equal to the surface area of the pyramid, so we have:

πr(r + l) = 2 × Area of the base + Perimeter × l

Substituting the known values, we get:

πr(r + 13) = 2 × 6,152.25 cm² + 314 cm × 13 cm

Simplifying and solving for r, we get:

πr² + 13πr - 4,059.5 = 0

Using the quadratic formula, we find:

r ≈ 17.44 cm (rounded to two decimal places).

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The volume of a standard size golf ball can be calculated using the formula for the volume of a sphere:

V = (4/3)πr^3

where r is the radius of the golf ball. The diameter of the golf ball is 1.680 inches, so the radius is 0.840 inches.

V = (4/3)π(0.840)^3

= 2.468 in^3

The weight of the golf ball can be calculated by multiplying its volume by the density of the material:

W = V × D

where D is the density of the material. The density of the material is 0.6523 ounces per cubic inch.

W = 2.468 in^3 × 0.6523 oz/in^3

= 1.6095 oz

Therefore, the weight of one golf ball is approximately 1.61 ounces (rounded to the nearest hundredth of an ounce).

Where the above mean exist, the values of x and y  are 10.5 and 3.5 respectively.

The total number of people surveyed is 24. So we can write:

Frequency of 0 sisters + Frequency of 1 sister + Frequency of 2 sisters + Frequency of 3 sisters = Total frequency

5 + x + 5 + y = 24

x + y = 14 --- (1)

Also, we know that the mean number of sisters is 1.25. This means that the total number of sisters divided by 24 should be equal to 1.25. So we can write:

0 × 5 + 1 × x + 2 × 5 + 3 × y = 1.25 × 24

x + 3y = 21 --- (2)

Now we have two equations (1) and (2) with two variables (x and y). We can solve for x and y by simultaneous equations.

Multiplying equation (1) by 3, we get:

3x + 3y = 42 --- (3)

Subtracting equation (2) from equation (3), we get:

2x = 21

x = 10.5

Substituting the value of x in equation (1), we get:

10.5 + y = 14

y = 3.5

Therefore, the values of x and y are 10.5 and 3.5 respectively.

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Answer:

B

Step-by-step explanation:

first you would need to do the inverse of sine to get the angle since normal sine would give you the length and you need the angle.

An easy way to remeber sine, cosine and tangent is

SOH CAH TOA

sin= opposite/ hypotenuse

cosine= adjacent/ hypotenuse

tangent= opposite/adjacent.

first label your triangle with the sides hypotenuse, adjacent and opposite.

hypotenuse is the longest side that is diagonal in this case like ab

opposite is the side that is opposite the angle you are looking for, so in thsi case line cb

adjacent is the like next to the angle you are trying to find so in thsi case like ac

and since we know sine inverse = opposite/hypotenuse = angle

(we are using sine for this question since that is what the question is asking for)

we simply do

sine inverse= 3/5

so the answer is B

i hope this helps! :)

Answer:B

Step-by-step explanation: im sure because i answer that in school im correct

The area of circle with radius 4 centimetres and the special math constant, pi to be 3. 142 is equals to the 50.3 cm².

Area of a shape is defined as the total spece covered by shape in two-dimensional. In geometry, the area enclosed circle is calculated by π times the square of radius of circle. Formula of Area = π × r², where 'r' is the radius. The units of area are square of units of radius that if radius in feet then unit of area will be square feet. We have a circle with radius say r = 4 cm.

The value of specific math constant, pi ( i.e., π) is equals to be 3.142. We have to determine the area of circle. The area of circle, A = π× 4²

=> A = 16π

=> A = 16× 3.142

=> A = 50.272 ~ 50.3 cm²

Hence, the required area value is 50.3 cm².

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Complete question:

The above figure completes the question.

Work out he area of this circle. Take pi to be 3. 142 and give your answer to 1 decimal place

it is important to note that the sample size of 1000 subjects is large enough for statistical inference, but the significance level must be taken into account when interpreting the results.

No. Since the tests were performed at the 1% significance level, as many as 10 subjects may have done significantly better than random guessing.

When conducting hypothesis testing, the significance level (in this case, 0.01 or 1%) is the probability of rejecting the null hypothesis when it is actually true. This means that there is a 1% chance of observing a significant result purely by chance, even if the null hypothesis (in this case, that the subjects do not have ESP) is true.

In this scenario, nine subjects performed significantly better than random guessing, which may suggest that they have ESP. However, due to the possibility of observing significant results by chance, it is not proper to conclude that these nine people have ESP. There is still a chance that these results are purely coincidental.

Additionally, it is important to note that the sample size of 1000 subjects is large enough for statistical inference, but the significance level must be taken into account when interpreting the results.

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[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 25\%\to \frac{25}{100}\dotfill &0.25\\ t=\textit{elapsed time}\dotfill &2\\ \end{cases} \\\\\\ A = 20000(1 - 0.25)^{2} \implies A=20000(0.75)^2\implies A = 11250[/tex]

The required expected number of employees who will pass the test from given 11 potential employees is equal to 10.

Probability of passing a drug test is 90%,

Then the probability of failing is 10%.

For each potential employee,

Probability of passing is 0.9, and the probability of failing is 0.1.

The number of potential employees who would be expected to pass the test,

Calculated using the binomial distribution with n = 11 and p = 0.9.

P(A = x) = (ⁿCₓ) × pˣ ×  (1-p)ⁿ⁻ˣ

where,

A is the number of potential employees who pass the test

x is the number of potential employees who pass the test

n is the number of potential employees

p is the probability of passing the test

Using this formula, the expected number of potential employees who would pass the test is,

E(A) = n ×p

      = 11 × 0.9

      = 9.9

Rounding to the nearest whole number, we can expect 10 potential employees to pass the test.

Therefore, the expected number of employees from the given  probability who would pass the the test is 10.

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If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.

What is hypothesis testing?

A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters through hypothesis testing.

Here,

We have to find the correct statement about hypothesis testing.

We concluded that  If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.

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Answer:

In this case, B is true.

Whether to use a one-sided or a two-sided test is typically decided BEFORE the data are gathered, not after.

Be careful while reading the options on the quiz, because depending on the question you get, the options may be worded slightly differently. Because of the wording, the answer may be different as well (on the FLVS quiz, I got different answer choices for this question). Be careful and read cautiously!

Have a great day.

"type of orange" because it is a bar graph therefore it is supposed to be categories, not numbers :)

In conclusion Rounding to four decimal places, we get:

f(t) = 9100e²(0.1398t)

How to solve?

To write the function F(t) = 9100(1.15)²t in the form f(t) = ae²(kt), we need to first take the natural logarithm of both sides:

ln(F(t)) = ln(9100(1.15)²t)

ln(F(t)) = ln(9100) + ln(1.15²t)

ln(F(t)) = ln(9100) + t × ln(1.15)

Now, we have the form ln(F(t)) = ln(a) + kt, where k = ln(1.15) and a = 9100. We can exponentiate both sides of this equation to get:

F(t) = e²(ln(a) + kt)

F(t) = e²ln(a) × e²(kt)

F(t) = a × e²(kt)

Substituting the values of a and k, we get:

F(t) = 9100 × e²(0.1398t)

Rounding to four decimal places, we get:

f(t) = 9100e²(0.1398t)

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The values of the variable x are 7 and -1. Options B and D

Functions are simply defined as those equations, expressions or laws that shows the relationship between two variables.

These variables are;

From the information given, we have that;

f(x) = 16

f(x) =  x² - 6x + 9

Now, equate the two functions, we have;

x² - 6x + 9 = 16

collect the like terms

x² - 6x + 9 - 16 = 0

subtract the values

x² - 6x - 7 = 0

solve the quadratic equation

x² - 7x + x - 7 = 0

x(x - 7) + 1( x - 7)

Then, x = 7 and -1

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Emily new boots cost a total of $71.4 with the tax included as 5% and the original cost of the boots being $68.

The sales tax rate in Emily's city = 5% and the cost of Emily's new boots is $68

we need to find the amount of sales tax Emily will pay for her boots,

The formula we will use =

Sale tax = Percent sales tax x Cost of the product

when we put the values in the formula, we get:

Sales tax = 5% x $68

= $3.4

now we need to also calculate the total cost for Emily's boots,

Therefore, the total cost = Cost of boots + Sales Tax

when we put the values in the formula, we get:

Total cost = $68 + $3.4

= $71.4

Therefore, the total cost Emily will pay for her boots is $71.4

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Answer:

x=7

Step-by-step explanation:

First, try to bring all your X's together

3x+9x=6x+42

   12x=6x+42

   -6x  -6x

    6x=42

    /6   /6

     x = 7

Answer:

24 sin(3x) cos(3x)

Step-by-step explanation:

To find:-

Answer:-

The given function to us is ,

[tex]:\sf\implies y = 4sin^2(3x) \\[/tex]

To find it's derivative we would have to use Chain rule of differentiation , which is ;

[tex]:\sf\implies \pink{ \dfrac{dy}{dx}=\dfrac{dy}{du}\cdot \dfrac{du}{dx}} \\[/tex]

Taking the given function,

[tex]:\sf\implies y = 4sin^2(3x) \\[/tex]

Differentiate both sides with respect to x,

[tex]:\sf\implies \dfrac{dy}{dx}=\dfrac{d}{dx}4sin^2(3x)\\[/tex]

We can take out the constant as ,

[tex]:\sf\implies \dfrac{dy}{dx}= 4 \dfrac{d}{dx}sin^2(3x) \\[/tex]

Multiply and divide by sin(3x) as ,

[tex]:\sf\implies \dfrac{dy}{dx}= 4 \bigg( \dfrac{d(sin^23x)}{d(sin3x)}\times \dfrac{d\ sin3x}{dx}\bigg)\\[/tex]

Differentiation of sin(nx) is n cos(nx) and

[tex]:\sf\implies \pink{ \dfrac{d(x^n)}{dx} = nx^{n-1} }[/tex]

So that ,

[tex]:\sf\implies \dfrac{dy}{dx}= 4 ( 2sin(3x) \cdot 3cos(3x))\\[/tex]

Simplify,

[tex]:\sf\implies\pink{ \dfrac{dy}{dx}= 24\ sin(3x) \ cos (3x)}\\[/tex]

Hence the derivative of the given function is 24 sin(3x) cos(3x) .

[tex]\rule{200}2[/tex]

Related formulae :-

[tex]\boxed{\boxed{\begin{minipage}{5cm}\displaystyle\circ\sf\;\dfrac{d}{dx}(sin\;x)=cosx \\\\ \circ \;\dfrac{d}{dx}(cos\;x) = -sinx \\\\ \circ \; \dfrac{d}{dx}(tan\;x) = sec^{2}x \\\\ \circ\; \dfrac{d}{dx}(cot\;x) = -csc^{2}x \\\\ \circ \; \dfrac{d}{dx}(sec\;x) = secx \cdot tanx \\\\ \circ \; \dfrac{d}{dx}(csc\;x) = -cscx \cdot cotx \\\\ \circ\; \dfrac{d}{dx}(sinh\;x)=coshx \\\\ \circ\; \dfrac{d}{dx}(cosh\;x)= sinhx \\\\ \circ\;\dfrac{d}{dx}(tanh\;x)=sech^{2}h \\\\ \circ\;\dfrac{d}{dx}(coth\;x)=-csch^{2}x \\\\ \circ\;\dfrac{d}{dx}(sech\;x) =-sechx \cdot tanhx \\\\ \circ\;\dfrac{d}{dx}(csch\;x) = -cschx \cdot cothx\end{minipage}}}[/tex]

[tex]\rule{200}2[/tex]

Answer:

[tex]\dfrac{\text{d}y}{\text{d}x}=12 \sin (6x)[/tex]

Step-by-step explanation:

To find the derivative of y = 4sin²(3x), use the chain rule.

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]

The given function can be written as:

[tex]y=4(\sin 3x)^2[/tex]

Let y = 4u², where u = sin(3x).

Differentiate the two parts separately.

[tex]\dfrac{\text{d}y}{\text{d}u}=8u \quad \text{and} \quad \dfrac{\text{d}u}{\text{d}x}=3 \cos (3x)[/tex]

Put everything into the chain rule formula:

[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x}& =\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}\\\\&=8u \times 3 \cos (3x)\\\\&=24u \cos (3x)\\\\&=24 \sin (3x) \cos (3x) \end{aligned}[/tex]

Simplify using the sine double angle identity:

[tex]\boxed{\sin (2 \theta)= 2 \sin \theta \cos \theta}[/tex]

[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x}&=24 \sin (3x) \cos (3x) \\\\&=12(2 \sin (3x) \cos (3x))\\\\&=12 \sin (2 \cdot 3x)\\\\&=12 \sin (6x)\end{aligned}[/tex]

Therefore:

[tex]\dfrac{\text{d}y}{\text{d}x}=12 \sin (6x)[/tex]

[tex]\hrulefill[/tex]

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Differentiating $\sin (ax)$}\\\\If $y=\sin(ax)$, then $\dfrac{\text{d}y}{\text{d}x}=a \cos (ax)$\\\end{minipage}}[/tex]

The area of the shaded segment of the circle is calculated by substracting the area of triangle from area of sector of circle So, area of shaded segment of the above circle is equals to the (12π - 9√3) cm².

Assume a sector having a radius r and a central angle of α degrees. The sector's area will be A= (α/360∘)πr². Similarly, different shapes have different area formulas. We have been provided a circle of radius 6cm. Assume that its center is O and the segment is AB. Radius of circle , r = 6 cm

Central angle,α = 120°

Area of shaded segment is calculated by the area of sector AOB of circle minus area of triangle AOB formed there. So, Area of sector AOB , A = (α/360∘)πr²

= ( 120°/360°) π6²

= (1/3) 36π = 12π cm²

As we know, OA = OB= 6cm

=> m∠OAB = m∠OBA

and m∠AOB + m∠OAB + m∠OBA = 180∘

=> 120∘ + m∠OAB + m∠OAB= 180∘

=> 2(m∠OAB) = 180∘− 120∘ = 60°

=> m∠OAB = 30° = m∠OBA

So, it is an isosceles triangle. Draw a perpendicular OC on AB then there is formed two right angled triangles. In right angled triangle OAC, 90°, 60°, 30° and OA = 6 cm then OC/6 = Sin 30°

=> OC= 3 cm and

AC = √36 - 9 = √27 = 3√3 cm

Similarly, BC = 3√3 cm so, AB = 6√3 cm. Now, area of triangle AOB = (1/2) × AB × OC = (1/2)× 6√3 ×3 = 9√3 cm²

So, required area = 12π cm² - 9√3 cm². Hence, required value is (12π - 9√3) cm².

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Complete question:

The above figure completes the question. Find the area of the shaded segment of the circle.

Just make a flat line for each time the car stops.

Hope this helps.

To find the area of the shaded polygon, we had to assume that each dotted line was one unit. In which case, the coordinates are:

Hence, the area of the polygon is A [tex]\approx[/tex] 11.15 units.

To get the area of the polygon, we must determine the length of all it's sides.

a) A-B is given by the distance formula:

distance = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using this formula, we can calculate the distance between points A(1,4) and B(5,6) as follows:

distance = √((5 - 1)² + (6 - 4)²)

= √(16 + 4)

= √(20)
A-B = 4.47213595

A-B [tex]\approx[/tex] 4.47

b)
To find B-C we use the same method:
B-C = 3.16 units.

c)
To find C- D we use the same method:
C- D  [tex]\approx[/tex] 3.16 units.

d) to find D-A  we use the employ the same method:
D - A [tex]\approx[/tex] 2.83



Since this is an irregular quadrilateral, we will require the use of the
length of one of it's diagonals which is also computed using the distance formula to get: 4.47 Units.


Calculate the perimeter of ABCD

Perimeter of ABCD = AB + BC + CD + AD

Perimeter of ABCD = 4.4721359549996 + 3.1622776601684 + 3.1622776601684 + 2.8284271247462

Perimeter of ABCD = 13.625118400083


Calculate the semi-perimeter (s) of ABCD

s  =   Perimeter ÷ 2

s  =   13.625118400083 ÷ 2

s = 6.8125592000413


Calculate the Area (A) using Brahmagupta's Formula

A = √[(s - a)(s - b)(s - c)(s - d)]

A = √(6.8125592000413 - 4.4721359549996)(6.8125592000413 - 3.1622776601684)(6.8125592000413 - 3.1622776601684)(6.8125592000413 - 2.8284271247462)

A = √(2.3404232450417)(3.6502815398729)(3.6502815398729)(3.9841320752951)

A = √(124.24555320337)
A = 11.14654893693

A [tex]\approx[/tex] 11.15 units.

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In the given problem,  the distance from point A to point B is approximately 658 feet (rounded to the nearest foot).

Let's define some variables:

Using trigonometry, we can write the following equations:

For triangle ACT, we have:

tan(15°) = h/d

For triangle BCT, we have:

tan(50°) = h/(d+x)

We want to find the value of x, so let's rearrange the second equation:

tan(50°) = h/(d+x)

tan(50°)*(d+x) = h

d+x = h/tan(50°)

x = h/tan(50°) - d

Substituting the given values:

x = 115/tan(50°) - d

Now we need to find the value of d. For that, we can use the first equation:

tan(15°) = h/d

d = h/tan(15°)

Substituting the given value:

d = 115/tan(15°)

Now we can substitute both values into the equation for x:

x = 115/tan(50°) - 115/tan(15°)

Using a calculator, we get:

x ≈ 658.4 ft

Therefore, the distance from point A to point B is approximately 658 feet (rounded to the nearest foot).

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The burger costs $0.625, the souvenir costs $3.75, and the pass costs $5.00.

Let's name the burger price "b," the souvenir price "s," and the pass price "p." Then, using the information provided, we can construct an equation system:

b + s + p = 35.75  (1) (The three things cost a total of $35.75.)

b = (1/6)s               (2) (the burger was one-sixth the price of the memento).

s = (3/4)p     (3) (the memento cost one-quarter the price of the pass)

b + s + p + 2 = 35.75       (4) (After purchasing these products, Dion had                        $2.00 left over.)

To remove s from the equations, we can apply equations (2) and (3):

b + (3/4)p + p = 35.75    (equations (1) and (3))

b = (1/6)(3/4)p                (Applying Equation (2))

b = (1/8)p

This expression can now be substituted by Input b into equation (1):

(1/8)p + (3/4)p + p = 35.75

(7/8)p = 35.75

p = 35.75 / (7/8)

p = $5.00

We may calculate the cost of the keepsake using equation (3):

s = (3/4)p = (3/4)($5.00) = $3.75

Finally, we can calculate the cost of the burger using equation (2):

b = (1/6)s = (1/6)($3.75) = $0.625

As a result, the burger costs $0.625, the souvenir costs $3.75, and the pass costs $5.00.

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Answer:

A. True

Step-by-step explanation:

If two angles of a triangle are congruent to the corresponding angles or the second triangle than the third angles must be congruent to each other.

The sum of the interior angles of a triangle is 180.  Let's say 2 angles to one triangle is 100 and the second angle is 35.  That forces the third angle to be 45 (100 + 35 + 45 = 180)

Helping in the name of Jesus.

Answer:

A. True

Step-by-step explanation:

In congruent triangles...All angles and sides have to be equal.

Answer:

Step-by-step explanation:

Answer: The median decreases to 6.5.

Step-by-step explanation:

The median before 4 was added was 6.75.

When 4 is added the median is 6.5.