A rectangular park had a dirt path across its diagonal that was yards long. The diagonal and the long side of the park formed an angle that measured . A person walked along the sidewalks outside the park, from the start to the end of the path, as shown by the arrows. The diagonal dirt path that cuts across the rectangular park and the sidewalks outside the park form a right triangle. The dirt path is the hypotenuse and it is labeled 100 yards. The start of the sidewalk is adjacent to the 30-degree angle, and it is labeled X. The end of the path is opposite the 30-degree angle, and it is labeled Y. Which expression shows the distance that he walked?

Answer: 22

Step-by-step explanation:

Number of floor tiles = (5.4m × 4.2m) ÷ 1m²

Number of floor tiles = 22.68

Minimum number of floor tiles = 22

Answer: [tex]\pm1,\pm3,\pm5, \pm15[/tex]

Step-by-step explanation:

We can list the possible rational roots of this polynomial using the Rational Root Theorem. This theorem states that all the possible rational roots of an equation follow the structure [tex]\frac{p}{q}[/tex], where p is any of the factors of the constant term and q is any of the factors of the leading coefficient.

In this example, -15 is the constant term and 1 is the leading coefficient ([tex]x^4[/tex] has a coefficient of 1).

The factors of -15 are [tex]\pm1,\pm3,\pm5, \pm15[/tex], while the factors of 1 are [tex]\pm1[/tex]. p is can be any one of the factors of -15, while q can be any of the factors of 1.

[tex]\frac{\pm1,\pm3,\pm5, \pm15}{\pm1}[/tex]

The possible roots can be any of the numbers on the top divided by any of the numbers on the bottom. Since dividing by 1 or -1 won't change any of the numbers on the top, the rational roots of this function are [tex]\pm1,\pm3,\pm5, \pm15[/tex].

The probability of 11 voters out of 15 voting candidate A is 0.9770

According to the statement

we have given that the percentage of voters is 81% and poll conducts are 15 and we have to find the probability that 11 of the 15 voters will prefer Candidate

So, For this purpose,  

the question in based on binomial probability which means the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes p and q and p+q=1

let probability of choosing candidate A be p

and probability of choosing candidate B be q

In question p=0.81 and q=0.16

n be total number of voters=15

x be number of successes

then P(x=x)= [tex]\frac{n}{x} p^{x} q^{n-x}[/tex]

P(x=11)= [tex]\frac{11}{15} 0.81^{11} 0.16^{4}[/tex]

= 0.9770

So, the probability of 11 voters out of 15 voting candidate A is 0.9770

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Answer:

t2=8/5

Step-by-step explanation:

using this formula

t1/s1 =t2/s2

4/5=t2/2

cross multiply

5t2=8

t2=8/5

The correct answer for the value of t₂ is [tex]1.6[/tex].

Given:

Time t₁ = 4,

Distance s₂ =2

Distance s₁ = 5.

To find value of t₂ , use the concept of proportion:

[tex]\dfrac{t_1}{s_1} = \dfrac{t_2}{s_2}[/tex]

Put value of [tex]t_1 ,s_1 ,s_2[/tex]:

[tex]\dfrac{t_2}{2} =\dfrac{4}{5}\\\\t_2 =\dfrac{8}{5}\\\\ t_2 = 1.6[/tex]

The correct value of [tex]t_2[/tex] is [tex]1.6[/tex].

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Take HJ = x, GH = y and GJ = z

put the value of x from equation 1 in equation 2

[tex]{ \qquad❖ \: \sf \:z = (y + 2) + y - 17} [/tex]

[tex]{ \qquad❖ \: \sf \:z = 2y - 15} [/tex]

now, put the value of x and z in equation 3

[tex]{ \qquad❖ \: \sf \:y + 2 + y + 2y - 15 = 73} [/tex]

[tex]{ \qquad❖ \: \sf \:4y - 13 = 73} [/tex]

[tex]{ \qquad❖ \: \sf \:4y = 86} [/tex]

[tex]{ \qquad❖ \: \sf \:y = 21.5 \: \: in} [/tex]

Now, we need to find HJ (x)

[tex]{ \qquad❖ \: \sf \:x = y + 2} [/tex]

[tex]{ \qquad❖ \: \sf \:x = 21.5 + 2} [/tex]

[tex]{ \qquad❖ \: \sf \:x = 23.5 \: \: in} [/tex]

[tex]{ \qquad \large \sf {Conclusion} :} [/tex]

Answer:

16

Step-by-step explanation:

when we multiply we have 16n so thats is d coefficient

Answer: 0

Step-by-step explanation:

Substituting in x=0, we get

[tex]\frac{0(0-2)}{2-2e^{2}(0)}=0[/tex]

Using Euler's Formula, the number of faces is given by: 8.

It states that the number of vertices, edges and faces is related by the following equation:

V - E + F = 2.

In this problem, the parameters are given as follows:

E = 15, V = 9.

Hence the number of faces is given by:

V - E + F = 2.

9 - 15 + F = 2

F - 6 = 2

F = 8.

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The expression that will help him to determine the total cost is as follows:

y = 60 + 4x

He signed up to provide snacks for his daughter and her school group's camping trip.

He found a package of granola bars in bulk for $60 that he thought would be enough for everyone for a few days.

He also wanted to buy some boxes of fruit snacks, which were $4 each.

The number to buy and the total cost can be expressed as follows:

let

y = total cost

x = number of boxes of fruit juice.

Therefore, the  expression that will help him to determine the total cost is as follows:

y = 60 + 4x

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The area of the region enclosed by the curves x + y = 1, x - 3 = y, y = √x and x = 0 is 16.815 square units.

In this question we must determine the area generated by four functions: three linear functions and a radical function. First, we plot the four functions to determine the required combinations of definite integrals need for calculation:

[tex]A = \int\limits^{0.382}_0 {[f(x) - g(x)]} \, dx + \int\limits^2_{0.382} {[h(x) - g(x)]} \, dx[/tex], where f(x) = √x, g(x) = x - 3 and h(x) = - x + 1.

[tex]A = \int\limits^{0.382}_{0} {[\sqrt{x} - x + 3]} \, dx + \int\limits^{2}_{0.382} {[- 2 \cdot x + 4]} \, dx[/tex]

[tex]A = \int\limits^{0.382}_{0} {\sqrt{x}} \, dx - \int\limits^{0.382}_{0} {x} \, dx + 3 \int\limits^{0.382}_{0}\, dx - 2 \int\limits^{2}_{0.382} {x} \, dx + 4 \int\limits^{2}_{0.382}\, dx[/tex]

[tex]A= 2 \cdot x^{\frac{3}{2} }|_{0}^{0.382} - \frac{x^{2}}{2}|_{0}^{0.382} + 3\cdot x |_{0.382}^{2} - x^{2} |_{0.382}^{2}+4\cdot x |_{0.382}^{2}[/tex]

[tex]A = 2 \cdot (0.382^{\frac{3}{2} }-0^{\frac{3}{2} })-\left(\frac{1}{2} \right)\cdot (0.382^{2}-0^{2}) + 3 \cdot (2 - 0.382) - (2^{2}-0.382^{2})+4\cdot (2^{2}-0.382^{2})[/tex]

A = 16.815

The area of the region enclosed by the curves x + y = 1, x - 3 = y, y = √x and x = 0 is 16.815 square units.

The statement reports an inconsistency with at least one function and needs to be modified in order to apply definite integrals in a consistent manner. New form is shown below:

Sketch the region enclosed by the given curves and find its area: (i) x + y = 1, (ii) x - 3 = y, (iii) y = √x, (iv) x = 0.

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The amount of the loss exists 1350.

Amount of Loss means an amount equivalent to the outstanding balance of the principal amount, less any amounts recognized by perfecting rights under a security agreement, together with such interest as the executive director shall permit, to a maximum of such interest as may be permitted by rule.

Given: Mr. Black purchased a television set for $450.00. He subsequently sold the television set at a defeat of 30%.

From the given information, we get

[tex]$4500\cdot \frac{30}{100}[/tex]

simplifying, we get

[tex]$4500\cdot \frac{30}{100}[/tex]

= 1350

Therefore, the amount of the loss exists 1350.

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Answer:

Step-by-step explanation:

Draw UT                         Construction

UT = UT                         Reflexive Property

BT = EU                           Given

BU = ET                           Given

ΔUBT = ΔEUT                SSS = SSS

<B = <E                             CPCTC

The bolded parts are the blanks you need to fill in.

Answer:

Draw UT                         construction

UT = UT                         reflexive property

BT = EU                           given

BU = ET                           given

ΔUBT = ΔEUT                SSS = SSS

<B = <E                             CPCTC

hope this helps!

Answer: 2.25 meters

Step-by-step explanation: 1 in = 2 meters. 0.75 is 75 percent of 1 so the length of the window is 75 percent of 2 which is 1.5. 1.5 squared is 2.25 so the length of the window is 2.25 meters

The required number is 7. The expression formed with the given information is x - 21 = 2(-x).

An expression is the combination of variables, constants, and coefficients.

If two expressions are related by an equal in between them, then that is said to be an equation.

From the given data,

Consider the required number = x

The number is decreased by 21 i.e., x - 21

Twice the opposite of the number = 2(-x)

So, on equating,

x - 21 = 2(-x)

On simplifying,

⇒ x - 21 = -2x

⇒ x + 2x = 21

⇒ 3x = 21

∴ x = 7

Thus, the required number is 7.

Check:

7 - 21 = -14 and 2(-7) = -14.

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The answer is 4) 140.

If we closely examine the pattern of the series, we see that after a number is subtracted by a value, it is multiplied by the same value, and then it moves on to the next natural number.

The next step, according to the pattern, would be to multiply 4.

[tex](x^2 - y^2) \, dx + 2xy \, dy = 0[/tex]

Multiply both sides by [tex]\frac1{x^2}[/tex].

[tex]\left(1 - \dfrac{y^2}{x^2}\right) \, dx + \dfrac{2y}x \, dy = 0[/tex]

Substitute [tex]y=vx[/tex], so [tex]v=\frac yx[/tex] and [tex]dy=x\,dv+v\,dx[/tex].

[tex](1-v^2) \, dx + 2v (x\,dv + v\,dx) = 0[/tex]

[tex](1 + v^2) \, dx + 2xv \, dv = 0[/tex]

Separate the variables.

[tex]2xv\,dv = -(1 + v^2) \, dx[/tex]

[tex]\dfrac{v}{1+v^2}\,dv = -\dfrac{dx}{2x}[/tex]

Integrate both sides

[tex]\displaystyle \int \frac{v}{1+v^2}\,dv = -\frac12 \int \frac{dx}x[/tex]

On the left side, substitute [tex]w=1+v^2[/tex] and [tex]dw=2v\,dv[/tex].

[tex]\displaystyle \frac12 \int \frac{dw}w = -\frac12 \int\frac{dx}x[/tex]

[tex]\displaystyle \ln|w| = -\ln|x| + C[/tex]

Solve for [tex]w[/tex], then [tex]v[/tex], then [tex]y[/tex].

[tex]e^{\ln|w|} = e^{-\ln|x| + C}[/tex]

[tex]w = e^C e^{\ln|x^{-1}|}[/tex]

[tex]w = Cx^{-1}[/tex]

[tex]1 + v^2 = Cx^{-1}[/tex]

[tex]1 + \dfrac{y^2}{x^2} = Cx^{-1}[/tex]

[tex]\implies \boxed{x^2 + y^2 = Cx}[/tex]

Your mistake is in the first image, between third and second lines from the bottom. (It may not be the only one, it's the first one that matters.)

You incorrectly combine the fractions on the left side.

[tex]\dfrac1{-2v} -\dfrac v{-2} = \dfrac1{-2v} - \dfrac{v^2}{-2v} = \dfrac{1-v^2}{-2v} = \dfrac{v^2-1}{2v}[/tex]

1. According to the affordability formulas given, Joe-Bob cannot afford to take out another loan.

2. Joe-Bob should follow the affordability formulas if he wants to live without financial stress caused by debts.

3. Joe-Bob may decide not to follow the affordability formula, if he can reduce his fixed monthly payments or increase his income.

4. Taking out the car loan will force Joe-Bob to increase his DTI and reduce his savings, investments, and discretionary spending.

Affordability refers to a person's financial ability to afford some fixed expenses without impacting negatively the variable expenses.

Affordability can be measured as a Debt To Income (DTI) ratio.

Current monthly income = $3,500

Monthly mortgage payment = $900

Monthly student loan payment = $350

Total monthly debt payment = $1,250

Debt To Income (DTI) = 35.7% ($1,250/$3,500 x 100)

Thus, with a DTI of 36%, Job Bob should not take out an additional car loan.

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The probability that the instructor asks one of Sam and John whose probabilities of being asked are as indicated in the task content is; 0.12.

It follows from the task content that the probability that Sam is being asked is; 0.05 while that for John being asked is; 0.07.

Consequently, we may conclude that the probability of either of the two classmates being asked the question in discuss is; the sum of the probabilities and hence, we have;

P(Sam or John) = 0.05 + 0.07

= 0.12.

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[tex]X[/tex] and [tex]Y[/tex] are independent and identically distributed with PMF

[tex]\mathrm{Pr}(X = x) = \begin{cases}1/6 & \text{if } x \in\{1,2,3,4,5,6\} \\ 0 & \text{otherwise}\end{cases}[/tex]

If [tex]Z=X-Y[/tex], then [tex]Z[/tex] has range/support

{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}

where we can get

and so on, so that the PMF of [tex]Z[/tex] is

[tex]\mathrm{Pr}(Z=z) = \begin{cases}1/36 & \text{if } z\in\{-5,5\} \\ 2/36 & \text{if } z\in\{-4,4\} \\ 3/36 & \text{if }z\in\{-3,3\} \\ 4/36 & \text{if } z\in\{-2,2\} \\ 5/36 & \text{if } z\in\{-1,1\} \\ 6/36 & \text{if } z =0 \\ 0 & \text{otherwise}\end{cases}[/tex]

Answer:

We lend 100% - 9.2% and this will equal 90.8%, then we will make this percentage of 42,600 which will give us 38,680 and we will add the 42,600 and this will give us a total of 81,460 copies.

Answer:

3%, 32%

Step-by-step explanation:

winning 1 game only: two possibilities

a. winning balltoss, losing dart, which is 20%*85% = 17%

b. winning dart, losing ball toss, which is 15%*80% = 12%

so winning 1 game only: 29%

winning both games:

20% * 15% = 3%

winning either one: winning both games+winning 1 game only

29% + 3% = 32%

The number of tickets sold are:

From the question, we have the following parameters:

Number of tickets = 63

Total amount = 444 Birr

Adult ticket = 8 Birr per adult

Children ticket = 6 Birr per adult

Represent the children tickets with x and adults ticket with y.

So, we have the following system of equations

x + y = 63

6x + 8y = 444

Express the equations as a matrix

x      y

1       1       63

6      8       444

Apply the following transformation

R2 = R2 - 6R1

This gives

x      y

1       1       63

0      2       66

Apply the following transformation

R2 = 1/2R2

x      y

1       1       63

0      1       33

From the above matrix, we have the following system of equations

x + y = 63

y = 33

Substitute y = 33 in x + y = 63

x + 33 = 63

Subtract 33 from both sides of the above equation

x = 30

Hence, 30 children tickets were sold and 33 adult tickets were sold

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Answer:

1/4 ,- 4, 1/2 2 1/2 4 1/4

Step-by-step explanation:

1/4, 4 1/2, 2,1/2,4, 1/4,

A)  Rotate by 90° counterclockwise.

B) Reflection transformation about the line y = 5.

C) Parallel Lines are C₂D₂ and A₂B₂; EF and E₁F₁.

D) Perpendicular lines are;  D₁F₁ and  E₁F₁; DF and EF; DC and AB.

E) Line segments with slope of 0 are; AB, C₂D₂, A₂B₂, EF and E₁F₁

F) Line segments on the boat that have an undefined slope are; Lines A₁B₁, DF and DC.

G) Slope of Line ED = 1

A) The blue segment CD is seen on the graph as a perpendicular line with 2 units while the line segment C₂D₂ is seen as a horizontal line. Thus, to match CD with C₂D₂, we will rotate by 90° counterclockwise.

B) The transformations that would be used on the blue triangle to get it to match with the red triangle is a reflection transformation about the line y = 5.

C) The line segments that are parallel to each other are; C₂D₂ and A₂B₂; EF and E₁F₁.

D) The line segments that are perpendicular are;  D₁F₁ and  E₁F₁; DF and EF; DC and AB.

E) Horizontal lines that are parallel to the x-axis have zero slope. Thus, AB, C₂D₂, A₂B₂, EF and E₁F₁ all have zero slopes.

F) Undefined slope is the slope of a vertical line. Thus, Lines A₁B₁, DF and DC have undefined slopes.

G) Slope of ED = (5 - 4)/(-10 - (-11))

Slope of ED = 1/1

Slope = 1

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Answer:

1 +-3i

Step-by-step explanation:

Answer:

answer is 1) x=±3i

Step-by-step explanation:

Answer:

[tex]\boxed {AB = 52 m}[/tex]

Step-by-step explanation:

This forms a right triangle.

Therefore, by using the Pythagorean Theorem, we can find AB.

AB = √AC² + BC²

I hope it helped you solve the problem.

Good luck on your studies!

Answer: Distance AB = 52 m

Step-by-step explanation:

Given information

Point A = 20 m north of point C

Point B = 48 m east of point C

Please refer to the attachment below for a graphical understanding

Concept

According to the graph drawn, Point A, Point B, and Point C form a right angle, and the distance between Point A and B would form a right triangle.

Therefore, we can use the Pythagorean theorem to find the distance between points A and B.

Given formula

a² + b² = c²

Substitute values into the formula

a² + b² = c²

(20)² + (48)² = c²

Simplify exponents

400 + 2304 = c²

Simplify by addition

2704 = c²

c = √2704

c = 52  or  c = -52 (reject, since no distance can be negative)

Therefore, the distance AB is [tex]\Large\boxed{52~m}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer: [tex]x=2, y=1[/tex]

Step-by-step explanation:

Subtracting the second equation from the first yields [tex]2x=4 \longrightarrow x=2[/tex].

This means that [tex]y=1[/tex].

So, the solution is [tex]x=2, y=1[/tex]

Answer:

Two Equal Angles = 45°

Third Angle = 90°

Step-by-step explanation:

Given information

Two equal angles of an isosceles triangle are half the third angle

Set variables

Let x be the angle of the equal angles of the isosceles triangle

Let 2x be the angle of the third angle

Set equations

x + x + 2x = 180 (Triangle angle sum theorem)

Combine like terms

2x + 2x = 180

4x = 180

Divide 4 on both sides

4x / 4 = 180 / 4

[tex]\Large\boxed{x=45^\circ}[/tex]

Substitute the x value into the expression to find the third angle

Third angle = 2x

                   = 2 (45)

                   = [tex]\Large\boxed{90^\circ}[/tex]

Hope this helps!! :)

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