I really need help with this problem.

The distance between the fire and station B is 10.7miles

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

The angle at A = 90- 35

= 55°

The angle at B = 90-49

= 41°

Angle at the fire = 180-(41+55)

= 180-96 = 84°

Using sine rule

sin84/13 = sin55/x

xsin84 = 13sin55

0.995x = 10.65

x = 10.65/0.995

x = 10.7 miles

Therefore the distance between the fire and station B is 10.7 miles.

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1. The product of the matrix MG would be [tex]\left[\begin{array}{ccc}1&k_1+9&4k_2+36\\2t_1&k_1t_1-17&3k_2-19t_1-11\\t_2+1&k_1-4t_2+5&k_2t_2-8\end{array}\right][/tex]

2. The values of k₁ = -9;  k₂ = -9; t₁ = 0; t₂ = -1

The values of the matrix M and G are;

M = [1, 4, 5;                       G = [2, k₁, -19;

      t₁, 3, -1;                             1, -4, k₂;

      1, t₂, 1]                              -1, 5, 11]

The product MG will be row 1

1×2 + 4×1 + 5×-1     1k₁+4×-4+ 5×5       1×-19+4k₂+5×11 ⇒1    k₁+9    4k₂+36

Row 2

t₁×2+3×1+-1×-1    t₁k₁+3×-4+-1×5       t₁×-19+3k₂+-1×11  ⇒ 2t₁    k₁t₁-17 3k₂-19t₁-11

Row 3

1×2+t₂×1+1×-1      1k₁+t₂×-4+-1×5      1×-19+t₂k₂+1×11 ⇒ t₂+1   k₁-4t₂+5    k₂t₂-8

Therefore MG =

1     k₁+9   4k₂+36

2t₁    k₁t₁-17    3k₂-19t₁-11

t₂+1   k₁-4t₂+5      k₂t₂-8

G = M⁻¹  should be an identity matrix which looks like

IM = [ 1 0 0

         0 1 0

        0 0 1 ]

MG and I to find the values of t₁, t₂, k₁, and k₂:

1 = 1,         k₁+9 = 0,       4k₂+36 = 0

2t₁ = 0     k₁t₁-17 = 1        3k₂-19t₁-11 = 0

t₂+1 = 0     k₁-4t₂+5 = 0   k₂t₂-8 = 1

k₁+9 = 0 ⇒k₁ = -9          

4k₂+36 = 0  ⇒  k₂ = -9          

2t₁ = 0 ⇒   t₁ = 0          

t₂+1 = 0 ⇒    t₂ = -1

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We can predict that there are approximately 2,250 Art majors in the total population of 7,500 students at ASU based on the sample data.

We have,

We can use the formula for estimating population proportion:

Population proportion = sample proportion x population size

where the sample proportion is the fraction of students in the sample who are Art majors, and the population size is the total number of students in the population.

From the sample of 250 students, 75 said that they are majoring in Art, so the sample proportion of Art majors.

sample proportion = 75/250 = 0.3

The population size is 7,500 students.

Using the formula above, we can estimate the number of Art majors in the total population:

population proportion = sample proportion x population size

population proportion = 0.3 x 7,500

population proportion = 2,250

Therefore,

We can predict that there are approximately 2,250 Art majors in the total population of 7,500 ASU students based on the sample of 250 students surveyed.

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To memorize knowledge there are several tips that can help us. Some are: Repeat some knowledge from time to time to memorize them.

To memorize knowledge there are several methods that can be useful when we need to learn something difficult. In this case, we must use some methods that can help us such as:

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We can expect a student to guess 17 correct answers on a test with 68 four-choice multiple choice questions with probability 0.25.

Since the probability of guessing the correct answer to a four-choice multiple choice question is 0.25, the probability of guessing an incorrect answer is 1 - 0.25 = 0.75.

We can model the number of correct guesses as a binomial distribution with n = 68 (the number of trials) and p = 0.25 (the probability of success, i.e., guessing correctly).

The expected value of a binomial distribution is given by the formula:

E(X) = n * p

So, in this case, the expected number of correct answers that a student should guess on the test is:

E(X) = 68 * 0.25 = 17

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Just add the powers while it is multiply

-1+(-3)

= -1 - 3

= -4

So it is [tex]2^{-4}[/tex]

Answer:

10 * 10^10 is equal to 100,000,000,000

The solution of the differential equation y'' + 2y' - y = xe is found to be [tex]y = Ce^{(-1-\frac{\sqrt{6}}{2})t} + C'e^{(-1+\frac{\sqrt{6}}{2})t} - \frac{4}{3}xe^{x} + Ce^{x}[/tex]

To solve the differential equation y'' + 2y' - y = xeˣ, we first find the complementary solution by solving the characteristic equation,

r² + 2r - 1 = 0

Using the quadratic formula, we get,

r = (-2 ± √(2² + 4(1)(1))) / 2

r = (-2 ± √6) / 2

So the roots are,

r₁ = -1 - √6/2

r₂ = -1 + √6/2

Therefore, the complementary solution is:

[tex]y_c = Ce^{r_{1}t} + C'e^{r_{2}t}\\y = Ce^{(-1-\frac{\sqrt{6}}{2})t} + C'e^{(-1+\frac{\sqrt{6}}{2})t}[/tex]

To find the particular solution, we use the method of undetermined coefficients. We assume a particular solution of the form,

y_p = Ax²eˣ + Bxeˣ + Ceˣ

Taking the first and second derivatives, we get,

y'_p = (2Ax + B + A)x eˣ + Beˣ + Ceˣ

y''_p = (4A + 2Ax + B + A)x eˣ + (2A + B)eˣ + Ceˣ

Substituting these expressions into the differential equation, we get,

(4A + 2Ax + B + A)x eˣ + (2A + B)eˣ + Ceˣ + 2[(2Ax + B + A)x eˣ + Beˣ + Ceˣ] - (Ax²eˣ + Bxeˣ + Ceˣ) = xeˣ

Simplifying, we get,

(3Ax² + 4Ax + B)x eˣ = xeˣ

Equating coefficients, we get,

3A = 1

4A + B = 0

Solving for A and B, we get,

A = 1/3

B = -4/3

Substituting these values into the assumed particular solution, we get,

y_p = (1/3)x²eˣ - (4/3)xeˣ + Ceˣ

Taking the first and second derivatives, we get,

y'_p = (2/3)x eˣ - 4/3eˣ + Ceˣ

y''_p = (2/3)eˣ + Ceˣ

Substituting the particular solution and its derivatives into the differential equation and simplifying, We get,

(2/3)xeˣ = xeˣ

This equation is true for all x, so there is no restriction on C. Therefore, the general solution is,

y = y_c + y_p

[tex]y = Ce^{(-1-\frac{\sqrt{6}}{2})t} + C'e^{(-1+\frac{\sqrt{6}}{2})t} - \frac{4}{3}xe^{x} + Ce^{x}[/tex]

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Complete question - y'' + 2y' - y = xeˣ solve the differential equation.

The values of the complex expressions are ✓(x - iy) = a - ib and x² + y² =  (a + ib)²(a - ib)²

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

✓(x + iy) = a + ib

Changing the signs, we have

✓(x - iy) = a - ib

Multiply both expressions

This gives

✓(x + iy) * ✓(x - iy) =  (a + ib)(a - ib)

Square both sides

So, we have

(x + iy) * (x - iy) =  (a + ib)²(a - ib)²

This gives

x² + y² =  (a + ib)²(a - ib)²

Hence, the values of ✓(x - iy) is a - ib and x² + y² is  (a + ib)²(a - ib)²

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The partitions coordinate are (7, -2).

We have the coordinates (8, -5) and (4, 7)

Ratio = 1 :3

Using Section Formula

x = ( 4 + 24)/ 4

x = 28/4

x= 7

and, y= (7 - 15)/4

y = -8/4

y= -2

Thus, the partitions coordinate are (7, -2).

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using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

The value of x in the quadrilateral is 70 degrees

To find the value of the fourth interior angle, we can use the fact that the sum of all four interior angles is equal to 360 degrees. We can set up an equation:

85 + 150 + 55 + x = 360

where x is the fourth interior angle we want to find. To solve for x, we can first simplify the left side of the equation by adding the known angles:

290 + x = 360

Then, we can isolate x by subtracting 290 from both sides:

x = 360 - 290

x = 70

Therefore, the value of x when the interior angles of the quadrilateral are 85, 150, and 55 degrees is 70 degrees. This means that the four interior angles of the quadrilateral are 85, 150, 55, and 70 degrees, and their sum is indeed equal to 360 degrees.

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Answer:

25% probability

Step-by-step explanation:

2x2=4

1x1=1

1 out 4 is shaded red

1 out of 4 is 1/4 which is 25%

The x value in the linear expression 6x - 2y = -17 is -13/6 when y = 0

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

The linear expression 6x - 2y = -17

To determine the value of x in the linear expression, we set y to any value say y = 2 and then calculate the value of x

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

6x - 2(2) = -17

Evaluate

6x = -13

Divide both sides by 6

x = -13/6

This means that the value of x is equal to -13/6

So, we have (-13/6, 0)

Hence, the ordered pairs of the linear expression is (-13/6, 0)

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The solution set of the inequality (2/5)*(10x - 15) ≥ 10 is:

[4, ∞)

Here we want to solve the inequality:

(2/5)*(10x - 15) ≥ 10

To solve this we need to isolate the variable x, to do so, we can start multiplying both sides by 5/2

(10x - 15) ≥ 10*(5/2)

10x - 15 ≥ 25

Now add 15 in both sides:

10x ≥ 25 + 15

Now divide both sides by 10.

x ≥ 40/10

x ≥ 4

So the solution set is the set of all real numbers equal or larger than 4.

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Mean - this is the average. Add up the numbers and divide by the count of the numbers in the data set.

11+13+14+16+17+18+20+20+21+24+25+29 = 228

There are 12 numbers, so divide by 12.

228/12 = 19. The mean is 19.

Median - - - this is the MIDDLE number. Your data is already in numerical order (hooray!) so there are 12 numbers. Since it's even, we'll take the average of the 2 middle numbers. The 6th number is 18 and the 7th number is 20. The average of these is 19. So the median is 19.

(Side note: yes, median and mean can be the same.)

Mode - - - this is repeat/most common numbers! 20 repeats. 20 is the mode.

Range - - - biggest number is 29, littlest is 11. The range is 29-11 = 18.

(A) The preimage is ABC.

(B) The image is A'B'C'.

(C) The coordinates of the output are:

A(0,9) reflects over the line of reflection to A'(0,-9).

B(-4,4) reflects over the line of reflection to B'(4,-4).

C(0,4) reflects over the line of reflection to C'(0,-4).

In geometry, a reflection is a type of transformation where a figure is flipped over a line, called the line of reflection. In this problem, ABC-A'B'C' is a reflection, which means that it is a transformation of a figure where each point of the original figure has a corresponding point in the reflected figure such that the line of reflection is the perpendicular bisector of the line segment joining each point to its corresponding point.

A) The preimage is the original figure, which is ABC.

B) The image is the reflected figure, which is A'B'C'.

C) The coordinates of the output are:

A(0,9) reflects over the line of reflection to A'(0,-9).

B(-4,4) reflects over the line of reflection to B'(4,-4).

C(0,4) reflects over the line of reflection to C'(0,-4).

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The maximum number of toothbrushes the dentist can purchase is 50.

Let's denote the number of toothbrushes the dentist orders by "x".

If the dentist orders less than 50 toothbrushes, then the cost of the toothbrushes will be 2.58x.

If the dentist orders 50 or more toothbrushes, then the cost of the toothbrushes will be 1.24x.

There is a base cost of [tex]$48[/tex] for printing the dentist's name and address on the toothbrushes.

The total cost of the order can be expressed as:

Total cost = 48 + (2.58x) for x < 50

Total cost = 48 + (1.24x) for x ≥ 50

The maximum number of toothbrushes the dentist can purchase, given that the budget is [tex]$110[/tex].

So we can set up an equation:

Total cost = 110

For x < 50:

48 + 2.58x = 110

2.58x = 62

x ≈ 24.03

For x ≥ 50:

48 + 1.24x = 110

1.24x = 62

x ≈ 50

The maximize number of toothbrushes, we choose the larger value of x, which is x ≈ 50.

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Answer:

28.57% chance

Step-by-step explanation:

add them all up which is 14, and if there are 4 white marbles that means its 4/14, which is 28.57 as a percent (2:7 as ratio)

Answer:

x = 78°

Step-by-step explanation:

Line q pass through the parallel line of s and r so their alternet interior angles are equal. the alternet interior angles of 135° is 57°+ x so they are equal .

57° + x = 135°

x = 135° - 57°

x = 78°

So the answer is D, 78°

Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

[tex]\sf P =\dfrac{F}{1+r\div n}^{(nt)[/tex]

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

[tex]\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}[/tex]

[tex]\sf P = \dfrac{1000}{(1.0375)^{10}}[/tex]

[tex]\sf P = \dfrac{1000}{1.4450}[/tex]

[tex]\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)[/tex]

Therefore, the price of the zero coupon bond is $692.04.

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The regular admission price for one adult is $17.50.

We have,

Let's first determine the total cost of admission after the coupons have been applied.

Since each person has a coupon for $5 off, the total discount for the group is $5 x 6 = $30.

The total cost of admission after the discount.

$105 - $30

= $75.

Let A be the regular admission price.

Since each person paid the same price after the discount, we can set up the following equation:

6(A - $5) = $75

We subtract $5 from the regular price A because that is the amount of the coupon discount.

We can simplify the equation as follows:

6A - $30 = $75

6A = $105

A = $17.50

Therefore,

The regular admission price for one adult is $17.50.

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The length of the given rectangular cuboid is: 9 cm

In geometry, a rectangular prism is defined as a polyhedron with two congruent as well as parallel bases. It is also referred to as a cuboid. A rectangular prism is one that possesses six faces, and then all the faces are located in a rectangle shape and possess twelve edges. Whenever its cross-section along the length, it is referred to as a prism.

The formula for the volume of a prism is given by the formula:

V = L * W * H

Where:

L is length

W is width

H is height

We have that Volume = 432 cm³

Thus:

6 * L * 8 = 432

48L = 432

L = 432/48

L = 9 cm

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The constraint of x for the function g(x) = -40(2x + 7)(x - 10) is given by, 0 [tex]\le[/tex] x [tex]\le[/tex]6.

Given that the function is,

g(x) = - 40(2x + 7)(x - 10)

where x stands for the number of years since the year 2003

and g(x) stands for the amount of sales of golf equipment in million dollar unit.

The mathematician used the data for the year span of 2003 - 2009.

Min of x = Number of years since 2003 when the year is 2003 = 2003 - 2003 = 0

Max of x = Number of years since 2003 when the year is 2009 = 2009 - 2003 = 6

So the constraint of x is, 0 [tex]\le[/tex] x [tex]\le[/tex] 6.

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30 gallons of 28% butterfat and 30 gallons of 16% butterfat should be combined to create a 60-gallon mixture that is 22 % butterfat.

Let x gallon of 28% butterfat mixed with the y gallon of 16% butterfat to obtain 60 gallons of 22.5% butterfat,

⇒ x + y = 60 ⇒ x = 60 - y ----(1),

Quantity of butterfat in x gallon + quantity of butterfat in y gallon = total quantity of butterfat,

⇒ 28% of x + 16% of y = 22% of 60

⇒ 0.28x + 0.16y = 0.22 × 60

⇒ 0.28x + 0.16y = 13.2

⇒ 28x + 16y = 1320

⇒ 14x + 8y = 660

From equation (1),

14(60-y) + 8y = 660

840 - 14y + 8y = 660

6y = 180

y = 30

Again from equation (1),

x = 60 - y

= 60 - 30

= 30

Hence, 30 gallons of 28% butterfat and 30 gallons of 16% butterfat are combined to create a 60-gallon mixture that is 22%

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Answer:

Right three

Step-by-step explanation:

Because the translation is applied inside the parentheses, we are shifting the function left/right. To determine whether it is shifted left or right, note that shifting right will have a negative number and shifting left will have a positive number. Since we have a negative number -3, it is shifted right.

Answer:

Step-by-step explanation:

Here if we put [tex]x=3[/tex] then then equation will give 0. Hence it will shift right side three unit .

Final answer: right 3

Answer:

C) 16

Step-by-step explanation:

(3x + 5) + 37 = 90

3x = 90 - 5 - 37

3x = 48

x = 48/3 = 16

Answer:

x = 16°

Step-by-step explanation:

It is 90° angle so their sum must be 90°( complement) .

3x + 5° + 37° = 90°

3x + 42° = 90° ... simplify the like term

3x = 90° - 42°

3x = 48°

3x/3 = 48°/3

x = 16°

So the answer is C, 16

Answer:

50313.28

See the below process

Step-by-step explanation:

Important formulae

A=Total Amount

P=Principal or amount of money deposit

R=Annual interest rate

N=Number of Times compounded per year

T=Time in years

For the formula:

[tex]a \: is \: equals \: to \: p(1 + \frac{r}{n}) \: n - t \\ p \: is \: equals \: to \: 5000 \: dollars \: comma \: r \: s \: equals \: to \: 8\% \: comma \: n \: is \: equals \: to \: 1 \: and \: t \: is \:equals \: to \: 30 \: years \: [/tex]

Solution:

A=5000(1+0.08 /1) to the power 1.30

5000×10.062657

Answer= 50313.28

-Thank You By MrIshaan

Probability of landing on space with polka dots = 3/8.

Probability of landing on space with stripes = 1/2.

Probability of landing on space with stripes and even numbers = 1/4.

Probability of landing on space with stripes or even numbers = 5/8.

Hence the code is 'AFCH'.

From the definition of Probability we know that,

Probability of event = (Number of Favorable outcomes)/(Total number of outcomes)

Here total number of spaces = 8.

Number of space with polka dots = 3 [space numbered 1, 4, 6]

Number of space with stripes = 4 [space numbered 0, 2, 3, 5, 7]

Number of space with stripes and even numbers = 2 [the space numbered 0 and 2]

Probability of landing on space with polka dots = 3/8 (A)

Probability of landing on space with stripes = 4/8 = 1/2 (F)

Probability of landing on space with stripes and even numbers = 2/8 = 1/4 (C)

So, Probability of landing on space with stripes or even numbers

= Probability of landing on space with polka dots + Probability of landing on space with stripes - Probability of landing on space with stripes and even numbers

= 3/8 + 1/2 - 1/4

= (3 + 4 - 2)/8

= 5/8 (H).

Hence the code will be 'AFCH'.

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