Find the area of the triangle

Answer:

12.6 units.

Step-by-step explanation:

According to cosine formula:

[tex]a^2=b^2+c^2-2bc\cos A[/tex]

Using cosine formula in triangle STU, we get

[tex](SU)^2=(ST)^2+(TU)^2-2(ST)(TU)\cos T[/tex]

[tex]t^2=(5)^2+(15)^2-2(5)(15)\cos (53^{\circ})[/tex]

[tex]t^2=25+225-150(0.60)[/tex]

[tex]t^2=160[/tex]

Taking square root on both sides.

[tex]t=\sqrt{160}[/tex]

[tex]t\approx 12.6[/tex]

Therefore, the value of t is 12.6 units.

Answer: $10,000

Step-by-step explanation:

Given the following :

Profit if economy remains strong = $30,000

Profit if economy grows at moderate pace = $10, 000

Loss if economy goes into recession = $30,000

Probability that economy will remain strong = 20% = 0.2

probability the economy will grow at a moderate pace = 70% = 0.7

probability the economy will slip into recession = 10% = 0.1

Expected value = sum of (x * p(x))

Here expected value equals;

Strong economy profit = $30,000 * 0.2 = $6000

Moderate economy profit = $10,000 * 0.7 = $7000

Loss on Recession = $30,000 * 0.1 = $3000

Expected profit = $(6000 + 7000 - 3000)

Expected profit = $10,000

Answer: Ask the king to draw first and read it. Explain that if the king selects "leave" the PM's choice could only be "stay". It is then unnecessary for the PM to draw. It avoids embarrassing the king in his lie, demonstrates the PM's intelligence, and keeps his job.

Step-by-step explanation:

The length of the arc s is 6.283 inches.

The length of an arc is given by the formula,

[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}[/tex]

where

θ is the angle, which arc creates at the center of the circle in degrees.

Radius, r = 8 in.

Angle, θ = 45°,

[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}[/tex]

[tex]\rm{ Length\ of\ the\ Arc\ s = 2\times \pi \times(8)\times\dfrac{45}{360}[/tex]

[tex]\rm{ Length\ of\ the\ Arc\ s =6.283\ inches.[/tex]

Hence, the length of the arc s is 6.283 inches.

Learn more about Length of an Arc:

https://brainly.com/question/1577784

The approximate length of arc s on the given circle is; 6.28inches

The length of an arc is given by the formula;

Therefore,

Length, L = (45/360) × 2 × 3.14 × 8

Read more on length of an arc;

https://brainly.com/question/2005046

Answer:

4.5 cm

Step-by-step explanation:

apothem=R/2=9/2=4.5 cm

Answer:

In 256 ways

Step-by-step explanation:

The number of answer choices will be; 4 * 3 = 12 answer choices

Okay, so per question we have 4 choices

The number of ways we can answer the first question is 4 ways since there are 4 choices

For the second question, 4 ways also

For the third 4 ways

And for the last question, four ways too

So the number of ways to correctly answer the question will be ;

4 * 4 * 4 * 4 = 256 ways

Answer:

[tex]\boxed{\sf \ \ 28 \ \ }[/tex]

Step-by-step explanation:

Hello,

Please find attached the graph

AB = 6-2 = 4

DA = 7-0 = 7

So the area of the rectangle is AB * DA = 4 * 7 = 28

Hope this helps

Answer:

El reloj está marcando:

las 4:00 horas

Step-by-step explanation:

El reloj avanzó a su mismo ritmo pero en sentido contrario a partir de las 6:45

si ahora son las 9:30 el reloj marca:

9:30 = 9horas 30minutos = 9h 30'

6:45 = 6horas 45minutos = 6h 45´

1 hora = 60'

9h 30' = 8h + 60' + 30' = 8h + 90' = 8h 90'

entonces:

 8h 90'

- 6h 45'

= 2h 45

entonces el reloj está marcando 2h 45' menos que la hora en que se dañó.

por tanto:

 6h 45'

- 2h 45'

= 4h 00'

El reloj ahora está marcando las

4 horas en punto.

Answer:

BCD

Step-by-step explanation:

Answer: B,C & D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The chord- chord angle 105° is half the sum of the arcs intercepted by the angle and its vertical angle, thus

[tex]\frac{1}{2}[/tex](120 + x) = 105 ( multiply both sides by 2 )

120 + x = 210 ( subtract 120 from both sides )

x = 90 → D

Answer:

Step-by-step explanation:

1.50x + 10[x/30] >= 450

x >= 246.3

check:

1.50*246 + 10*8 = 449

$450

Answer:

y = 9.1

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{WX}}=\frac{\text{SinX}}{\text{WY}}[/tex]

[tex]\frac{\text{SinW}}{\text{w}}=\frac{\text{SinY}}{\text{y}}=\frac{\text{SinX}}{\text{x}}[/tex]

Since m∠W + m∠X + m∠Y = 180°

m∠W + 58° + 106° = 180°

m∠W = 180° - 164°

m∠W = 16°

[tex]\frac{\text{Sin16}}{\text{w}}=\frac{\text{Sin106}}{\text{y}}=\frac{\text{Sin58}}{\text{8}}[/tex]

[tex]\frac{\text{Sin106}}{\text{y}}=\frac{\text{Sin58}}{\text{8}}[/tex]

y = [tex]\frac{8\times (\text{Sin106})}{\text{SIn58}}[/tex]

y = 9.068

y ≈ 9.1

Answer: 16,384

Step-by-step explanation:

The seven marbles have different colours, so we can differentiate them.

Now, suppose that for each marble we have a selection, where the selection is in which jar we put it.

For the first marble, we have 4 options ( we have 4 jars)

For the second marble, we have 4 options.

Same for the third, for the fourth, etc.

Now, the total number of combinations is equal to the product of the number of options for each selection.

We have 7 selections and 4 options for each selection, then the total number of combinations is:

C = 4^7 = 16,384

Answer:

the answer is 16384

Step-by-step explanation:

have a nice day.

Answer:

DE = 4.24

Step-by-step explanation:

The diagram is not shown; However, the question can still be solved without the diagram.

Having said that,.

Given that

DF = EF = 3

This implies that DE is the hypothenus and will be solved using Pythagoras theorem.

DE² = EF² + DF²

Substitute 3 for EF and DF

DE² = 3² + 3²

DE² = 9 + 9

DE² = 18

Take Square Root of both sides

DE = √18

DE = 4.242640687119285

DE = 4.24 (Approximated)

Answer:

Step-by-step explanation:

from cosines theorem:

t² = 11² + 14² - 2•11•14•cos87°

t² = 121 + 196 + 308•0.05236

t² = 333.12688

t = √333.12688

t = 18.2517... ≈ 18.3

Answer:

A

Step-by-step explanation:

Type in the equation of the graphing calculator and press graph

Answer:

10

Step-by-step explanation:

[tex]\left(x-h\right)^{2}+\left(y-k\right)^{2}=r^2[/tex]

[tex]\left(x-6\right)^{2}+\left(y-0\right)^{2}=r^2\\[/tex]

We used (2,-3)

[tex]\left(2-6\right)^{2}+\left(-3-0\right)^{2}=25[/tex]

[tex]r^2=25\\[/tex] , so [tex]r = 5[/tex]

But this one is asking for the diameter, and to find it. It's simply 2r.

2*5 = 10

Answer:

167.55

Step-by-step explanation:

so it varies jointly so

A-area if cylinder

so

[tex]a \: \alpha \: \pi \: r \: ^{2} h[/tex]

so

[tex]a = k\pi \: r^{2}h[/tex]

where k is the constant

so apply the first set of values to get k=2/3

then substitute the k with the second set of values

Answer:

T = 1.5s

Step-by-step explanation:

Hello,

To find the time the pincone hits the ground, we need to use the equation given.

Note that h = 0 when the pinecones hits the ground.

This question relates to motion under gravity.

h = -16t² + 36

0 = -16t² + 36

Make t² the subject of formula

16t² = 36

t² = 36 / 16

t² = 2.25

Take the square root of both sides

t = √(2.25)

t = 1.5s

The time it takes the pinecone to hit the ground is 1.5s.

Answer:

42

Step-by-step explanation:

7 times as large as 6   = 7 * 6

7 * 6 = 42

Hope this helps

Answer:

42

Step-by-step explanation:

Answer:

518 / 3.

Step-by-step explanation:

(74 / 3) * 7 = (74 * 7) / 3 = 518 / 3 = 172 and 2/3 = 172.6666666667.

Hope this helps!

Answer: Pam's total salary is $41666.666

Step-by-step explanation:

Assume her total earning or salary per year = y

Personal expenses spent yearly = $7500

Personal expenses yearly ($7500) = 18% of y

100%y =

18% of y = 7500

(18/100)y = $7500

100% y = Total salary

0.18y = $7500 - - - - - - - (1)

1y = Total salary

(Total salary * 0.18y) = (7500 * y)

Total salary = 7500y / 0.18y

Total salary = 7500/0.18

Total salary = $41666.666

Answer:

[tex]\dfrac{y^2}{64}-\dfrac{x^2}{9}=1[/tex] .

Step-by-step explanation:

Since vertices lie on y-axis. So, it is a vertical parabola of the form

[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]

where, (h,k) is center, [tex](h,k\pm c)[/tex] is focus and [tex](h,k\pm a)[/tex] is vertex.

Center is (0,0). So, h=0 and k=0.

Foci are [tex](0,\pm \sqrt{73})[/tex]. So [tex]c=\sqrt{73}[/tex].

Vertices are [tex](0,\pm 8)[/tex]. So [tex]a=8[/tex].

We know that,

[tex]a^2+b^2=c^2[/tex]

[tex]8^2+b^2=(\sqrt{73})^2[/tex]

[tex]b^2=73-64[/tex]

[tex]b=3[/tex]

Put h=0,k=0, a=8 and b=3 in equation (1).

[tex]\dfrac{(y-0)^2}{8^2}-\dfrac{(x-0)^2}{3^2}=1[/tex]

[tex]\dfrac{y^2}{64}-\dfrac{x^2}{9}=1[/tex]

Therefore, the required equation is [tex]\dfrac{y^2}{64}-\dfrac{x^2}{9}=1[/tex] .

Answer:

x = 125°

Step-by-step explanation:

The given polygon is a hexagon with 6 sides.

The sum of the interior angles for any given polygon = (n - 2)180, where n is the number of sides of the polygon.

Therefore:

[tex] x + 117 + 124 + 102 + 145 + 107 = (6 - 2)180 [/tex]

[tex] x + 595 = (4)180 [/tex]

[tex] x + 595 = 720 [/tex]

Subtract both sides by 595 to solve for x:

[tex] x + 595 - 595 = 720 - 595 [/tex]

[tex] x = 125 [/tex]

x = 125°

Answer: 1/5

Step-by-step explanation:

Given the following :

Total number of ducks in pool = 30

Mark 1 = 15 ducks

Mark 2 = 9 ducks

Mark 3 = 6 ducks

Probability of picking a duck with Mark 3:

Probability = (number of required outcomes / total possible outcomes)

Number of required outcomes = number of ducks with mark 3 = 6 ducks

P(picking a duck with Mark 3) = 6/30

6/30 = 1/5

= 1/5

Answer:

x=6 and x=5.1

Step-by-step explanation:

Answer:

$95.42  more

Step-by-step explanation:

To find out how much money was made with Investment A after 2 years:

First, we are told that 160 dollars is saved per month for 2 years.  There are 24 months in 2 years, so we have to multiply $160 by 24 months.

160 *24=$3840 after 2 years.

Next, we learn thar 2.5% interest rate is added to the total amount saved in those two years.  So, we must turn 2.5% in to a decimal, which is 0.025.

Now, multiply 3840*0.025 to get $96.

We have to add that on the the amount saved, so 3840+96=$3936.

Investment A made $3936 after 2 years.

To find out how much money was made with Investment B.

So, we have to find compound interest.  The formula for compound interest is:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

In this problem: P=3800, r=3% or 0.03, n=1, and t=2.

So, lets write it out: [tex]A=3800(1+\frac{0.03}{1} )^{2*1}[/tex]

That becomes: [tex]A=3800(1.03)^{2}[/tex]

Simplify it even further: [tex]A=3800(1.0609)[/tex]

Multiply the last two numbers to get: [tex]A=4031.42[/tex]

Investment B made $4031.42 after 2 years.

The question asks us to find out how much more money Investment B made than Investment A after 2 years.  It's simple.  Just subtract Investment A's amount from Investment B's amount.

4031.42-3936=95.42

Investment B made $95.42 more than Investment A after 2 years.

Hey there! :)

Answer:

Third choice: 13π/15 in.

Step-by-step explanation:

Begin by finding the circumference of the entire circle. Use the formula

C = 2rπ to solve:

C = 2(3)π

C = 6π.

Next, we can set up a proportion to find the arc length of AQB:

[tex]\frac{6\pi }{360}= \frac{x}{52}[/tex]

Cross multiply:

52 · 6π = 360 · x

312π = 360x

Divide both sides by 360:

312π/360 = 360x/360

x = 13π/15 in.

Answer:

The answer is 77n/15 inches :)

Step-by-step explanation:

Answer:

900

Step-by-step explanation:

a heptagon has 7 sides, so we take the hexagon's sum of interior angles an and add 180 to it's getting us, 720 + 180 = 900 degrees