A tree is 18 feet tall. A wire runs from the top of the tree to a point 4 feet from its base. The wire is √340 feet long. Estimate the length of the wire to the nearest hundredth of a foot. The wire is about (Blank) feet long.

Answer:

yeah the answer is right

The length of the Hypotenuse is, \(\sqrt{5}x\) units.

What is Pythagoras Theorem?

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Let the one leg of a right triangle is twice as long as the other.

Suppose the shorter leg is x.

So the longer leg is 2x.

Let, the hypotenuse is h.

By Pythagoras Theorem,

\(x^2 + (2x)^2 = h^2\\x^2 + 4x^2 = h^2\\5x^2 = h^2\\h = \sqrt{5} x\)

Hence, the hypotenuse as a function of the length of the shorter leg, is \(\sqrt{5}x\) units.

To know more about the Pythagoras Theorem, click on the link

https://brainly.com/question/343682

#SPJ4

Answer: 5 1/2 rounded

5.33

Step-by-step explanation:

Answer:

2sqrt3

Step-by-step explanation:

because it's a 60 30 right triangle. and you have to leave your answer in radical form.

Her mental age would be 8 yrs old.

IQ [ Intelligent Quotient ]  is a type of standard score that indicates how far above, or how far below, his/her peer group an individual stands in mental ability.

IQ of a person is given by the formula -

IQ = MA/CA * 100

IQ = Mental Age / Chronological Age * 100

According to the question, IQ = 100, CA = 8

⇒ 100 = MA / 8 *100

⇒1 = MA / 8

⇒ MA = 8 Yrs

Hence, the estimated mental age of susan is 8 yrs old.

To understand more about Division and Multiplication refer -

https://brainly.com/question/28768606

#SPJ4

Answer:

a is the answer I hope you have a great day

Answer:

A.)

B.)

Step-by-step explanation:

i looked it up and only a and b show 10

Answer:

Step-by-step explanation:

Yes it is a quadratic equation

5x^2 + 40x = -7

5x^2 + 40x + 7 = 0

a = 5

b = 40

c = 7

-40/10 + (sqrt(1600 - 4(5)(7)))/10

-4 + (sqrt(1600-160))/10

-4 + (sqrt(1440))/10

-4 + 12(sqrt(10))/10

-4 + 6/5(sqrt(10))

The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

Learn more about trigonometrical ratios on https://brainly.com/question/23130410

#SPJ1

The cash price of the bond is $10,898.92.The accrued interest is $315.32.

The cash price of the bond, we need to determine the present value of the bond's future cash flows. The bond has a face value (redeemable at par) of $22,000 and a coupon rate of 5.3%. Since the interest is payable semi-annually, each coupon payment would be half of 5.3%, or 2.65% of the face value. The bond matures on May 12, 2008, and the purchase date is June 07, 2001, which gives a total of 28 semi-annual periods.

Using the formula for present value of an annuity, we can calculate the present value of the coupon payments. The yield is 9.8% compounded semi-annually, so the semi-annual discount rate is half of 9.8%, or 4.9%. Plugging in the values into the formula, we get:

Coupon payment = $22,000 * 2.65% = $583

Present value of coupon payments = $583 * [(1 - (1 + 4.9%)^(-28)) / 4.9%] = $10,315.32

To calculate the present value of the face value, we need to discount it to the present using the same discount rate. Plugging in the values, we get:

Present value of face value = $22,000 / (1 + 4.9%)^28 = $5883.60

Finally, we add the present value of the coupon payments and the present value of the face value to obtain the cash price of the bond:

Cash price = Present value of coupon payments + Present value of face value = $10,315.32 + $5,883.60 = $10,898.92.

Accrued interest refers to the interest that has accumulated on the bond since the last interest payment date. In this case, the last interest payment date was on June 7, 2001, and the purchase date is also June 7, 2001, so no interest has accrued yet.

The accrued interest can be calculated by multiplying the coupon payment by the fraction of the semi-annual period that has elapsed since the last interest payment. Since no time has passed between the last interest payment and the purchase date, the fraction is 0. Thus, the accrued interest is $583 * 0 = $0.

Learn more about multiplying : brainly.com/question/620034

#SPJ11

Answer:

-11

Step-by-step explanation:

-1/2y=1/2+5

- 1/2 y = 1+10 (by taking lcm)

               2  

 \(\frac{-1}{2}\) x 2y = 11

y = -11

\( \frac{ - 1}{ \: \: \: 2} y = \frac{1}{2} + 5\)

\( \frac{ - 1}{ \: \: \:2} \times y = \frac{1}{2} + 5\)

\( \frac{ - 1}{ \: \: \:2} \times y = \frac{11}{2} \)

\(y = \frac{11}{2} \div \frac{ - 1}{ \: \: \:2} \)

\(y = \frac{11}{2} \times \frac{ \: \: \: 2}{ - 1} \)

\(y = \frac{ \: \: 22}{ - 2} \)

\(y = - 11\)

The value of y = -11

Therefore :-

\( \frac{ - 1}{ \: \: \:2} \times - 11 = \frac{1}{2} + 5\)

Answer:

Step-by-step explanation:

49 hours of work

Answer:

Formula of reflection the y axis is

P(x,y)→P'(-x,y)

Now

By using formula

E(1,3)=E'(-1,3)

F(1,0)=F'(-1,0)

P(4,2)=P'(-4,2)

R(2,0)=R'(-2,0)

Step-by-step explanation:

After 3 weeks, the expected number of bacteria is approximately 2008.55.

If the growth rate of the number of bacteria at any time   (t  ) is proportional to the number present at   (t  ) and triples in 1 week, we can model the growth using the exponential growth equation:

 (N(t) = N_0     c dot e^{kt}  )

where:

 (N(t)  ) is the number of bacteria at time   (t  ),

 (N_0  ) is the initial number of bacteria,

 (k  ) is the growth constant.

Given that the number of bacteria triples in 1 week, we can determine the value of the growth constant   (k  ). Since tripling corresponds to multiplying the initial number by 3, we have:

 (3N_0 = N_0     c dot e^{k     c dot 1}  )

Simplifying, we find:

 (e^k = 3  )

Taking the natural logarithm of both sides, we have:

 (k =   ln(3)  )

Now we can calculate the number of bacteria after 3 weeks (  (t = 3  )) with an initial number of 100 (  (N_0 = 100  )):

 (N(3) = 100   c dot e^{  ln(3)   c dot 3}  )

Simplifying, we find:

 (N(3) = 100     c dot e^{3   ln(3)}  )

Using a calculator, we can evaluate this expression:

 (N(3)   approx 100     c dot 20.0855  )

Therefore, after 3 weeks, the expected number of bacteria is approximately 2008.55.

Learn more about natural logarithm from :

https://brainly.com/question/305900

#SPJ11

The point where the line through (5, 2) with slope 4 crosses the vertical axis is (0, -18).

To do this, we can use the point-slope form of a line equation:

y - y1 = m(x - x1)

Here, (x1, y1) is the given point (5, 2) and m is the slope, which is 4. Let's plug in these values:

y - 2 = 4(x - 5)

Now, we need to find the point where the line crosses the vertical axis (y-axis). When a point is on the y-axis, its x-coordinate is 0. So, we will substitute 0 for x and solve for y:

y - 2 = 4(0 - 5)
y - 2 = -20
y = -20 + 2
y = -18

Therefore, the point where the line through (5, 2) with slope 4 crosses the vertical axis is (0, -18).

Learn more about "line": https://brainly.com/question/24644930

#SPJ11

To determine the concentration of the analyte in the unknown using the fit parameters and the linear model, you need to substitute the given signal value into the equation y = mx + b.

In this case, the linear model is represented by the equation y = mx + b, where:

y is the signal value (80.77 in this case),

m is the slope obtained from the regression analysis, and

b is the y-intercept obtained from the regression analysis.

You haven't provided the values of m and b, so I'll use placeholders for now.

Let's assume the slope (m) obtained from the LINEST formula is m = 2.5 and the y-intercept (b) is b = 10.

Substituting these values into the equation:

y = mx + b

80.77 = 2.5x + 10

To find the concentration (x), we can rearrange the equation:

2.5x = 80.77 - 10

2.5x = 70.77

x = 70.77 / 2.5

x ≈ 28.31

Therefore, based on the given fit parameters and the linear model, the concentration of the analyte in the unknown is approximately 28.31 ppm Co2+.

To learn more about regression : brainly.com/question/32505018

#SPJ11

Answer: 0

Step-by-step explanation:

1/3 times 21 = 7 -1/2 times 12 = -6

7-1-6 = 0

Answer:

The answer is 6.4

Step-by-step explanation:

Since a^2+b^2=c^2, then 5^2+4^2=6.4^2

Answer:

6

Step-by-step explanation:

if we always go from right to left it will start with lin segment BC   BD    BA   CD  CA    and DA those are all the posible segments for this line

Answer:

0.75

Step-by-step explanation:

9+3 = 12

a half is 50%, a quarter is 25% so a half quarter would be 75%.

75 ÷ 100 = 0.75

Answer:

10 & 4

Step-by-step explanation:

Let the numbers are a and b.

Their average = 7

= > ( a + b ) / 2 = 7

= > a + b = 2 * 7 = 14 ...( 1 )

Also,

= > 3 times of difference between a and b = 18

= > 3( a - b ) = 18

= > a - b = 6 ... ( 2 )

adding ( 1 ) & ( 2 ) :

= > ( a + b ) + ( a - b ) = 14 + 6

= > 2a = 20

= > a = 10

Thus,

= > a + b = 14 → 10 + b = 14

= > b = 14 - 10 = 4

Answer:

400

Step-by-step explanation:

The area of sides and add then up

The sample is a systematic sample.

What is sample?

In statistics, a sample is a subset of individuals or objects selected from a larger population. Samples are used in statistical analyses to draw conclusions or make inferences about the entire population.

A sample is typically less time-consuming and less expensive to collect and analyze than the entire population, making it a practical and efficient way to conduct research.

A systematic sample is a type of probability sampling method in which every nth member of a population is selected to be included in the sample.

In this case, the network administrator is analyzing the company's network logs every third day, which means they are selecting every third day's data for analysis.

This is a systematic approach to selecting the data for analysis, making it a systematic sample.

Therefore, the sample is a systematic sample.

To learn more about sample visit:

https://brainly.com/question/24466382

#SPJ1

The division will give a value of 0.15 × 10^10.

The information is to divide the quantity 1.365 times ten raised to the eighteenth power end quantity divided by the quantity 9.1 times ten raised to the eighth power end quantity.

This will be:

(1.365 × 10^18) / (9.1 × 10^8)

= 1.365/9.1 × 10^10

= 0.15 × 10^10

Learn more about division on:

brainly.com/question/25289437

#SPJ1

Answer:  Step-by-step explanation:

I believe that is it 100, since it is the only number listed that has factors and multiples.

Hope this helps!

Using proportions, her commission would be of $3,700.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Her commissions are divided as follows:

Hence the total commission is:

0.15 x 5000 + 0.25 x 1000 + 0.3 x 9000 = $3,700.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

2.25

Step-by-step explanation:

Answer: It seems that you have provided two equations to represent the number of men and women receiving bachelor's degrees over the years, where x represents the number of years after 1970. However, you haven't specified what the question or task is. It's essential to provide further instructions or ask a specific question so that I can assist you accordingly.

Answer:

Weighted mean.

Step-by-step explanation: