3. Use a proportion to find the distance across the water from C to D.

Answer:

A) Yes, because the sum of any two side lengths is greater than the third side length.

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, 4 + 8 = 12, which is greater than 10, and the other two combinations (4 + 10 and 8 + 10) also satisfy this rule. Therefore, the given side lengths do form a triangle.

Step-by-step explanation:

Answer:

64°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

let the third angle be x , then

x + 90° + 26° = 180°

x + 116° = 180° ( subtract 116° from both sides )

x = 64°

the other angle is 64°

The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

We have,

Recall the trigonometric identities:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b))

Using these identities, we can find the exact values of the expressions given.

(a) Sin (α + β)

sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

= (√5/5)(-3/5) + (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 - 8/25

= (-6√5 - 8)/25

(b) Cos (α + β)

cos(α + β) = cos(α)cos(β) - sin(α)sin(β)

= (2/5)(-3/5) - (√5/5)(-4/5) (using the values given for sin and cos)

= -6/25 + 4√5/25

= (4√5 - 6)/25

(c) Sin (α - β)

sin(α - β) = sin(α)cos(β) - cos(α)sin(β)

= (√5/5)(-3/5) - (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 + 8/25

= (-6√5 + 8)/25

(d) tan (α - β)

tan(α - β) = (tan(α) - tan(β))/(1 + tan(α)tan(β))

= ((√5/5) - (-4/5))/(1 + (√5/5)(-4/5)) (using the values given for sin and cos)

= (9√5/5)/(1 - 4/5√5)

= (-9√5 + 45)/4

Therefore,

The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ1

Answer: B

Step-by-step explanation: The first X was 1. If you add 1 too the 1/2 in the equation, its 1 & 1/2. theres only one graph that has 1 & 1/2, and its B

Answer:

x > -5, so the correct answer is C.

Answer:

Please give brainliest

Step-by-step explanation:

c

Answer:

54,390

Step-by-step explanation:

Answer:

54, 390

Step-by-step explanation:

What is 54,392 close to? 90 or 100? (In this case, 54,300)

I hope this helped at all.

Answer:-111

Step-by-step explanation:

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

Learn more about expression at https://brainly.com/question/1859113

#SPJ1

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Answer:

a)H0: β1= 1 and Ha: β1 ≠1

b) The test statistic is____.t= b- β/ sb

c) The p-value is____.0.999144

(d) Therefore, we can conclude that:_____. there is not enough evidence to reject the null hypothesis.    

The data provides no evidence at the 0.1 significance level that these thermometers are not consistent.

Step-by-step explanation:

This is called testing hypotheses about β, the population regression co efficient.

The null and alternate hypotheses are

H0: β1= 1 and Ha: β1 ≠1

The significance level is ∝=0.1 and ∝/2 is 0.05

The critical region at t ∝/2 (29)=  t ≤ - 1.699 , t ≥ 1.699

The test statistic is

t= b- β/ sb

which has t distribution with υ= 31-2= 29 degrees of freedom.

Calculations

Ŷ = a +bX

b = SPxy /SS x= Σ(xi-x`)(yi-y`)/Σ(xi-x`)²

b = 39671.6/39680= 0.9998

a = y` - bx`

x`= 60

y`= 59.989

a = 59.989 -0.9998*60 = 0.001734

Syx²= Σ( yi -y`)²/ n-2= 39663.3857/ 29=1367.68965

Syx= 36.9822

Sb= Syx/ √∑  (x-x`)²

Sb= 36.9823/ √39680

Sb= 36.9823/ 199.984

Sb= 0.18493

x-x`                 y-y`                    (x-x`)²     (x-x`)(y-y`)

-60                 -59.969            3600              3598.1419

-56                  -55.999           3136          3135.9458

-52                 -52.079             2704          2708.1097

-48                -47.959              2304           2302.0335

-44                 -43.899              1936          1931.5574

-40                -39.989               1600          1599.5613

-36              -36.009                1296            1296.3252

-32               -31.899              1024              1020.769

-28               -28.049             784                785.3729

-24                -23.959             576               575.0168

-20               -19.989             400                  399.7806

-16                 -15.939            256                  255.0245

-12               -12.039             144                    144.4684

-8                  -7.989             64                       63.9123  

-4                 -4.119                16                      16.4761

0                 -0.08903           0                         0

4                  3.921              16                      15.6839

8                7.961                64                       63.6877

12                12.121             144                     145.4516

16                16.031             256                   256.4955

20               20.021           400                  400.4194

24               24.111              576                   578.6632

28                28.071           784                     785.9871

32                 31.751            1024                    1016.031

36               36.031           1296                    1297.1148

40                39.961          1600                    1598.4387

44                43.881           1936                     1930.7626

48               48.021           2304                     2305.0065

52              52.001             2704                     2704.0503

56             56.051              3136                       3138.8542

60            60.041                3600                     3602.4581

∑0          0                 39680 (SSx)     39671.6 (SPxy)

Putting the values

The test statistic is

t= b- β/ sb

t= 0.9998-1/ 0.18493

t=-0.0010815

Since the calculated t=-0.0010815  does not lie in the critical region  t ∝/2 (29)=  t ≤ - 1.699 , t ≥ 1.699 we conclude that these thermometers seem to be measure temperatures.

The p-value is  ≈ 0.999144

there is not enough evidence to reject the null hypothesis.    

The comparisons of the fractions given above is enumerated below.

1) To compare 1/8 and 1/9, I can find a common denominator by multiplying the denominators together. The common denominator is 8 x 9 = 72.

Then, I can convert each fraction to have a denominator of 72 by multiplying the numerator and denominator of each fraction by the appropriate factor. The result is 9/72 and 8/72. Since 9/72 is bigger than 8/72, I know that 1/8 is smaller than 1/9.

2) To compare 7/8 and 8/9, I can find a common numerator by multiplying the numerators together. The common numerator is 56. Then, I can convert each fraction to have a numerator of 56 by multiplying the numerator and denominator of each fraction by the appropriate factor. The result is 49/56 and 64/72. Since 64/72 is bigger than 49/56, I know that 8/9 is bigger than 7/8.

3) To compare 15/38 and 5/13, I can find a common numerator by multiplying the numerators together.

The common numerator is 195. Then, I can convert each fraction to have a numerator of 195 by multiplying the numerator and denominator of each fraction by the appropriate factor.

The result is 75/195 and 75/195. Since the numerators are the same, I can compare the denominators. Since 195 is bigger than 169, I know that 15/38 is smaller than 5/13.

4) To compare 5/9 + 7/12 and 1/2, I can compare each fraction to 1/2 separately.

First, 5/9 is smaller than 1/2 because 9 is bigger than 18, so each ninth is smaller than each half.

Next, 7/12 is also smaller than 1/2 because 12 is bigger than 6, so each twelfth is smaller than each half.

Therefore, both fractions added together (without actually adding them) will be smaller than 1/2.

Learn more about fractions at:

https://brainly.com/question/10708469

#SPJ1

The median, mean, range and mode will be 6, 5.4, 9 and 7.

What is median?

The median is the middle number in the data set when the data set is written from least to greatest.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

To know more about median check the below link:

https://brainly.com/question/14532771

#SPJ1

Considering the triangle given the variables are calculated to be

x = (5√6)/3

y = (10√6) / 3

Information given in the question

right angle triangle

The unknown variables is calculated using SOH CAH TOA

Definition of variables for the  right angle triangle

hypotenuse = y

opposite = 5√2

adjacent = x

The variable x is solved using tan, TOA, the angle is 60

tan 60 = Opposite / Adjacent

tan 60 = (5√2) / x

x = (5√2) / tan 60

x = (5√6)/3

The variable y is solved using sin, SOH, the angle is 60

sin 60 = Opposite / Hypotenuse

sin 60 = (5√2) / y

y = (5√2) / sin 60

y = (10√6) / 3

Learn more about SOH CAH TOA here:

brainly.com/question/29334128

#SPJ1

Answer:

10

Step-by-step explanation:

the max is 18 it currently has 8 the owner used 2

16- (8-2)

16-6

10

111 I guess? good luck ig

Answer:

brainliest?

Step-by-step explanation:

the amount of space taken up by the cylinder, measured in cubic units ... A cylindrical container is used to hold water. It has a diameter of 30 ... A brand new filled can of chicken broth is 10 cm tall and has a radius of 10 cm. Mishka ... Isabella's Ice Cream Parlor uses waffle cones that are 5 inches in diameter and 6 inches tall.

Carrying value on June 30, 2024  is $176 million, total  Interest revenue  is $12.44 million

To calculate the interest revenue for the first six months, we need to find the carrying value of the bonds on June 30, 2024.

The carrying value is the purchase price plus the accrued interest, which is calculated as follows:

Accrued interest = Face value x Coupon rate x Time

where Time = 6/12 = 0.5 (since interest is paid semiannually)

Accrued interest = $200 million x 6% x 0.5 = $6 million

Carrying value on June 30, 2024 = Purchase price + Accrued interest

= $170 million + $6 million

= $176 million

The interest revenue for the first six months is calculated as follows:

Interest revenue = Carrying value x Market rate x Time

= $176 million x 8% x 0.5

= $7.04 million

For the second six months, the carrying value is the fair value of $180 million, since the bonds were revalued at December 31, 2024.

The interest revenue for the second six months is calculated as follows:

Interest revenue = Carrying value x Coupon rate x Time

= $180 million x 6% x 0.5

= $5.4 million

Total interest revenue = Interest revenue for first six months + Interest revenue for second six months

= $7.04 million + $5.4 million

= $12.44 million

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ1

Answer:

i dont have any idea.....my brain is full of BTS

Step-by-step explanation:

Question 4: \(\frac{8}{1}\)

Question 5: \(\frac{4}{5}\)

Question 6: \(\frac{2.5}{1}\)

Question 7: \(\frac{1}{1}\)

The way to solve these types of questions, also know as "slope" is solved in the format \(\frac{y-y}{x-x}\) (y minus y over x minus x) which also can be known as \(\frac{rise-rise}{run-run}\) (rise minus rise over rune minus run). To solve this you can choose any two sets of numbers (the top and the bottom of a chart is 1 set) and you use its numbers to find the slope. One important rule when solving for slope is to never write your answer in decimal form and rarely write your answer as a whole number always answer questions in fraction form!!!! Anyway, the y and the x are already given so no need to find those as well. Here's the solving of all questions:

for this question I choose the number sets:\(\frac{24}{3} and, \frac{32}{4} in. ..equation... written... as, \frac{24-32}{3-4}\)

so, now the easy part, 24-32=-8

Next we solve the bottom, 3-4=-1

so we end up with \(\frac{-8}{-1}\) and when we simplify it can be written as \(\frac{8}{1}\) or just 8 (I recommend to always write in fraction form because some teachers will remove points if its not in fraction form).

Now, for the rest of the problems I wont explain the solving process.

\(\frac{60}{185} and\frac{100}{235} written...as,\frac{60-100}{185-235}\)

60-100=-40

185-235=-50

\(\frac{-40}{-50} simplify...to,\frac{4}{5}\)

\(\frac{12.5}{5} and\frac{25}{10} written...as,\frac{12.5-25}{5-10}\)

12.5-25=-12.5

5-10=-5

\(\frac{-12.5}{-5}simplify...to,\frac{2.5}{1}\) or 2.5 (I recommend to always write in fraction form because some teachers will remove points if its not in fraction form).

\(\frac{4}{2} and\frac{5}{3} written...as,\frac{4-5}{2-3}\)

4-5=-1

2-3=-1

\(\frac{-1}{-1}simplify...to,\frac{1}{1}\) or 1 (I recommend to always write in fraction form because some teachers will remove points if its not in fraction form).

Hope this helped, please give mw brainiest I spent half an hour on this :D

        -Thanks for your time.

Answer:

Falling action

Step-by-step explanation:

Falling action in a basic plot structure is the events that happen after the climax and before the resolution. This part of your story is often used to show the consequences of the climax and how it affects the characters.

Answer:

12 and -10

Step-by-step explanation:

a coefficient is a number multiplied by a variable

Answer:

1/4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

1/8+1/8=2/8 simplified its 1/4 but if you dont want it simplified its 2/8

If a piece of fruit snack which is 1 foot long is cut into two pieces, and one part is 3/4 of a foot long, then what we have is;

To arrive at 4/4 as shown in step 2, we take the LCM of both expressions.

On the left is 1/1 and on the right is 3/4. The LCM of the denominators (that is 1 and 4) is 4. Hence 1 can now be re-written as 4/4.

Answer:

There is a 20% probablity that the marble will be green :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: Your answer is 23.5in²

Hope it helped :D

Good Luck!

Answer:

its 3/10

Step-by-step explanation:

V = 3/10

3

--

10

Answer:

I speak English.

Step-by-step explanation:

I  am from America.

To prove congruence using SAS Theorem, you must understand that pairs of two angles are congruent as well as the pair of sides that are next to one of the specified angles.

In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.

All triangles are contained in a single plane if all geometry is on the Euclidean plane, but in higher-dimensional Euclidean spaces, this is no longer the case.

The definition of the terminology used to classify triangles can be found on the first page of Euclid's Elements, which dates back more than two thousand years. In modern classification, names are either directly transliterated from Euclid's Greek or translated from Latin.

Hence, To prove congruence using S Theorem, you must understand that pairs of two angles are congruent as well as the pair of sides that are next to one of the specified angles.

learn more about triangle click here:

brainly.com/question/1058720

#SPJ4

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.