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9514 1404 393

Answer:

Step-by-step explanation:

The acute angles in a right triangle are complementary, so ...

  C = 90° -50°

  C = 40°

__

SOH CAH TOA reminds you of the relations ...

  Cos = Adjacent/Hypotensue

  Sin = Opposite/Hypotenuse

Then ...

  cos(50°) = c/9

  c = 9·cos(50°) ≈ 5.79

  sin(50°) = a/9

  a = 9·sin(50°) ≈ 6.89

the clock lost 2 seconds per day

Answer:

Option 4

Step-by-step explanation:

Let any two real number a and b (no matter +ve, -ve or 0). a ≥ b

The average of them will always lie in between them or be equal(if 0).

Let's prove : According to the statement,

a ≥ (a + b)/2 ≥ b

2a ≥ a + b ≥ 2b

2a ≥ a + b and a + b ≥ 2b

a ≥ b and a ≥ b, as we assumed.

Moreover, as the average exists in between a and b, we have the average (a + b)/2. Similarly, there exists one more average of (a + b)/2 and a or b, which definitely lie between a and b as (a + b)/2 lies there and smaller than a and b.

In the same order, we can have many average and the process would stop. This leads to infinite number between a and b.

Notice that we talked about all the numbers moreover there are many irrational(non-terminating like 9.898989.... etc numbers as well.

Option (4), infinite solutions.

Note: we solved for all the number (not specifically odd, even, natural, whole, integer, etc).

Answer:

1. 156 2. 84 3. 74

Step-by-step explanation:

1. b x h. 8 x 8 is every side on the square so one side is 64 and the one behind it is 64 also which is 128 and since that is the case with the other sides its 128 + 128 = 156

2. 1/2 x b x h = 1/2 x 4 x 3 = 6 x 2 because of the side behind it that is the same = 12. 6 x 5 = 30; 6 x 4 = 24; 6 x 3 = 18. 12 + 30 + 24 + 18 = 84

3. b x h. 2.5 x 2 = 5 x 2 because of the other side = 10; 7 x 2.5 = 17.5 x 2 = 35; 7 x 2 = 14 x 2 = 28. 10 + 35 + 28 = 76

Answer:

A

Step-by-step explanation:

Answer:

[tex]x=15[/tex]

Step-by-step explanation:

Pythagorean theorem: [tex]c^2 = a^2 + b^2[/tex], where c is the longest side (hypotenuse), a and b are the other sides of the right angled triangle.

In this question, c is labelled as [tex]x[/tex].

Therefore, we can use the theorem to find [tex]x[/tex].

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

So, substitute in the other sides and solve for [tex]x[/tex].

[tex]x^2 = (9)^2 + (12)^2\\x^2 = 81 + 144\\x^2 = 225\\x = 15[/tex]

We can see the answer is correct because it is meant to be the largest side and [tex]15> 12>9[/tex].

Answer:

[tex]g(f(x)) = x^{[2]} +[-1][/tex]

Step-by-step explanation:

Given

[tex]f(x) = x^2[/tex]

[tex]g(x) =x -1[/tex]

Required

[tex]g(f(x))[/tex]

We have:

[tex]g(x) =x -1[/tex]

Replace x with f(x):

[tex]g(f(x)) = f(x) -1[/tex]

Substitute [tex]f(x) = x^2[/tex]

[tex]g(f(x)) = x^2 -1[/tex]

Hence:

[tex]g(f(x)) = x^{[2]} +[-1][/tex]

Answer:

From Pythagoras Rule

c=√1²+2²

c=√5 cm

c= 2.2cm

To the Nearest tenth..

Answer:

About 220 of the students scored less than 96

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 156 and a standard deviation of 23.

This means that [tex]\mu = 156, \sigma = 23[/tex]

Proportion that scored less than 96:

p-value of Z when X = 96. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{96 - 156}{23}[/tex]

[tex]Z = -2.61[/tex]

[tex]Z = -2.61[/tex] has a p-value of 0.00453.

About how many of the students scored less than 96?

0.00453 out of 48592.

0.00453*48592 = 220.1.

Rounding to the closest integer:

About 220 of the students scored less than 96

Answer:

220

Step-by-step explanation:

#platolivesmatter

Answer:

[tex] (x-1.3) ^2 + (y+3.5) ^2= 37 [/tex]

Step-by-step explanation:

Radius of the circle [tex] r = \sqrt {37}\: units [/tex]

Center of the circle (h, k) = (1.3, - 3.5)

Equation of the circle in center radius form is given as:

[tex] (x-h) ^2 + (y-k) ^2= r^2 [/tex]

Plugging the values of h, k and r in the above equation, we find:

[tex] (x-1.3) ^2 + (y+3.5) ^2= (\sqrt {37})^2 [/tex]

[tex] (x-1.3) ^2 + (y+3.5) ^2= 37 [/tex]

This is the required equation of the circle.

Answer:

The second one

O (1-6) (2-5) (3-4) (4-3) (5-2) (6-1)

Step-by-step explanation:

Favorable outcome is the outcome that we are looking for

The outcome that we are looking for when rolling two = die is a sum of 7

The set (1-6) (2-5) (3-4) (4-3) (5-2) (6-1) all add up to equal 7

( 1 , 6 ) 1 + 6 = 7

( 2 , 5 ) 2 + 5 = 7

( 3 , 4 ) 3 + 4 = 7

etc.

Which means that they are the favorable outcomes for rolling a seven

Answer:

The line equation is Y=(1/2)x+2

Step-by-step explanation: Start with the standard from: y=mx+b

Find the slope, or change in the y value divided by change in the x value.

For this graph the slope is 1/2 meaning the y value goes up once every time the x value goes up two. this is represented by the m value

Now we need to find the y intercept, or where the graph passes through the y intercept, this is represented by b

We find the intercept by inserting a point n the line into our equation and solving for b:

Point: (2,3) Equation: y=(1/2)x+b

3=(1/2)2+b

3=1+b

-1  -1

2=b

Answer: [tex]322\ lb[/tex]

Step-by-step explanation:

Given

The magnitude of the force [tex]F=350\ \text{Pounds}[/tex]

The force makes an angle of [tex]67^{\circ}[/tex] with the horizontal

So, the components of the force are

[tex]\Rightarrow F\cos 67^{\circ}, F\sin 67^{\circ}\\\Rightarrow F\cos 67^{\circ}=350\cos 67^{\circ}\\\quad \quad =136.75\ lb\\\text{Similarly, }\\\Rightarrow F\sin 67^{\circ}=350\sin 67^{\circ}\\=322.17\ lb[/tex]

The larger among the two is [tex]F\sin 67^{\circ}[/tex] i.e. [tex]322\ lb[/tex]

9514 1404 393

Answer:

  C.  y = 11.27(0.7^x)

Step-by-step explanation:

The table value (x, y) = (0, 11.27) tells you the multiplier of the exponential term will be 11.27. The decreasing values tell you the base of the exponential term is less than 1. Only answer choice C matches these requirements.

Answer:

x = 10

Step-by-step explanation:

Answer:

Your answer would be 4^-3.

Step-by-step explanation:

So, a negative exponent by definition, is writing out 1/x^y. Where x is the number and y is the negative exponent.

In this case, 4 would be the number and -3 would be the negative exponent.

So we're going from 1/x^y to x^-y in order to solve this. Therefore, this is something where the numbers can just be plugged in.

1/x^y ---> x^-y

1/4^3 ---> 4^-3

Your answer would be 4^-3.

Answer:

6(3x - 4)

Step-by-step explanation:

From the question, we can deduce the following points;

- 6 is multiplied by 3x minus 4

Translating the word problem into an algebraic expression, we have;

6 * (3x - 4)

Answer: speed is  540 km/h

Step-by-step explanation:   Lets mark speed as v.

Because distenace is same, you can mark   6 h · 900 km/h = 10 h · v

and v = 5400 km / 10 h = 540 km/h.

Or using inverse proportions :   10 h / 6 h  =  v / 900 km/h  .

Before multiplying you turn lastproportion around :

10 h / 6 h = 600 km/ h / v   ,which gives   10 v = 6 · 900 km/h

and result is same

Answer:

[tex]\implies f(x) = ( x + 2)^2[/tex]

Step-by-step explanation:

Given :-

And we need to rewrite the function by completing the square. The function is ,

[tex]\implies f(x) = x^2+8x + 4[/tex]

[tex]\implies ( a + b)^2= a^2+b^2+2ab [/tex]

Rewriting the function :-

[tex]\implies f(x) = x^2+8x + 4\\\\\implies f(x) = x^2 + 2.2.2x + 2^2[/tex]

[tex]\implies f(x) = ( x + 2)^2[/tex]

Hence the function in whole square form is (x + 2)² .

Answer:

69.12

Step-by-step explanation:

12x5.76

Answer

69

Step-by-step explanation:

12×5.75=69

Step-by-step explanation:

Answer:  No puedo responder a esto sin que me muestres el problema.

Answer:

0.0623 ± ( 2.056 )( 0.0224 ) can be used to compute a 95% confidence interval for the slope of the population regression line of y on x

Step-by-step explanation:

Given the data in the question;

sample size n = 28

slope of the least squares regression line of y on x or sample estimate = 0.0623

standard error = 0.0224

95% confidence interval

level of significance ∝ = 1 - 95% = 1 - 0.95 = 0.05

degree of freedom df = n - 2 = 28 - 2 = 26

∴ the equation will be;

⇒ sample estimate ± ( t-test) ( standard error )

⇒ sample estimate ± ( [tex]t_{\alpha /2, df[/tex]) ( standard error )

⇒ sample estimate ± ( [tex]t_{0.05 /2, 26[/tex]) ( standard error )

⇒ sample estimate ± ( [tex]t_{0.025, 26[/tex]) ( standard error )

{ from t table; ( [tex]t_{0.025, 26[/tex]) = 2.055529 = 2.056

so we substitute

⇒ 0.0623 ± ( 2.056 )( 0.0224 )

Therefore, 0.0623 ± ( 2.056 )( 0.0224 ) can be used to compute a 95% confidence interval for the slope of the population regression line of y on x

Answer:

[tex] a^{5} [/tex]

Step-by-step explanation:

Given the mathematical expression;

a⁸/a³

To rewrite the expression in the form [tex] a^{m} [/tex]

We would have to apply the law of indices.

[tex] Law \; of \; division = \frac {a^{x}}{a^{y}} = a^{x - y} [/tex]

[tex] Law \; of \; division = \frac {a^{8}}{a^{3}} = a^{8 - 3} [/tex]

[tex] a^{m} = a^{8 - 3} = a^{5} [/tex]

Explanation:

The period of a function measures how long a cycle takes. Think of tides on a beach. There's a regular pattern that can be predicted whether its high tide or low tide. Time is often the critical component with the period. Since choice D mentions time and the key term "repeat", this is why it's the answer.

The other values, while useful elsewhere, aren't going to tell us anything about the period. The initial value being 5 doesn't tell us when y = 5 shows up again, and if the function is repeating itself at this point or not. So info about choice A is not sufficient to determine the period. The same goes for choices B and C as well.

Answer:

For a general function f(x), the domain is the set of the possible values of x that we can input in the function.

The trick to find the domain is first to assume that the domain is the set of all real numbers, and then let's try to find the values of x that cause a problem in the function. (If the graph is cut in some value of x, such that it ends with an open or a closed point, then these values define the domain).

Such that one of these problems can be like x = 1 in the function:

g(x) = 1/(x - 1)

Because that value causes the denominator to be equal to zero, then the domain of that function will be the set of all real numbers except the value x = 1.

In this case, we have:

f(x) = x^2 - 4

There is no value of x that causes a problem for this function, then the domain is the sett of all real numbers.

Correct option D.

Answer:

x - 5 = 63

x = 63 - 5

x = 58 years

Answer:

she will be 34

Step-by-step explanation:

x - Joseph age

(x-5)+x=63

2x=68

x=34

34- 5 =29 Angeles age

in 5 years she will be 29+5=34

Answer:

17.46 ft

Step-by-step explanation:

The inclined plane is in the shape of a right triangle, therefore we can use the Pythagorean theorem to find the length of the inclined plane. The formula for this theorem is the following

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

Where a and b are the two sides and c is the hypotenuse/inclined side. Therefore, we can simply plug in the lengths of the two sides into the formula and solve for c.

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

[tex]7^{2} + 16^{2} = c^{2}[/tex]

[tex]49 + 256 = c^{2}[/tex]

[tex]305 = c^{2}[/tex]   ... square root both sides

17.46 = c

Answer:

yes it does. good job on your A.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation: