Let θ be an angle in quadrant IV such that sinθ = -2/5 .
Find the exact values of secθ and tanθ.

If x = -1, you have

2(-1) + 3 cos(-1) + e ⁻¹ ≈ -0.0112136 < 0

and if x = 0, you have

2(0) + 3 cos(0) + e ⁰ = 4 > 0

The function f(x) = 2x + 3 cos(x) + eˣ is continuous over the real numbers, so the intermediate value theorem applies, and it says that there is some -1 < c < 0 such that f(c) = 0.

Answer:

0.0667 = 6.67% probability that all seven machines are nondefective.

Step-by-step explanation:

The machines are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

10 machines means that [tex]n = 10[/tex]

2 defective, so 10 - 2 = 8 work correctly, which means that [tex]k = 8[/tex]

Seven are selected, which means that [tex]n = 7[/tex]

What is the probability that all seven machines are nondefective?

This is P(X = 7). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 7) = h(7,10,7,8) = \frac{C_{8,7}*C_{2,0}}{C_{10,7}} = 0.0667[/tex]

0.0667 = 6.67% probability that all seven machines are nondefective.

Answer:

x = 5 and -6

Step-by-step explanation:

Using the intersecting chord theorem which states that the products of the lengths of the line segments on each chord are equal.

Hence:

let

a = 6, b = 5, c = x+1 and d = x

Therefore, ab = cd

6*5 = x(x+1)

30 = x²+x

x²+x - 30 = 0

x²+ 6x - 5x - 30 = 0

x(x+6) - 5(x+6) =0

(x-5)(x+6) = 0

x-5 =0 and x+6 = 0

x = 5 and -6

Answer:

The 95% confidence interval for the mean time for all players, in minutes, is: (7.95, 11.01).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 10 - 1 = 9

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.2622\frac{2.14}{\sqrt{10}} = 1.53[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 9.48 - 1.53 = 7.95 minutes.

The upper end of the interval is the sample mean added to M. So it is 9.48 + 1.53 = 11.01 minutes.

The 95% confidence interval for the mean time for all players, in minutes, is: (7.95, 11.01).

Answer:

D

Step-by-step explanation:

Answer:

0.6827

Step-by-step explanation:

Given that :

Mean, μ = 3

Standard deviation, σ = 0.1

To produce an acceptable cork. :

P(2.9 < X < 3.1)

Recall :

Z = (x - μ) / σ

P(2.9 < X < 3.1) = P[((2.9 - 3) / 0.1) < Z < ((3.1 - 3) / 0.1)]

P(2.9 < X < 3.1) = P(-1 < Z < 1)

Using a normal distribution calculator, we obtain the probability to the right of the distribution :

P(2.9 < X < 3.1) = P(1 < Z < - 1) = 0.8413 - 0.1587 = 0.6827

Hence, the probability that the first machine produces an acceptable cork is 0.6827

Answer:

3.5

Step-by-step explanation:

in order to find the maximum, we are basically solving to find the vertex of the graph. to find the vertex use :

-b/2a

the 'b' is 112

the 'a' is -16

so :

-112/-32 = 3.5

the answer is B, 3.5

9514 1404 393

Answer:

  (x +3)² +(y -4)² = 145

Step-by-step explanation:

The center of the circle is the midpoint of the given segment PQ. If we call that point A, then ...

  A = (P +Q)/2

  A = ((-12, -4) +(6, 12))/2 = (-12+6, -4+12)/2 = (-6, 8)/2

  A = (-3, 4)

The equation of the circle for some radius r is ...

  (x -(-3))² +(y -4)² = r² . . . . . . where (-3, 4) is the center of the circle

The value of r² can be found by substituting either of the points on the circle. If we use Q, then we have ...

  (6 +3)² +(12 -4)² = r² = 9² +8²

  r² = 81 +64 = 145

Then the equation of the circle is ...

  (x +3)² +(y -4)² = 145

Answer:

y = -x + 5

Step-by-step explanation:

The point is in quadrant 2, so the line must pass through points that look like (a, 0) and (0, a) where a is a positive number.  The slope of such a line is -1.

If (x, y) is a point on the line, then the slope between points (x, y) and (-5, 10) is 1, and you can write

[tex]\frac{y-10}{x-(-5)}=-1\\y-10 = -1(x+5)\\y-10=-x-5\\y=-x+5[/tex]

Answer:

we know that all Lenght of circle is 2πr so 2*π*7=14π

Step-by-step explanation:

14π equal to 360°

but we need just 135° so we should write it kind of radian(π)

if 14π=360°

x=135°

14π*135=360°*x 14π*27=72*x ........= 14π*3=8*x

7π*3=4*x ....... X=21π/4

The length of the arc is 21/π4 in

An answer is an option A. 21/π4 in

The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.

⇒angle= arc/radius

 ⇒  135°=arc/7

⇒ arc =135°*7

  ⇒arc=135°*π/180° *7in

⇒arc = 21/π4 in

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Answer: 8.1

Step-by-step explanation:

4^2 + X^2 = 9^2

16 + X^2 = 81

X^2 = 81-16

X = sqrt 65 = 8.1

Answer:

3/4

Step-by-step explanation:

There are 13 hearts in a 52 deck.

52-13=39

39/52=3/4

The probability that you are not dealt a heart from the deck of cards is 3/4.

Probability determines the chances that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that you are not dealth with a heart = 1 - (number of hearts / total number of cards)

1 - 13/52 = 39/52 =  3/4

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Answer:

$7800

Step-by-step explanation:

1. Principal x interest x rate

So: $7500 + 4% (0.04) x 1 year = $300

2. Interest + Principal

So: $7500 + $300

Mrs Lee had $7800 in the bank.

Answer:

B) Its final coordinates are (8,-6)

Step-by-step explanation:

1. Translated 1 unit up and 4 units left

(-2,7) becomes (-6, 8)

2. Reflected about the x-axis

(-6,8) becomes (-6, -8)

3. Rotated 90° anticlockwise about the origin

(-6, -8) becomes (8, -6) because when rotating 90 degrees anticlockwise about the origin, point A (x,y) becomes point A' (-y,x). In other words, switch the x and y and make y negative.

Answer:

10/21 of the distance

Step-by-step explanation:

2/7 distance

------------------

3/8 tank

The rest of the tank is 8/8 - 3/8 = 5/8

2/7 distance         x

------------------ = ----------------------

3/8 tank              5/8 tank

Using cross products

2/7 * 5/8 = 3/8x

10/56 = 3/8x

Multiply each side by 8/3

10/56 * 8/3 = 3/8x * 8/3

10/3 * 8/56=x

10/3 * 1/7 =x

10/21 =x

10/21 of the distance

Multiplying block matrices works just like multiplication between regular matrices, provided that component matrices have the right sizes.

[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf{IW}+\mathbf{0Y}&\mathbf{IX}+\mathbf{0Z}\\\mathbf{KW}+\mathbf{IY}&\mathbf{KX}+\mathbf{IZ}\end{bmatrix}[/tex]

[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W+\mathbf 0&\mathbf X+\mathbf 0\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]

[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W&\mathbf X\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]

(I assume I is the identity matrix and 0 is the zero matrix.)

Answer:

Result is statistically significant.

Step-by-step explanation:

Given that :

Chisquare statistic, χ² = 67.81

Critical value for the distribution, χ²critical = 3.84

α = 0.05

The Decison region :

If χ² statistic > Critical value ; Reject H0 ; this. Eans that result is statistically significant.

Therefore, since, 67.81 > 3.84 ; This means that the result is statistically significant at 0.05

Answer:

x=  $6,284.15

Step-by-step explanation:

7300 = x(1 + .025/12)^72

x = [tex]\frac{7300}{(1 + \frac{.025}{12} )^{72} }[/tex]

x=  $6,284.15  

Answer:

f(x) = 6 when -5 < x ≤ -1

Step-by-step explanation:

Answer:

27 by 27

Step-by-step explanation:

Let the sides be x and y. The problem is essentially asking:

Given 2(x+y)=108, maximize xy.

We know that x+y=54. By the Arithmetic Mean - Geometric Mean inequality, we can see that [tex]\frac{x+y}{2} \ge \sqrt{xy[/tex]. Substituting in x+y=54, we get [tex]27\ge\sqrt{xy}[/tex], meaning that [tex]729 \ge xy[/tex]. Equality will only be obtained when x=y (in this case it will generate the maximum for xy), so setting x = y, we can see that x = y = 27. Hence, 27 is the answer you are looking for.

Answer:

$9986

Step-by-step explanation:

You got 13*4=52 quarters in 13 years.

Amount = 830*(1+0.049)^52

Amount = 9986.27

Answer:

138 gallons - milk containing 8% butterfat , 92 gallons -  milk containing 3% butterfat

Step-by-step explanation:

Firstly, find the quantity of butterfat in  the dairy needs of milk

230/100*6= 2.3*6=13.8 gallons of butterflat

1) Consider gallons each of milk containing 8% butterfat and milk containing 3%, suppose we need x gallons of milk containing 8 percents butterfat, then we need 230-x gallons of milk containing 3percent butterfat.

Then the quantity of the butterfat in the 8percents fat milk is x/100*8= 0.08x

the quantity of the butterfat in the 3percents fat milk is (230-x)/100*3=

=0.03 (230-x) = 6.9-0.03x The amount of butterfat of the both milk containing 8% butterfat and milk containing 3%is equal to 13.8 gallons

Then 0.08x+6.9-0.03x=13.8

0.05x=6.9

x=6.9/0.05= 138 -milk 8 percents

230-x= 230-138= 92

Answer:

-2

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals

Take the slope of AB = 1/2

-1/(1/2)

-1 * 2/1

-2

The slope of a line perpendicular is -2

9514 1404 393

Answer:

 6 minutes, 11 seconds

Step-by-step explanation:

In seconds the average transaction time is ...

  6 min 52 s = 6(60 s) +52s = 412 s

Reducing this by 10% will cut it to 1 -10% = 90% of this value, or ...

  (412 s)(0.9) = 370.8 s

In minutes and seconds, this is 6(60 s) +10.8 s = 6 min 10.8 s.

The average transaction time must be reduced to about 6 min 11 s.

Lo siento mucho, necesito los puntos porque estoy en una prueba.

Step-by-step explanation:

By the law of exponent :

(a^n)^m=a^n×m

Option C

b^n×m is the correct answer...

hope it helps

Here we have the quadratic function:

f(x) = -16*x^2 + 60*x + 16

We can see that it is in standard form:

y = a*x^2 + b*x + c

a) First we want to completely factorize the function f(x).

To do it, we first need to find the roots of f(x).

Remember that for a generic quadratic equation:

a*x^2 + b*x + c = 0

whit roots x₁ and x₂, the factorized form is:

a*(x - x₁)*(x - x₂)

And the roots are given by:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]

Then for the case of f(x) = -16*x^2 + 60*x + 16, the roots are:

[tex]x = \frac{-60 \pm \sqrt{60^2 - 4*(-16)*16} }{2*(-16)} = \frac{-60 \pm 68}{-32}[/tex]

So the two roots are:

x₁ = (-60 + 68)/-32 = -0.25

x₂ = (-60 - 68)/-32 = 4

Then the factorized form is:

f(x) = -16*(x - 4)*(x + 0.25)

B) We already found the roots, which are:

x₁ =  -0.25

x₂ =  4

These are the x-intercepts:

(-0.25, 0) and (4, 0)

C) We can see that the leading coefficient is negative.

This means that the arms of the graph go downwards, so as |x| increases, the value of f(x) tends to negative infinity.

D) To graph f(x) we can find some of the points of the graph (like the x-intercepts and some more of them) and then connect them with a parabola curve, the graph that you will get is the one that you can see below.

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Answer:

The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.

Step-by-step explanation:

Suppose that, in the past, 40% of all adults favored capital punishment. Test if the proportion has increased:

At the null hypothesis, we test if the proportion is still of 40%, that is:

[tex]H_0: p = 0.4[/tex]

At the alternative hypothesis, we test if the proportion has increased, that is, is greater than 40%, so:

[tex]H_1: p > 0.4[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that [tex]\mu = 0.4, \sigma = \sqrt{0.4*0.6}[/tex]

Random sample of 15 adults, 8 favor capital punishment.

This means that [tex]n = 15, X = \frac{8}{15} = 0.5333[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.5333 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{15}}}[/tex]

[tex]z = 1.05[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion of 0.5333 or more, which is 1 subtracted by the p-value of z = 1.05.

Looking at the z-table, z = 1.05 has a p-value of 0.8531.

1 - 0.8531 = 0.1469.

The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.

Answer:

x=(-2,0) and x=(5/2,0)

Step-by-step explanation:

To find x-intercepts you set f(x), or y, to 0 and then solve.

[tex]0=2x^2-x-10\\Factor!\\0=(x+2)(2x-5)\\x+2=0\\x=2\\2x-5=0\\2x=5\\x=\frac{5}{2}[/tex]

The x-intercepts of the graph of f(x) is (-2, 0) and (5/2, 0).

The function is given as:

[tex]f(x) = 2x^2 - x - 10[/tex]

We need to find the points at which the given function crosses the x-axis.

It is the point at which the given function crosses the x-axis.

The x-intercept is found by setting y = 0 or f(x) = 0.

Given function,

[tex]f(x) = 2x^2 - x - 10[/tex]

Let's set f(x) = 0.

[tex]2x^2 - x - 10 = 0[/tex]

Solve the equation for x.

[tex]2x^2 - x - 10\\2x^2 - (5 - 4)x - 10\\2x^2 - 5x + 4x - 10\\x(2x-5) +2(2x - 5)\\(x+2)(2x-5)[/tex]

Now we have,

x+2 = 0 and 2x - 5 = 0

x = -2 and x = 5 / 2

We already know that y = 0 so the points at which the function intercepts with the x-axis are:

(-2, 0) and (5/2, 0).

The x-intercepts of the graph of f(x) is (-2, 0) and (5/2, 0).

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