let (-3,-7) be a point on the terminal side of theta. find the exact values of sin theta, sec theta, and tan theta

Answer:

Option C: 38 is p more than 25

Step-by-step explanation:

the equation 25 + p = 38

can be read as 38 is 25 plus p units, or similarly ;

38 is p units more than 25.

Therefore from the three sentences you are showing, only the last one (option C) is the correct one.

Answer:

start with -29, multiply each term by 4

start with 60, multiply each term by 0.1

start with 97 and multiply each term by 0.5

3.03 cells

Step-by-step explanation:

1. The first sequence begins with -29. -116 ÷ -29 = 4, -464 ÷ -116 = 4, etc. Each value is multiplied by 4 to get the next value.

2. The second sequence begins with 60. 6 ÷ 60 = 0.1, 0.6 ÷ 6 = 0.1, etc. Each value is multiplied by 0.1 to get the next value.

3. The colony starts with 97 cells. Splitting into two is the same as multiplying by 0.5.

4. Multiply 97 by 0.5, 5 times for 5 minutes.

97 · 0.5 · 0.5 · 0.5 · 0.5 · 0.5 = 3.03

Answer:

x = 4

Step-by-step explanation:

===============================================

Explanation:

Use the distance formula to get this answer. The idea is you subtract the x coordinates together, and do the same for the y coordinates as well. Square each result and add up those squares. The last step of the formula is to apply the square root to get the distance from A to B, which is also the length of segment AB.

[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(-3-5)^2+(-2-(-4))^2}\\\\d = \sqrt{(-3-5)^2+(-2+4)^2}\\\\d = \sqrt{(-8)^2+(2)^2}\\\\d = \sqrt{64+4}\\\\d = \sqrt{68}\\\\[/tex]

Therefore, [tex]AB = \sqrt{68}[/tex]

Answer:

s = 8 degrees

Step-by-step explanation:

12s + 42 + 42 = 180

12s + 84 = 180

12s = 96

s = 8 degrees

[tex]-6w-16>44[/tex]

Add both sides by 16

[tex]-6w>60[/tex]

Divide both sides by -6 (Note: Since we're dividing by a negative number, the inequality symbol needs to be reversed)

[tex]w<-\dfrac{60}{6}[/tex]

[tex]w<10[/tex]

This is the solution to the inequality. Let me know if you need any clarifications, thanks!

Answer:

Step-by-step explanation:

You're given a coordinate in the form of (x, y) and you're also given the vertex in the form of (h, k). We will use those in the vertex form of the equation

[tex]y=a(x-h)^2+k[/tex] and solve for a. Filling in:

[tex]-11=a(4-2)^2-3[/tex] which simplifies a bit to

[tex]-11=a(2)^2-3[/tex] and a bit more to

[tex]-11=4a-3[/tex]. Add 3 to both sides to get

-8 = 4a so

a = -2

The equation, then, is

[tex]y=-2(x-2)^2-3[/tex]

Answer:

  262°

Step-by-step explanation:

The relationship between the angle at B (82°) and the arcs of the circle, CGF and CDF, is that the angle is half the difference of those arcs. Of course the sum of those arcs is 360°, since together they make a full circle. So. we have ...

  CGF +CDF = 360

  (CGF -CDF)/2 = 82

We need to solve this system of equations to find CGF.

__

Multiplying the second equation by 2 and adding the first, we get ...

  2((CGF -CDF)/2) +(CGF +CDF) = 2(82) +(360)

  2CGF = 524 . . . . . simplify

  CGF = 262 . . . . . . divide by 2

The measure of arc CGF is 262°.

_____

Alternate solution

Here's another way to get there. Arc CDF is the supplement to angle B, so is ...

  CDF = 180° -∠CBF

Of course, arc CGF is 360° minus arc CDF, so ...

  CGF = 360° -(180° -∠CBF)

  CGF = 180° +∠CBF . . . . . simplify . . . please note this is a general solution

Then ...

  arc CGF = 180° +82° = 262°.

Answer:

  80 square units

Step-by-step explanation:

The area formula refers to a generic triangle ABC in which side lengths 'a' and 'b' are known and angle C is between those sides.

In the given figure, we have known side lengths of 12 and 14, and the angle between them is 72°.

Putting these numbers into the formula, we find the area to be ...

  A = (1/2)(12)(14)sin(72°) ≈ 79.9 ≈ 80 . . . . square units

The area of the triangle is about 80 square units.

Answer:

C. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 11​%±3​%.

Step-by-step explanation:

Data provided in the questions

Number of respondents = 1,000

Choose chocolate pie = 11%

margin of error = ±3 percentage points

Based on the above information,

The lower limit is

= 0.11 - 0.03

= 0.08

And, the upper limit is

= 0.11 + 0.03

= 0.14

So based on the above computation, the option c is correct as it represents the true population percentage of people with respect to the chocolate pie preference

Step-by-step explanation:

I believe the answer is

The fuction roughly matches the data

Answer:

The function fits very well

Step-by-step explanation:

The equation for the stats is

y=-0.039866x²+3.99375x-0.4785714

Answer:

I answered it

Step-by-step explanation:

I answered it

Answer:

∠ V ≈ 33.6°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos V = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{UV}{TV}[/tex] = [tex]\frac{5}{6}[/tex] , thus

∠ V = [tex]cos^{-1}[/tex] ([tex]\frac{5}{6}[/tex] ) ≈ 33.6° ( to the nearest tenth )

Answer:

D

Step-by-step explanation:

Hello, This is a geometric sequence where the first term is [tex]a_1=-1[/tex].

It means that the sequence is [tex](a_n)_{n\geq 1}[/tex].

In other words, as the common ratio is 7 the sequence is defined by

[tex]a_1=-1[/tex]

[tex]a_{n+1}=a_n\cdot 7 \ \ \text{ for n }\geq 1[/tex]

For instance, we can estimate the first terms:

[tex]a_1=-1\\\\a_2=7a_1=-7\\\\a_3=7a_2=-49[/tex]

And we know that we can even find a formula for the [tex]n^{th}[/tex] term of the sequence by:

[tex]a_n=a_1\cdot 7^{n-1}=-7^{n-1}[/tex]

Now, to answer the question, the domain for n is all integers where [tex]n\geq 1[/tex].

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term.

.

Answer:

Hey there!

S would be 2 times 7, or 14.

Hope this helps :)

Answer:

14

Step-by-step explanation:

This is a 30-60-90 triangle, so the sides corresponding are x, 2x, and xsqrt3. the side, s, that we want is the 2x, and the x is 7. So, s is 14.

Answer:

we can calculate it by applying trigonometric ratios

Step-by-step explanation:

tan 45 = length of wall/distance between ladder and wall

1 = length of wall/15

length of wall = 15m

(length of wall[tex])^{2}[/tex] + (distance between ladder and wall[tex])^{2}[/tex] = (length of ladder[tex])^{2}[/tex]

length of ladder = [tex]\sqrt{15^{2} + 15^{2} }[/tex]

                           = [tex]\sqrt{450}[/tex]

                           = 21.21 m

Answer:

A 95​% confidence interval for the proportion of students who eat cauliflower on​ Jane's campus is [0.012, 0.270].

Step-by-step explanation:

We are given that Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 ​students, she finds 2 who eat cauliflower.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                              P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of students who eat cauliflower

           n = sample of students

           p = population proportion of students who eat cauliflower

Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                   of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

Now, in Agresti and​ Coull's method; the sample size and the sample proportion is calculated as;

[tex]n = n + Z^{2}__(\frac{_\alpha}{2})[/tex]

n = [tex]24 + 1.96^{2}[/tex] = 27.842

[tex]\hat p = \frac{x+\frac{Z^{2}__(\frac{\alpha}{2}_) }{2} }{n}[/tex] = [tex]\hat p = \frac{2+\frac{1.96^{2} }{2} }{27.842}[/tex] = 0.141

95% confidence interval for p = [ [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

 = [ [tex]0.141 -1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] , [tex]0.141 +1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] ]

 = [0.012, 0.270]

Therefore, a 95​% confidence interval for the proportion of students who eat cauliflower on​ Jane's campus [0.012, 0.270].

The interpretation of the above confidence interval is that we are 95​% confident that the proportion of students who eat cauliflower on​ Jane's campus is between 0.012 and 0.270.

Answer: 5.0693 ounces

Step-by-step explanation:

For a 6 ounce cup to overflow, then the cup content is beyond 6 ounce, at 2%

P(x > 6) = 2% = 0.02; similarly

P(x<6) = 1 - P(x > 6)'.

P(x<6) = 1 - 0.02 = 0.98

The z-score for 0.98 = 2.326

The z - formular for a normally distributed goes thus :

Zscore =(observed score - mean) / standard deviation

Substituting the vamus :

2.326 = (6 - mean) / 0.4

2.326 × 0 4 = 6 - mean

0.9304 = 6 - mean

Mean = 6 - 0.9304

Mean = 5.0693

Answer:

1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x ← is in slope- intercept form

with slope m = 1

Answer:

1

Step-by-step explanation:

Answer 158Step-by-step explanation: you have to multiply the fraction by the numerator and divided by itsself and the subtract everything thren get myy642565780

Answer:

148 cm ^2

Step-by-step explanation:

Hey there!

Well is the area of the base is 30 then we can conclude that the side lengths are 5 and 6.

Then if the volume is 120 we can do,

120 ÷ 30 = 4

So the height is 4 cm.

Now we already have the area of the base we just need to find the area of the rest of the rectangles.

If the bottom base is 30 then the top base is also 30.

30 + 30 = 60cm^2

Now we can do the two rectangles on the side that have side lengths of 5 and 4.

5*4 = 20

20+20 = 40 cm^2

Now we can do the two final rectangles that have side lengths of 6 and 4.

6*4=24

24 + 24 = 48 cm^2

Now we can add all the areas up,

48 + 40 + 60

= 148 cm^2

Hope this helps :)

x = 108

y = 36

z = 72

=============================================================

Explanation:

Check out the diagram below. I have added letters of x, y and z in places to help find the values of y and z. Note the triangle on top is isosceles (since a regular polygon has all sides equal; therefore the triangle on top has the top diagonal sides equal).

Before we find either y or z, let's find x.

For any regular polygon, the interior angles are all the same measure. They sum to 180(n-2). In this case, n = 5, so the angles sum to 180(5-2) = 540. Each individual interior angle is 540/n = 540/5 = 108 degrees

x = 108

Another way to find this interior angle is to first find the exterior angle. For any convex polygon (regular or not), the exterior angles always add to 360. When we talk about regular polygons, each individual exterior angle is 360/n. So in this case, we have 360/5 = 72 as one exterior angle. The adjacent interior angle is therefore x = 180-72 = 108. So there are two ways to find the measure of an interior angle.

--------

Referring to the diagram, specifically the isosceles triangle on top, we can see that it has angles of x, y and y. They add to x+y+y = x+2y. Set this equal to 180, plug in x = 108 and solve for y

x+2y = 180

108+2y = 180

2y = 180-108

2y = 72

y = 72/2

y = 36

--------

The bottom most triangle is a congruent copy of the triangle on top. We have another isosceles triangle with the same side lengths as before. This triangle also has x, y and y as mentioned above.

Notice the adjacent angles of y and z in the bottom left corner. They must add to 108 as this was the measure of the interior angle of a regular pentagon. So,

y+z = x

36+z = 108

z = 108-36

z = 72

Answer:

P((1 or 2) and Tail) = 1/6 = StartFraction 1 over 6

Step-by-step explanation:

A six-sided die and a coin.

Probability of getting <3 and tail.

P((1 or 2) and Tail)

= 2/6 * 1/2

= 1/6

Answer:

1/6

Step-by-step explanation:

5.23 m

in cm 523 cm

nearest tenth 520cm

Step-by-step explanation:

60 / 360 × 2 ×22/7 × 5

110/ 21

5.23m

Answer:

5,2(3) meters

Step-by-step explanation:

Formula

arc length = 2π·r (x°/360°)

= 2π·5m(60°/360°)

= 2·3,14·5m·1/6

= 31,4m/6

= 5,2(3) meters

At a MINIMUM, during dry weather conditions, you should have at least 2 seconds of space between you and the vehicle in front of you (3 seconds is better). Do this by using a fixed object such as a bridge, tree, or even a crack or shadow in the roadway.

Calculate the gap between you and the car in front of you by selecting an inanimate object along the lane. If the other car goes past the target, then "1000 one, 1000 two ..." count. You are three seconds behind this car when you get to "one thousand three" before you go through the piece.

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

Hope this helps!

Brainliest would be great!

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

With all care,

Forbidden

Answer:

  [tex]6y^2\sqrt{10}+12\sqrt{5y}[/tex]

Step-by-step explanation:

Use the distributive property and the rules for forming and simplifying square roots.

  (√a)(√b) = √(ab)

  √(a²b) = a√b

__

  [tex]3\sqrt{10}\cdot(y^2\sqrt{4}+\sqrt{8y})=(3\sqrt{10})(2y^2) +(3\sqrt{10})(\sqrt{8y})\\\\=6y^2\sqrt{10}+3\sqrt{80y}\\\\=6y^2\sqrt{10}+3\sqrt{(4^2)(5y)}\\\\=\boxed{6y^2\sqrt{10}+12\sqrt{5y}}\qquad\text{matches the first choice}[/tex]

Answer:

   a

Step-by-step explanation:

Answer:

Step-by-step explanation:

I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me....

Answer:

3

Step-by-step explanation:

210=60(1)+50y

210=60+50y

-60  -60

150=50y

divide

y=3

Answer:

x = 2; y = 6.

Step-by-step explanation:

If the two triangles will be congruent by the HL Theorem, the hypotenuses and side lengths have to be equal. That means that...

x + 3 = y - 1

2x - 1 = y - 3

x + 3 = y - 1

y - 1 = x + 3

y = x + 4

2x - 1 = y - 3

y - 3 = 2x - 1

y = 2x + 2

2x + 2 = x + 4

x = 2

y = 2x + 2

y = 2 * 2 + 2

y = 4 + 2

y = 6

y = x + 4

y = 2 + 4

y = 6

Hope this helps!

Answer: 0.216 km .

Step-by-step explanation:

Given, The area of a square plot is 0.0324 hectares.

Since , 1 hectare =10,000 meters

Then, the area of a square plot = 10,000 x 0.0324

= 324 meters

Area of square = side²

[tex]\Rightarrow\ (\text{side})^2=324\\\\\Rightarrow\ \text{side}=\sqrt{324}=18\ m[/tex]

Perimeter = 4(side) = 4 x 18 = 72 m

Since it  was fenced using 3  strands of wire.

So, Total length of wire used =  3 (Perimeter) = 3 (72)m

= 216 m

Hence, the total length of wire used 216 m.

In km , 216 m = 0.216 km   [ 1 m = 0.001 km]

Hence, the correct option is 0.216 km .