In the diagram, which pair of angles are corresponding angles?
​

Answer:

1. The train is will cross the tunnel in 2 minutes.

The train is traveling at 30 km every hour or 60 minutes, so it will move 1 km every 60/30 minutes, or every 2 minutes.

2. Explanation here first: 22 free throws means 22 points and 22 field goals.

184-22=162 points they still needed to get, and

85-22=63 goals they still needed to score

We can now use a system of equations, (where x is 3-point goals, and y is 2-point goals) to solve the problem:

3x+2y=162

x+y=63 (-2)

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

3x+2y=162

-2x-2y= -126

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

x=36, and y=27 so the NBA players got 36 3-point goals, and 27 2-point goals

We can check this:

(36*3) + (27*2) + 22 = 108+54+22 = 184 total points

Step-by-step explanation:

Hope this helps!

Answer:

The answer is StartFraction 5 over 7 EndFraction

Answer:

The probability of the complement of the original event is 5/7.

Step-by-step explanation:

The probability of the complement of an event is 1 less the probability of the event, so

We get:  1 - 2/7, or 5/7

The probability of the complement of the original event is 5/7.

Note that  5/7  and 2/7  add up  to 7/7, or 1.

Answer:

a) [tex]cos(\alpha)=-\frac{3}{5}\\[/tex]

b)  [tex]\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]

c) [tex]\frac{4+3\sqrt{3} }{10}\\[/tex]

d)  [tex]\alpha\approx 53.1^o[/tex]

Step-by-step explanation:

a) The problem tells us that angle [tex]\alpha[/tex] is in the second quadrant. We know that in that quadrant the cosine is negative.

We can use the Pythagorean identity:

[tex]tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}[/tex]

Where we have used that the secant of an angle is the reciprocal of the cos of the angle.

Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:

[tex]cos(\alpha)=-\frac{3}{5}[/tex]

b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:

[tex]cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]

where we took the positive value, since we know that the angle is in the first quadrant.

c) We can now find [tex]sin(\alpha -\beta)[/tex] by using the identity:

[tex]sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\[/tex]

Notice that we need to find [tex]sin(\alpha)[/tex], which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:

[tex]sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}[/tex]

Then:

[tex]sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}[/tex]

d)

Since [tex]sin(\alpha)=\frac{4}{5}[/tex]

then  [tex]\alpha=arcsin(\frac{4}{5} )\approx 53.1^o[/tex]

Answer:

(- 1, 5 )

Step-by-step explanation:

Since the x- coordinate of Q, x = - 1 lies on the line of reflection.

The point Q will remain unchanged, that is

coordinates of image are (- 1, 5 )

Answer:

(a) y = -3/5 x + 13/5

(b) y = 5/3 x + 1/3

Step-by-step explanation:

(a) The slope of the tangent line is dy/dx.  Use implicit differentiation:

x² + y² + 4x + 6y − 21 = 0

2x + 2y dy/dx + 4 + 6 dy/x = 0

2x + 4 + (2y + 6) dy/dx = 0

x + 2 + (y + 3) dy/dx = 0

(y + 3) dy/dx = -(x + 2)

dy/dx = -(x + 2) / (y + 3)

At the point (1, 2), the slope is:

dy/dx = -(1 + 2) / (2 + 3)

dy/dx = -3/5

Using point-slope form of a line:

y − 2 = -3/5 (x − 1)

Simplifying to slope-intercept form:

y − 2 = -3/5 x + 3/5

y = -3/5 x + 13/5

(b) The normal line is perpendicular to the tangent line, so its slope is 5/3.  It also passes through the point (1, 2), so point-slope form of the line is:

y − 2 = 5/3 (x − 1)

Simplifying to slope-intercept form:

y − 2 = 5/3 x − 5/3

y = 5/3 x + 1/3

Answer:

12 rational

Step-by-step explanation:

2√3×√12 =

= 2√3×√2²·3

= 2√3×2√3

= 2×2×√3×√3

= 4×3

= 12

Answer:

x >5

Step-by-step explanation:

-4(3-X) > 8

Divide by -4, remembering to flip the inequality

-4/-4(3-X) < 8/-4

3-x < -2

Subtract 3 from each side

3-x-3 < -2-3

-x <-5

Divide by -1, remembering to flip the inequality

x >5

Answer:

[tex]c.[/tex] [tex]5<x[/tex]

Step-by-step explanation:

[tex]-4(3-x)>8\\3-x>-2\\-x>-5\\x>5[/tex]

Answer: 5x + 1

Step-by-step explanation:

f(x) - g(x)

(3x + 2) - (-2x + 1)       Here you distribute the negative sign to (-2x + 1)

3x + 2 + 2x - 1            Here you combine like terms

5x + 1                         This is the answer.

Answer:

See the explanation

Step-by-step explanation:

The function given to us is:

f(x) = (1/3)⁻ˣ

We can convert the negative power into positive one by interchanging the numerator and denominator.

f(x) = (3/1)ˣ

f(x) = 3ˣ

Substitute value for x= -3 , -2, -1, 0, 1, 2, 3

f(-3) = 3⁻³ = 0.037

f(-2) = 3⁻² = 0.111

f(-1) = 3⁻¹ = 0.333

f(0) = 3⁰ = 1

f(1) = 3¹ = 3

f(2) = 3² = 9

f(3) = 3³ = 27

f(4) = 3⁴ = 81

and so on

The table of the found values of f(x) or y for the corresponding values of x, along with their graph is given below.

Answer:

The number is 5250

Step-by-step explanation:

5/6 * x = 4375

Multiply each side by 6/5 to isolate x

6/5 * 5/6 x = 4375 * 6/5

x =5250

Answer:

5250

Step-by-step explanation:

5/6x= 4375

x= 4375*6/5

x= 5250

Answer:

the answer is 12

Step-by-step explanation:

because (6, 12) x axis is 6, and the 12 is the y axis. Meaning that you would go 12 along the y axis.

Answer:

I believe the answer is 12

Answer:

30.25

Step-by-step explanation:

Answer:     2.345

Step-by-step explanation:

The square root of 5.5 is 2.345.

Answer:

The area of a rectangle is the product of the length and the width of the rectangle.

The dimensions chosen for length and width of a rectangle must be the lengths of two adjacent sides. The area is the product of the two dimensions. It does not make a difference which one you call length and which one you call width since length * width = width * length because of the commutative property of multiplication.,

Answer:

To find the area you need both the length and width

A= lw

Practically it doesn't matter which one you call length or width  as long as both of them used in the calculation. The product of them doesn't change.

Answer:

2/$5.00

Step-by-step explanation:

It's the only one that makes sense

Answer:

4,10

It is the only option on the table

Step-by-step explanation:

Answer:

D. a³+b³=(a+b)(a²-ab+b²)

Explanation:

That is the form of the Sum of Cubes identity

Answer:

Option A.

Step-by-step explanation:

Note: The given function should be [tex]f(x)=\dfrac{2}{5}(10)^x[/tex] instead of [tex]f(x)=(10)^x[/tex].

Consider the given function is  

[tex]f(x)=\dfrac{2}{5}(10)^x[/tex]

We need to find the function which represents a reflection of f(x) across the x-axis.

If a function f(x) is reflected across the x-axis, then the new function is

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

Using this rule, we get

[tex]g(x)=-\dfrac{2}{5}(10)^x[/tex]        [tex][\because f(x)=\dfrac{2}{5}(10)^x][/tex]

Therefore, the correct option is A.

Answer:

A: There is only one solution since the two lines meet up. If it was parallel or the two lines where on top of each other there would be either an infinite amount of solutions or zero.

B:(3,5)

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

We know that the mean is 15 and the median is 18. In order to solve this problem, we can work backwards. First, image the scenario:

15, 15, 15, 15, 15.

We want the median to be 18, we we can add 3 to the middle number and then subtract three from the first number (in order to keep the mean constant). Thus, we have:

12, 15, 18, 15, 15.

Now, we can subtract and add in order to find the largest number. For instance, we can subtract 11 from 12 and add that 11 to the last number:

1, 15, 18, 15, 26

Next, we can subtract 13 (not 14 because each of the numbers should be different) from the second number and add that to 26:

1, 2, 18, 15, 39.

Finally, the most we an do is to add 4 to the fourth number and subtract 4 from 39 because we want to keep the median 18. Thus:

1, 2, 18, 19, 35.

Each value is distinct.

The largest possible value is 35.

Answer:

35.

Step-by-step explanation:

Since the mean of the five different positive integers is 15, you can assume that they all add up to be 5 * 15 = 75. The median is 18, which means that the rest of the four numbers add to be 75 - 18 = 57, with two numbers higher than 18 and two numbers lower.

You want to find the highest possible values for the maximum, you want to have very low minimums (so you can keep the maximum high). Since the question asks for different positive integers, the lowest numbers you can have are 1 and 2. So far, you have 1, 2, and 18 in your data set, so you have 57 - 3 = 54 to work with for your maximum.

You still want the highest value for the largest of the integers, so the fourth number will be 19. That is because that is the lowest you can go that is still higher than the median. Then, in your data set, you will have 1, 2, 18, and 19, which add up to be 40.

Since all five numbers add to be 75, the maximum will be 75 - 40 = 35.

To make sure this is correct, check your work. 1 + 2 + 18 + 19 + 35 = 75. 75 / 5 = 15. The mean is 15. The middle number is 18, so the median is 18. All five are different positive integers.

And there you have it! The maximum possible value of the largest of these five integers is 35.

Hope this helps!

Answer:

1. equilateral triangle

2. rectangle

3. circle area

4. trapezoid

5. circle circumference

6. parallelogram

7. regular polygon

8. triangle

Hope that helps.

Answer:

The probability that the combined sample tests positive  for the virus is 0.083

Since the probability that combined sample test positive for the virus is greater than 0.05, it is not likely for such a combined  sample to test positive.

The probability that the combined sample will test positive is 0.083

Step-by-step explanation:

Given that:

The probability of a randomly selected adult in one country being infected with a certain virus is 0.003.

P = 0.003

number of blood sample size n = 29

The probability mass function of X is as follows;

[tex]P(X=x) = \left[\begin{array}{c}{29}&x\\\end{array}\right] (0.003)^x (1-0.003)^{29-x}[/tex]

Thus; the required probability is;

[tex]P(X \geq 1) = 1 - P ( X < 1)[/tex]

[tex]P(X \geq 1) = 1 - P ( X =0)[/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} \dfrac{29!}{0!(29-0)!} \ \ \times 0.003)^0 \times (1-0.003)^{29-0}}\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} 1 \times 1 \times ( 0.9166)\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - 0.9166[/tex]

[tex]P(X \geq 1) = 0.0834[/tex]

Therefore; the probability that the combined sample tests positive  for the virus is 0.083

Is it unlikely for such a combined  sample to test positive?

P(combined  sample test positive  for the virus ) = 0.0834

Since the probability that combined sample test positive for the virus is greater than 0.05, it is not likely for such a combined  sample to test positive.

The probability of a randomly selected adult in one country being infected with a certain virus is 0.003.

P = 0.003

number of blood sample size n = 29

The probability mass function of X is as follows;

[tex]P(X=x) = \left[\begin{array}{c}{29}&x\\\end{array}\right] (0.003)^x (1-0.003)^{29-x}[/tex]

Thus; the required probability is;

[tex]P(X \geq 1) = 1 - P ( X < 1)[/tex]

[tex]P(X \geq 1) = 1 - P ( X =0)[/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} \dfrac{29!}{0!(29-0)!} \ \ \times 0.003)^0 \times (1-0.003)^{29-0}}\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} 1 \times 1 \times ( 0.9166)\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - 0.9166[/tex]

[tex]P(X \geq 1) = 0.0834[/tex]

The probability that the combined sample will test positive is 0.083

Answer:

336 cm3

Step-by-step explanation:

Using Cavalieri’s principle, this volume is the same as for a right rectangular prism with these dimensions. Apply the formula for volume of a rectangular prism:

V = lwh

V = (6)(4)(14)

V = 336 cm3

Answer:

19.625 cm^2

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

V = 3.14 * 5^2 * .25

V =19.625 cm^2

Answer:

[tex]\frac{13}{3}[/tex] ÷ [tex](-\frac{5}{6})[/tex]

Step-by-step explanation:

[tex]4\frac{1}{3}/(-\frac{5}{6})=\\\\\frac{13}{3}/(-\frac{5}{6})[/tex]

Answer:

13/3  ÷ - 5/6

Step-by-step explanation:

4 1/3 ÷ - 5/6

Change the mixed number to an improper fraction

4 1/3 = (3*4 +1)/3 = 13/3

13/3  ÷ - 5/6

Answer:

The answer would be A. because AB/EF=BC/DE

Step-by-step explanation:

AB = 2

EF = 5

BC = 1

DE = 2.5

2/5 = 0.4

1/2.5 = 0.4

The equation AB/EF=BC/DE is correct. All of the others are not.

The slope of line segment AC the same as the slope of line segment DF in the figure below because AB/EF = BC/DE.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

We need to find the proportionality statement for the ratio of the sides of the triangles.

If two triangles are similar, then the corresponding sides are proportional.

ABC ≈ DEF,

Here AB, BC, and AC are corresponding sides of DE, EF, and DF respectively.

Using the definition of similarity we ge

AB = 2

EF = 5

BC = 1

DE = 2.5

2/5 = 0.4

1/2.5 = 0.4

The equation AB/EF = BC/DE is correct. All of the others are not.

Learn more about a triangle;

https://brainly.com/question/7116550

#SPJ2

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

12x + 3y = 15

Express it in the form y = mx + c

3y = -12x + 15

Divide all terms by 3

y = - 4x + 5

From the equation m = - 4

Since the lines are parallel their slope are also the same

So the slope of the parallel line is also - 4

Hope this helps you

Answer:  A

Since you already have an equation just put in how many stickers and erasers she wants to get: 0.35(2)+0.99(2)+0.59≤4.

Then you multiply: .35(2)=.70. .99(2)=1.98.

Then add: .70+1.98+.59=3.27, so yes she can since 3.27 is less than 4 so the answer is A

Answer:

A. yes, because the total will be $3.27

Step-by-step explanation:

0.35x + 0.99y + 0.59 ≤ 4

0.35(2) + 0.99(2) + 0.59 ≤ 4

0.70 + 1.98 + 0.59 ≤ 4

3.27 ≤ 4

Hey there! :)

Answer:

56.7 kg.

Step-by-step explanation:

Use the density formula to solve for the mass:

D = m/V.

Rearrange in terms of mass, or 'm':

DV = m.

Solve for the volume:

0.06 × 0.9 × 1.5 = 0.081 m³.

Plug this into the equation along with the density:

700 × 0.081 = 56.7 kg.

Answer:

C. -3

Step-by-step explanation:

Plugging both of those points into the slope formula gets you a slope of -3.

Answer:

0.16 P(Yellow or Brown)=0.16

Answer: 0.44

Step-by-step explanation:

0.4 + 0.28 = 0.68

1.00 - 0.68 = 0.32

0.32 divided by 2.0 = 0.16

Total answer is 0.44

GLAD TO HELP:)

HAVE A NICE DAY!

BTW: I WAS DOING A TEST, BUT TOOK MY TIME TO HELP YOU! :)

PLEASE BRAINLEST ME!

Hey there! :)

Answer:

5.

Step-by-step explanation:

The pattern of this puzzle is to take the bottom two numbers of the triangle, find the sum, then divide by the top number. For example:

8 + 4 = 12 --> 12/3 = 4.

5 + 13 = 18 --> 18/6 = 3.

9 + 5 = 14 --> 14/2 = 7.

Therefore:

14 + 6 = 20 --> 20/4 = 5. The missing number is 5.

Answer: 5

Step-by-step explanation: