Imagine each letter of the word “Mathematical” is written on individual pieces of paper and placed in a bag. Should you pick a random letter from that bag, what is the probability that you pick a vowel?

For this case we have that by definition[tex]\pi[/tex] equals 180 degrees.

We must convert 135 degrees to radians, then:

[tex]135 * \frac {\pi} {180} =\\135 * \frac {3.14} {180} =\\\frac {423.9} {180} = 2.355[/tex]

Rounding off we have:

2.4 radians.

Answer:

2.4 radians

Answer:

Step-by-step explanation:

We will check whether the given pair x = 3 and y = 2 is the solution of the first equation.

4(3) - 5(2) = 12 - 10 = 2 CORRECT

Put x = 3 and y = 2 to the equation 6x + 7y = Q:

Q = 6(3) + 7(2)

Q = 18 + 14

Q = 32

y= mx+b ( equation for slope)

y= 4/5x-3

The slope (m)is 4/5

The y- intercept(b) is -3

Answer: slope is 4/5

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

In this case:

m = 4/5

b = -3

This means that 4/5 is the slope of this line.

Hope this helped!

~Just a girl in love with Shawn Mendes

Final answer:

To find the length of the pole, we can use the Pythagorean theorem.

Explanation:

To find the length of the pole, we can use the Pythagorean theorem. Since the base of the pole is 7 feet away from the wall and the top of the pole reaches 21 feet up the wall, we can envision a right triangle with the pole as the hypotenuse. Using the Pythagorean theorem, we can calculate:

c^2 = a^2 + b^2

Where c is the length of the pole, a is the base length (7 feet), and b is the height reached by the pole (21 feet).

Plugging in the values, we get:

c^2 = 7^2 + 21^2

Solving for c, we find that the length of the pole is √(7^2 + 21^2) feet.

Answer:

27.778 hours

Step-by-step explanation:

just 2500 divided by 90 and that is 27.778

Final answer:

The time to drive 2500 km at a speed of 90 km/h would be 27.78 hours, but this is only a theoretical minimum as actual driving would include stops.

Explanation:

The question is asking about the time it would take to drive a certain distance at a constant speed. This is a straightforward application of the formula for calculating travel time, which is:

Time = Distance / Speed

Given the distance from Thunder Bay to Vancouver is approximately 2500 km and the car travels at a constant speed of 90 km/h, the calculation would be:

Time = 2500 km / 90 km/h

This simplifies to approximately 27.78 hours.

Answer:

The second choice

Step-by-step explanation:

The histogram shows the following:

3 children are within the ages of 5-10

7 children are within the ages of 11-13

4 children are within the ages of 14-18

So all you need to do is find the set of data that shows that fit the intervals. So find the data that have three values within 5 to 10; seven values with the 11-13; and four values within 14 to 18.

Answer:

(2,4)

Step-by-step explanation:

We have the system:

y=x+2

y=3x-2.

This is already setup for substitution.

I'm going to replace my first y with what the second y equals.

That is, I'm going to write 3x-2=x+2.

Time to solve the following for x:

3x-2=x+2

Subtract x on both sides:

2x-2= 2

Add 2 on both sides:

2x. = 4

Divide both sides by 2:

x. = 2

Now that we know x=2 and we have an equation that relates x to y: either y=x+2 or y=3x-2, doesn't matter which we use, we can find y.

So we y=x+2 with x=2 which means y=2+2=4.

So the solution, the intersection, is (2,4).

Answer:

(2, 4 )

Step-by-step explanation:

Given the 2 equations

y = x + 2 → (1)

y = 3x - 2 → (2)

Substitute y = 3x - 2 into (1)

3x - 2 = x + 2 ( subtract x from both sides )

2x - 2 = 2 ( add 2 to both sides )

2x = 4 ( divide both sides by 2 )

x = 2

Substitute x = 2 into (1) for the corresponding value of y

y = x + 2 = 2 + 2 = 4

As a check

Substitute x = 2 into the 2 equations and check validity

(1) → y = 2 + 2 = 4 ← Correct

(2) → y = (3 × 2) - 2 = 6 - 2 = 4 ← Correct

Solution is (2, 4 )

Answer:

6

Step-by-step explanation:

30 x 40 x 50 x 60 x 70 = 252,000,000

There are six zeros at the end. So there are 6 terminal zeros.

Answer:

a) 51 feet

b) 3.5 seconds

Step-by-step explanation:

The y-coordinate of the vertex of the given parabola is what we are looking for.

We first need to find the t-coordinate of the vertex.

The t-coordinate can be found using -b/(2a).

We need to compare

-16t^2+56t+2

to

at^2+bt+c

to identify a,b, and c.

a=-16

b=56

c=2

We are ready to compute -b/(2a).

-b/(2a)=-56/(2*-16)=-56/-32=7/4.

The vertex occurs at t=7/4.

To find y, we use y=2+56t-16t^2

y=2+56(7/4)-16(7/4)^2

y=51

So the maximum height is 51 feet.

Part b)

Hitting ground means the height between the ball and the ground is 0.

So we need to replace h(t) with 0.

0=2+56t-16t^2

I'm going to use quadratic formula.

a=-16

b=56

c=2

The quadratic formula is:

[tex]t=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]t=\frac{-56 \pm \sqrt{56^2-4(-16)(2)}}{2(-16)}[/tex]

Computing the thing inside the square root and the thing in the denominator using my handy dandy calculator:

[tex]t=\frac{-56 \pm \sqrt{3264}}{-32}{/tex]

I'm going to do the square root of 3264 now:

[tex]t=\frac{-56 \pm 57.131427428}{-32}[/tex].

I'm going to compute both

[tex]\frac{-56 + 57.131427428}{-32}[/tex] and [tex]-56-57.131427428}{-32}[/tex] using my handy dandy calculator:

[tex]-0.035357[/tex] while the other one is [tex]3.535357[/tex]

The negative value doesn't make sense for our problem so the answer is approximately 3.5 seconds.

Answer:

[tex]\large\boxed{5\dfrac{1}{3}\ units}[/tex]

Step-by-step explanation:

ΔZYW and ΔWYX are similar. Therefore corresponding sides are in proportion:

[tex]\dfrac{ZY}{YW}=\dfrac{YW}{YX}[/tex]

We have:

[tex]ZY=3,\ YW=4,\ YX = a[/tex]

Substitute:

[tex]\dfrac{3}{4}=\dfrac{4}{a}[/tex]          cross multiply

[tex]3a=(4)(4)[/tex]

[tex]3a=16[/tex]          divide both sides by 3

[tex]a=\dfrac{16}{3}\\\\a=5\dfrac{1}{3}[/tex]

Answer:

Hello guys im also here for that answer

Step-by-step explanation:

Answer: -16

Step-by-step explanation:

input is x

output is y

9x-7=y

9(-1)-7=y

-9-7=-16

Answer:

The answer is -16

Step-by-step explanation:

input is x

output is y

9x-7=y

9(-1)-7=y

-9-7=-16

Answer:

1/81

Step-by-step explanation:

Answer: 1/81

Step-by-step explanation:

9 to the power of -2 = 1^2/9^2

1/81

Hope it helps

Answer:

See below.

Step-by-step explanation:

All the equations are one-step equations.

In each case, see what operation is being done to the variable, and do the opposite operation to both sides.

1.

t + 1.32 = 3.48

1.32 is being added to t.

Subtract 1.32 from both sides.

t + 1.32 - 1.32 = 3.48 - 1.32

t = 2.16

2.

b - 4.22 = 7.08

4.22 is being subtracted from b.

Add 4.22 to both sides.

b - 4.22 + 4.22 = 7.08 + 4.22

b = 11.3

4.

h + 4/9 = 7/9

4/9 is being added to h.

Subtract 4/9 from both sides.

h + 4/9 - 4/9 = 7/9 - 4/9

h = 3/9

h = 1/3

5.

-5/8 = x - 1/4

1/4 is being subtracted from x.

Add 1/4 to both sides.

-5/8 + 1/4 = x - 1/4 + 1/4

-5/8 + 2/8 = x

-3/8 = x

x = -3/8

7.

3.2c = 9.6

c is being multiplied by 3.2.

Divide both sides by 3.2.

3.2c/3.2 = 9.6/3.2

c = 3

8.

-5.04 = 1.26d

c is being multiplied by 1.26.

Divide both sides by 1.26.

-5.04/1.26 = 1.26d/1.26

-4 = d

d = -4

10.

-2/3 = 3/4t

t is being multiplied by 3/4.

Divide both sides by 3/4 which is the same as multiplying both sides by 4/3.

-2/3 * 4/3 = 3/4t * 4/3

-8/9 = t

t = -8/9

11.

w/2.5 = 4.2

w is being divided by 2.5.

Multiply both sides by 2.5.

w/2.5 * 2.5 = 4.2 * 2.5

w = 10.5

Answer:

third graph (open circle on 518, colored to the right)

Step-by-step explanation:

The record is 518 cm. That means that 518 cm has already been accomplished. Anything less than 518 cm is not a record. 518 cm is also not a record. Only distances greater than 518 cm are records.

Answer: third graph (open circle on 518, colored to the right)

Answer:

The correct option for the graph is C.

Step-by-step explanation:

Consider the provided information.

The school record in the long jump is 518 cm.

Now we need to find the graph represents the set of jump distances in centimeters that would set a new school record.

Here, school already set a record in the long jump i.e 518 cm, it means anything less then or equal to the 518 cm is not a record.

As we need to exclude the numbers 518. So use an open dot at 518.

For record the distances should be greater than 518 cm. Thus, use the arrow moving right to 518.

Hence, the correct option for the graph is C.

Answer:

8.555 in.

Step-by-step explanation:

So the area of the square is x^2.

This makes that the area of the circle is x^2 - 20 pie.

The radius of the circle is half of the diameter, so it is 0,5x.

The formula for the circle area is:

Area = pie * r^2.

x^2 - 20 pie = pie * (0,5x)^2

x^2 - 20 pie = pie * 0,25x^2

x^2 - pie * 0,25x^2 = 20 pie

x^2 * (1 - 0,25 pie) = 20 pie

x^2 = 20pie / (1 - 0,25 pie)

x = square root (20pie / (1 - 0,25 pie)) = 17.11

So the radius is 0,5 * 17.11 = 8.555 in.

Answer:

{ - 1, 1, 7, 23 }

Step-by-step explanation:

To find the range substitute the values from the domain into g(x)

g(-2) = -2(- 2) + 3 = 4 + 3 = 7

g(- 10) = - 2(- 10) + 3 = 20 + 3 = 23

g(1) = - 2(1) + 3 = - 2 + 3 = 1

g(2) = - 2(2) + 3 = - 4 + 3 = - 1

Range is { - 1, 1, 7, 23 }

Answer:

(0,7)

Step-by-step explanation:

This equation you are given is in slope-intercept form, the form y=mx+b.

It is called slope-intercept from because it gives us the slope and the y-intercept.

The slope is m.

The y-intercept is b.

If we compare y=8x+7 to y=mx+b, we should make the conclusion that m=8 and b=7.

This tells the slope is 8 while the y-intercept is 7.

The y-intercept is 7 is sometimes required to be represented by a point.  Since it is the y-intercept, the x is 0 so the point that represents the y-intercept is (0,7).

Answer:

0,7

Step-by-step explanation:

Answer:

y=1/6x+1 because the formula is written as y=mx+b

Answer:

y=1/6x+1

Step-by-step explanation:

slope is the change in y over the change in . 2-1 is 1 and 6-0 is 6 so the slope will be 1/6. the y intercept is given by the second coordinate (0,1) which is why you add 1.

Answer:

Given an exponential function of the form

y = a*(b)^x

The values of b that will result in the desired percentage values are:

Case 1

b = 23% decrease

1 - 0.23 = 0.77

y = a*(0.77)^x

Case 2

b = 8% increase

1 + 0.08 = 1.08

y = a*(1.08)^x

Case 3

b = 15% decrease

1 - 0.15= 0.85

y = a*(0.85)^x

Case 4

b = 120% increase

1 + 1.2 = 2.2

y = a*(2.2)^x

See attached picture for examples

The value of b in an exponential function is calculated as : For a 23% decrease = 0.77, For an 8% increase = 1.08, For a 15% decrease = 0.85, For a 120% increase = 2.20.

The student is trying to determine the corresponding exponential function base value (b) for a given percent rate of change.

In an exponential function y = abx, a positive b models exponential growth, while a value of b less than 1 models exponential decay.

We can convert the percent increase or decrease to a decimal and then add or subtract it from 1 to find the corresponding value of b.

For a 23% decrease, b = 1 - 0.23 = 0.77.

For an 8% increase, b = 1 + 0.08 = 1.08.

For a 15% decrease, b = 1 - 0.15 = 0.85.

For a 120% increase, b = 1 + 1.20 = 2.20.

Answer:a and b

Step-by-step explanation:

Answer:

[tex]A\subset B[/tex]

Step-by-step explanation:

Let A and B, be two non-empty sets, then set A is a subset of set B if all elements in set A can be found in set B.

The given sets are:

A={1,2} and B={1,2,3,4}

We can observe that, all the elements in set A are also in set B.

This means that set A is a subset of B.

We write this as:

[tex]A\subset B[/tex]

The correct answer is option D.

Answer: 190°

Step-by-step explanation:

Angle CAE is 1/2 times the measure of arc CBA, therefore:

95° x 2=190°

The  measure of arc CBA =190°

To understand the relationship between angle CAE and arc CBA, we need to delve into the properties of angles and arcs in circles. Here is a step-by-step explanation:

Step 1: Understanding Inscribed Angles

In a circle, an inscribed angle is an angle formed by two chords that intersect on the circle. The measure of an inscribed angle is always half the measure of the intercepted arc.

Step 2: Relationship between Angle CAE and Arc CBA

Given:

- Angle CAE is inscribed in the circle.

- Arc CBA is the intercepted arc for angle CAE.

According to the properties of inscribed angles:

[tex]\[ \text{Measure of Angle CAE} = \frac{1}{2} \times \text{Measure of Arc CBA} \][/tex]

Step 3: Using the Given Information

Let's denote:

[tex]- \( \angle CAE \)[/tex] as the measure of angle CAE.

[tex]- \( \text{Arc CBA} \)[/tex] as the measure of arc CBA.

From the given information, the measure of arc CBA is 95°. Using the inscribed angle property:

[tex]\[ \angle CAE = \frac{1}{2} \times \text{Arc CBA} \][/tex]

[tex]\[ \angle CAE = \frac{1}{2} \times 95^\circ \][/tex]

[tex]\[ \angle CAE = 47.5^\circ \][/tex]

However, if we are interpreting the problem differently and consider that angle CAE is given as 95°, and we need to find the measure of the arc intercepted by this angle when doubled, then we would calculate:

[tex]\[ \text{Arc CBA} = 2 \times \angle CAE \][/tex]

[tex]\[ \text{Arc CBA} = 2 \times 95^\circ \][/tex]

[tex]\[ \text{Arc CBA} = 190^\circ \][/tex]

Therefore, if angle CAE is half the measure of arc CBA, and given the angle CAE as 95°:

[tex]\[ \text{Arc CBA} = 2 \times 95^\circ = 190^\circ \][/tex]

This shows that the measure of arc CBA is 190°.

Answer:

A, C, E

Step-by-step explanation:

substitute for x in each option and check if the value of y satisfies the inequality

Answer:

Option A, C and E

Step-by-step explanation:

We have to find points which are solution to the linear inequality ( y<0.5x + 2)

(a) For (-3, -2)

-2 < (0.5 × 3 + 2)

-2 < 1.5 + 2

-2 < 3.5

True, It's a solution.

(b) For (-2, 1)

1 < 0.5 × (-2) + 2

1 < -1 + 2

1 < 1

False, it's not a solution

(c) For (-1, -2)

-2 < 0.5 (-1) +2

-2 < -1 + 2

-2 < 1

True, It's a solution.

(d) For (-1, 2)

2 < 0.5 (-1) + 2

2 < -1 + 2

2 < 1

False, It's not the solution.

(e) For (1, -2)

-2 < 0.5 (1) + 2

-2 < 2.5

True It's a solution

Therefore, Option A, C and E are the solutions.

Answer:

look at explanation:

Step-by-step explanation:

1st picture: angle bisector

2nd picture: angle bisector

3rd picture: perpendicular bisector

4th picture: angle bisector

5th picture: perpendicular bisector

6th picture: perpendicular bisector

Answer:

-5

Step-by-step explanation:

Let's find the answer by dividing [tex](-2m^{3}-m+m^{2}+1)[/tex] by  [tex](m+1)[/tex], like this:

[tex](-2m^{2})*(m+1)=-2m^{3}-2m^{2}[/tex] and:

[tex](-2m^{3}-m+m^{2}+1)-(-2m^{3}-2m^{2})=3m^{2}-m+1[/tex] then:

[tex](3m)*(m+1)=3m^{2}+3m[/tex] and:

[tex](3m^{2}-m+1)-(3m^{2}+3m)=-4m+1[/tex] then:

[tex](-4)*(m+1)=-4m-4[/tex] and:

[tex](-4m+1)-(-4m-4)=5[/tex] notice that the remainder is 5 so we need to subtract the remainder.

Based on the previous procedure we can define:

[tex](-2m^{3}-m+m^{2}+1)/(m+1)=(-2m^{2}+3m-4) + 5[/tex]

In conclusion the smallest integer that can be added to the polynomial is -5, so the polynomial will be [tex](-2m^{3}-m+m^{2}-4)[/tex].

Answer:

Draw a line across  the points (6,0) and (0,3)

Step-by-step explanation:

This is the equation of a line, so it is enough to find two points (x,y), locate them and draw a straight line passing trough then,

Having said that, lets start.

The first easy point to find is the one that makes y=0, so we have the following equation: 0=-1/2 x +3, which gives that x=6, this point is (6,0)

The other easy point to find is the one that makes x=0, so we have the following equation y=-1/2 * 0 +3, which gives that y=3, this point is (0,3)

We have two points (6,0) and (0,3)

Answer: 8.55 minutes.

Step-by-step explanation: To find the time to run a mile, divide the total minutes by the total number of miles.

94/11=8.55

It will take 8.55 minutes to run one mile.

Step-by-step explanation:

Write a proportion.  3 laps is to 2 km as 5 laps is to x km.

3 / 2 = 5 / x

Cross multiply:

3x = 10

Divide:

x = 10/3

x = 3⅓

Madison will have run 3⅓ kilometers.

Answer:

R(p) = -6p^2 + 60p....

Step-by-step explanation:

Revenue, R = quantity sold * price

Price = p

Quantity sold = q = -6p + 60

R(p) = q*p

where q=-6p + 60

= (-6p + 60) * p = -6p^2 + 60p

Answer: R(p) = -6p^2 + 60p....

Answer:

Geometric Sequence.

[tex]a_{n}=(2)^{n-1}[/tex]

Step-by-step explanation:

The x-coordinates represent the number of terms of the sequence while the y-coordinates represent the term of the sequence. So the series shown on the graph is:

1, 2, 4, 8

We can see that the ratio of two consecutive terms of the above sequence is constant. i.e.

2/1 = 2

4/2 = 2

8/4 = 2

Such a sequence in which the ratio of two consecutive terms is a constant is known as Geometric Sequence and this constant ratio is known as common ratio.

The general term of a geometric sequence is represented as:

[tex]a_{n}=a_{1}(r)^{n-1}[/tex]

Using the values for the given sequence we get:

[tex]a_{n}=1(2)^{n-1}[/tex]

[tex]a_{n}=(2)^{n-1}[/tex]

Where n represents the number of term.

Answer:

y = -7/4 + 5

Step-by-step explanation:

Parallel lines have the same slope.

Step 1: Identify the slope of the given equation.

From my understanding, the equation is actually

y= -7/4x - 2

slope is m from y=mx + c

slope = m= -7/4

Slope of parallel line = -7/4

Step 2: Find the y-intercept (c) from the coordinates (4, -2)

y=mx + c

-2 = -7/4(4) + x

-2 = -7 + c

c = 5

Step 3: Write the equation of the parallel line.

slope = m = -7/4

y-intercept = c = 5

y = mx + c

y = -7/4 + 5

!!