Help ASAP!!!

Find the given angle, to the nearest degree.

Answer:

AB = 20 tan55°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{20}[/tex] ( multiply both sides by 20 )

20 tan55° = AB

Answer:

interior angle (2)= 70

interior angle (3)= 60

Step-by-step explanation:

Given:

exterior angle=120°

interior angle (1)=50°

Required:

interior angle (2)=?

interior angle (3)=?

Formula:

exterior angle=interior angle (1) + interior angle (2)

Solution:

exterior angle=interior angle (1)+ interior angle (2)

120°=50°+interior angle (2)

120°+50°=interior angle (2)

70°=interior angle (2)

interior angle (3)= 180°-interior angle (1)- interior angle (2)

interior angle (3)=180°-50°+70°

interior angle (3)=180°-120°

interior angle (3)= 60°

Theorem:

Theorem 1.16

The measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

Hope this helps ;) ❤❤❤

Answer:

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

Step-by-step explanation:

You can understand the statement from many perspectives, but in terms of proposition logic it is best to understand it as   "negation of a" or "  b" in mathematical terms is written like this

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

You can show that they are logically equivalent because they have the same truth table.

Answer:

The answer is (1,-5). (i.e x=1 and y=-5).

Hope it helps..

Answer:

(1,-5)

Step-by-step explanation:

Answer:

Step-by-step explanation:

∆ BCD ~ ∆ DCA

[tex] \frac{bc}{dc} = \frac{dc}{ac} [/tex]

Plug the values:

[tex] \frac{5}{y} = \frac{y}{6 + 5} [/tex]

[tex] \frac{5}{y} = \frac{ y}{11} [/tex]

Apply cross product property

[tex]y \times y = 11 \times 5[/tex]

Calculate the product

[tex] {y}^{2} = 55[/tex]

[tex]y = \sqrt{55} [/tex]

Hope this helps...

Good luck on your assignment..

Answer:

x= 45

Step-by-step explanation:

In this diagram, there is an angle that is split into 2 angles.

The angle is a 90 degree angle. We know this because of the little square in the corner that denotes a right angle.

Therefore, the 2 angles inside of the right angle must add to 90 degrees. The 2 angles that make up the right angle are x and 45.

x+45=90

We want to find x. We need to get x by itself. 45 is being added on to x. The inverse of addition is subtraction. Subtract 45 from both sides.

x+45-45=90-45

x= 90-45

x=45

The measure of angle x is 45 degrees.

Answer:

Step-by-step explanation:

1. Preferred Share dividends.

There are 300,000 preference shares and each of them got $2.85. Total dividends are;

= 300,000 * 2.85

= $855,000‬

2. Total dividends = $3,500,000

Dividends left for Common Shareholders (preference gets paid first)

= 3,500,000 - 855,000

= $2,645,000

Common shares number 2,500,000

Dividend per share of common stock = [tex]\frac{2,645,000}{2,500,000}[/tex]

= $1.06

Looks like the given function is

[tex]f(x)=\dfrac1{9-x}[/tex]

Recall that for |x| < 1, we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

We want the series to be centered around [tex]x=4[/tex], so first we rearrange f(x) :

[tex]\dfrac1{9-x}=\dfrac1{5-(x-4)}=\dfrac15\dfrac1{1-\frac{x-4}5}[/tex]

Then

[tex]\dfrac1{9-x}=\displaystyle\frac15\sum_{n=0}^\infty\left(\frac{x-4}5\right)^n[/tex]

which converges for |(x - 4)/5| < 1, or -1 < x < 9.

Answer:

3 pairs

Step-by-step explanation:

Top and Bottom

Front and Back

Side and Side.

Cereal Boxes have 6 sides

Answer:

See Image Below.

Step-by-step explanation:

The Shaded region is the area of numbers that this equation satisfies.

Answer:

Please see attached image

Step-by-step explanation:

In order to graph the inequality, start from plotting the boundary line defined by the equality;

y = 3 x

You just need two points to accomplish such. so let's use two simple values for x and find what the y-values are:

for x = 0 then y = 3 (0) = 0

for x = 1 then y = 3 (1) = 3

Then use the points (0, 0) and (1, 3) to plot the boundary line.

After this, grab any point on the plane either clearly above the boundary line, or clearly below it and check if the inequality satisfies. For example, you can pick the point (3, 0) which is on the x line, 3 units to the right of the origin, and clearly below the boundary line we just plot.

When you use it in the inequality, you get:

(0)  [tex]\leq[/tex] 3 (3)

0   [tex]\leq[/tex] 9

which is a true statement, therefore, the points below the boundary lie are also solutions of the inequality.

Then the solution consists of all the points in the boundary line we just plotted (and indicated by drawing a solid line), plus all the points below the line, as depicted in the attached image.

Answer:

A. a straight line passing

Step-by-step explanation:

Answer:

a straight line passing

Step-by-step explanation:

Answer:

x≤9  

Step-by-step explanation:

x−15≤−6

Add 15 to each side

x−15+15≤−6+15

x≤9  

Answer:

[tex]\boxed{x\leq 9}[/tex]

Step-by-step explanation:

[tex]x-15 \leq -6[/tex]

[tex]\sf Add \ 15 \ to \ both \ parts.[/tex]

[tex]x-15 +15 \leq -6+15[/tex]

[tex]x\leq 9[/tex]

Answer:

D (13,5)

Step-by-step explanation:

X 2 3 4 5

Y 2 5 9 13

So the ordered pairs are (2,2),(3,5), (4,9), (5,13)

and the ordered pairs for the inverse are

(2,2),(5,3), (9,4), (13,5)

from which D (13,5) is found among the options.

Answer:

b

Step-by-step explanation:

Answer:

59 accidents were investigated.

Step-by-step explanation:

The question above is a probability question that involves 2 elements: causes of accidents.

Let

A = Alcohol

E = Excessive speed

In the question, we are given the following information:

18 accidents involved Alcohol and Excessive speed =P(A ∩ E)

26 involved Alcohol = P(A)

12 accidents involved excessive speed but not alcohol = P( E ) Only

21 accidents involved neither alcohol nor excessive speed = neither A U B

We were given P(A) in the question. P(A Only) = P(A) - P(A ∩ E)

P(A Only) = 26 - 18

= 8

So, only 8 accident involved Alcohol but not excessive speed.

The Total number of Accidents investigated = P(A Only) + P( E only) + P(A ∩ E) + P( neither A U B)

= 8 + 12 + 18 + 21

= 59

Therefore, 59 accidents were investigated.

Answer:

Option C.

Step-by-step explanation:

In the given figure we have two parallel lines AB and CD.

A transversal line FB intersect the parallel lines at point B and C.

We know that the if a transversal line intersect two parallel lines, then corresponding angles are congruent.

[tex]\angle ABC=\anle ECF[/tex]

[tex]x=y[/tex]

To prove this by translation, we need a translation along the directed line segment CB maps ine CD onto line AB and angle y onto angle x.

Therefore, the correct option is C.

Working backwards, on Wednesday morning we have 60 / (1/2) = 120 pounds of ice.

2/3 melts on Tuesday so 120 pounds must be 1/3 of the ice.

120 / (1/3) = 360

Answer: D. 360

Answer:

The beryllium atom; 1.99 times larger.

Step-by-step explanation:

The beryllium atom is 0.000000000112 meters, while the nitrogen atom is 0.000000000056 meters. So, the beryllium atom is larger than the other.

(1.12 * 10^-10) / (5.6 * 10^-11)

= (1.112 / 5.6) * (10^-10 + 11)

= 0.1985714286 * 10

= 1.985714286 * 10^0

So, the beryllium atom is about 1.99 times larger than the other.

Hope this helps!

Answer:

16 hours

Step-by-step explanation:

From the above question, we are given the following information

For one wall, working alone,

Amy can paint for 12 hours

Which means, in

1 hour , Amy would have painted = 1/12 of the wall

Bob can paint for 18 hours

Which means ,

in 1 hour, Bob would have painted = 1/18 of the wall.

We are told Amy painted the wall for 4 hours and then Bob took over and completed the wall.

Step 1

Find the portion of the wall Amy painted before Bob took over.

Amy painted the wall for 4 hours before Bob took over.

If:

1 hour = 1/12 of the wall for Amy

4 hours =

Cross multiply

4 × 1/12 ÷ 1

= 4/12 = 1/3

Amy painted one third(1/3) of the wall

Step 2

Find the number of hours left that Bob used in painting the remaining part of the wall

Let the entire wall = 1

If Amy painted 1/3 of the wall

Bob took over and painted = 1 - 1/3

= 2/3 of the wall

If,

Bob painted 1/18 of the wall = 1 hour

2/3 of the wall = ?? = Y

Cross multiply

2/3 × 1 = 1/18 × Y

Y = 2/3 ÷ 1/18

Y = 2/3 × 18/1

Y = 36/3

Y = 12 hours.

This means, the number of hours Bob worked when he took over from Amy = 12 hours.

Step 3

The third and final step is to calculate how many hours it took them to paint the wall

Number of hours painted by Amy + Number of hours painted by Bob

= 4 hours + 12 hours

= 16 hours

Therefore, it took them 16 hours to paint the entire wall.

Answer:

Point of faulty equipment car = 0.2614 (Approx)

Step-by-step explanation:

Given:

Total number of car = 700

Faulty equipment car = 183

Find:

Point of faulty equipment car

Computation:

Point of faulty equipment car = Faulty equipment car / Total number of car

Point of faulty equipment car = 183 / 700

Point of faulty equipment car = 0.261428571

Point of faulty equipment car = 0.2614 (Approx)

Answer:

EB = 9

Step-by-step explanation:

CD = AB

The line with the value of five that also forms a right angle with EB is a perpendicular bisector to AB.

So the value of EB is half of AB (AB is equal to CD).

18/2 = 9

Answer:

the null hypothesis would be: p = 70%/0.7

The alternative hypothesis would be: p < 0.7

Step-by-step explanation:

The null hypothesis is most of the time always the default statement while the alternative hypothesis is tested against the null and is its opposite.

In this case study the null hypothesis would be: the proportion of men who own cats is 70%: p = 0.7

The alternative hypothesis would be: the proportion of men who own cats is smaller than 70% : p < 0.7

Answer:

0

Step-by-step explanation:

Hope this helps

In general, if we have [tex]x^a=x^b,[/tex] then [tex]a=b.[/tex] Thus, the first answer choice is correct.

Answer:

[tex]\boxed{\red{2x - 1 = 5x - 14}}[/tex]

First answer is correct.

Step-by-step explanation:

we know that,

[tex] {x}^{a} = {x}^{b} [/tex]

[tex]a = b[/tex]

So, according to that,

[tex] {5}^{(2x - 1)} = {5}^{(5x - 14)} [/tex]

Therefore,

[tex]2x - 1 = 5x - 14[/tex]

Steps to solve:

1 = -4 + 3/8x

~Add 4 to both sides

1 + 4 = -4 + 4 + 3/8x

~Simplify

5 = 3/8x

~Multiply 8/3 to both sides

5 * 8/3 = 3/8x * 8/3

~Simplify

13 1/3 = x

As we look through the answer choices, we can see that none resembles any of the steps I did above but by looking at the answers for each one, the only logical answer is B since it has a final answer of x = 40/3 or 13 1/3.

Best of Luck!

Answer:

Third option

Step-by-step explanation:

We can't factor this so we need to use the quadratic formula which states that when ax² + bx + c = 0, x = (-b ± √(b² - 4ac)) / 2a. However, we notice that b (which is 6) is even, so we can use the special quadratic formula which states that when ax² + bx + c = 0 and b is even, x = (-b' ± √(b'² - ac)) / a where b' = b / 2. In this case, a = 1, b' = 3 and c = 7 so:

x = (-3 ± √(3² - 1 * 7)) / 1 = -3 ± √2

let us build equation for unknown legs

If we keep the length pf one leg as x

the other leg would be x +3

so we can build a relationship using pythagoras theorem

x^2 + (x+3)^2 = 15^2

x^2 + x^2 + 6x + 9 = 225

2x^2 + 6x + 9 = 225

2x^2 + 6x+ 9-225 = 0

2x^2 + 6x - 216 = 0

x^2 + 3x - 108 = 0 dividing whole equation by 2

x^2 + 12x - 9x - 108 = 0

x ( x + 12 ) - 9 (x + 12) = 0

(x -9) ( x +12) = 0

solutions for x are

x = 9 or x = -12

as lengths cannot be negative

one side length is 9cm

and other which is( x + 3)

9 + 3

12cm

The lengths of the legs of the right angled triangle is 9 feet and 12 feet.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:

Hypotenuse² = First Leg² + Second leg²

Let x represent the length of one leg. The other leg is three more = x + 3, hypotenuse = 15 ft. Hence:

15² = x² + (x + 3)²

x² + 6x + 9 + x² = 225

2x² + 6x - 216 = 0

x² + 3x - 108 = 0

x = - 12 or x = 9

Since the length cant the negative hence x= 9, x + 3 = 12

The lengths of the legs of the right angled triangle is 9 feet and 12 feet.

Find out more at: https://brainly.com/question/10040532

Answer:

P = 0.0714

Step-by-step explanation:

If two faces of the larger cube that share and edge are painted blue, it means that 28 of the 64 unit cubes are painted in at least one side and 36 cubes have no painting faces.

Additionally, from the 28 cubes painted only 4 have exactly two painted faces.

Then, to calculate the number of ways in which we can select x elements from a group of n, we can use the following equation:

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

So, the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces is:

[tex]P=\frac{4C1*36C1}{64C2}=0.0714[/tex]

Because there are 64C2 ways to select 2 cubes from the 64, and from that, there are 4C1*36C1 ways to select one cube with exactly two painted faces and one cube with no painted faces.

Answer:

a = 16

b = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Length of the design 16 inches is represented by the point (0, 16) and length of 12 inches by (1, 12).

That means these points lie on the graph of the function 'f' represented by,

f(x) = a(b)ˣ

For the point (0, 16),

f(0) = a(b)⁰

16 = a(1)

a = 16

For another point (1, 12),

f(1) = a(b)¹

12 = ab

12 = 16(b) [Since a = 16]

b = [tex]\frac{12}{16}[/tex]

b = [tex]\frac{3}{4}[/tex]

Therefore, values of a and b are 16 and [tex]\frac{3}{4}[/tex] respectively.

Answer:

the car overtake the truck at time 11:40 am.

Step-by-step explanation:

We have both vehicules going at constant speed from city a to city b. The distance is unknown, but can be written as d.

We will express the time in hours (and decimals of hours).

The truck speed can be calculated estimating the time between arrival and start:

- The arrival time is 1.15 pm. This is t2=13.25.

- The starting time is 9:15 am. This is t1=9.25.

The truck took t2-t1=13.25-9.25=4 to go from city a to b.

The average speed is then:

[tex]v_t=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{4}[/tex]

We can write the equation for the position x(t) for the truck as:

[tex]x(t)=x_0+v_t\cdot t=x_0+\dfrac{d}{4}t\\\\\\x(13.25)=x_0+\dfrac{d}{4}(13.25)=d\\\\x_0=d-3.3125d=-2.3125d\\\\\\x(t)=-2.3125d+0.25d\cdot t[/tex]

For the car we have:

- The arrival time is 12:45 am. This is t2=12.75.

- The starting time is 10 am. This is t1=10.

The car took t2-t1=12.75-10=2.75.

The average speed is then:

[tex]v_c=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{2.75}[/tex]

We can write the equation for the position x(t) for the car as:

[tex]x(t)=x_0+v_c\cdot t=x_0+\dfrac{d}{2.75}t\\\\\\x(12.75)=x_0+\dfrac{d}{2.75}(12.75)=d\\\\x_0=d-4.6363d=-3.6363d\\\\\\x(t)=-3.6363d+0.3636d\cdot t[/tex]

The time at which the car overtake the car is the time when both vehicles have the same position:

[tex]x(t)/d=-2.3125+0.25\cdot t = -3.6363+0.3636\cdot t\\\\-2.3125+3.6363=(0.3636-0.25)t\\\\1.3238=0.1136t\\\\t=1.3238/0.1136\approx11.65[/tex]

The car overtakes the truck at t=11.65 hours or 11:39 am.

Answer:

99.5% Confidence interval = (-0.025, 0.547)

= -0.025 < p < 0.547

Step-by-step explanation:

             | A | B | C | Total

Male      | 5 | 4 | 17 | 26

Female | 6 | 2 | 15 | 23

Total     | 11 | 6 | 32 | 49

If p represent the proportion of all female students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p to three decimal places.

All female students = 23

Female students that score an A = 6

p = (6/23) = 0.2608695652 = 0.261

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = (6/23) = 0.261

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 99.5% confidence interval for sample size of 23 is obtained from the t-tables since information on the population standard deviation is not known.

we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 23 - 1 = 22.

Significance level for 99.5% confidence interval

(100% - 99.5%)/2 = 0.25% = 0.0025

t (0.0025, 22) = 3.119 (from the t-tables)

Standard error of the mean = σₓ = √[p(1-p)/N]

p = 0.261

N = sample size = 23

σₓ = √(0.261×0.739/23) = 0.091575

99.5% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.261 ± (3.119 × 0.091575)

CI = 0.261 ± 0.2856

99.5% CI = (-0.0246, 0.5466)

99.5% Confidence interval = (-0.025, 0.547)

= -0.025 < p < 0.547

Hope this Helps!!!