Answer choice
D) A worker with 15 years of service gets 5 weeks of vacation and each year.

Answer:

518 / 3.

Step-by-step explanation:

(74 / 3) * 7 = (74 * 7) / 3 = 518 / 3 = 172 and 2/3 = 172.6666666667.

Hope this helps!

Answer:

D

Step-by-step explanation:

The chord- chord angle 105° is half the sum of the arcs intercepted by the angle and its vertical angle, thus

[tex]\frac{1}{2}[/tex](120 + x) = 105 ( multiply both sides by 2 )

120 + x = 210 ( subtract 120 from both sides )

x = 90 → D

Answer: 16,384

Step-by-step explanation:

The seven marbles have different colours, so we can differentiate them.

Now, suppose that for each marble we have a selection, where the selection is in which jar we put it.

For the first marble, we have 4 options ( we have 4 jars)

For the second marble, we have 4 options.

Same for the third, for the fourth, etc.

Now, the total number of combinations is equal to the product of the number of options for each selection.

We have 7 selections and 4 options for each selection, then the total number of combinations is:

C = 4^7 = 16,384

Answer:

the answer is 16384

Step-by-step explanation:

have a nice day.

Answer:

Step-by-step explanation:

from cosines theorem:

t² = 11² + 14² - 2•11•14•cos87°

t² = 121 + 196 + 308•0.05236

t² = 333.12688

t = √333.12688

t = 18.2517... ≈ 18.3

Answer:

Hey there!

Sine is equal to opposite/hypotenuse

Tangent is equal to opposite/adjacent

opposite=a

hypotenuse=b

adjacent=c

Thus, tangent x= a/c.

Hope this helps :)

Answer:

tan x = a/sqrt(b^2 - a^2)

Step-by-step explanation:

sin x = a/b = opp/hyp

tan x = opp/adj

adj^2 + opp^2 = hyp^2

adj^2 + a^2 = b^2

adj = sqrt(b^2 - a^2)

tan x = a/sqrt(b^2 - a^2)

Answer:

Null hypothesis: Policy B remains more effective than policy A.

Alternate hypothesis: Policy A is more effective than policy B.

Step-by-step explanation:

Remember, a hypothesis is a  usually tentative (temporary until tested) assumption about two variables– independent and the dependent variable.

We have two types of hypothesis errors:

1. A type I error occurs when the null hypothesis (H0) is wrongly rejected.

That is, rejecting the assumption that policy B remains more effective than policy A when it is actually true.

2. A type II error occurs when the null hypothesis H0, is not rejected when it is actually false. That is, accepting the assumption that policy B remains more effective than policy A when it is actually false.

Answer:

y=10 ( number of acrobat)

Step-by-step explanation:

let x be the elephant and y the acrobat

elephant has 4 legs and acrobat 2

4x+2y=40

x+y=15  ⇒x=15-y

substitute for x in the equation:

4(15-y)+2y=40

60-4y+2y=40

-2y=40-60

y=-20/-2

y=10 ( number of acrobat)

number of elephant=15-10=5 elephants

Answer:

the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%  is 0.0042

Step-by-step explanation:

Given that :

A film distribution manager calculates that 9% of the films released are flops

Let p be the probability for the movies that were released are flops;

[tex]\mu_p = P = 0.9[/tex]

If the manager is right, what is the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%

now; we know that our sample size = 442

the standard deviation of the variance  is [tex]\sigma_p= \sqrt{\dfrac{p(1-p)}{n}}[/tex]

[tex]\sigma_p= \sqrt{\dfrac{0.9(1-0.9)}{442}}[/tex]

[tex]\sigma_p= \sqrt{\dfrac{0.9(0.1)}{442}}[/tex]

[tex]\sigma_p= \sqrt{\dfrac{0.09}{442}}[/tex]

[tex]\sigma_p= \sqrt{2.0361991 \times 10^{-4}}[/tex]

[tex]\sigma _p = 0.014[/tex]

So; if the manager is right; the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% can be calculated as:

[tex]P(|p-P|>0.04)=1 -P(p-P|<0.04)[/tex]

[tex]P(|p-P|>0.04)=1 -P(-0.04 \leq p-P \leq 0.04)[/tex]

[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{\sigma_p} \leq \dfrac{ p-P}{\sigma_p} \leq \dfrac{0.04}{\sigma_p})[/tex]

[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{0.014} \leq Z\leq \dfrac{0.04}{0.014})[/tex]

[tex]P(|p-P|>0.04)=1 -P( -2.8571 \leq Z\leq 2.8571)[/tex]

[tex]P(|p-P|>0.04)=1 -[P(Z \leq 2.8571) -P (Z\leq -2.8571)[/tex]

[tex]P(|p-P|>0.04)=1 -(0.9979 -0.0021)[/tex]

[tex]P(|p-P|>0.04)=1 -0.9958[/tex]

[tex]\mathbf{P(|p-P|>0.04)=0.0042}[/tex]

∴

the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%  is 0.0042

Answer: $10,000

Step-by-step explanation:

Given the following :

Profit if economy remains strong = $30,000

Profit if economy grows at moderate pace = $10, 000

Loss if economy goes into recession = $30,000

Probability that economy will remain strong = 20% = 0.2

probability the economy will grow at a moderate pace = 70% = 0.7

probability the economy will slip into recession = 10% = 0.1

Expected value = sum of (x * p(x))

Here expected value equals;

Strong economy profit = $30,000 * 0.2 = $6000

Moderate economy profit = $10,000 * 0.7 = $7000

Loss on Recession = $30,000 * 0.1 = $3000

Expected profit = $(6000 + 7000 - 3000)

Expected profit = $10,000

Answer:

18

Step-by-step explanation:

Answer:

18.

Step-by-step explanation:

[4 + (3 - 1)] * 3

= (4 + 2) * 3

= 6 * 3

= 18

Hope this helps!

Answer:

10

Step-by-step explanation:

[tex]\left(x-h\right)^{2}+\left(y-k\right)^{2}=r^2[/tex]

[tex]\left(x-6\right)^{2}+\left(y-0\right)^{2}=r^2\\[/tex]

We used (2,-3)

[tex]\left(2-6\right)^{2}+\left(-3-0\right)^{2}=25[/tex]

[tex]r^2=25\\[/tex] , so [tex]r = 5[/tex]

But this one is asking for the diameter, and to find it. It's simply 2r.

2*5 = 10

Answer: Ask the king to draw first and read it. Explain that if the king selects "leave" the PM's choice could only be "stay". It is then unnecessary for the PM to draw. It avoids embarrassing the king in his lie, demonstrates the PM's intelligence, and keeps his job.

Step-by-step explanation:

Answer: 1/5

Step-by-step explanation:

Given the following :

Total number of ducks in pool = 30

Mark 1 = 15 ducks

Mark 2 = 9 ducks

Mark 3 = 6 ducks

Probability of picking a duck with Mark 3:

Probability = (number of required outcomes / total possible outcomes)

Number of required outcomes = number of ducks with mark 3 = 6 ducks

P(picking a duck with Mark 3) = 6/30

6/30 = 1/5

= 1/5

Answer:

Yes, it would be statistically significant

Step-by-step explanation:

The information given are;

The percentage of jawbreakers it produces that weigh more than 0.4 ounces = 60%

Number of jawbreakers in the sample, n = 800

The mean proportion of jawbreakers that weigh more than 0.4 = 60% = 0.6 = [tex]\mu _ {\hat p}[/tex] =p

The formula for the standard deviation of a proportion is [tex]\sigma _{\hat p} =\sqrt{\dfrac{p(1-p)}{n} }[/tex]

Solving for the standard deviation gives;

[tex]\sigma _{\hat p} =\sqrt{\dfrac{0.6 \cdot (1-0.6)}{800} } = 0.0173[/tex]

Given that the mean proportion is 0.6, the expected value of jawbreakers that weigh more than 0.4  in the sample of 800 = 800*0.6 = 480

For statistical significance the difference from the mean = 2×[tex]\sigma _{\hat p}[/tex] = 2*0.0173 = 0.0346 the equivalent number of Jaw breakers = 800*0.0346 = 27.7

The z-score of 494 jawbreakers is given as follows;

[tex]Z=\dfrac{x-\mu _{\hat p} }{\sigma _{\hat p} }[/tex]

[tex]Z=\dfrac{494-480 }{0.0173 } = 230.94[/tex]

Therefore, the z-score more than 2 ×[tex]\sigma _{\hat p}[/tex] which is significant.

Answer:

Step-by-step explanation:

min 452, max 507, so 494 is not unusual.

Answer:

3.9

Step-by-step explanation:

Pythagorean theorem:

a^2 + b^2 = c^2

a^2 + 1^2 = 4^2

a^2 + 1 = 16

a^2 = 15

a = sqrt(15)

a = 3.9

Answer a = 3.9 yards

Answer:

[tex]\boxed{3.9}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

Apply Pythagorean theorem.

[tex]a^2 + b^2 = c^2[/tex]

[tex]a^2 + 1^2 = 4^2[/tex]

[tex]a^2 + 1 = 16[/tex]

[tex]a^2 = 15[/tex]

[tex]a=\sqrt{15}[/tex]

[tex]a \approx 3.872983[/tex]

Answer:

Step-by-step explanation:

1.50x + 10[x/30] >= 450

x >= 246.3

check:

1.50*246 + 10*8 = 449

$450

Answer:

1 = 90°, 2 = 66°

Step-by-step explanation:

Since the diagonals of a rhombus are perpendicular, ∠1 = 90°. Using the Exterior Angles Theorem (exterior angle = sum of remote interior angles, we see that ∠2 = 90 - 24 = 66°.

Answer:

Since ΔABC is equilateral, ∠ACB = 60°. Since ΔCED is isosceles (we know this because CE = ED from the graph), ∠ECD = ∠EDC from Base Angles Theorem, and since the sum of angles in a triangle is 180°, they measure (180 - 32) / 2 = 74° each. Since BCD is a straight line, it measures 180° so we can write:

60 + x + 74 = 180

134 + x = 180

x = 46°

Answer:

46 degrees

Step-by-step explanation:

Since triangle ABC is equilateral that means each angle in that triangle is 60 degrees.

We also know that for triangle ECD angle C and angle D have to be 74 degrees, because a triangle has 180 degrees in total and the only unique angle is at the top which is 32. So it is 180-32=148, than 148/2=74.

We than know that a half circle is 180 degrees aswell, so we do 180-60=120

120-74=46

Answer:

y=3

Step-by-step explanation:

10=2y+4

10-4=2y

6=2y

3=y

Answer:

2x-(3x+5) = -x-5

Step-by-step explanation:

     2x + 0

-

     3x + 5

-———————-

     -x - 5

Answer:

6π

Step-by-step explanation:

First we need to find the circumference of the circle. We know that the radius is 4 and the formula is πd or 2πr

Leaving it in terms of pi, the circumference is 8π

Now we need to find the length of the arc.

Since the missing part of the circle is labeled with a right angle, we know that it's exactly 1/4 of the whole circle. That means the arc we need to find is 3/4 of the circumference.

3/4 of 8π is 6π

Answer:

T = 1.5s

Step-by-step explanation:

Hello,

To find the time the pincone hits the ground, we need to use the equation given.

Note that h = 0 when the pinecones hits the ground.

This question relates to motion under gravity.

h = -16t² + 36

0 = -16t² + 36

Make t² the subject of formula

16t² = 36

t² = 36 / 16

t² = 2.25

Take the square root of both sides

t = √(2.25)

t = 1.5s

The time it takes the pinecone to hit the ground is 1.5s.

Answer:

[tex]\boxed{\sf \ \ 28 \ \ }[/tex]

Step-by-step explanation:

Hello,

Please find attached the graph

AB = 6-2 = 4

DA = 7-0 = 7

So the area of the rectangle is AB * DA = 4 * 7 = 28

Hope this helps

Answer:

x=6 and x=5.1

Step-by-step explanation:

Answer:

  D.  p + q = 7

Step-by-step explanation:

The slope of AB is ...

  mAB = (y2 -y1)/(x2 -x1) = (1 -4)/(6 -p) = -3/(6 -p)

The slope of BC is ...

  mBC = (q -1)/(9 -6) = (q -1)/3

We want the product of these slopes to be -1:

  mAB·mBC = -1 = (-3/(6 -p))·((q -1)/3)

  -(q-1)/(6 -p) = -1 . . . . cancel factors of 3

  q -1 = 6 -p . . . . . multiply by -(6 -p)

  q + p = 7 . . . . . matches choice D

Answer:

C p+q=7

Step-by-step explanation:

I did it on plato and it was right

Answer:

-30

Step-by-step explanation:

7m + 2n - 8p/n

Let  m = –4, n = 2, and p = 1.5

7(-4) + 2 ( 2) -8*(1.5)/2

-28 + 4 - 4*1.5

-28+ 4 - 6

-30

Answer:

-30

Step-by-step explanation:

Hey there!

Well given,

m = -4

n = 2

p = 1.5

We need to plug those number into,

7m + 2n - 8p/n

7(-4) + 2(2) - 8(1.5)/(2)

-28 + 4 - 12/2

-28 + 4 - 6

-24 - 6

-30

Hope this helps :)

Without further context I can't say much other than the radius is perpendicular to the tangent. In other words, the radius and tangent line form a 90 degree angle. This is one particular radius and its not just any radius. The radius in question must have the point of tangency as its endpoint.

The radius, AB  is perpendicular to the tangent line,  BC  so their slopes are negative reciprocals of one another. Because I generated a circle at random for this activity, this conclusion likely applies to any tangent line to a circle. In other words, the tangent line to any circle is perpendicular to the radius at their point of intersection.

Answer:

167.55

Step-by-step explanation:

so it varies jointly so

A-area if cylinder

so

[tex]a \: \alpha \: \pi \: r \: ^{2} h[/tex]

so

[tex]a = k\pi \: r^{2}h[/tex]

where k is the constant

so apply the first set of values to get k=2/3

then substitute the k with the second set of values

Answer:

BCD

Step-by-step explanation:

Answer: B,C & D

Step-by-step explanation: