A bowl in the shape of a hemispere is filled with water to a depth h=3 inches. The radius of the bowl is R inches. Express the radius of the bowl R as a function of the angle theta.

Answer:

The value of x is 3 cm.

Step-by-step explanation:

Given,

Total surface area of cuboid = 112 cm^2

Height of cuboid = 10 cm

Breadth of cuboid = 2 cm

Length of cuboid = x cm

Solution,

Formula for total surface of cuboid = [tex]2\times(length\times breadth +breadth\times height+height\times length)[/tex]

∴[tex]112=2(x\times2+2\times10+10\times x)\\112=2(2x+20+10x)\\112=2(12x+20)\\12x+20=\frac{112}{2}\\12x+20=56\\12x=56-20\\12x=36\\x=\frac{36}{12}=3[/tex]

Thus the length of cuboid is 3 cm.

Answer:

the answer is (-4,2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is (-4,2)

Answer: 50 tissue boxes

Step-by-step explanation:

The students want to make care packages for unhoused people for winter season.

They would like to put 5 boxes of tissues into each care package.

If they have 450 boxes pack, to determine how many tissue boxes that they need to complete the boxes, we will divide the total number of boxes pack that they have by the number of tissues that will go into one pack. It becomes

450/9 = 50

Answer:

a)550

b)910

c)730

Step-by-step explanation:

The given model is

[tex]v(t) = 10t^2 ft/s[/tex]

Use the interval [0,6], with n=6 rectangles

Then, the interval width is

[tex]\Delta t = \frac{b-a}{n}[/tex]

[tex]\Delta t = \frac{6-0}{6}[/tex]= 1

so, the sub intervals are

[0,1], [1,2], [2,3], [3,4],[4,5],[5,6]

Now evaluating the function values

[tex]f(t_0)= f(0) = 0[/tex]

[tex]f(t_1)= f(1) = 10[/tex]

[tex]f(t_2)= f(2) = 40[/tex]

[tex]f(t_3)= f(3) = 90[/tex]

[tex]f(t_4)= f(4) = 160[/tex]

[tex]f(t_5)= f(5) = 250[/tex]

[tex]f(t_6)= f(6) = 360[/tex]

a) left hand sum is

L_6 = [tex]\Delta t [f(t_0)+ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)][/tex]

=[tex]1 [0+ 10+40+90+160+250][/tex]

= 550

b) right hand sum

R_6 = [tex]\Delta t [ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)+f(t_6)][/tex]

= [tex]1 [10+40+90+160+250+360][/tex]

= 910

c) average of two sums is

[tex]\frac{L_5+R_5}{2}[/tex]

= [tex]\frac{550+910}{2}[/tex]

=730

Kyle is correct in saying that 3/5 is equal to 60% because 3/5 is equivalent to 60/100.

Kyle says that 3/5 is equal to 60%. This statement can be explained by saying that 3/5 is equivalent to 60/100. To convert a fraction to a percentage, you multiply the top number (numerator) by 100 and then divide by the bottom number (denominator). In this case, multiplying 3 by 100 gives you 300, and when you divide 300 by 5, it equals 60. Hence, 3/5 is indeed equivalent to 60%, which makes Kyle's statement correct.

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Answer:

From three condition the it is proved that Δ ABC and  Δ DEF are similar Triangles .  

Step-by-step explanation:

Given as :

To Proof : Triangle Δ ABC and Triangle Δ DEF are similar

There are three methods for two Triangles to be similar

A ) SAS  i.e side angle side

B ) AA i.e angle angle

C ) SSS i.e side side side

Now,

A) If two triangle have a pair of equal corresponding angles and sides are proportional then triangle are similar

So, If in  Δ ABC and  Δ DEF

∠ B = ∠ E

and , [tex]\dfrac{AB}{DE}[/tex] =  [tex]\dfrac{BC}{EF}[/tex]

Then Δ ABC  [tex]\sim[/tex] Δ DEF

I.e SAS   similarity

B ) If two triangles have equal corresponding angles , then triangles are similar .

So, If in  Δ ABC and  Δ DEF

∠ B = ∠ E   and   ∠ A = ∠ D

Then Δ ABC  [tex]\sim[/tex] Δ DEF

I.e AA similarity

C ) If two triangles have three pairs of corresponding sides proportional then triangles are similar .

So, If in  Δ ABC and  Δ DEF

[tex]\dfrac{AB}{DE}[/tex] =  [tex]\dfrac{BC}{EF}[/tex] = [tex]\dfrac{AC}{DF}[/tex]

Then Δ ABC  [tex]\sim[/tex] Δ DEF

I.e SSS similarity

Hence From three condition the it is proved that Δ ABC and  Δ DEF are similar Triangles .   answer

Answer: Neither

Step-by-step explanation:

Got it wrong bc of the person it top of me but yea

Answer:

A. pay for each individuals tipping fee at landfills with taxes

Step-by-step explanation:

Because it is a recyclic methodology .It is a service provide to household for dispose of the waste and recycled it. So as a  municipality wanting to waste management so Curbside recycling can be used.

Municipal should attract business that utilize source reduction in their manufacturing.

They should offer much to its resident.

They maintain a hazardous waste collection site for its residents as well.

Answer:

a)[tex]P(X\geq 11) = 0.198[/tex]

b)[tex]P(X\leq 2) = 0.000565[/tex]

c) Mean = 8.8

Step-by-step explanation:

1) Previous concepts

Binomial Distribution is a "discrete probability distribution which is used to calculate the probabilities for the independent trials and for each trial there is only two outcomes success or failure and probability for each success remains constant throughout each trial".

The Binomial distribution is a type of Bernoulli experiment with following properties:

a)There are two possible outcomes; success or failure.

b) Outcomes are independent on preceding result of a trial.

c) The probability of success remains constant throughout the experiment.

d)The number of successes are fixed.

The probability mass function for the Binomial distribution is given by:

[tex]P(X=a)=(nCa)(p)^x (1-p)^{n-x}[/tex]

Where [tex]p[/tex] is the probability of success, n the number of trials and x the number of successes that we want on the n trials.

[tex]X[/tex] represent the number federal inmates that are serving time for drug dealing

[tex]p=0.55[/tex] represent the proportion of federal inmates that are serving time for drug dealing

[tex]n=16[/tex] random sample selected

2) Part a

The random variable X follows this distribution [tex]X \sim Binom(n,p)[/tex]

On this case we want the following probability, and since says greater or equal than 11 we can express like this:

[tex]P(X \geq 11)=P(X=11)+P(x=12)+P(x=13)+P(x=14)+P(x=15)+P(x=16)[/tex]

[tex]P(X=11)=(16C11)(0.55)^{11} (1-0.55)^{5} =0.112[/tex]

[tex]P(X=12)=(16C12)(0.55)^{12} (1-0.55)^{4} =0.0572[/tex]

[tex]P(X=13)=(16C13)(0.55)^{13} (1-0.55)^{3} =0.0215[/tex]

[tex]P(X=14)=(16C14)(0.55)^{14} (1-0.55)^{2} =0.00563[/tex]

[tex]P(X=15)=(16C15)(0.55)^{15} (1-0.55)^{1} =0.000918[/tex]

[tex]P(X=16)=(16C16)(0.55)^{16} (1-0.55)^{0} =0.00007011[/tex]

[tex]P(X \geq 11)=0.112+0.0572+0.0215+0.00563+0.000918+0.00007011=0.198[/tex]

3) Part b

[tex]P(X \leq 2)=P(X=0)+P(x=1)+P(x=2)[/tex]

[tex]P(X=0)=(16C0)(0.55)^{0} (1-0.55)^{16} =0.00000283[/tex]

[tex]P(X=1)=(16C1)(0.55)^{1} (1-0.55)^{15} =0.0000552[/tex]

[tex]P(X=2)=(16C2)(0.55)^{2} (1-0.55)^{14} =0.000507[/tex]

[tex]P(X \leq 2)=0.00000283+0.0000552+0.000507=0.000565[/tex]

4) Part c

The expected value for the binomial distribution is given by the following formula:

[tex] E(X)=np=16*0.55=8.8[/tex]

So then the average number of federal inmates that are serving time for drug dealing on a sample of 16 is approximately 9.

Answer:

option C) (7, -2)

Step-by-step explanation:

By the graph, the initial coordinates of point A are ( -5, -4)

first reflection along the line x=1, only the x coordinate will change.

the new x coordinate is = x = 7

thus the point becomes (7, -4)

similarly, reflection along y= -3, only the y coordinate will change.

the new y coordinate is = y = -2

thus the final coordinates are (7, -2)

Answer:

a) There are no evidence that Calvin is correct.

b) There are evidence that Calvin is correct.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 1 ounce

Sample size, n = 23

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 1\text{ ounce}\\H_A: \mu < 1\text{ ounce}[/tex]

P-value =  0.086

a) Significance level = 5% = 0.05

Since

P-value > Significance level

We fail to reject the null hypothesis and accept it. Thus, the chips bag contain one ounce of product. Thus, there are no evidence that Calvin is correct.

b) Significance level = 10% = 0.10

Since

P-value < Significance level

We reject the null hypothesis and accept the alternate hypothesis. Thus, the chips bag contain less than one ounce of product. Thus, there are evidence that Calvin is correct.

Answer:

1: C(n) = 2.50 + 16n

2: $66.50

Step-by-step explanation:

Part 1

Each ticket costs $16 per person. If tickets for n persons were purchased, the total cost would be 16n.

There is also a one-time service fee of $2.50 that must be paid. Thus, for n tickets the total cost is

C(n) = 2.50 + 16n

Part 2

For n = 4, the expression evaluates to

C(4) = 2.50 + 16 (4) = $66.50

Answer:

easey

Step-by-step explanation:

Answer:

The answer to your question is x = 4

Step-by-step explanation:

                                   2x² - bx - 20 = 0

One root is -2.5

Process

Get the value of the equation when x = -2.5

                                   2(-2.5)² - b(-2.5) - 20 = 0

                                   2(6.25) + 2.5b  - 20 = 0

                                   12.5 + 2.5b - 20 = 0

                                   2.5b = 20 - 12.5

                                   2.5b = 7.5

                                   b = 7.5 / 2.5

                                  b = 3

Then

                                  2x² - 3x - 20 = 0

Factor the polynomial

                                  2 x -20 = -40

                                  2x² -8x + 5x - 20 = 0

                                  2x(x - 4) + 5(x - 4) = 0

                                  (x - 4)(2x + 5) = 0

                                  x₁ - 4 = 0               2x₂ + 5 = 0

                                 x₁ = 4                     x₂ = -5/2

                                                               x₂ = -2.5

Answer:

The "other" or "second" root is 4.

Step-by-step explanation:

We are told that -2.5 is a root of the equation.  The coefficient b of the x term is unknown, and must be determined.  Because -2.5 is a root, synthetic division with -2.5 as divisor must return a remainder of zero.

Setting up synthetic division, we arrive at:

-2.5    /    2    -b    -20

                     -5     +12.5 + 2.5b

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

                2   -5-b    -7.5 + 2.5b

The remainer, -7.5 + 2.5b, must be zero (0).  Thus, 2.5b = 7.5, and b = 3.

Then the other factor has the coefficients {2, -5-b}, and because b = 3, this comes out to coefficients {2, -8}.

The other factor is 2x - 8, which, if set equal to 0, yields x = 4.  This is the "other root."

Answer:

b) 0.2464

c) 0.0580

d) 0.2952

Step-by-step explanation:

Probability of those that purchased regular gas = 88% = 0.88

2% purchased mid grade gas

10% purchased premium gad

Given that a driver bought regular gas, 28% paid with credit card

Given that a driver bought mid grade gas, 34% paid with credit card

Given that a driver bought premium gas, 42% paid with credit card

Let R represent drivers that bought regular gas

Let M represent drivers that bought mid grade gas

Let P represent drivers that bought premium gas

Let C represent credit card payment

Let NC represent non-credit card payment

Pr(R) = 88% = 0.88

Pr(M) = 2% = 0.02

Pr(P) = 10% = 0.10

Pr(C|R) = 28%= 0.28

Pr(C|M) = 34%= 0.34

Pr(C|P) = 42%= 0.42

Pr(NC|R) = 1 - 0.28= 0.72

Pr(NC|M) = 1 - 0.34 = 0.66

Pr(NC|P) = 1 - 0.42 = 0.58

Using multiplication rule

Pr(AnB) = Pr(A) * Pr(B|A) = Pr(B) * Pr(A|B)

Using conditional probability,

P(B|A) = Pr(AnB) / Pr(A)

Pr(CnR) = Pr(R) * Pr(C|R)

= 0.88*0.28

= 0.2464

Pr(CnM) = Pr(M) * Pr(C|M)

= 0.02*0.34

= 0.0068

Pr(CnP) = Pr(P) * Pr(C|P)

= 0.10*0.42

= 0.0420

b) the probability that an automobile driver filled with regular gasoline AND paid with a credit card =

Pr(CnR)

= 0.2464

c) the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card = Pr(P n NC) = Pr(NC|P) * Pr(P)

= 0.58 * 0.10

= 0.0580

d) The probability of those that paid with credit card is given as

Pr(CnR) + Pr(CnM) + Pr(CnP)

= 0.2464 + 0.0068 + 0.042

= 0.2952

This problem involves calculating different probabilities pertaining to customers' selection of gas type and payment method. These probabilities are found by multiplying corresponding probabilities together for intersecting events, and adding different possibilities together for compound events.

The subject of this question is probability, used in Mathematics. Let's solve each part step-by-step:

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∠A = ∠B

6x + 12 = 3x + 63

6x - 3x = 63 - 12

3x = 51

x = 51 ÷ 3

x = 17

6(17) + 12

102 + 12

∠A = 114°

Answer:

114

Step-by-step explanation:

Answer

The answer

it is y ≥ -2|x + 1| + 3

since the -2 or A controls the negative or positive of an absolute value graph its negative so it's down.

| x+1| if it's like that then you must reverse the sign so it is -1

and for the +3 that controls your vertical line meaning up or down. & in this case it went up so its +3

Answer:

Step-by-step explanation:

Lines p and line r are parallel. This actually means that they will extend continuously without meeting at a point.

Let us assign an alphabet to an angle to make it easy for reference. The diagram is shown in the attached photo

From the photo,

Angle T is equal to 34 degrees. This is because angle T and 34 degrees are corresponding angles.

Angle G = angle T. This is because angle T is vertically opposite to angle G. Therefore

G = 34 degrees

Answer:

Step-by-step explanation:

If you plot the vertex and the point that it goes through, the point it goes through is above the vertex, so the vertex is a positive one that opens upwards.  The general vertex form of a parabola of this type is

[tex]y=a(x-h)^2+k[/tex]

We have the x, y, h, and k.  We will plug all those in and solve for a.  That looks like this:

[tex]-5=a(6-4)^2-13[/tex] which simplifies to

-5 = 4a - 13 and

8 = 4a so

a = 2

That means that the paraobola in vertex form is

[tex]y=2(x-4)^2-13[/tex]

Answer:

a) 95% confidence interval estimate of the true weight is (3.026, 3.274)

b) 99% confidence interval estimate of the true weight is (2.944, 3.356)

Step-by-step explanation:

Confidence Interval can be calculated using M±ME where

And margin of error (ME) can be calculated using the formula

ME=[tex]\frac{t*s}{\sqrt{N} }[/tex] where

Using the numbers 95% confidence interval estimate of the true weight is:

3.150±[tex]\frac{2.776*0.1}{\sqrt{5} }[/tex]≈3.150±0.124

And 99% confidence interval estimate of the true weight is:

3.150±[tex]\frac{4.604*0.1}{\sqrt{5} }[/tex]≈3.150±0.206

Answer:

r=68.64 m

Step-by-step explanation:

Given that

Weight ,wt= 14100 N

mass m = 1410 kg             ( g = 10 m/s²)

Friction force = Weight

Fr= 14100 N

v= 26.2 m/s

Lets take radius of the curve =  r

To balance the truck ,radial force should be equal to the friction force

[tex]\dfrac{mv^2}{r}=Fr[/tex]

mv² = Fr x r

1410 x 26.2² = 14100 x r

r=68.64 m

Therefore radius of the curve will be 68.64 m

Answer - r=68.64 m

The minimum safe curve radius that the truck could negotiate at 26.2 m/s in good driving conditions is approximately 78.94 meters. This relies on the principles of centripetal force and friction, and requires converting the weight of the truck into its mass. The resulting radius ensures that the centripetal force, provided by the friction between the tires and the road, is enough to keep the truck on its path.

The subject of this question is related to Centripetal Force and Friction in physics. Centripetal force is the net force on an object moving in a circular path and it points towards the center of the circular path. This force keeps the object moving along this path and is provided by the frictional force between the truck's tires and the road.

In this case, if friction equates to the weight of the truck (14100 N), it will be the centripetal force. The equation for centripetal force is given by:

where Fc is the centripetal force, m is the mass of the object, v is the velocity of the object and r is the radius of the circular path. We can arrange this formula to calculate the safe curve radius(r) the truck can negotiate:

However, in this case, the mass of the truck is given as a force (Weight = 14100 N). So first we need to convert this weight into mass. We can do this by using the formula: Weight = mass (m) × acceleration due to gravity (g). Here, g = 9.8 m/s²:

Now we can substitute m = 1438.78 kg, v = 26.2 m/s and Fc = 14100 N into our radius equation to find the minimum safe curve radius for the truck:

So, the minimum safe curve radius that the truck could negotiate at 26.2 m/s in good driving conditions is approximately 78.94 meters.

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Answer:

  y(x) = e^(-2x +3)

Step-by-step explanation:

The graphed line has a "y-intercept" of 3 and a slope of -2, so its equation is ...

  ln(y) = -2x +3

Taking antilogs, we get ...

  y(x) = e^(-2x +3)

Answer:

Step-by-step explanation:

We have four equations here.  Let's actually solve them, using factoring if possible and some other method if factoring is not possible.

A)  x^2 + 5x + 4 factors into (x + 1)(x + 4), but x^2 + 5x - 4 does not.

B)  x^2 + 6x + 9 factors into (x + 3)^2.

C) x^2 + 3x - 4 factors into (x + 4)(x - 1).

D) x^2 - x - 6 factors into (x - 3)(x + 2)

x^2 + 5x - 4 = 0 can be solved, but not by factoring.

Answer:

The worth of the automobile after an year with 15% depreciation  is $22,100.

Step-by-step explanation:

The current cost of the automobile car = $26,000

The percentage of depreciation  = 15%

Now, calculating the depreciated amount:

15% of $26,000  = [tex]\frac{15}{100}  \times 26,000 = 3,900[/tex]

So, the depreciated amount of the car in the next year = $3,900.

Now, the worth of the car after an year

= CURRENT WORTH - THE DEPRECIATED AMOUNT

= $26,000 - $3,900.

= $22,100

Hence, the worth of the automobile after an year  is $22,100.

Final answer:

The stone is approximately 583 feet high 4 seconds later.

Explanation:

To find the height of the stone 4 seconds later, we can use the equation of motion for an object in free fall:

h = h0 + v0t + (1/2)gt^2

Where:

h = height at time t

h0 = initial height

v0 = initial velocity

g = acceleration due to gravity

t = time

Substituting the given values:

h = 775 + 16(4) + (1/2)(-32)(4)^2

h = 775 + 64 - 256

h = 583 feet

Therefore, the stone is approximately 583 feet high 4 seconds later.

Answer: No

Step-by-step explanation:

X does not represent the cost of fabric. X represents the number of yards of fabric used.

15x + 250

Could be read as ($15 × # of yards) + $250

So she has to pay $15 per yard of fabric plus an additional $250 base amount for having them made and hung in the first place.

She could use an additional variable to represent the cost of fabric.

Example: Y

Y= 15x

Cost of fabric is equal to $15 per yard × # of yards.

The equation for the total cost depending on the number of students in Emma's Extreme Sports classes is C = 50 + 20x.

C = 50 + 20x

Where C represents the total cost, 50 is the fee per class, and 20 is the cost per student.

Answer:

she will need to dance for 26 hours

Step-by-step explanation:

500=15(26)+110

Answer:

26 hours

Step-by-step explanation:

One group will donate $15 per hour, while the other is offering a flat sum of $110. She wants $500, so we can set up the equation

15x + 110 = 500 (with x being the number of hours Traci dances). You subtract 110 from 500 to isolate the variable with its coefficient, resulting in

15x = 390 . Then, dividing 390 by 15 to get x by itself, the answer of 26 hours is found.

Answer:

B) x + y = 3

Step-by-step explanation:

This is a specific way to give details without a detailed written explanation of the function. There will be NO exponents when trying to find out information about something:

[tex]\displaystyle x + y = 3 → y = -x + 3[/tex]

I am joyous to assist you anytime.

Answer:

  C)  28√17

Step-by-step explanation:

The perimeter is twice the sum of the two given side lengths, so is ...

  P = 2(L +W) = 2(2√153 +4√68)

  = 2(6√17 +8√17) = 2(14√17)

  P = 28√17 . . . . . matches choice C

_____

This is about simplifying radicals. The applicable rules are ...

  √(ab) = (√a)(√b)

  √(a²) = |a|

__

  153 = 9×17, so √153 = (√9)(√17) = 3√17

  68 = 4×17, so √68 = (√4)(√17) = 2√17

_____

Comment on the problem presentation

It would help if there were actually radicals in the radical expressions. We had to guess based on the spacing and the answer choices.

In any event, this problem can be worked with a calculator. Find the perimeter (≈115.45) and see which answer matches that. (That's what I did in order to verify my understanding of what the radical expressions were.)