Use the distributive property

Answer:

x=2 or 5/3

Step-by-step explanation:

the explanation is in the picture

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Answer:

x = 5/3

x = -2

Step-by-step explanation:

6x² + 2x - 20 = 0

(6x - 10)(x + 2)

= 6x² + 12x - 10x - 20

= 6x² + 2x - 20

6x - 10 = 0

6x = 10

x = 10/6

x = 5/3

x + 2 = 0

x = -2

Answer:

Step-by-step explanation:

Use the point-slope formula.

y - y_1 = m(x - x_1)  when :     x_1 = -5  and    y_1 =3 and   m= -6/5

the equation :   y - 3 = -6/5(x +5)

Answer:

y=-6/5x-3

Step-by-step explanation:

Answer:

1 out of 6 for green die and 1 out of 6 for red die

Step-by-step explanation:

As we know there are six numbers on both of the dices

so if we toss a die there is a 1 out of 6 outcomes that a 4 comes out for the green die and 1 out of 6 outcomes again for the red die

The probability that a 4 shows on the green die and a 5 shows on the red die is given by P ( C ) = 1/36

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that a 4 shows on the green die and a 5 shows on the red die be represented as P ( C )

Now , the number of outcomes in a roll of die = { 1 , 2 , 3 , 4 , 5 , 6 } = 6 outcomes

And , probability that a 4 shows on the green die P ( A ) = 1/6

The probability that a 5 shows on a red die P ( B ) = 1/6

Now , it is an independent experiment

So , the compound probability is P ( C ) = P ( A ) . P ( B )

And , the probability that a 4 shows on the green die and a 5 shows on the red die P ( C ) = ( 1/6 ) ( 1/6 )

The probability that a 4 shows on the green die and a 5 shows on the red die P ( C ) = 1/36

Hence , the probability is P ( C ) = 1/36

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Answer:

The second, third and fifth are true.

Step-by-step explanation:

1) False, the radius is d÷2=8÷2=4 cm

2) True, C = 2×π×r = π×d = 8π

3) True, C = 8π = 8 × 22/7 = 176÷6 ≈ 25,14

4) False, C = 25,14 ≈ 25

5) True, C = 8π = 8×3,14 = 25,12

Answer: B,C,E

Step-by-step explanation:

Answer:

3:4

Step-by-step explanation:

Before we start to deal with the ratio, we need all lengths in the same units.

The width is 18 inches.

The height is 2 feet.

Let's convert the height to inches. Then we will have both dimensions in the same units, inches.

2 ft * (12 in.)/ft = 24 in.

Now we have:

width = 18 in.

height = 24 in.

ratio of width to height = 18 in. to 24 in. = 18/24 = 3/4 = 3:4

The ratio of the width to the height of the bonsai tree is 3:4 after converting the height into inches and simplifying the ratio.

The question asks to find the ratio of the width of a bonsai tree to its height. Since the width is given in inches and the height in feet, we first need to convert the height into inches to have a consistent unit of measure. There are 12 inches in 1 foot, so the bonsai tree's height is 2 feet times 12 inches/foot, which equals 24 inches.

Now, we can write the ratio of the width to height as 18 inches (width) to 24 inches (height). This simplifies to 3:4 after dividing both terms by the greatest common factor, which is 6.

Answer:

option a all real values of x where x < −1

Step-by-step explanation:

Answer:

Probability of selecting a ball from the first ball if it is a blue ball =  = 0.75

Step-by-step explanation:

Number of blue balls in the first box = 3

Number of blue balls in the second box = 1

Total number of blue balls = 3 + 1

Total number of blue balls = 4

Probability = (Number of possible outcomes)/(Number of total outcomes)

Probability of selecting a ball from the first ball if it is a blue ball = 3/4

Probability of selecting a ball from the first ball if it is a blue ball =  = 0.75

Answer: 8cxs^c= -3 csc (x) +1

Step-by-step explanation:

To solve for c you need to simplify both sides of the equation, then isolating the variable

Answer:

x = - π/2   or x = - π/2 + 2nπ       n = integer

Step-by-step explanation:

4csc²x+3cscx-1=0

(csc x + 1) (4csc x - 1) = 0

csc x = - 1 or csc x = 1/4

1/ sin x = - 1      or 1 / sin x = 1/4

sin x = - 1      or sin x = 4  (x no solution when sin x = 4)

sin x = - 1

x = - π/2   or x = - π/2 + 2nπ       n = integer

Answer:

Step-by-step explanation:

sin(-295°)=-sin (295)=-sin (360-65)=-(-sin 65°)=sin (65°)

Answer:

Step-by-step explanation:

Answer:

The correct option is;

(Choice B) Both the mean and median will increase, but the mean will increase by more than the median.

Step-by-step explanation:

Here, we are expected to show the differences (advantages/properties) of the mean and median

Note that the definition of the mean is the sum of the value of all data points divided by the number of data points

Assuming the four accountants each earn $ 55,000.00

Therefore, initial mean before getting rd of the part-time accountant is

(55+ 55+ 55 + 55 + 10)/5 = 46

Final mean after the part-time accountant is gone =(55+ 55+ 55 + 55 )/4 = 55

Therefore the mean increases

However, the median is given by the middle value when the list of values are arranged in increasing order as

55, 55, 55, 55, 10

Therefore the initial median is 55

Final median after the part-time accountant is gone is

55, 55, 55, 55

Therefore, final = (55 + 55)/2 = 55

That is the median remains the same that is little or increase.

Therefore, since the range of values for the full time accountants salaries weigh less than the difference between the average full time salary and a single part time, both the mean and the median will increase but the mean will increase more than the median

Answer:

b

Step-by-step explanation:

Answer:

θ = 170°

Step-by-step explanation:

Given angle is in radian as,

[tex]\theta^{c} = \dfrac{17 \pi}{18}[/tex]

Here, [tex]\theta^{c}[/tex] symbol represents the angle is in radian.

To convert given angle into degree, multiply the given angle with conversion factor as follows,

[tex]\theta^{\circ} = \theta^{c} \times \left(\frac{180}{\pi }\right)^{\circ}[/tex]

Substituting the values,

[tex]\theta^{\circ} =  \dfrac{17 \pi}{18} \times \left(\dfrac{180}{\pi }\right)[/tex]

Cancelling out the common terms,

[tex]\theta^{\circ} =17\times \left(10\right)[/tex]

Therefore,

[tex]\theta^{\circ} =170^{\circ}[/tex]

Therefore the value of given angle in degree is 170°

To convert radians to degrees, utilize the conversion factor 180/π. In this instance, we have the angle (17π / 18) radians, which simplifies to 170 degrees when converted to the degree format.

The subject topic of this conversation is about converting radians to degrees. Specifically, we're looking at how to convert the radian measurement = 17 / 18 into degrees.

One radian is equivalent to 180/ degrees. As such, to convert radians to degrees, you multiply the radian measurement by this conversion factor (180/).

Have a look at the calculation: = (17 / 18) * (180/).

The cancels out leaving us with / * . This calculation gives us = 170 degrees.

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Answer:

The height of the right circular cone when constructed this way is [tex]\sqrt3[/tex] cm.

The radius of the right circular cone when constructed this way is [tex]\sqrt6[/tex] cm.

The volume of the right circular cone when constructed this way is [tex]6\sqrt3 \pi[/tex] cm³.

Step-by-step explanation:

Given that,

A right triangle whose hypotenuse is 3 cm long is revolved .

Then other two legs of the triangle will be radius and height of the cone.

Assume the height and radius of the cone be h and r respectively.

From Pythagorean Theorem :

h²+r²=3²

⇒ r²= 9 - h²

Then the volume of the cone is

V= π r²h

⇒ V= π(9-h²)h                [ ∵ r²= 9 - h²]

⇒V= π(9h - h³)

Differentiating with respect to h

V'=π(9 - 3h²)

Again differentiating with respect to h

V''= π(-6h)

⇒V''= (-6πh)

To maximum or minimum ,we set V'=0

π(9 - 3h²)=0

⇒3h²=9

⇒h²=3

[tex]\Rightarrow h=\sqrt3[/tex]

Now, [tex]V''|_{h=\sqrt3}=-6\pi (\sqrt3)<0[/tex].

Since at [tex]h=\sqrt3[/tex],V''<0.

The volume of cone is maximum at [tex]h=\sqrt3[/tex] cm when constructed this way.

The height of the right circular cone when constructed this way is [tex]\sqrt3[/tex] cm.

The radius of the right circular cone when constructed this way  [tex]r=\sqrt{9-(\sqrt3)^2[/tex]

   =  [tex]\sqrt{9-3}[/tex]

   [tex]=\sqrt6[/tex] cm.

The volume of the  right circular cone when constructed this way is

=π r²h

[tex]=\pi (\sqrt6)^2\sqrt3[/tex]

[tex]=6\sqrt3 \pi[/tex] cm³

Step-by-step explanation:

I just finished the assignment and got everything right ;)

Hope i helped!

Answer:

c

Step-by-step explanation:

Answer: 6 and 6

Step-by-step explanation:6x6=36

6+6=12

Answer:

247.3 Ft

Step-by-step explanation:

c=3.14(78.75)

c=247.245 *rounded*

The question was about calculating the circumference of a circle using its diameter. The diameter was given, and the formula for circumference 'C = πd' was used, where 'd' was 78.75 feet and 'π' was approximated at 3.14. The circumference comes out to be approximately 247.35 feet when rounded to the nearest tenth.

The subject in this question is the measurement of the circumference of a cookie given its diameter, a basic concept in geometry in the field of Mathematics. Circumference which is the distance around a circle can be calculated using the formula 'C = πd', where 'C' is the circumference, 'd' is the diameter and 'π' is a constant approximately equal to 3.14.

In this case, the diameter 'd' of the cookie is 78.75 feet. So, by substituting the values into the formula, we get: C = 3.14 * 78.75.

After performing this calculation, you'll find that the approximate circumference of the cookie is 247.35 feet when rounded to the nearest tenth.

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Answer:

4/5

Step-by-step explanation:

cos B = 3/5

cos Ф = adjacent/hypothesis

hypothesis ² = adjacent² + opposite²

5²= 3²+ o²

25 = 9+o²

25-9=o²

16 = o²

√16 = o = 4

Sin B = opposite/hypothesis = 4/5

Answer:

55/4

Step-by-step explanation:

13 3/4

(13×4 + 3)/4

55/4

Answer:

hope this helps!

Answer:

We can use the sample about 42 days.

Step-by-step explanation:

Decay Equation:

[tex]\frac{dN}{dt}\propto -N[/tex]

[tex]\Rightarrow \frac{dN}{dt} =-\lambda N[/tex]

[tex]\Rightarrow \frac{dN}{N} =-\lambda dt[/tex]

Integrating both sides

[tex]\int \frac{dN}{N} =\int\lambda dt[/tex]

[tex]\Rightarrow ln|N|=-\lambda t+c[/tex]

When t=0, N=[tex]N_0[/tex] = initial amount

[tex]\Rightarrow ln|N_0|=-\lambda .0+c[/tex]

[tex]\Rightarrow c= ln|N_0|[/tex]

[tex]\therefore ln|N|=-\lambda t+ln|N_0|[/tex]

[tex]\Rightarrow ln|N|-ln|N_0|=-\lambda t[/tex]

[tex]\Rightarrow ln|\frac{N}{N_0}|=-\lambda t[/tex].......(1)

                            [tex]\frac{N}{N_0}=e^{-\lambda t}[/tex].........(2)

Logarithm:

130 days is the half-life of the given radioactive element.

For half life,

[tex]N=\frac12 N_0[/tex],  [tex]t=t_\frac12=130[/tex] days.

we plug all values in equation (1)

[tex]ln|\frac{\frac12N_0}{N_0}|=-\lambda \times 130[/tex]

[tex]\rightarrow ln|\frac{\frac12}{1}|=-\lambda \times 130[/tex]

[tex]\rightarrow ln|1|-ln|2|-ln|1|=-\lambda \times 130[/tex]

[tex]\rightarrow -ln|2|=-\lambda \times 130[/tex]

[tex]\rightarrow \lambda= \frac{-ln|2|}{-130}[/tex]

[tex]\rightarrow \lambda= \frac{ln|2|}{130}[/tex]

We need to find the time when the sample remains 80% of its original.

[tex]N=\frac{80}{100}N_0[/tex]

[tex]\therefore ln|{\frac{\frac {80}{100}N_0}{N_0}|=-\frac{ln2}{130}t[/tex]

[tex]\Rightarrow ln|{{\frac {80}{100}|=-\frac{ln2}{130}t[/tex]

[tex]\Rightarrow ln|{{ {80}|-ln|{100}|=-\frac{ln2}{130}t[/tex]

[tex]\Rightarrow t=\frac{ln|80|-ln|100|}{-\frac{ln|2|}{130}}[/tex]

[tex]\Rightarrow t=\frac{(ln|80|-ln|100|)\times 130}{-{ln|2|}}[/tex]

[tex]\Rightarrow t\approx 42[/tex]

We can use the sample about 42 days.

Final answer:

The radioactive sample can be used for approximately 390 days.

Explanation:

The half-life of a radioactive element is the time it takes for half of the radioactive nuclei to decay. In this case, the half-life is 130 days. The sample is considered no longer useful when 80% of the nuclei have decayed. To determine how many days the sample can be used, we need to find the number of half-lives it takes for 80% of the nuclei to decay.

80% is the same as 0.8, which means 20% (or 0.2) of the nuclei remain. Each half-life reduces the amount of nuclei by half, so we can set up an equation:

0.2 = (1/2)^n

where n is the number of half-lives.

To solve for n, we can take the logarithm of both sides:

n = log_base(1/2)(0.2)

Using a calculator, we find n ≈ 2.737.

Since we can't have a fraction of a half-life, we round up to the nearest whole number, which gives us n = 3.

Now, we can find the number of days by multiplying the half-life by the number of half-lives:

Number of days = 130 days * 3 = 390 days.

Therefore, the sample can be used for approximately 390 days.

Answer:

it is a 7 step process explained in explanation section

Step-by-step explanation:

Step one

fill 7 litre bucket then pour it in 4 liter bucket

output: 7 litre bucket has 3 litres and 4 litres bucket has 4 liter in it

Step two

drain four liter bucket and pour 3 liter from 7 litre bucket in it

output: 7 litre bucket has 0 litres and 4 litres bucket has 3 liter in it

step 3

fill 7 litre bucket and transfer water from it in 4 liter bucket which has already 3 liter in it

output: 7 litre bucket has 6 litres and 4 litres bucket has 4 liter in it

step 4

drain four liter bucket and pour 4 liter from 7 litre bucket which has 6 litre in it

output: 7 litre bucket has 2 litres and 4 litres bucket has 4 liter in it

step 5

drain 4 litre bucket and pour 2 litre from 7 litre bucket

output: 7 litre bucket has 0 litres and 4 litres bucket has 2 liter in it.

step 6

fill 7 liter bucket fully

output: 7 litre bucket has 7 litres and 4 litres bucket has 2 liter in it.

step 7

pour water from 7 liter bucket in 4 litre bucket which has already 2 litre in it

output: 7 litre bucket has 5 litres and 4 litres bucket has 4 liter in it.

Answer:

<1 and <2 are alternate exterior angles

<3 and <4 are consecutive interior angles

Step-by-step explanation:

<1 and <2 are alternate exterior angles

Alternate exterior angles are on opposite outside of the lines

<3 and <4 are consecutive interior angles

Consecutive interior angles are on the same side on the inside of the line

Answer: I think it's 50.2 but I might be wrong

Answer: 10.3 pounds of CO2 is produced

Step-by-step explanation:

Assuming there are 30 days in a month, if the microwave is run for 10 minutes per day, then the number of minutes for which the microwave is run in a month is

30 × 10 = 300 minutes

We would convert from minutes to hours

60 minutes = 1 hour

Therefore,

300 minutes = 300/60 = 5 hours

Also,

1000 watts = 1 kW

Therefore,

1500 watts = 1500/100 = 1.5kw

Therefore, the number of kWh is

1.5 × 5 = 7.5 kWh

If 1.37 pounds CO2 per kWh, then

If 1kWh = 1.37 pounds CO2, then

7.5 kWh = 7.5 × 1.37 = 10.3 pounds rounded to the nearest tenth

Final answer:

A 1500-watt microwave running for 10 minutes per day for one month emits approximately 10.3 pounds of CO2 when rounding to the tenths place.

Explanation:

The question is how much carbon dioxide is produced from running a 1500-watt microwave for 10 minutes a day for a month. To solve this, we first need to calculate the total energy used by the microwave in kWh. Since the microwave uses 1500 watts and is used for 10 minutes daily, we convert this to hours:

10 minutes = 10/60 hours = 1/6 hour

Power in kWh = Power in watts / 1000

Energy used per day in kWh = (1500 watts / 1000) x (1/6 hour) = 0.25 kWh

Next, we need to calculate the monthly energy use:

Energy used per month in kWh = 0.25 kWh/day x 30 days = 7.5 kWh

Using the given conversion factor of 1.37 pounds of CO2 per kWh, the total CO2 emissions can be calculated:

CO2 emissions = 7.5 kWh x 1.37 pounds CO2/kWh = 10.275 pounds of CO2

Finally, rounding to the tenths place:

CO2 emissions for the month = 10.3 pounds (rounded)

Answer: the third answer. Explanation below.

Step-by-step explanation:

The first passage shows Antigone as a rebel because she chooses to defy the State. The second passage shows Boadicea as a warrior because she "herself led the soldiers, encouraging them with her brave words."

Antigone and Boadicea are presented with different archetypal roles across the passages; Antigone as a warrior, tragic heroine, rebel, and villain; and Boadicea as a tragic heroine, sage, warrior, and sage again.

The archetypes presented in these passages are different in the roles and characteristics assigned to Antigone and Boadicea. In the first set of passages, Antigone is depicted as a warrior, then as a tragic heroine, next as a rebel, and lastly as a villain. Conversely, Boadicea is presented as a tragic heroine, followed by a sage, then as a warrior, and finally as a sage once again. These variations represent unique depictions of these mythical figures, giving us different lenses to interpret their actions and significance within their respective narratives.

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Answer:

22?

Step-by-step explanation:

Just take 40 and subtract the 7 to get 33 and then 2 to get 31 and 9 to get 22.

Answer:

22 more rolls

Step-by-step explanation:

if she needs to sell 40 and she has sold 9+7+2=18 than you subtract 18 from 40 getting 22 more rolls

Answer:

a) The antibiotic is made with a greater initial amount of active ingredient

b) The two medications will have the same amount of active ingredients in the blood stream at exactly 8 hours after first taking the medication.

Step-by-step explanation

Active ingredient of Nasal spray left in the bloodstream is modelled as

n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))

Active ingredient of Antibiotic left in the bloodstream is modelled as

a(t) = 9/(t+3)

with t in hours.

a) At the instance of usage, the active ingredient for both drugs are at their initial concentration as they appear in the drugs.

So, we find the amount of active ingredient for each drug in the bloodstream at t=0 and compare.

For nasal spray,

n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))

At t = 0

n(0) = (1/5) + (18/15) = 1.4

For antibiotics,

a(t) = 9/(t+3)

At t=0

a(0) = (9/3) = 3

3 > 1.4

Hence, the antibiotic is made with a greater initial amount of active ingredient.

b) when both medications will have the same amount of active ingredients in the bloodstream, n(t) = a(t)

n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))

a(t) = 9/(t+3)

Note that (t² + 8t + 15) = (t + 3)(t + 5)

When n(t) = a(t)

((t + 1)/(t + 5)) + (18/(t² + 8t + 15)) = 9/(t+3)

Multiplying through by (t² + 8t + 15) or more properly written as (t + 3)(t + 5)

(t+1)(t+3) + 18 = 9(t+5)

t² + 4t + 3 + 18 = 9t + 45

t² - 5t - 24 = 0

Solving the quadratic equation

t = 8 or t = -3

Time can't be negative, hence, t = 8 hours.

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