The volume of a right cone is 1824 � π units 3 3 . If its circumference measures 24 � π units, find its height.

The solution to the equation 3x² + x - 12 = 1 is x = -1/4; and x = 4

An equation is an expression that shows the relationship between numbers and variables using mathematical operators.

The polynomial is classified based on degree as linear, quadratic, cubic and so on.

Given the equation:

3x² + x - 12 = 1

subtracting 1 from both sides:

3x² - 11x - 4 = 0

3x² - 12x + x - 4 = 0

3x(x - 4) + 1(x - 4) = 0

(3x + 1)(x - 4) = 0

3x + 1 = 0; and x - 4 = 0

x = -1/4; and x = 4

The solution to the equation is x = -1/4; and x = 4

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[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=20\\ \theta =65 \end{cases}\implies a=\cfrac{(65)\pi (20)^2}{360} \\\\\\ A=\cfrac{650\pi }{9}\implies A\approx 226.89[/tex]

The single transformation that maps shape triangle a onto shape b is  [tex]\:\begin{pmatrix}-5\\ -5\end{pmatrix}[/tex]

From the figure, we have the following highlights

Both triangles are congruent

Triangle B is 5 units down from triangle A

Triangle B is 5 units left of triangle A

The above highlights mean that the triangle A must be translated 5 units left and 5 units down to get triangle B.

This is represented as (x,y) -> (x - 5, y - 5)

By vector representation, we have: [tex]\:\begin{pmatrix}-5\\ -5\end{pmatrix}[/tex]

Hence, the single transformation that maps shape a onto shape b is  [tex]\:\begin{pmatrix}-5\\ -5\end{pmatrix}[/tex]

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The graph of the inequality y ≥ x² is shown in the image attached below.

In order to to graph the solution to the given linear equation on a coordinate plane, we would use an online graphing calculator to plot the given quadratic function and then take note of the x-intercept, zeros, or roots.

In this scenario and exercise, we would use an online graphing calculator to plot the given quadratic function as shown in the graph attached below;

y ≥ x²

Based on the graph (see attachment), we can logically deduce that the possible solution to the given quadratic function is given by the ordered pair (0, 0).

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Answer:

14.4

Step-by-step explanation:

1) 16^2-7^2=207

2) square root of 207 is 14.4 (to 1 decimal place).

The main answer to the question "How many pounds of laundry detergent does Andrew make?" is 4.125 pounds.

he total amount of borax used to make 3 batches is:

8 ounces/batch x 3 batches = 24 ounces

The total amount of washing soda used to make 3 batches is:

10 ounces/batch x 3 batches = 30 ounces

The total amount of soap used to make 3 batches is:

6 ounces/batch x 3 batches = 18 ounces

To find the total weight of the laundry detergent, we need to add up the weight of each ingredient. Since 1 pound is equal to 16 ounces, we can convert the total weight from ounces to pounds by dividing by 16.

Total weight of laundry detergent = (24 + 30 + 18) ounces / 16 = 4.125 pounds

Therefore, Andrew makes 4.125 pounds of laundry detergent.

Answer: Donald and 2nd one A

Step-by-step explanation:

Hence ,the percentage of students that take exactly one course is 71.43% and the value of N(P ∩ M) and  N(P ∩ E) is 36 and 30 respectively.

Principle of Inclusion and Exclusion is an approach which derives the method of finding the number of elements in the union of two finite sets. This is used for solving combinations and probability problems when it is necessary to find a counting method, which makes sure that an object is not counted twice.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, although the abbreviations pct., pct, and sometimes pc are also used. A percentage is a dimensionless number; it has no unit of measurement.

Let  P, M, and E be the  sets of students  taking  Physics,  Mathematics,  and  English,  respectively.  Then:

|P| = 90, |M| = 72, |E| = 162

Let  X  be  the  set of students  taking all three  courses, Y be  the set of students taking  exactly  two courses,  and Z  be  the  set of  students  taking exactly one  course. Then:

|X| = ?, |Y| = ?, |Z| = ?

We know that , the  Principle of Inclusion and Exclusion (PIE) to  determine  the values  of |X|, |Y|, and |Z|. that means,

|P ∪ M ∪ E| = |P| + |M| + |E| - |P ∩ M| - |P ∩ E| - |M ∩ E| + |P ∩ M ∩ E|

We know that |P ∪ M ∪ E| = 252, so we can substitute the values we have to get:

252 = 90 + 72 + 162 - |P ∩ M| - |P ∩ E| - |M ∩ E| + |X|

To compute |P ∩ E| and |M ∩ E|,  according to given problem,

[tex]\frac{1}{3}[/tex] of  those  that take  physics take English, so |P ∩ E| =[tex]\frac{1}{3}[/tex] * |P| = 30

[tex]\frac{1}{4}[/tex] of  those  that take mathematics take English, so |M ∩ E| =[tex]\frac{1}{4}[/tex]* |M| = 18

[tex]\frac{1}{2}[/tex] of  those that take mathematics  take physics, so |P ∩ M| = [tex]\frac{1}{2}[/tex] * |M| = 36

Substituting these values, we get:

252 = 90 + 72 + 162 - 36 - 30 - 18 + |X|

|X| = 252-324+84=-72+84=12

So, there are 12  students who take all three courses.

now, To find  |Y|,  by using this formula:

|Y| = |(P ∩ M) ∪ (P ∩ E) ∪ (M ∩ E)|

We  already  know  in question |P ∩ E|  and  |M ∩ E|,  so we just need to find |P ∩ M ∩ E|.   from given problem

we know that:

|P ∩ M ∩ E| =[tex]\frac {(P ∩ E)}{P}[/tex]* |M| = ([tex]\frac{30}{90}[/tex]) * 72 = 24

Substituting these values, we get:

|Y| = |(P ∩ M) ∪ (P ∩ E) ∪ (M ∩ E)| = |P ∩ M| + |P ∩ E| + |M ∩ E| - |P ∩ M ∩ E| = 36 + 30 + 18 - 24 = 60

So, there  are  60 students  who take exactly two courses.

now, To  find |Z|, by using this  formula:

|Z| = |P| + |M| + |E| - |X| - |Y|

Substituting  the  values we have found, we get:

|Z| = 90 + 72 + 162 - 12 - 60 = 252 - 72 = 180

So, there   are 180 students  who take exactly one course.

Now ,To find the percentage of  students that  take exactly  one course, we can determine,

[tex]\frac{|Z|}{252}* 100%\\ =\frac{180}{252} * 100%\\=0.7143*100%\\=71.43%[/tex]%

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Correct question is:

The school of engineering of a polytechnic required all student to take physics, mathematics or English in a graduating class of 252 students.90 students take physics,72 students take mathematics and 162 take English. 1/3 of those that take physics take English, 1/4 of those that take mathematics take English and 1/2 of those that take mathematics take physics. How many students take all courses, how many student take two more courses,what is the percentage of students that take exactly one course,what is the the value of N(P ∩ M) and N(P ∩ E).

Answer:

57

Step-by-step explanation:

We know that parentheses come first in the order of operations. Therefore, we will first evaluate (3 × 5).

3 × 5 = 15

↓ substituting this value back in for the parentheses

[tex]12+[15+2(15)][/tex]

Next, we will deal within the brackets, which act like parentheses. Multiplication comes before addition, so we will execute 2(15) first.

2(15) = 2 × 15 = 30

↓ substituting this value back in

[tex]12+[15+30][/tex]

Now, executing the addition:

15 + 30 = 45

↓ substituting this value back in for the brackets

[tex]12 + 45[/tex]

Finally, all there is to do is execute the addition.

12 + 45 = 57

[tex]\boxed{57}[/tex]

Answer:

-2

Step-by-step explanation:

Plug in the values of 'x' and 'y':

[tex]\frac{2+-4}{3-2} =\frac{2-4}{1} =\frac{-2}{1} =-2[/tex]

Answer: So, the value of the expression 2+x/3-y when x=-4 and y=2 is -4/3.

Step-by-step explanation: To evaluate the expression 2+x/3-y for x=-4 and y=2, we can substitute the values of x and y into the expression. This gives us:

2 + (-4)/3 - 2

Solving this expression following the order of operations, we first solve the division:

2 + (-4/3) - 2

Then we solve the addition and subtraction from left to right:

= 2 - 4/3 - 2

= (6/3) - (4/3) - (6/3)

= -4/3

So, the value of the expression 2+x/3-y when x=-4 and y=2 is -4/3.

Answer: 2

Step-by-step explanation:

Hace 2+3=5 collares. Para cada collar usa 2/5 por eso

5(2/5)=2

Answer:

B. $436,72

Step-by-step explanation:

500,000 = R * ((1 - (1 + 0.02/12)^(-12*40)) / (0.02/12))

Resolviendo para R, obtenemos:

R = 436.72

Por lo tanto, Jesse necesitará invertir $436.72 en su IRA cada mes para alcanzar su meta de $500,000 en 40 años, suponiendo una tasa de interés del 2% compuesto mensualmente. La respuesta correcta es la opción B.

Two half-lives would be necessary for a sample of parent isotopes to decay to the point that only one-fourth of the sample is composed of parent isotopes.

Each half-life reduces the amount of parent isotopes by half, so after one half-life, the sample would consist of one-half parent isotopes and one-half daughter isotopes.

After the second half-life, half of the remaining parent isotopes would decay, leaving only one-fourth of the original sample as parent isotopes.

Number of half-lives = log(base 2) (original amount/final amount)

For example, if the half-life of a radioactive isotope is 5 years and you start with 100 atoms of the isotope, after one half-life (5 years), you will have 50 atoms remaining.

Thus, to get to one-fourth of the original amount, you need to go one more half-life, for a total of four half-lives.

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The area of a segment of a circle is (12π-9√3) square inches.

We have to determine the area of a segment of a circle.

The formula for the area of the sector that:

Arc length = πr² (θ/360)

Where r = the radius of the circle,

θ = the angle (in degrees) subtended by an arc at the center of the circle.

As per the shown figure, it is given that:

Central angle θ = 120°

The radius of a circle r = 6 in.

The area of the sector A₁ = π(6)² (120/360)

The area of the sector A₁  = 12π in²

The area of the triangle within the sector:

A₂ = 1/2 × (6√3)(3) = 9√3 in²

Now, the area of the segment is:

A₁ - A₂ = (12π - 9√3) in²

Therefore, the area of a segment of a circle is (12π-9√3) square inches.

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The intercepts of the rational function m(x)=4(x-5)(x+8)/(x^2-2x-15) are given as follows:

The rational function in the context of this problem is defined as follows:

m(x)=4(x-5)(x+8)/(x^2-2x-15)

The denominator can be simplified as follows:

x² - 2x - 15 = (x - 5)(x + 3).

Simplifying the x - 5 terms, the function can be written as follows:

m(x) = 4(x + 8)/(x + 3).

The x-intercept is the value of x when y = 0, hence:

x + 8 = 0

x = -8.

The y-intercept is the value of y when x = 0, hence:

m(0) = 4 x 8/3

m(0) = 32/3.

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Answer:

Area of a sector= θ/360×π×r×r

=76/360×22/7×4×4

(Do your division and multiplication)

=10.615 units

To nearest hundredth=10.620units

Julia scored at least 20 points. Inequality for the situation is: x ≥ 20, where x represent score of Julia.

Let the score of Julia be  "x". The inequality for this given situation would be:

x ≥ 20

According to this inequality, Julia's score, denoted by the letter "x," is greater than or equal to 20. Greater than or equal to is indicated by the sign "≥". The minimum score Julia must achieve is shown by the number 20 on the right side of the inequality. The "≥" sign makes sure Julia's score can be 20 or any number higher than 20, but it can never be less than 20.

The fact that Julia received at least 20 points is therefore indicates by the inequality : x ≥ 20

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Answer:

area of the triangle BCD is

1/2.8.10 sq unit

=40 sq unit

BCD is a right angle triangle

so, BC^2+CD^2=BD^2

=> 8^2+10^2=BD^2

=> 64+100=BD^2

=> BD^2=164

=> BD=√164=2√41

BD=2√41 unit

1/2.BD.x=40

=> x=40.2/BD

=> x=80/2√41=40/√41

The area of the shaded region is given as follows:

0.0475.

Here, we have to obtain probabilities using the normal distribution:

The z-score of a measure X of a variable that has mean symbolized by  and standard deviation symbolized by  is obtained by the rule presented as follows:

Z = X - μ / σ

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.

Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.

The mean and the standard deviation for the IQ scores are given as follows:

μ = 100, σ = 15

The shaded region is the area to the right of 125, hence it's area is one subtracted by the p-value of Z when X = 125, hence:

Z = (125 - 100)/15

Z = 1.67

Z = 1.67 has a p-value of 0.9525.

Hence:

1 - 0.9525 = 0.0475.

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Missing Information

The shaded region is the area to the right of 125.

18 liters of 15% acid, 18 liters of 35% acid, and 36 liters of 65% acid should be used.

Let x is the volume of 15% acid, y is the volume of 35% acid, and z is the volume of 65% acid.

Given that, the total mixture is 72 liters,

Implies that,

x + y + z = 72

Also,65% solution is used two times as 35% solution is used.

z = 2y

The amounts of acid add up to the final amount.

0.15x + 0.35y + 0.65z = 0.45 (72)      

Substitute the value of z here,

0.15x + 0.35y + 0.65 (2y) = 0.45 (72)

Simplify

x + 3y = 72

0.15x + 1.65y = 32.4      

Solve for x in the first equation, then substitute into the second.

x = 72 − 3y

0.15 (72 − 3y) + 1.65y = 32.4

Solve for y.

10.8 − 0.45y + 1.65y = 32.4

1.2y = 21.6

y = 18

Now find x and z.

x = 72 − 3y = 18

z = 2y = 36

18 liters of 15% acid, 18 liters of 35% acid, and 36 liters of 65% acid should be used.

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Answer:

Step-by-step explanation:

−UPDATE!! The answer is 1/3 so harray

The equations which are equivalent to Negative one-fourth (x) + three-fourths = 12 are:

Negative 1 (StartFraction x over 4 EndFraction) + three-fourths = 12

StartFraction negative x + 3 over 4 EndFraction = 12

(StartFraction negative x over 4 EndFraction + three-fourths = 12

Given equation is,

Negative one-fourth (x) + three-fourths = 12

This can be written numerically as,

-1/4 x + 3/4 = 12

-x/4 + 3/4 = 12, which is the last option.

This can be written as,

-1 (x/4) + 3/4 = 12, which is the second option.

Since the denominators are same in left hand side, adding the fractions, we get,

(-x + 3) / 4 = 12, which is the third option.

Hence the second, third and last options are equivalent equations.

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Sample space for the given experiment is:

OGRI, OGRS, OGII, OGIS, OPRI, OPRS, OPII, OPIS, GGRI, GGRS, GGII, GGIS, GPRI, GPRS, GPII, GPIS.

In probability theory, the sample space is the set of all possible outcomes of a random experiment or process. The sample space of an experiment refers to the set of all possible outcomes that can occur when the experiment is conducted. In this case, the experiment is choosing toppings for a salad at a restaurant. The sample space would consist of all possible combinations of the toppings and dressings that can be chosen.

There are two choices for the extra toppings: olives or garbanzo beans. There are also two choices for the meat: pepperoni or shrimp. Lastly, there are two choices for the dressing: ranch or Italian.

To find the sample space, we can list out all possible combinations of these choices. Using the given letters to represent each choice, the sample space would be:

{OGI, OGI, OPI, OPS, ORI, ORG, OGS, OPI, OPS, OSI, OSG, OSI, GGI, GPI, GPS, GRI, GRG, GGS, GGI, GPI, GPS, GSI, GSG, GSI}

This set contains all 24 possible outcomes that can occur when selecting toppings and dressing for the salad.

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Complete question:

Answer:

Step-by-step explanation:

12

Answer:

Penelope

Step-by-step explanation:

I don't think there is enough information - To find if two triangles are similar, you need 2+ common angles or at least some correlation between the lengths of the sides (not an exact definition). These rules cannot be applied to the 2 triangles.

The outcomes that make the complement of rolling a two are given as follows:

Hence the probability of the complement is given as follows:

p = 5/6.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The complement of an event are all the events out of the total outcomes that are not the event.

Supposing a dice with six sides, the complement of rolling a two is all outcomes which are not two.

And hence the probability of the complement is given as follows:

p = 5/6. (rolling a two is the only non-desired outcome).

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Answer:

B

Step-by-step explanation:

Using the data:

6 students sent 0-4 emails

4 students sent 5-9 emails

2 students sent 10 - 14 emails

3 students sent 15-19 emails

Option B graphs this data correctly

Answer:b

Step-by-step explanation:

have a nice day

After factoring the given expression which is -2bk² - 4bk + 30b, we get -2b(k + 5)(k - 3). So, the correct answer is (a) .

To factor the expression -2bk² - 4bk + 30b, we first need to factor out the greatest common factor of -2b.

-2b(k² + 2k - 15)

Next, we need to factor the quadratic expression k² + 2k - 15.

We can find two numbers that multiply to -15 and add up to 2 by using trial and error or by using the quadratic formula. The two numbers are 3 and -5.

Therefore, we can write:

-2b(k + 5)(k - 3)

Therefore, the correct answer is (a) -2b(k + 5)(k - 3).

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Answer:  10,450

Step-by-step explanation:

If 5% of the 11,000 people who entered a drawing won a prize, that means that 95% of the people did not win a prize.

To find out how many people did not win a prize, we can calculate 95% of the total number of people who entered the drawing:

95% of 11,000 = 0.95 x 11,000 = 10,450

Therefore, 10,450 people did not win a prize.

Robin's graph of the function g(x) = -x² = -f(x)  is the reflection of Giselle’s graph over the x-axis. Robin’s graph is a reflection of Giselle’s graph over the x-axis.

What is  linear equation?

An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.

                         The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.

To reflect a function across the x-axis, replace y with -y.

To reflect a function across the y-axis, replace every x with -x.

To translate a function vertically, add or subtract a number to the end of the function.

To translate a function horizontally, add or subtract a number before any exponents are applied.

The difference between Robin's and Giselle's functions are the negative in front of x².  This is the same as making y negative; this is a reflection across the x-axis.

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If the claim is approved, the homeowner's insurance policy will pay an amount of for the damages.

Given that,

Annual premium = $650

Deductible = $1,350 per claim.

Amount of damage formed in windstorm = $35,500

Amount of the damage that the insurance company will pay is the amount of the damage which deducts the deductible amount.

Amount insurance company pays = $35,500 - $1,350 = $34,150

Hence the amount paid by the company is $34,150.

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