i need an answer for this question in the simplest radical form please

Answer: x= 3

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

So the equation is 90=12x+54. You get x by itself. To do that you subtract 54 from 90. You get 36. Then you divide.

Answer:

27

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Volume of a cylinder = area of the base x height.

v = [(pi)(r)^2] x height

188.4 = [(3.14)(2)(2)] x h

188.4 = 12.56h

h = 15

Please let me know if you have questions

Answer:

cos(θ) =  -3/√10

sin(θ) =   1/√10

tan(θ) =  -1/3

Step-by-step explanation:

When we have a point (x, y), the angle generated between the positive x-axis and a ray that connects the origin and the point, is defined by:

cos(θ) = x/(√(x^2 + y^2))

sin(θ) = y/(√(x^2 + y^2))

tan(θ) = y/x

Now we have the point (-3, 1), then we have:

x = -3

y = 1

√(x^2 + y^2) = √((-3)^2 + 1^2) = √10

Then we just need to replace these values in the given formulas:

cos(θ) = x/(√(x^2 + y^2)) = -3/√10

sin(θ) = y/(√(x^2 + y^2)) =  1/√10

tan(θ) = y/x = 1/-3 = -1/3

Answer:

(-2,-3)

Step-by-step explanation:

A=(8,-5)

M=(3,-4)

The difference between them is that m is 5 to the left and 1 up. We need to do the same thing to find B.

B=(-2,-3)

Answer

C

Step-by-step explanation:

The simplified form of the given expression \(7\sqrt[3]{2x}-3\sqrt[3]{16x} -3\sqrt[3]{8x}\) is \(\sqrt[3]{2x} -6\sqrt[3]{x}\).

The given expression is,

\(7\sqrt[3]{2x}-3\sqrt[3]{16x} -3\sqrt[3]{8x}\)

It is required to solve the given expression.

Write all the terms in the form of power of primes and then take the cube root of that term.

Simplify the given expression as,

\(7\sqrt[3]{2x}-3\sqrt[3]{16x} -3\sqrt[3]{8x}=7\sqrt[3]{2x}-3\sqrt[3]{2^4x} -3\sqrt[3]{2^3x}\\ =7\sqrt[3]{2x}-6\sqrt[3]{2x} -6\sqrt[3]{x}\\ =\sqrt[3]{2x} -6\sqrt[3]{x}\)

Therefore, the simplified form of the given expression \(7\sqrt[3]{2x}-3\sqrt[3]{16x} -3\sqrt[3]{8x}\) is \(\sqrt[3]{2x} -6\sqrt[3]{x}\).

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Answer:

C

Step-by-step explanation:

apparenlty

The Stony Brook University has been ranked as the third best university to pursue a degree in applied mathematic among all the other public and private universities.

Stony Brook University—SUNY is placed #77 in the Best Colleges rating for 2022–2023's National Universities category.

The tuition fees is $10,556 and $28,476 for in-state and out-of-state respectively. The Stony Brook University comes under the state University of New York along with the other 64 universities.

The Stony Brook AMS major has reportedly been listed by College Factual as one of the top five undergraduate applied mathematics degrees in the US for a number of years, according to USA Today. The top five schools for 2020 are CalTech, Stanford, Harvard, Brown, and Stony Brook.

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S1: m || n

S2: m∠2 ≅ m ∠3

R3: Corresponding angles postulate

R5: Linear pair angles are also supplementary angles

S7: m∠1 + m∠2 =180°

What is linear pair?

An angle pair that is linear is produced when two lines intersect at a single point. The terms "linear" and "rectangular" are used to describe angles that follow the intersection of two lines in a straight line. Total angles of a linear pair are always equal to 180°.

Given that line m and line n are parallel to each other.

Statement 1: m || n

Reason 1: Given

Corresponding angles postulate: When a transversal divides two parallel lines, the resulting angles are congruent.

Statement 2: m∠2 ≅ m ∠3

R2: Corresponding angles postulate

S3: m∠2 ≅ m ∠3

R3: Corresponding angles postulate

Statement 5: ∠1 is supplementary to ∠2.

Reason 5: The linear pair angles are also supplementary angles.

Statement 7: m∠1 + m∠2 = 180°

Reason 7: Substitution property of equality

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Answer:inequality form  x  ≤  -1

for 3x + 9  ≤ 6

Step-by-step explanation:isolate the variable by dividing eash side by factors that dont contain the variable

Answer:

Answer Varies

Step-by-step explanation:

For the 1st equation, there are a lot of numbers that could fit x, such as any negative number, such as -1,-2,-3, etc. For the 2nd equation, 9 and below would work. Please correct me if I am wrong because everybody makes mistakes.

The null hypothesis for the sample data set is given by H₀ : μ = 2 and the alternate hypothesis for the data is H₁ : μ > 2 .

a)H₀ : μ = 2

H₁ : μ > 2

We cannot reject the null hypothesis and conclude that no significant evidence exists to confirm that the mean tree-planting time differs from two hours.

Given :

X = 23.71,17.79, 29.87,18.78,28.76

b)Sample mean, x = Σx / n = 22/10 = 2.2

c) Standard deviation, s = 0.516

H0 : μ = 2

H1 : μ > 2

Test statistic :

(x - μ) ÷ (s/√(n))

n = 10

d) Test statistic :

=(2.2 - 2) ÷ (0.516/√(10))

=0.2 / 0.1631735

Test statistic = 1.23

Using the P-value from T-score we get the degrees of freedom:

df

= n - 1

= 10 - 1

= 9

P-value (1.23, 9) = 0.1249

e) Since, P-value > α ; We fail to reject the null and conclude that no significant evidence exists to support that mean tree-planting time differs from two.

A hypothesis is thetheory put up to explain a phenomenon. If a hypothesis cannot be tested by the scientific method, it cannot be referred to as a scientific hypothesis.

Scientific theories frequently start with historical observations that can't be adequately explained by the body of knowledge at this time. A hypothesis is a tested assertion regarding the relationship between two or more variables in the scientific area or a theory put out to explain an observed phenomena.

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9514 1404 393

Answer:

  180

Step-by-step explanation:

The smallest such number is 4·5·9 = 180. Any multiple of 180 will be divisible by 4, 5, and 9.

Answer:

5p-q = 5. (-6) - 5 = -30 - 5 = -35

5pq= 5. (-6) . 5 = -30 . 5 = -150

Step-by-step explanation:

The administration's willingness to pay to save a student's statistics life is no more than option c) $100,000.

To estimate the administration's willingness to pay to save a student's statistical life, we need to calculate the cost per statistical life saved. Currently, the probability of a student dying from the plague is 1/3,000. If the rats are eradicated, this probability is reduced to zero. The cost of eradicating the rats is $1,000,000. To calculate the cost per statistical life saved, we divide the cost by the number of statistical lives saved.

The number of statistical lives saved is the product of the number of students on campus (30,000) and the reduction in probability (1/3,000).
Cost per statistical life saved = $1,000,000 / (30,000 * (1/3,000))
                         = $1,000,000 / (30,000 * 1/3,000)
                         = $1,000,000 / 10
                         = $100,000
Therefore, the correct answer is option c) $100,000.

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The RREF of [a| b] obtained above does not have such a row, so the system is consistent for all values of b.

To find all possible values of b such that rank(a) = rank([a| b]), we need to consider the augmented matrix [a| b] and perform row operations to obtain its reduced row echelon form (RREF). If the RREF has the same number of nonzero rows as the RREF of a, then rank(a) = rank([a| b]).

Performing row operations on [a| b] gives:

1 4 3 1 -1 | b1
3 9 3 0 9 | b2
2 6 2 4 -2 | b3
1 3 1 2 -1 | b4

R2 - 3R1 -> R2:
1 4 3 1 -1 | b1
0 -3 -6 -3 12 | b2 - 3b1
2 6 2 4 -2 | b3
1 3 1 2 -1 | b4

R3 - 2R1 -> R3 and R4 - R1 -> R4:
1 4 3 1 -1 | b1
0 -3 -6 -3 12 | b2 - 3b1
0 -2 -4 2 0 | b3 - 2b1
0 -1 -2 1 0 | b4 - b1

R2/(-3) -> R2 and R3/(-2) -> R3 and R4/(-1) -> R4:
1 4 3 1 -1 | b1
0 1 2 1 -4 | (3b1 - b2)/3
0 1 2 -1 0 | (2b1 - b3)/2
0 1 2 -1 0 | b4 - b1

R3 - R2 -> R3 and R4 - R2 -> R4:
1 4 3 1 -1 | b1
0 1 2 1 -4 | (3b1 - b2)/3
0 0 0 -2 4 | (2b1 - b3)/2 - (3b1 - b2)/3
0 0 0 -2 4 | b4 - b1 - (3b1 - b2)/3

R3/(-2) -> R3 and R4/(-2) -> R4:
1 4 3 1 -1 | b1
0 1 2 1 -4 | (3b1 - b2)/3
0 0 0 1 -2 | (b2 - 2b1 + b3)/3
0 0 0 1 -2 | (b1 - b4 + (3b1 - b2)/3)/2

R2 - 2R4 -> R2 and R1 - 3R4 -> R1:
1 4 3 0 1 | (5b1 - b2 + 2b4)/6
0 1 2 0 -8/3 | (-4b1 + b2 + 2b4)/3
0 0 0 1 -2 | (b2 - 2b1 + b3)/3
0 0 0 0 0 | (5b1 - b2 - 3b4)/6

Since the last row of the RREF has all zeros except for the last entry, we can conclude that rank(a) = rank([a| b]) if and only if 5b1 - b2 - 3b4 = 0. Therefore, all possible values of b are given by b4 = (5b1 - b2)/3.

To find all possible values of b such that the system ax = b is inconsistent, we need to check if the RREF of [a| b] has a row of the form [0 0 ... 0 | c] with c ≠ 0. If such a row exists, then the system is inconsistent for all values of b corresponding to that row.

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Answer:

1 1/4 cups

Step-by-step explanation:

Answer:

1 1/4 cups of punch.

Step-by-step explanation:

Since 2 1/2 cups of sherbet are needed to make 24 cups, and we need to make 12 cups of punch, it's basically 24 divided by 2. So we need to divide 2 1/2 by 2, which would be 1 1/4 cups.

Answer:

4/5 or .8

Step-by-step explanation:

Solution:

Given the triangle ABC;

The sum of interior angles of a triangle is 180 degrees. Thus;

We have;

Thus, the measure of angle C is;

The minimum cross-sectional area is zero. As a result, the beam can support no load.

Beams are structural members that are used to bear loads and to transmit these loads to the supporting structure. They are characterized by their length and cross-section.

They're designed to bend and resist bending when loaded by gravity, snow, wind, and other loads. Beams are generally horizontal, but they may also be slanted or curved.

The allowable tensile stress (σallow)t is given as 2.1 ksi, and the allowable compressive stress (σallow)c is given as 3.6 ksi. Thus, the allowable axial load on the beam may be computed using the following equations:

For tension,Allowable tensile stress :σt= 2.1 ksi

Cross-sectional area of beam : A P = σt × A

Rearranging the above equation, A = P/ σt

:= P/2.1 ...(1)

For compression,Allowable compressive stress : σc= 3.6

ksi Cross-sectional area of beam :A P = σc × A

Rearranging the above equation, A = P/ σc

= P/3.6 ...(2)

In Equations 1 and 2, P is the allowable axial load on the beam. The smallest of these two equations determines the allowable axial load on the beam because it governs the beam's strength.

The minimum value for A can be found by combining the equations.

We can equate the two equations to obtain:

P/2.1 = P/3.6

Rearranging the equation, we get

3.6P = 2.1P

P = 0

Therefore, the minimum value for A can be obtained by substituting P = 0 into either equation. Since the load is zero, the beam is weightless and the smallest cross-sectional area that can support no load is zero.

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Answer:

Look at the explanation.

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

it is 66

The total number of fish in the entire sampling area is 600

Sampling:

The process of selecting the group that you will actually collect data from in your research is called sampling.

Given,

Consider a case where 400 fish are tagged and released during a first outing. During a second outing in the same area, 400 fish are again caught and released, of which half are already tagged.

Here we need to find the total number of fish in the entire sampling area.

Let us consider N be the number of fish in the entire sampling area.

While looking through the given question,

We have identified the following,

Number of fish tagged = 400

Next time number of fish caught = 400

We know the half of them are tagged, so the untagged fishes are

=> 400/2

=> 200

Therefore, the total number of fishes is

=> 400 + 200

=> 600

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The storm rainfall flux is 0.00127 m2/hr, 1.27 kg liquid water/m2hr, 2.8 lb liquid water/m2hr, 1.27 liters liquid water/m2hr, and 0.335 gallons liquid water/m2hr. The amount of liquid water fell on the garden is 80.6 L, 21.3 gallons.

Dimensions of outdoor vegetable garden = 2 m × 2 m

Storm rainfall = 0.8 inches of rain

Time of storm = 1 hr(

a) The rainfall flux is the amount of rainfall per unit area and unit time. It is given as:

Rainfall flux = (Amount of rainfall) / (Area × Time)

Given the area of the garden is 2 m × 2 m, and the time is 1 hr, the rainfall flux is:

Rainfall flux = (0.8 inches of rain) / (2 m × 2 m × 1 hr)

Converting inches to meters, we get:

1 inch = 0.0254 m

Therefore,

Rainfall flux = (0.8 × 0.0254 m) / (2 m × 2 m × 1 hr) = 0.00127 m/hr

Converting the rainfall flux to other units:

In kg/hr:

1 kg of water = 1000 g of water

Density of water = 1000 kg/m3

So, 1 m3 of water = 1000 kg of water

So, 1 m2 of water of depth 1 m = 1000 kg of water

Therefore, 1 m2 of water of depth 1 mm = 1 kg of water

Therefore, the rainfall flux in kg/hr = (0.00127 m/hr) × (1000 kg/m3) = 1.27 kg/m2hr

In lbs/hr:

1 lb of water = 453.592 g of water

So, the rainfall flux in lbs/hr = (0.00127 m/hr) × (1000 kg/m3) × (2.20462 lb/kg) = 2.8 lbs/m2hr

In liters/hr:

1 m3 of water = 1000 L of water

So, 1 m2 of water of depth 1 mm = 1 L of water

Therefore, the rainfall flux in L/hr = (0.00127 m/hr) × (1000 L/m3) = 1.27 L/m2hr

In gallons/hr:

1 gallon = 3.78541 L

So, the rainfall flux in gallons/hr = (0.00127 m/hr) × (1000 L/m3) × (1 gallon/3.78541 L) = 0.335 gallons/m2hr

(b) To calculate the amount of water that fell on the garden, we need to calculate the volume of water.

Volume = Area × Depth.

The area of the garden is 2 m × 2 m.

We need to convert the rainfall amount to meters.

1 inch = 0.0254 m

Therefore, 0.8 inches of rain = 0.8 × 0.0254 m = 0.02032 m

Volume of water = Area × Depth = (2 m × 2 m) × 0.02032 m = 0.0806 m3

Converting the volume to other units:

In liters:

1 m3 of water = 1000 L of water

Therefore, the volume of water in liters = 0.0806 m3 × 1000 L/m3 = 80.6 L

In gallons:

1 gallon = 3.78541 L

Therefore, the volume of water in gallons = 80.6 L / 3.78541 L/gallon = 21.3 gallons.

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Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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The equation of the tangent would be y = -4x/3 - 25/3 and the equation of the normal would be y = 3x/4.

What is a parabola?

A parabola is a plane curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits several seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.

The given equation is x² + y² = 25 ; (4, 3)

Now when we put x = 4 and y = 3

then LHS = RHS.

Now find the slope:

      2x + yy' = 0

       ⇒ y' = -x/y

Now at (4, 3) slope would be y' = -4/3.

The equation of the tangent would be

      y - y1 = m(x - x1)

      y - 3 = (-4/3)(x-4)

     3y - 9 = -4x + 16

     4x + 3y = 25

     y = -4x/3 - 25/3

Now equation of the normal is:

  y - y1 = (-1/m)(x - x1)

  y - 3 = 3/4(x - 4)

  y = 3x/4

Hence, the equation of the tangent would be y = -4x/3 - 25/3 and the equation of the normal would be y = 3x/4.

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Answer:

Here are your answers! :)

Step-by-step explanation:

15) -21

16) -11

17) 26

18) 23

19) -32

20) -20

21) 65

22) 420

23) 16

24) -13

25) 20

(I hope this helps!!)

Answer:

1/12 mile

Step-by-step explanation:

He walks 7/12 mile in 7 minutes.

In 1 minute, he walks 1/7 of the distance.

1/7 of 7/12 mile = 1/12 mile