help please a.-5 b.-1/5 c1/5 d.5

Answer:

Below in bold.

Step-by-step explanation:

(a) Using the Pythagoras theorem:

30^2 = 21^2 + p^2

p^2 = 30^2 - 21^2 = 459

p = √459

  = 21.4 cm to nearest tenth.

(b) cos P = 21/30 = 0.70

   m < P = 45.57 degrees to nearest hundredth.

Answer:

a)  p = 21.4 cm (nearest tenth)

B)  P = 45.6° (nearest tenth)

Step-by-step explanation:

As triangle PQR is a right triangle, we can use Pythagoras Theorem to find the length of p.

Pythagoras Theorem

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

where:

From inspection of the triangle:

Substitute the given values into the formula and solve for p:

[tex]\implies 21^2+p^2=30^2[/tex]

[tex]\implies 441+p^2=900[/tex]

[tex]\implies 441+p^2-441=900-441[/tex]

[tex]\implies p^2=459[/tex]

[tex]\implies \sqrt{p^2}=\sqrt{459}[/tex]

[tex]\implies p=\pm 3\sqrt{51}[/tex]

As p is the length, p can be positive only.

Therefore, p = 21.4 cm (nearest tenth)

To find the angle P, use the cosine trigonometric ratio.

Cosine trigonometric ratio

[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]

where:

From inspection of the triangle:

Substitute the given values into the formula and solve for P:

[tex]\implies \sf \cos P=\dfrac{21}{30}[/tex]

[tex]\implies \sf P=\cos^{-1}\left(\dfrac{21}{30}\right)[/tex]

[tex]\implies \sf P=45.572996^{\circ}[/tex]

Therefore, the measure of angle P is 45.6° (nearest tenth).

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Answer:

the correct answer is c (x+8)

Step-by-step explanation:

x+8=0

=x= -8

put x= -8 in the given polynomial

(-8)²+5(-8)-24

= 64-40-24

=24-24= 0

Hence, the age of his brother when brain is [tex]11[/tex] is [tex]19.[/tex]

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here given that,

Brian is [tex]8[/tex] and his brother is twice his age.

As age of brain is [tex]8[/tex].

His brother is twices than his age is [tex]8(2)=16[/tex]

When the age of brain is [tex]11[/tex] then [tex]3[/tex] added to his present age.

Then the age of his brother is [tex]16+3=19[/tex]

Hence, the age of his brother when brain is [tex]11[/tex] is [tex]19.[/tex]

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Answer: right

Step-by-step explanation:

[tex]-499 > -500[/tex], and larger numbers are to the right of numbers smaller than them on the number line.

Answer:

A= 54

B=3

Step-by-step explanation:

I hope this helps!

Answer:

Zero real number solutions

Step-by-step explanation:

Doesn't intercept the x-axis -> No real solutions

Multiplicative rule's probability is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

According to the statement

we have to explain about the those law which is used when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

So, For this purpose we know that the

According to multiplicative rule of probability ,

If A and B are two independent events in a probability experiment, then the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B) In case of dependent events , the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B | A)

and we see that these conditions are fulfilled by the definition of the multiplicative rule.

So, Multiplicative rule is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

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In a proportionate stratified sample of 120, there are 72 Whites, 24 Latinos, 18 Blacks and 6  others.

Proportionate Stratified Sample

A proportionate stratified sample is one in which the size of the strata in the sample is proportional to the size of the strata in the population; in other words, the chance of selecting a unit from a stratum depends on the relative size of that stratum in the population.

Calculating the Proportionate Stratified Sample

The given percentage of -

Whites = 60%

Latinos = 20%

Blacks = 5%

Strength of the sample = 120

⇒ Number of Whites = 60% of 120

= 0.6 × 120

=72

Number of Latinos = 20% of 120

= 0.2 × 120

=24

Proportionate Stratified Sample of Blacks and Others

Count of Blacks = 15 % of 120

= 0.15 × 120

= 18

Count of others = 5% of 120

= 0.05 × 120

6

Thus, in a Proportionate Stratified Sample of 120, 72 are Whites, 24 are Latinos, 18 are Blacks, and 6 are others.

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Answer:

Step-by-step explanation:

Assuming that the question is:

12 * (3 + 2^2) : 2 - 10 =       remember PEMDAS

12 * (3 + 4) : 2 - 10 =

12 * 7 : 2 - 10 =

84 : 2 - 10 =

42 - 10 =

32

Answer:

-10.5

Step-by-step explanation:

[tex]\frac{12*(3+2^2)}{2-10}[/tex]

2²= 4

3+4=7

12×7=84

2-10=-8

84÷-8= -10.5

Hope it helped, comment below if you need more assistance! :)

Answer: [tex]f^{-1}(x)=\frac{x}{4}[/tex]

Step-by-step explanation:

Let [tex]f(y)=x[/tex].

[tex]x=4y\\\\y=\frac{x}{4}\\\\\therefore f^{-1}(x)=\frac{x}{4}[/tex]

Considering concepts of divisibility, the amount of numbers in the set that are divisible by 2 but not by 10 is:

(C) 19.

The data-set has (55 - 10) + 1 = 46 numbers, hence 23 are divisible by 2. 20, 30, 40 and 50 are also divisible by 10, that is, 4 numbers have to be removed, hence the amount is:

23 - 4 = 19.

Which means that option C is correct.

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The planning value for the population standard deviation is 4330.

Given the confidence interval 20000 and 35000.

We have to find the planning value of standard deviation.

Standard deviation is measuring dispersion of data. Uniform probability distribution has two bounds a and b. The standard deviation is given by :

s=[tex]\sqrt{(b-a)^{2}/12 }[/tex].

Annual starting salaries for college graduates be between 20000 and 35000.

It is uniform in the interval so, a=20000, b=35000.

Now we have to just put the values of a and b in the above formula to get the value of standard deviation.

s=[tex]\sqrt{(35000-20000)^{2} /12}[/tex]

=[tex]\sqrt{(15000)^{2} /12}[/tex]

=[tex]\sqrt{225000000/12}[/tex]

=[tex]\sqrt{18750000}[/tex]

=4330

Hence the planning values for the population standard deviation is 4330.

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Question is incomplete as it should includes the confidence interval of $20000 and $35000.

On the number line the position of point F is at point 4.

According to the statement

We have a given that the on a number line , point D is at -3, and point E is at 6. The point F lies on the ratio of to is 2 : 3.

and we have to find the F point on the number line.

Firstly,

Number line is a line on which numbers are marked at intervals, used to illustrate simple numerical operations.

So, According to given information,

Point D is at -3, and point E is at 6.

Ratio of point E to F = 6*2/3

Then

Ratio of point E to F = 6*2/3

After solving it

The point F = 2*2

The point F = 4.

So, On the number line the position of point F is at point 4.

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There can be 36 combinations.

The total number of combinations of the dial can be found by using permutations without any number repeating.

There are four integers on the dial. They are 0, 1, 2, and 3.

It is also given that the numbers shouldn't repeat on the adjacent dial.

Therefore, we can say that there are 4 possible numbers on the first.

Similarly, on the second dial, only 3 numbers are possible since no two adjacent dials can have the same.

This is also the case for the third dial. It can also have 3 possible numbers.

Therefore, the total number of combinations is given by 4*3*3 = 36 combinations.

Therefore, we have found that there can be 36 combinations.

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Option 2. The equation of the parabola is given as y = one eighthx² + 5

We have the coordinate plane to be passing through the graph at point C on the y axis. This is used to represent the slope.

Hence the slope is 5

The equation of the line is given as  y=x²+C

Hence we can see that there is a rising slope. So the answer is Option 2.

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Answer: y=-1/5x+ 8/5    (Third one down)

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt[4]{x - 4} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: x - 4 = (3) {}^{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x - 4 = 81[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 81 + 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 85[/tex]

So, the correct choice is 85

Answer:

Step-by-step explanation:

4√(x-4) = 3

√(x-4) = 3/4

Square both sides:

x - 4  = 9/16

x = 4 + 9/16

x = 4 9/16.

The best interpretation of 0.8^a in this exponential equation is that: C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.

An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:

f(x) = aeˣ

Based on the information provided, we can logically deduce that the atmospheric pressure (p) exerted on an airplane flying at an altitude of a miles above sea level is defined by the following exponential function:

p = 14.63 × 0.8^a

Next, we would evaluate as follows;

At a = 0, we have:

p = 14.63 × 0.8^(0)

p = 14.63 psi.

At a = 1, we have:

p = 14.63 × 0.8^(1)

p = 11.704 psi, and this is 20% less than a mile before.

At a = 2, we have:

p = 14.63 × 0.8^(2)

p = 9.3632 psi, and this is 20% less than a mile before.

At a = 2, we have:

p = 14.63 × 0.8^(3)

p = 7.4906 psi, and this is 20% less than a mile before.

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Complete Question:

Atmospheric pressure, measured in pounds per square inch (psi) is the force exerted by Earth's atmosphere over a given area. The atmospheric pressure, p, exerted on an airplane flying at an altitude of a miles above sea level can be approximated by the model shown below. What is the best interpretation of 0.8^a in this equation?

p = 14.63 × 0.8^a

A. If the airplane reaches the outer extent of the Earth's atmosphere, the atmospheric pressure will be 0.8 psi.

B. If the airplane is at sea level, the atmospheric pressure will be 0.8 psi.

C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.

D. For each mile that the altitude increases, the atmospheric pressure increases 20%.

The value of r in the exponential decay function 7000 = 20000(1-r)^10 is 10%

The equation is given as:

7000 = 20000(1-r)^10

The above equation is an exponential decay function.

So, we have:

7000 = 20000(1-r)^10

Divide both sides of the equation by 20000

0.35 = (1-r)^10

Take the 10th root of both sides

0.35^(1/10) = 1 - r

Evaluate the exponent

0.9 = 1 - r

Add r to both sides

0.9 + r = 1

Subtract 0.9 from both sides

r = 1 - 0.9

Evaluate

r = 0.1

Express as percentage

r = 10%

Hence, the value of r in the exponential decay function 7000 = 20000(1-r)^10 is 10%

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Answer:

2/3x

Step-by-step explanation

Answer:

(x³-3x²-3x-1) / (27x³)

Step-by-step explanation:

((x-1) / (3x))³

= (x-1)³ / /3x)³

(x-1)³ = (x-1)(x-1)(x-1) = x³ - 3x² - 3x - 1

then:

(x-1)³ / (3x³) = (x³-3x²-3x-1) / (27x³)

Answer:

Let "x" and y" be the two numbers.

We have

xy = 5/6, (1) and x/y = 15/8. (2)

Multiply (1) and (2) (both sdes). You will get

x^2 = (5*15)/(6*8) = 25/16.

Hence, x = +/- 5/4.

Next, divide (1) by (2) (both sides). You will get

y^2 = 5/6:15/8 =

(5*8)/(6*15) = 4/9.

Hence, y=+/-2\/3.

Answer. There are two solutions: (x, y)=(5\/4,2\/3) and (x,y) = (-5/4,-2/3).

// We should exclude the second solution, since the numbers are negative.

Answer:

x=1/3

Step-by-step explanation:

Answer:

The water in pot X is hoter than that of pot Y

Answer:

A is the answer

Step-by-step explanation:

Any complex number [tex]z[/tex] can be written in polar/exponential form as

[tex]z = |z| e^{i\arg(z)} = |z| (\cos(\arg(z)) + i \sin(\arg(z)))[/tex]

In the complex plane, the given complex number belongs to the third quadrant since both its real and imaginary parts are negative. This means the argument must be between π and 3π/2, so the first two options are eliminated.

The difference between the remaining two options is the coefficient [tex]|z|[/tex]. We have

[tex]z = -2\sqrt3 - 6i \implies |z| = \sqrt{(-2\sqrt3)^2 + (-6)^2} = 4\sqrt3[/tex]

so (D) (the last option) is the correct choice.

The cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is d(t) = 6cos([tex]\pi[/tex]t).

As long as its length is constant, a pendulum completes each swing (or oscillation) in precisely the same amount of time. Any particular pendulum oscillates for a fixed amount of time.

Calculation for the cosine function-

The given function is: cosine function, d = acos(bt).

As, the pendulum takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right.

The total time 't' by the pendulum is 2 sec.

Calculate the angular speed of the pendulum by-

ω = 2[tex]\pi[/tex]f

   = 2[tex]\pi[/tex]×(1/2)

ω = [tex]\pi[/tex] which is 'b' value of the given function.

As given, the distance of the pendulum from the centre is half of the total distance.

a = 12/2

a = 6

Substitute the obtained values in the cosine function, d = acos(bt),

d(t) = 6cos([tex]\pi[/tex]t)

Therefore, the cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is  d(t) = 6cos([tex]\pi[/tex]t).

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The complete question is -

Starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right. Write a cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds).

Answer:

a=6

The period is 2 seconds.

b=pi

t=0.5

d=4.243

Step-by-step explanation:

1) [tex]\overline{AB} \perp \overline{BD}[/tex], [tex]\overline{AB} \cong \overline{DB}[/tex], [tex]\overline{AC} \cong \overline{DE}[/tex] (given)

2) [tex]\angle ABD[/tex] is a right angle (perpendicular lines form right angles)

3) [tex]\triangle ABD[/tex] and [tex]\triangle DEB[/tex] are right triangles (a triangle with a right angle is a right angle)

4) [tex]\triangle ABD \cong \triangle DEB[/tex] (HL)

5) [tex]\angle ACB \cong \angle DEB[/tex] (CPCTC)

The length of the wall = 125m

The area of the Playground = 10000[tex]m^{2}[/tex]

What is geometry?

A branch of mathematics that broadly deals with the measurement, properties, and connections of points, lines, angles, surfaces, and solids: the investigation of qualities of given elements that hold true even after being subjected to predetermined transformations.

Given data:

Perimeter of the playground=410m

length of the wall = 80m

The playground's width can be calculated as follows if its length is 80 meters:

(Formula of Perimeter of a rectangle)

P=2(L+B)              

410=2(80 +B)

410= 160 + 2B

2B= 410-160

2B= 250

B= 125 m

This results in a 125 m length for the playground.

The area of playground.

Area = Length x Width

Area = 80 x 125

area = 10000[tex]m^{2}[/tex]

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \:x = - \dfrac{ 9}{20} [/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:2(3x + 1) + 3(5x + 2) = x - 1[/tex]

[tex]\qquad❖ \: \sf \:6x + 2 + 15x + 6 = x - 1[/tex]

[tex]\qquad❖ \: \sf \:(6x + 15x - x) + (2 + 6 + 1) = 0[/tex]

[tex]\qquad❖ \: \sf \:20x + 9 = 0[/tex]

[tex]\qquad❖ \: \sf \:20x = - 9[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \:x =- \cfrac{ 9}{20} [/tex]

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

________________________________

→ 2(3x + 1) + 3(5x + 2) = x – 1

→ 6x + 2 + 15x + 6 = x – 1

→ 21x + 8 = x – 1

→ 21x – x = – 1 – 8

→ 20x = – 9

→ x = –9/20

________________________________

Answer:

In order to go from the first point to the second, we need to rise from 4 to 7, i.e. by 3. We also need to run from -4 to -2, i.e. by 2. Therefore the slope is 32 .

Step-by-step explanation: