Put the following equation of a line into slope-intercept form, simplifying all
fractions.
y - 2 = -5

If a₁ = 9 and aₙ = 4 + (aₙ - 1) in an arithmetic sequence, then the value of fifth term a₅ is equal to 25.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

From the information provided, we know that the common difference is equal to 4.

Substituting the given parameters into the formula, we have;

a₅ =  9 + (5 - 1)4

a₅ =  9 + 4(4)

a₅ =  9 + 16

a₅ =  25

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Complete Question:

If a₁ = 9 and aₙ = 4 + (aₙ - 1), then find the value of a₅.

Answer:

1/10

Step-by-step explanation:

The probability of the first is 2/5 and the second is 1/4. Multiply them together and you get 2/20. Simplify to 1/10

Answer:

b = 12

Step-by-step explanation:

a² + b² = c²

a and b are the length of the sides in the right triangle and c is the hypotenuse.

since we know one leg and the hypotenuse, we can find the other leg.

9² + b² = 15²

81 + b² = 225

b² = 225 - 81

b² = 144

b = 12

Answer:

The answer is 12

Step-by-step explanation:

the formula is A^2+B^2=c^2

9² + b² = 15²

81 + b² = 225

b² = 225 - 81

b² = 144

b = 12

The true speed and direction of the football thrown by the  quarterback is 39.139 mph and 7⁰ respectively.

The true speed and direction of the football is determined by applying the concept of relative velocity.

Vr/w = Vb - Vw

where;

Vr/w is the velocity of the football with respect to the wind

Vb is the velocity of the football

Vw is the velocity of the wind

Vr/w = 42 mph - 13 mph = 29 mph

The direction speed can be determined by a triangle

Direction of the speed, θ = (360 - 345) - (180 - 172)

                                      θ = 15 - 8 = 7⁰

Resultant speed;

\(R^2 = 42^2 + 13^2 - 2(42 \times 13 \times cos7)\\\\R^2 =849.139\\R = \sqrt{849.139}\\R = 29.139 mph\)

Thus, the true speed and direction of the football thrown by the  quarterback is 39.139 mph and 7⁰ respectively.

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Answer:

29.140 ; 175

Step-by-step explanation:

Answer:

4x3+6x6=48

Step-by-step explanation:

PEMDAS

4x3=12

6x6=36

12+36=48

therefore, the answer is 48

Answer:15

Step-by-step explanation:

it could be 15 but (three times) is geting me off

sorry if i was no help and all the number's wow

The mean total expenditure on beverages is $736 with a variance of $8.1912.

If X and Y have a bivariate distribution with covariance zero, this implies that the variables show no linear relationship.

Given that an individual's per kg expenditure on coffee is distributed with mean $2.32 and variance 0.09.

Each individual in the population drinks 3 kg of tea and 2 kg of coffee.

Let T and C be the amount spent on tea and coffee respectively by an individual.

Then,

Total expenditure on coffee = 2 × 2.32 × 100 = $232

and,

Total expenditure on tea = 3 × 1.68 × 100 = $504

We know that the covariance of T and C is zero.

Thus, Mean of the total expenditure on beverages = 232 + 504 = $736,

The variance of the total expenditure on beverages = 4 × variance of expenditure on coffee + 9 × variance of expenditure on tea

= 4 × 0.09 × (2.32)² + 9 × 0.04 × (1.68)²

= $8.1912

Hence, the mean total expenditure on beverages is $736 with a variance of $8.1912.

If X and Y have a bivariate distribution with covariance zero, this implies that the variables show no linear relationship.

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Answer:

\(\fbox{3\sqrt{2}}\)\(3\sqrt2\)

Step-by-step explanation:

Step 1:

Let us figure out the measurements of all the angles first. We are given one angle of 45º, and another of 90º. The angles of a triangle must add up to 180º, hence we can use basic addition and subtraction to find the last angle.

\(\angle=180-90-45\\\angle=45\)

Great our angle is 45º! Notice something...?

Step 2:

We now have two 45º angles in our triangle. This means we have an isosceles triangle.

According to BATh (base angle theorem), in an isosceles triangle, the angles opposite the congruent sides are congruent. Thus, y is congruent to the given side of \(3\sqrt2\).

y=\(\fbox{3\sqrt{2}}\)\(3\sqrt2\)

I hope this helps! Let me know if you have any questions :)

Four friends go out to eat and their meal cost $86. 50. The sales tax 6. 75% and they should tip the waiter 20%.each person must pay $27.7 for their meal

Four friends go out to eat and $86.50 for their meals.

The sales tax is 6.75%, and the waiter is tipped 20%.

M = 86.5 * 10675 / 10000 = 92.34

92.34$, and the total amount of money that four friends will give, including waiter tip, is

T=92.35 * 120 / 100 = 110.80

and each person must give

110.8/4= $27.7

each person must pay $27.7

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Describe four common ways in which individuals respond to perceived inequity are -

Equity, also known as shareholders' equity (or shareholders' equity for private companies), is the sum of money which would be handed back to a company ’s creditors if each of its assets have been liquidated and all of its debt was paid off in the event of liquidation.

Some key features regarding the equity are-

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Check the picture below.

so for the equation y = 40 + 20x, what's an appropriate domain? or namely, what could be some valid values for "x"?

well, Jessica is going to put in 20 bucks only for 12 weeks, so whatever "x" is going to be, is must be from 0 to 12, or in interval notation [0 , 12].

Answer:

A bird drops a stick to the ground from a height of 80 feet. The equation 0=−16x2+64x+80 gives the number of seconds that have passed when it hits the ground. After about how many seconds did the stick hit the ground?

Step-by-step explanation:

h = -16t^2 + 80   Stick hits the ground when h = 0:

0 = -16t^2 + 80    

16t^2 = 80

t^2 = 80/16 = 5

t = POSITIVE root 5 (due to the real world nature of the problem)

t approximately 2.236 seconds.

========================================

Graph is a downward opening parabola with h-intercept of 80, t-intercept(s) of sqrt(5), - sqrt(5)

Symmetric about h-axis, though I would only graph on the right side of the h-axis since  

that is where t >= 0.

Answer:

31 ≤ x

Step-by-step explanation:

22 ≤ x - 9;

22 + 9 ≤ x - 9 + 9;

31 ≤ x

Answer:

7. I attached my answer ... have a nice day

Answer:  2x−4

Step-by-step explanation:

pictue to show you the answer have a bless day

The sum of the given expression is 2x-4

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given are two expressions, −4x+1 and 6x−5, we are asked to find the sum,

On adding, we get,

= −4x+1 + 6x−5

= -4x+6x-5+1

= 2x-4

Hence, the sum of the given expression is 2x-4

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Using the formula T1/2 = 0.693/λ, we may determine decay from half-life.

The half-life is the amount of time needed for half of the initial population of radioactive atoms to decay.

T1/2 = 0.693/λ describes the relationship between the half-life, T1/2, and the decay constant.

A percentage is used to represent the degradation rate.

Simply decreasing the percent and dividing it by 100 yields the decimal equivalent.

The decay factor b = 1-r can therefore be calculated.

For instance, the exponential function's decay rate is 0.25, and the decay factor b = 1- 0.25 = 0.75 if the rate of decay is 25%.

Nearly all decay processes that are exponential, or nearly exponential, are referred to by the phrase "half-life".

Therefore, using the formula T1/2 = 0.693/λ, we may determine decay from half-life.

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Answer:

Your answer is:

1) f >= 17

2) f <= -8

Step-by-step explanation:

Hope this helped : )

a. There are 8 possible birth orders, with probabilities listed in a distribution table; b. The probability of 2 boys and a girl is 3/8; c. The probability of 2 girls and a boy is 1/8; d. The probability of at least one girl is 7/8; e. The probability of at least two boys is 1/2 or 4/8.

a. There are 8 possible birth orders, which are:

BBB

BBG

BGB

GBB

BGG

GBG

GGB

GGG

The probability distribution table is:

Birth Order Probability

BBB 1/8

BBG 3/8

BGB 3/8

GBB 3/8

BGG 3/8

GBG 3/8

GGB 3/8

GGG 1/8

b. The probability of two boys and a girl is 3/8, since there are three birth orders that satisfy this condition (BBG, BGB, and GBB) out of a total of eight possible birth orders.

c. The probability of two girls and a boy in that order is 1/8, since there is only one birth order that satisfies this condition (GGB) out of a total of eight possible birth orders.

d. The probability of at least one girl is 7/8, since there are seven birth orders that have at least one girl (BBG, BGB, GBB, BGG, GBG, GGB, GGG) out of a total of eight possible birth orders.

e. The probability of at least two boys is 4/8 or 1/2, since there are four birth orders that have at least two boys (BBB, BBG, BGB, and GBB) out of a total of eight possible birth orders.

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Answer:

15-10-11-14

Step-by-step explanation:

15+10= 25

25+11= 36

36+14= 50

The weighting of a bit is determined by the value 2^n  in a binary system, by the value 3^n in ternary system and by the value b^n in any base.

The weighting of a bit in a binary system is determined by the value 2^n, where n is the position of the bit. So in a 4-bit binary number, the weighting of the first bit (the far right bit) is 2^0 = 1, the weighting of the second bit is 2^1 = 2, the third bit is 2^2 = 4, and the fourth bit is 2^3 = 8.

In a ternary system, the weighting of a bit is determined by the value 3^n, and for any base the weighting is determined by the value b^n, where b is the base of the system and n is the position of the bit.

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A closed under addition can be proved if the sum of any two members of the set also belongs to the set.

We can take any two even integers and add them together. The result is an even integer. A set is closed under scalar multiplication if the product of any member and a scalar is also in the set. In other words, if x is in S and a is any scalar then ax will be in the set if the set is closed under scalar multiplication. For example, the set of 2 x 2 diagonal matrices is closed under scalar multiplication.

For example,

A = {( x, y) , y = 0 }

B= { (x, y) , x+ y = 1 }

Typical elements of A are (1,0), (2,0). The element (1,1) is an element not in A. Typical elements of B are (1,0), (1/2,1/2). The element (1,1) is an element not in B. Now A and B carry an addition that is  (x, y)+(x', y')=(x + y, x' + y')). Saying that A is closed under addition just means that whenever you take two elements in A, the sum of those elements is again in A. Let's check if this is the case: two elements in A have the form (x, 0) and (x', 0). The sum of those elements is (x + x', 0), and this is again in A. Thus A is closed under addition.

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In quadrant IV, \(\cos(A)\) is positive. So

\(\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} \approx 0.6258\)

Then by the definition of tangent,

\(\tan(A) = \dfrac{\sin(A)}{\cos(A)} \approx \dfrac{-0.78}{0.6258} \approx \boxed{-1.2465}\)

Answer:

True

Step-by-step explanation:

We need to verify whether 15 and 20 are the correct solution to the rule of "The difference between the 2 number is 5 and the number are in the ratio 3 : 4". Let's see,

First rule → The difference between the 2 numbers is 5

20 - 15 = 5 ⇒ Correct

Second rule → The numbers are in the ratio 3 : 4

15 : 20 ( ÷ 5 to both ratio's ) 3 : 4 ⇒ Correct

Answer:

please see the attached picture for full solution

hope it helps...

Good luck on your assignment..

According to the given statement Betsy has traveled a total distance of 60 yards.

To find the total distance Betsy has traveled, we need to calculate the distance between each location and sum them up.

Given that one unit on the coordinate grid equals 10 yards, we can determine the distance between each location by finding the difference in their coordinates and multiplying it by 10.

The coordinates for Betsy's path are:
Location 1: (0, 0)
Location 2: (1, 0)
Location 3: (2, 0)
Location 4: (3, 0)

The distance between Location 1 and Location 2 is 1 unit, which is equal to 1 * 10 = 10 yards.

The distance between Location 2 and Location 3 is also 1 unit, which is equal to 1 * 10 = 10 yards.

The distance between Location 3 and Location 4 is 1 unit, which is equal to 1 * 10 = 10 yards.

To return back to Location 1, Betsy will need to travel from Location 4 to Location 1.

The distance between these two locations is 3 units, which is equal to 3 * 10 = 30 yards.

Summing up the distances:
10 yards + 10 yards + 10 yards + 30 yards = 60 yards

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Answer:

To answer this u need the formula v=pi r^2h. Since r=9 and h= 2, we could solve the equation by plugging in the variables. v= (3.14)(9)^2(2) is equal to 508.94

#a

\(\\ \rm\Rrightarrow f(-4)\)

\(\\ \rm\Rrightarrow 3(-4)+2\)

\(\\ \rm\Rrightarrow -12+2\)

\(\\ \rm\Rrightarrow -10\)

#b

#1

\(\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}\)

\(\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}\)

Find y

\(\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}\)

Inverse is

\(\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}\)

#2

\(\\ \rm\Rrightarrow gof(x)\)

\(\\ \rm\Rrightarrow g(f(x))\)

\(\\ \rm\Rrightarrow g(3x+2)\)

\(\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}\)

\(\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}\)

\(\\ \rm\Rrightarrow \dfrac{6x+3}{3}\)

If we factor out

\(\\ \rm\Rrightarrow \dfrac{2x+1}{1}\)

\(\\ \rm\Rrightarrow 2x+1\)

#c

\(\\ \rm\Rrightarrow f(x)=g(x)\)

\(\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}\)

\(\\ \rm\Rrightarrow 3(3x+2)=2x-1\)

\(\\ \rm\Rrightarrow 9x+6=2x-1\)

\(\\ \rm\Rrightarrow 7x=-7\)

\(\\ \rm\Rrightarrow x=-1\)

Answer:

Given functions:

\(f(x)=3x+2\)

\(g(x)=\left(\dfrac{2x-1}{3}\right)\)

Part (a)

\(\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}\)

Part (b)(i)

\(\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}\)

Part (b)(ii)

\(\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}\)

Part (c)

\(\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}\)

Given Information:

Mean = μ = 12.2

Standard deviation = σ = 2.5

Required Information:

1. z-value = ?

2. P(12.2 < X < 14.3) = ?

3. P(X < 10.0) = ?

Response:

1. z-value = 0.72

2. P(12.2 < X < 14.3) = 29.96%

3. P(X < 10.0) = 18.94%

Normal Distribution is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

1. We want to find out the z-value associated with 14

\(P(X=14)=P(Z=\frac{\text{x}-\mu}{\sigma})\)

\(P(X=14)=P(Z=\frac{14-12.2}{2.5})\)

\(P(X=14)=P(Z=\frac{1.8}{2.5})\)

\(P(X=14)=P(Z=0.72)\)

Therefore, the z-value associated with X = 14 is 0.72

2. We want to find out the proportion of the population that is between 12.2 and 14.3.

\(P(12.2 < X < 14.3)=P(\frac{\text{x}-\mu}{\sigma} < Z < \frac{\text{x}-\mu}{\sigma})\)

\(P(12.2 < X < 14.3)=P(\frac{12.2-12.2}{2.5} < Z < \frac{14.3-12.2}{2.5})\)

\(P(12.2 < X < 14.3)=P(\frac{0}{2.5} < Z < \frac{2.1}{2.5})\)

\(P(12.2 < X < 14.3)=P(0 < Z < 0.84)\)

\(P(12.2 < X < 14.3)=P(Z < 0.84)-P(Z < 0)\)

The z-score corresponding to 0 is 0.50

The z-score corresponding to 0.84 is 0.7996

\(P(12.2 < X < 14.3)=0.7996-0.50\)

\(P(12.2 < X < 14.3)=0.2996\)

\(P(12.2 < X < 14.3)=29.96\%\)

Therefore, the proportion of the population that is between 12.2 and 14.3 is 29.96%

3. We want to find out the proportion of the population that is less than 10.0

\(P(X < 10.0)=P(Z < \frac{\text{x}-\mu}{\sigma} )\)

\(P(X < 10.0)=P(Z < \frac{10.0-12.2}{2.5} )\)

\(P(X < 10.0)=P(Z < \frac{-2.2}{2.5} )\)

\(P(X < 10.0)=P(Z < -0.88)\)

The z-score corresponding to -0.88 is 0.1894

\(P(X < 10.0)=0.1894\)

\(P(X < 10.0)=18.94\%\)

Therefore, the proportion of the population that is less than 10.0 is 18.94%

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.0, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.6 then go for 0.00 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

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The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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