The population of a city has increased by 24% since it was last measured. If the current population is 65,100, what was the previous population?

Answer:

16.25

65 x 0.25 = 16.25

If another type of question the total price would be 48.75 :)

The probability of a female being born to a couple using this​ technique is 0.923.

Yes, it is effective in increasing the likelihood that a baby will be a​ female.

Given:

In a test of a​ sex-selection technique, results consisted of 215 female babies and 18 male babies.

Total = 215+18

= 233

1.

The probability of a female being born to a couple using this​ technique is:

p = 215/233

p = 0.923.

hence the probability of the female being born to a couple is 0.923.

2.

Yes it is effective in increasing the likelihood that a baby will be a​ female because the probability of female is higher than the probability of male to be born.

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The equation to find rent difference C from given values of E and L is 1.75M + 3.25. After adding the values of E and L.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The meanings of the word equation and its translations into various languages can vary slightly.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables.

Let E represent Economy

Let L represent Luxury

Let M be the number of miles driven

Let C be how much it cost to rent a luxury car than economy

E = -0.70M + 11.95

L = 1.25M + 17.30

C = L - E

C =(1.25M + 17.30) - (-0.70M + 11.95)

C = 1.25M + 17.30 + 0.70M - 11.95

collect like terms

C = 1.25M + 0.70M + 18.20 - 14.95

C = 1.95M + 3.25

The rent difference between luxury car and economy car is 1.95M +3.25 .

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The value of the function f(5) is - 17.

A linear function is a function that represents a straight line on the coordinate plane.

A linear function in slope intercept form is as follows:

y = mx + b

where

Therefore, for the linear function,  f(4) = −13 and  f(−4) = 19.

f(5) can be found as follows;

-13  = 4m + b

19 = -4m + b

2b = 6

b = 6  /2

b = 3

-13 - 3 = 4m

-16 = 4m

m = -4

Hence,

f(5) = -4(5) + 3

f(5) = -20 + 3

f(5) = - 17

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Answer:

25.1 cm

Step-by-step explanation:

4 * 2 * 3.142 = 25.136 = 25.1 cm

We can rewrite the given logarithmic expression as [tex]ln(\frac{\sqrt{x}(x-1)^3 }{\sqrt[3]({x+1})^2 })[/tex].

So option (D) is the correct answer.

What is a logarithmic expression?

A logarithmic equation is one that involves the logarithm of a variable-containing expression. To solve exponential equations, first, determine whether both sides of the equation can be written as powers of the same number.

The given logarithmic expression can be expressed as

[tex]=\frac{1}{2}\ln}\left(x\right)+3\left(\ln\left(x-1\right)-\frac{2}{9}\ln\left(x+1\right)\right)[/tex]

[tex]=\frac{\ln\left(x\right)}{2}+3\left(\ln\left(x-1\right)-\frac{2}{9}\ln\left(x+1\right)\right)[/tex]

[tex]=\frac{\ln\left(x\right)}{2}+3\ln\left(x-1\right)-\frac{2\ln\left(x+1\right)}{3}[/tex]

By using the logarithmic properties, we get

[tex]=ln(\frac{\sqrt{x}(x-1)^3 }{\sqrt[3]({x+1})^2 })[/tex]

We can rewrite the given logarithmic expression as [tex]ln(\frac{\sqrt{x}(x-1)^3 }{\sqrt[3]({x+1})^2 })[/tex].

So option (D) is the correct answer.

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Answer:

square root of 12, 3,  square root of 21

Step-by-step explanation:

a

3.5 in

b

3 in

c (hypotenuse)

4.60977 in

Area

5.25

in²

The set of side measurements  √12, 3, and √21 could be used to form a right triangle. which is the correct answer would be option (D).

Pythagoras's theorem states that a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

We have to apply Pythagoras's theorem in all the given options to find the right triangle.

As per option (A),

6, 12, 60

6² + 12² = 60²

36 + 144 = 3600

180 = 3600

This equation is not true.

As per option (B),

4, 5, 7

4² + 5² = 7²

16 + 25 = 49

41 = 49

This equation is not true.

As per option (C),

√27, √35, 62

(√27)² + (√35)² = 62²

27 + 35 = 3844

This equation is not true.

As per option (D),

√12, 3, √21

(√12)² + (3)² = (√21)²

12 + 9 = 21

21 = 21

The above equation is true and satisfies Pythagoras's theorem which means these measurements could be used to form a right triangle.

Hence, the correct answer would be an option (D).

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The Angle-Side-Angle Postulate (ASA) asserts that two triangles are congruent if their two angles and included sides are congruent with each other.

We are given that,

BC = EF

∠B = ∠E

∠C = ∠F

We say that by ASA criterion: Δ ABC ≅ ΔDEF.

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Answer:

16

Step-by-step explanation:

12+1=13

13+1=14
14+1=15
15+1=16

1+1=2
2+1=3
3+1=4

---------
4+6=10

10+6=16

(6+6=12)

The equation that best represent the relationship on the scatter plot is y = 6 / 5 x + 18 / 5.

The line of best fit is used to express a relationship in a scatter plot of different data points.

The line of best fit (or trendline) is an educated guess about where a linear equation might fall in a set of data plotted on a scatter plot.

Therefore, the line of best fit will pass through (2, 6)(7, 12) and (12, 18).

Therefore, the equation of the line can be represented as follows;

y = mx + b

where

Therefore,

m = 12 - 6 / 7 - 2

m = 6 / 5

Let's find y-intercept using (2, 6)

6 = 6 / 5(2) + b

6 - 12 / 5 = b

b = 18 / 5

Therefore, the equation is y = 6 / 5 x + 18 / 5

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241,864,704  many different passwords are possible.

The total characters of the password is six in which it is given that first character should start with W, X, Y or Z. So the first character can be filled in 4 ways.

For next five characters it can be any letter of the alphabet or any numeric digit so it will be 26 + 10 = 36.

So second, third, fourth, fifth and sixth space can be taken by 36 characters.

Therefore the total no. of passwords will be 4 * 36 * 36 * 36 * 36 * 36 that is equal to 241,864,704.

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The volume of the right circular cone is, 131.95 cubic centimeter.

What is cone?

A cone is a smooth-tapering three-dimensional geometric object with a flat base and an apex or vertex. The base of a cone is made up of all the points on a plane other than the apex, and the apex is connected to all the other points on the base by a series of line segments, half-lines, or lines.

Here, the radius, r = 3 cm, and height h = 14 cm.

We have to find the volume of right circular cone.

Since,

Volume = [tex]\pi r^2\frac{h}{3}[/tex]

[tex]V = \pi (3)^3(\frac{14}{3})\\ V = \pi (3)(14)\\V = 42\pi \\V = 131.95 cm^3[/tex]

Hence, the volume of the right circular cone is, 131.95 cubic centimeter.

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The amount of interest he would pay for a  loan of $10,000 with a 2% interest rate and for 18 months is $300

Amount of money taken as a loan = $10000

The rate of interest = 2%

The time period of interest is 18 months = 1.5 year

Interst = prt/100

= 10000x 2 x 1.5/100

= 300

Therefore, the amount of interest he would pay for a  loan of $10,000 with a 2% interest rate and for 18 months is $300

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Answer:

a) $4089.55

b) $19089.55

c) $56.80

Step-by-step explanation:

a) (100 + 4.1)/100 = 1.041. So, 15000 × 1.041⁶ = 19089.55. Interest that will be paid: 19089.55 - 15000 = $4089.55 (2 dp).

b) $19089.55 (with interest and principal)

c) 4089.55/72 = $56.80

Answer:X<-2

Step-by-step explanation:

7x+1<-13

7x<-13-1

7x<-14

Answer:

Step-by-step explanation:

the answer is A: x<-2

The maximum value of the function z is 120

The objective function is given as

z = 8x + 3y

While the constraints are given as

x + y ≤ 15

2x + y ≤ 18

x ≥ 0 and y ≥ 0

To determine the feasible region, we simply plot the graphs of x + y ≤ 15 and 2x + y ≤ 18

And we subset the graph to where x ≥ 0 and y ≥ 0

From the graph, we have the feasible coordinates to be

(x, y) = (0, 18), (3, 12) and (15, 0)

Substitute (x, y) = (0, 18), (3, 12) and (15, 0) in z = 8x + 3y

z = 8(0) + 3(18) = 54

z = 8(3) + 3(12) = 60

z = 8(15) + 3(0) = 120

Hence, the maximum value is 120

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For a parallelogram having (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles, if [∠2 = (4x - 20)] and [∠4 = (3x - 11)], then the measure of ∠1 will be 164°.

As per the question statement, a parallelogram has (∠1 and ∠3) and         (∠2 and ∠4) as the two pairs of opposite angles, and [∠2 = (4x - 20)] and [∠4 = (3x - 11)],

Then, we are required to calculate the measure of ∠1.

To solve this question, first we will need to know about two important properties of a parallelogram,

(a) The sum of all the four interior angles of a parallelogram is equal to 360°,

(b) Opposite angles of a parallelogram are equal.

Now since our concerned parallelogram has (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles,

Therefore, (∠1 = ∠3) and (∠2 = ∠4),

And [(4x - 20) = (3x - 11)]...[∵(∠2 = ∠4)]

Or, [(4x - 3x) = (20 - 11)]

Or, [x = 9]

Therefore, [∠2 = ∠4 = (4x - 20) = 16°].

Now, [(∠1 + ∠2 + ∠3 + ∠4) = 360°]

Or, [(∠1 + ∠2 + ∠1 + ∠2) = 360°]...[∵(∠1 = ∠3) and (∠2 = ∠4)]

Or, [{(∠1 + ∠1 ) + (∠2 + ∠2)} = 360°]

Or, [(2∠1 + 2∠2) = 360°]

Or, [2∠1 = {360 - (2 * 16)}°]

Or, [2∠1 = (360 - 32)°]

Or, [2∠1 = 328°]

Or, [∠1 = (328/2)°]

Or, [∠1 = 164°]

That is, for a parallelogram having (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles, if [∠2 = (4x - 20)] and [∠4 = (3x - 11)], then the measure of ∠1 will be 164°

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The runway is 12,130 feet long.

To find are you have to times the two sides, in this case it's 190 X 12,130. To find the length of one of these sides you must divide the area by one known side, in this case 2,304,700/190, which means the answer is 12,130 feet

The unknown variable t has a value of t = (V - 7πr²)/6πr

From the question, we have the following parameters that can be used in our computation:

Formula; V = 6πrt+7πr*2

Rewrite the formula properly

So, we have the following representation

V = 6πrt + 7πr²

Subtract the expression 7πr² from both sides of the equation

So, we have

V - 7πr² = 6πrt + 7πr² - 7πr²

Evaluate the difference

V - 7πr² = 6πrt

So, we have

6πrt/6πr = (V - 7πr²)/6πr

Evaluate

t = (V - 7πr²)/6πr

Hence, the value is t = (V - 7πr²)/6πr

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Answer:

[tex]t = \dfrac{V-7\pi r^2}{6\pi r}[/tex]

Step-by-step explanation:

V = 6πrt + 7πr²

Subtract the term without t from both sides.

V - 7πr² = 6πrt

Now you have a single term with t on the right side and two terms without t on the left side.

Switch sides.

6πrt = V - 7πr²

Divide both sides by 6πr.

[tex] t = \dfrac{V - 7\pi r^2}{6\pi r} [/tex]

Answer:

The slope would be 1/9.

Step-by-step explanation:

From 3 to 4 it would be 1. From -4 to 5 it would be 9, the equation for slope is y/x so it would be 1/9.

solution

slope M =(Y' - Y)/(x' - x)

Indicated by (-4, 3) and (5 , 4)

x = -4 , x' = 5 , y = 3 , y' = 4

M = (4 - 3)/( 5 + 4)

M = 1/9 Ans

0 is an integer number.

A number without a decimal or fractional element is known as an integer, which encompasses both positive and negative numbers, including zero.

i.e. the set of integers is

Z = {... -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, ...}

The integers do not contain any fraction or rational number.

Here,

2.3 is a fraction number so it is not an integer.

And -3/4 is a rational number and rational numbers are not integers.

And pi is irrational number

So,

This three numbers are not an integer

Now,

0 is an integer as per the definition of integers.

Hence,

0 is the integer number

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Answer: 8/7 Or In Mixed Number Form 1 1/7

Step-by-step explanation: Get the common denominator which is 21 because you get 6/7 and multiply the number and denominator by 3. You will get 18/21. Now you add. 18/21 + 6/21 = 24/21. Simplify them by the greatest common factor and so I divide by 3 and get 8/7.

Hoped This Helped!

Answer:

Step-by-step explanation:

6/21 + 6/7

6/21 + 18/21

   24/21   = 1  1 / 7

6 x 3      18

____ =  __

7 x 3      21

- You need common denominators to add fractions together!!

Part (a)

The term "disjoint" is the same as "mutually exclusive".

If events E and F are disjoint, then we know that P(E and F) = 0. In other words, the two events have nothing in common. Therefore, it's impossible for them both to occur simultaneously.

P(E or F) = P(E) + P(F) - P(E and F)

P(E or F) = 0.4 + 0.5 - 0

P(E or F) = 0.9

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

Part (b)

If events E and F are independent, then P(E and F) = P(E)*P(F).

P(E or F) = P(E) + P(F) - P(E and F)

P(E or F) = P(E) + P(F) - P(E)*P(F)

P(E or F) = 0.4 + 0.5 - 0.4*0.5

P(E or F) = 0.4 + 0.5 - 0.2

P(E or F) = 0.9 - 0.2

P(E or F) = 0.7

The equation of line in slope - intercept form is, y = 2x - 13.

What is slope-intercept form of the line?

Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. y = mx + b is the equation in slope intercept form.

Consider the given equation of line y = 2x + 1.

And the point given is, (6, -1).

We have to find the equation of line parallel to the given line and passes through the point (6, -1).

First we have to find the slope of the parallel line.

Since, Slope of the parallel line is same as the slope of the given line.

Here, the slope of the line is 2.

So, the slope of the parallel line is also 2.

Now consider the point slope form of the line,

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex](x_1, y_1)=(6, -1) , m = 2[/tex]

⇒

[tex]y-(-1)=2(x-6)\\y+1=2x-12\\y=2x-12-1\\y=2x-13[/tex]

Hence, the equation of the line parallel to the given line in slope intercept form is, y = 2x - 13.

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Answer:

Step-by-step explanation:

1. x^2 + 4x + 5/x-1

2. x^3-3x^2 + 9x-2 + 3/x+3

3. 2x^2 - 2x+5- 14/3x+1

4.3x2^2- 4x+3 - 13/ 2x-1

5. 3x^2 + 6x + 7 + 12/2x-3

The time taken for the rocket to reach its maximum height as determined from the given information is; 2.25 seconds.

The maximum height reached by the toy rocket is; 88 feet.

It follows from the task content that the maximum height reached by the rocket is to be determined.

The given function is; h (t) = -16 t² + 72t + 7.

Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.

Therefore; at maximum height;

h'(t) = 0

h'(t) = -32t + 72 = 0

-32t = -72

t = -72/-32

t = 2.25 seconds.

Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.

Also, the maximum height reached by the rocket is at; h (2.25);

h(2.25) = -16(2.25)² + 72 (2.25) + 7

= -81 + 162 + 7

= 88.

The maximum height reached is; 88 feet.

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Answer:

1 ) Slope of the line

[tex]m = 2[/tex]

2 ) Equation of the line

[tex]y=2x-2[/tex]

3 ) Values of a and b

a = 5

b = 6

4 ) What is the y-coordinate when?

The y-coordinate is the vertical position of a point in terms of distance and direction along the y-axis.

In this graph, when x = 2 they y-coordinate is also 2 so it is 2 units from the y-axis.

Hope this helps! :)

The domain and range are [−4, 1] & [−4, 5].

What are the domain and range of a graph?

Graphs can also be used to determine the domain and range of functions. Because the domain refers to the set of possible input values, the domain of a graph includes all of the input values shown on the x-axis. The range is the set of possible output values shown on the y-axis.

We have given the graph,

The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis.

The range is the set of possible output values, which are shown on the y-axis.

We can observe that the graph extends horizontally from −4 to the right 1.  so the domain of function h is [−4, 1].

The vertical extent of the graph is 0 to –4, so the range of function h is [−4, 5].

Therefore, the domain and range are [−4, 1] & [−4, 5].

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