The 4th term of an A.P. is 27. and the sum of the 1st and the fourth term is 42. Find the common difference

Answer:

Step-by-step explanation:

the answer is 46.989

tenths, ones, decimal, hundredths, thousandths

the answer must be greater than 46.98 but less than 47.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.105ft2 is the area of given figure.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

The given figure has rectangle and semi circle.

Area of rectangle=length * Breadth

=10*8

=80 ft2

Area of semicircle=1/2πr2 (r=4ft)

=1/2*3.14*(4)^2

=3.14*4*2=25.12ft2

Therefore area of figure is

=Area of rectangle+Area of semicircle

=80ft2+25.12ft2

=105ft2.

Therefore area of figure is 105ft2.

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Answer:

0.2

Step-by-step explanation:

Divide 2 by 9. You’ll get 0.222222…

So, you have to round it down to 0.2

I hope this helps. Please mark me brainliest.

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Explanation:

Define the following three events:

Notation like P(A) = 12/20 means the probability of event A (aka picking the plain biscuit) is 12/20 since there are 12 plain biscuits out of 20 total. I'll leave the fraction un-reduced so we can see where the 12 and 20 come from. Going from 12/20 to 3/5 has us lose vital information about the original values.

Notation like AB means a plain biscuit was selected first and then a chocolate biscuit is selected second in that exact order. I'm assuming the first selection is not replaced. This makes the probability of the second selection dependent on the first.

So,

P(AB) = P(A)*P(B given A) = (12/20)*(5/19) = 3/19

P(AC) = P(A)*P(C given A) = (12/20)*(3/19) = 9/95

P(BC) = P(B)*P(C given B) = (5/20)*(3/19) = 3/76

The last step is to add those results to get the probability of event AB, event BC or event AC of occurring. Addition is possible since the events are mutually exclusive.

P(AB)+P(AC)+P(BC) = 3/19 + 9/95 + 3/76 = 111/380

I've skipped a few steps, so let me know if you need to see the finer details. Also feel free to ask about any questions in general if they come up.

The height of the pine tree shaped like a cone is 58.03 feet.

The curved surface of a cone is when we only consider the surface area of the sides.

We know the general formula for the volume of a cone is (1/3)πr²h.

Given, the volume of a pine tree shaped like a cone is 3887.2 cubic feet also given that it has a radius of 8 feet,

∴ We can obtain the height of the pine tree by equating given volume with the formula and substituting the value of radius.

So, (1/3)π(8)²h = 3887.2.

(1/3).(3.14).(64)h = 3887.2.

(200.96/3)h = 3887.2.

h = (3887.2×3)/200.96.

h = 11661.6/200.96.

h = 58.03 feet.

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Answer:

$690.63

Step-by-step explanation:

45 minutes = 0.75 hr, so he worked for 48.75 hrs.

This means he worked 8.75 hours of overtime, so his pay is

[tex]40(13)+(8.75)(13)(1.5) \approx \$690.63[/tex]

-15_, -9, -3_, 3, 9...

First of all we understand about what is sequence ?

A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function. Sequences can be both finite and infinite.

Now we know that

Arithmetic = each new term differs from the previous term by a fixed amount.

an = a1 + d (n − 1)

Geometric = each element after the first is obtained by multiplying the previous number by a constant factor

an = a1 (r)^(n − 1)

Given pattern is

_,-9,_,3,9

find out the blanks by following a pattern ..

The term to term rule of a sequence describes how to get from one term to the next.

There is the difference of +6

hence The common different is +6.

-15_, -9, -3_, 3, 9...

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The sequence is -2 1/4, - 1.2, -0.7, 2 1/2, 2 3/4.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

We have given number as

-2 1/4 = -2.25

-1.2

-0.7

2.5

2.75

So, the arrangement from least to greatest is -2 1/4, - 1.2, -0.7, 2 1/2, 2 3/4.

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If the mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by y = 3.50x + 6.00, then the number of games you can bowl for $34 is equal to 8.

A linear function can be described as an equation in which the highest power of the variables is not more than 1. As the linear function given is;

y = 3.50x + 6.00

Here y represents the total cost and x represents the number of games played.

We can find the number of games you can bowl for $34 as follows;

y = 3.50x + 6.00

34 = 3.50(x) + 6.00

34 - 6.00 = 3.50(x)

28 = 3.50(x)

x = 28 ÷ 3.50

x = 8

Hence, the number of games you can bowl for using the equation y = 3.50x + 6.00 is calculated to be 8.

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The statement which are true for triangle LMN are :

1 ) The angle at vertex L is acute.

2) The angle at vertex N is acute.

What is obtuse angle ?

An obtuse angle is defined as an angle measuring less than 180 degrees and greater than 90 degrees. Examples of obtuse angle degrees include 165°, 135°, 110°, 179°, 91°, etc., which lie between 90° and 180°.

Here, it is given that triangle LMN has an obtuse angle at vertex M that is :

The angle formed by vertex L and N will be acute angle that is less then 90 degrees as to satisfy the triangle law of addition (all sum of all the angles of a triangle is 180 degree).

Therefore, option A and D are correct.

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Answer:  1, 2 and 5

Step-by-step explanation:

Analyzing Obtuse Triangles
see picture

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

Explanation:

Central angle AOC is 144 degrees. This means arc ABC is 144 degrees because the central angle subtends this arc.

The remaining bit of the circle is 360-144 = 216 degrees. If we placed point E somewhere on the edge of the circle, toward the bottom, then major arc AEC is 216 degrees in measure.

Notice how inscribed angle ADC subtends this 216 degree arc. So according to the inscribed angle theorem, angle ADC is half of the 216 degree arc at 216/2 = 108 degrees.

Angle APD = 180 - (angle APC) = 180 - 145 = 35 degrees

------------------------

Focus solely on triangle ADP. We have these interior angles

The three interior angles must add to 180

A+D+P = 180

A+108+35 = 180

A+143 = 180

A = 180-143

A = 37 which is the measure of angle BAD.

Answer:

b) $1,391.25

Step-by-step explanation:

Noon is at 12pm, so 8am-12pm will be 4 hours.
8821-3256=5565, so the snack bar made $5565 in 4 hours, to find how much it made in 1 hour we need to divide 5565 by 4.

5565/4=1391.25

The Approximate assessment probability that next year is temperature year 16 will be in the 90s is 0.53

In the image that we have, there are 8 years out of a total of 15 years that would be having the temperature in the 90s.

This can be written in the fraction as 8 / 15 = 0.53

The probability can be defined as the chances of having something happening.

Hence we would say that the Approximate assessment probability that next year is temperature year 16 will be in the 90s is 0.53

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The logarithmic form of 5⁻³ = 1/125 is , [tex]log_5(\frac{1}{125} ) =-3[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function or equation

           x define expression

Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms :

According to statement,

5⁻³ = 1/125

as, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex]

Here,

a= 5, x= -3, N = 1/125

therefore logarithmic form is :  [tex]log_5(\frac{1}{125} ) =-3[/tex]

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The simplified value of the expression is [tex]-2^{2/3}[/tex].

The cube root of any given number is that number which we can multiply 3 times by itself to get the original number. It is denoted by ∛, for example- the cube root of x will be ∛x. It can also be written as (x)^1/3.

Here, we are given the expression ∛4 - 2∛4

We can also write this expression as follows-∛4 (1 - 2)= ∛4(-1)= - ∛4

Further, 4 can be written as: 2 × 2 = 2² = - (∛2)² = [tex]-2^{2/3}[/tex]

We cannot simplify this expression any further.

Thus, the value of the expression comes out to be [tex]-2^{2/3}[/tex].

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Since Jasmine wants to enter a career with median earnings of at least $33,500, but she doesn’t want to go to college, the occupation that fits her will be C Private detective.

It should be noted that from the information, Jasmine wants to enter a career with median earnings of at least $33,500, but she doesn’t want to go to college.

A Makeup artist earns $31,820.

A Mathematician earns $86,930.

A Private detective earns $33,750

A Massage therapist earns $33,400.

Therefore, the best occupation for her since she doesn't want to go to college and earns above $33500 is the private detective.

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Answer:

C. Private detective

Step-by-step explanation:

Answer:

Toyota

Step-by-step explanation:

im not sure im a 5th grder that just guessed

Answer:

a) 33/50         b) 17/50

Step-by-step explanation:

total cars = 250

toyotas = 165

The probablity of the first car to leave being a toyota is

165/250

Simplify it to 33/50

The probability of the first car to leave not being a toyota is

(250 - 165)/250

= 85/250

= 17/50

The amount of fuel required to drive 250 miles will be 25.14 liters.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that a car consumes 25.00 liters of fuel when driving a distance of 400.0 km. The amount of fuel required for 250 miles will be calculated as:-

1 km = 0.6213 miles

400 km = 400 x 0.6213 miles

400 km = 248.52 miles

248.52 miles = 25 litres

1 mile = 25 / 248.52 litres

250 miles = ( 250 x 25 ) / 248.52 litres

250 miles = 25.14 litres

Therefore, the amount of fuel required to drive 250 miles will be 25.14 liters.

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Answer:

B. 2(5+3)

Step-by-step explanation:

PEMDAS

2(5+3)

5+3= 8

2 × 8 = 16

10 + 6 = 16

Answer:

26

Step-by-step explanation:

[tex]2(4)^0+4! \\ \\ =2(1)+24 \\ \\ =26[/tex]

Using the absolute value function, we have that:

1) The table is:

2) The graph is given at the end of the answer.

3) The rule is: g(x) = |x - 3|.

4) The rule is: D(x) = |x| - 5.

5) The rule is: K(x) = |x - 3| - 5.

The absolute function is defined by:

It measures the distance of a point x to the origin.

Hence, applying the rule, the table is completed as follows:

The function is graphed at the end of the answer.

A translation right of 3 units is given by:

f(x - 3).

Hence:

g(x) = |x - 3|.

A translation down 5 units is given by:

f(x) - 5.

Hence:

D(x) = |x| - 5.

For item 5, the function was shifted 5 units down and 3 right, hence it is given by:

K(x) = |x - 3| - 5.

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Answer: 140

Step-by-step explanation: 25x20=500

32x20=640

640-500= 140!!

The image of Quadrilateral ABCD after transformation is shown in graph with coordinates A' (0, 2), B' (2, 4), C' (5, 4) and D' (4, 3).

What is Transformation?

Transformation is the act or process of changing completely.

The rule of transformation is given as;

(x, y) --> (x-2, y+5)

Now, The coordinates of Quadrilateral ABCD are;

A (2, -3) , B (4, -1), C (7, -1) and D (6, -2)

Apply the rule of transformation to find the coordinates of the image of Quadrilateral ABCD as;

A' (2-2, -3+5) = (0, 2)

B' (4-2, -1+5) = (2, 4)

C' (7-2, -1+5) = (5, 4)

D' (6-2, -2+5) = (4, 3)

Hence, The coordinates of image of Quadrilateral ABCD are;

A' (0, 2), B' (2, 4), C' (5, 4) and D' (4, 3).

And, The image of Quadrilateral ABCD after transformation is shown in graph.

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x + 2 is the graph of the function g, whose graph is a horizontal reduction of the graph of f by a factor of 1/2.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

The translation is a way of changing the position of an object on a xy-plane.

The function that results from shrinking a function f(x) horizontally by a factor of 1/a is given as;

g(x) =1/a f(x)

Give the function f(x) = 2x + 4, which will result in the following function if the function is shortened horizontally:

g(x) = 1/2(2x+4)

g(x) = x + 2

Hence the function g whose graph is a horizontal shrink of the graph of f by a factor of 1/2 is x + 2.

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Equation that has the specified asymptotes for the translation of y=2/x. x=4 and y=-8  is :

y = 2 / x- 4   -  8

The graph is shifted by that many units in the positive direction if you deduct a constant from your original function's x.

The original function's graph is shifted downward by that many units if a constant is subtracted from the y value.

Your first formula was y=2/x. The vertical asymptote is discovered when the denominator's root is solved for. It is x=0 in this instance, or the y-axis.

And when x changes to ∞, y=2/∞=0. This indicates that the y-axis, or your horizontal asymptote, is at y=0.

After seeing the first graph

Now, you can see the transformation of y=2/x below. As is evident, it has shifted 2 units to the right and 8 units down with vertical asymptote at x=4 and horizontal asymptote at y=−8.

you can see the second graph here...

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Yes, the claim is correct because √16 + π = 4 + π and  4 + π  is an irrational number

Rational numbers are numbers that can be expressed as the ratio of two integers while Irrational numbers cannot be expressed as the ratio of two numbers.

The sum of a rational and an irrational number is always an irrational number.

Example:

Consider a rational number: 4 and an irrational number: 2.7582...

When we add these two numbers, we get,

4 + 2.7582... = 6.7582....

Thus, it is clear that this sum is also an irrational number as the numbers after decimal are non-terminating and non-recurring.

Thus, the correct option is that the claim is correct because √16 + π = 4 + π which is an irrational number

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x = 6 is the extraneous solution of the equation

The equation given is

[tex]\sqrt{3x + 7}[/tex] = x -1

To find the Extraneous solution we need to square on both sides of the equation

[tex](\sqrt{3x + 7} )^{2}[/tex] =[tex](x - 1)^{2}[/tex]

3x + 7 = [tex]x^{2}[/tex] --2x + 1

[tex]x^{2}[/tex] - 5x - 6 = 0

[tex]x^{2}[/tex] - 6x + x - 6 = 0

x(x - 6) +1(x -6) =0

(x-6)(x+1) = 0

x = -1, 6

Now we need to put the value of x in the equation

x = -1

[tex]\sqrt{(3 * -1) + 7}[/tex] = -1 -1

[tex]\sqrt{4}[/tex] = -2

2≠ -2

Now put

x = 6

[tex]\sqrt{3 * 6 + 7}[/tex] = 6 -1

[tex]\sqrt{25}[/tex] = 5

5=5

Therefore we get to know that x = -1 is the extraneous solution and x = 6 is the solution of the equation

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Answer: x=7

Step-by-step explanation: 15x=120, x=8, 8-1= 7 brainliest?

Answer:

1. y = 0.5x – 0.5 or y =  1/2x -1/2

2. y = -1.5x – 2   or  y= -3/2x- 2

3. y= -x -5

4. y=x+3

i dk how to do the last picture