Use estimation to evaluate 8,627.5 ÷ 35

 y = 3/8x + 1/4 is equation of linear equation .

What in mathematics is a linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. with m the slope and b the y-intercept as the single constant and a first-order (linear) term.

                   The aforementioned is occasionally referred to as a "linear equation of two variables," where y and x are the variables.

                 There are three main types of linear equations: point-slope form, standard form, and slope-intercept form.

3/2x -4y+1=0

  -4y = -3/2x - 1

    y = 3/8x + 1/4

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The complete question is -

Which equation is equivalent to 3/2x -4y+1=0

As per area of rectangle, the dimensions of the box that yield the lowest cost is (1,1,6)

Area of rectangle:

The standard formula for area of rectangle is calculated as,

A = length x breadth

Given,

A closed rectangular box with volume 6 cubic feet is made from two different types of cardboard. the top and bottom are made with a heavy-duty cardboard that costs 30 cents per square foot. The sides are made from a light-weight cardboard that costs 5 cents per square foot.

Here find the dimensions of the box that yield the lowest cost.

Here let's consider the dimensions of the rectangular box be length l, breadth is b, and height is h.

Now, from the given information, the total cost can be derived as,

=> C=2lb×48+(2bh+2lh)×8

=> C=96lb+16bh+16lh

=> C=16(6lb+bh+lh) -----------------→(1)

Then the given volume is, V = lbh = 6 ---------------→(2) cubic feet.

Then the equation 2,

=> lbh = 6h = 6/lb

And then we have to substitute the value of h in equation 1, we get

=> C(l,b,h)=16(6lb+6/l+6/b)

Now we need to minimize the resulting function of two variables.

Therefore, we need to partially derivative the above function with respect to l,b. And set these equal to zero.

And the for l=0,b is undefined. So we can eliminate l=0.

Here we have to substitute l=1,b=112⇒1 in equation 2, we get

=> lbh=6(1)(1)h=6h=6h=6

Therefore, the critical point is, (1,1,6)

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y=3 is the equation of a horizontal line that passes through the point (9, 3)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

If a line passes through a point (x₁, y₁) and has a slope of m, then the

equation of the line is given by (y-y₁) = m(x-x₁).  

Because the question states the line is horizontal, the slope is zero, or m=0.

Plugging the information into the slope equation gives:

(y-(3)) = 0(x-(9)).

y-3= 0

y= 3.

Hence, y=3 is the equation of a horizontal line that passes through the point (9, 3).

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Answer: 12 years

Step-by-step explanation:

We know that the population decrease rate is 4% each year

So take 7900 times 0.04% = decrease 316 people each year

Then take 7900 - 4300 = 3600 people need to get there

Then take 3600 divided by 316 = 12 years

The discounted price of an item did the price increased after the weekend by a fraction of 1/5.

A fraction can be referred to or considered as a divisional representation of a whole number or a percentage, usually represented as a bigger numerical. A fraction denotes the representation of a number in such a way that the meaning or the accuracy of the number is not disturbed, but is shown differently. One-fifth is 20 percent of the total five parts of a number, and thus, the price increased by 1/5th after the weekend.

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Answer: whats up

hello

Step-by-step explanation:

The expression when Ahmad thinks of a number, n. He adds 4 then multiplies the result by 3 is 3(n + 4).

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this scenario, Ahmad thinks of a number, n. He adds 4 then multiplies the result by 3.

This will be:

= (n + 4) × 3

= 3(n + 4).

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the truth table of expression (A+B).A is T ,T ,F,F . A truth table has one column for each input variable (such as P and Q) and a final column that lists all potential outcomes.

Truth tables are mathematical tables that are used in logic, specifically in relation to Boolean algebra, Boolean functions, and propositional calculus. They contain the functional values of logical expressions on each of their functional arguments, or more specifically, for each combination of values that their logical variables can take.

given

( A+B) . A

A          B      (A + B)      (A+B).A

T           T         T                  T

T           F         T                 T

F           T         T                 F

F           F         F                 F

So , the truth table of expression (A+B).A is T ,T ,F,F .

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An Excel Combo Chart can display two different data series as different series type. A single Excel chart with two Y-axis that allows users to compare data is known as a combo chart.

Step 1: Arrange the data in the worksheet's columns and rows.

Step 2: Choose the information.

Step 3: Click the Combo chart icon on the Ribbon under the Charts group on the INSERT tab.

Step 4: Click each icon with your mouse.

step 5 Double-click the chart type that suits your data.

A combo chart combines two column charts, two line graphs, or a column chart and a line graph into one visual representation.

An Excel Combo Chart can display two different data series as different series type. A single Excel chart with two Y-axis that allows users to compare data is known as a combo chart.

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Answer:

$8 per pound

Step-by-step explanation:

16/2 = 8

Answer: $8

Step-by-step explanation:

16 divided by 2 = $8 per pound

For the given conditions convention B attendance is decreasing at a greater rate.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that, the number of people attending convention A can be modeled by the function as,

f(x) = 1200 • 0.95ˣ

where x is the number of years that the convention has been occurring.

The number of people attending convention A in year 1,

f(x) = 1200 × 0.95¹

f(x) = 1140

The number of people attending convention A in year 2,

f(x) = 1200 × 0.95²

f(x) = 1083

The number of people decreasing in the Convention A,

=1140 - 1083

=57

If the number of people attending Convention B was 2200 in year 1 and 2100 in year 2. The number of people decreasing in the Convention B,

=2200-2100

=100

Thus, for the given conditions convention B attendance is decreasing at a greater rate.

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Answer: 250 grams/packet = 8 packets.

Step-by-step explanation:

To find the number of 250g packets of biscuits that can be made from 2kg of biscuits, we need to first convert the weight of the biscuits to the same unit of measurement. Since 1 kilogram is equal to 1000 grams, 2kg of biscuits is equal to 2000 grams. Therefore, the number of 250g packets of biscuits that can be made from 2kg of biscuits is 2000 grams / 250 grams/packet = 8 packets.

Step-by-step explanation:

1 kg = 1000 g

as k stands for "kilo" meaning 1000.

250 g fit therefore 4 times into 1 kg.

and then 2×4 = 8 times into 2×1 = 2 kg.

so, there can be 8 250 g packets made from 2 kg.

The area of the ring between these two circles if the radius of the larger and the smaller circle is 10 and 6 is 200.96.

Given:

two circles have the same center $c.$

the larger circle has radius $10$

and the smaller circle has radius $6.$

we are asked to determine the  the area of the ring between these two circles.

⇒ Area of the ring =  Area of larger circle - area of smaller circle

⇒ Area of circle = πr²

⇒ Area of larger circle  = π(10)²

= 100π

⇒ Area of small circle = π(6)²

= 36π

Area of the ring =  Area of larger circle - area of smaller circle

Area of the ring = 100π - 36π

= 64π

= 200.96

Hence the area of the ring is 200.96

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The disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values ​​is m, the alternative will be -1/m.

A relationship between two terms on either side of an equal sign is depicted by a straightforward equation.

Simple equations also pursue one or a mixture of the four arithmetic computations of addition, simple arithmetic, multiplication, and division.

There are three basic forms of the system of equations: point-slope form, standard form, and slope-intercept form.

So, Shannon's error:

In a rectangle, the neighboring sides are perpendicular to one other, whereas parallel runs between the opposing sides.

The slope of line segments is equal, and the slope, of a perpendicular line to some other line with a slope, m, is -1/m , thus the slopes of the axis of symmetry should be equal, which gives:

The equation should consist of two sets of linear equations with equal slopes: B. Pair y = -x + 6 and y = -x - 5

Therefore, the slopes of the other two lines are -1/-1 = 1 and the equations of the other two lines are y = x - 4 and y = x - 5 respectively.

Therefore, the disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values ​​is m, the alternative will be -1/m.

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Answer:

first option

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

then the nature of the roots can be found using the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 , then the 2 roots are real and irrational

• If b² - 4ac > 0, and a perfect square, then 2 roots are real and rational

• If b² - 4ac = 0 , then 2 roots are real and equal

• If b² - 4ac < 0 , then 2 roots are not real

3x² + 4x - 2 = 0 ← is in standard form

with a = 3, b = 4 and c = - 2 , then

b² - 4ac = 4² - (4 × 3 × - 2) = 16 - (- 24) = 16 + 24 = 40

since b² - 4ac > 0 , then 2 real and irrational roots

Answer:

2. d = 40; 2 rational

Step-by-step explanation:

The discriminant (d) of a quadratic equation [tex]ax^2 + bx + c = 0[/tex] is:

[tex]\boxed{\mathrm{d =} \ b^2 - 4ac}[/tex].

If:

• d > 0, then there are two real solutions

• d = 0, then there is a repeated real solution

• d < 0, then there is no real solution.

In this question, we are given the quadratic equation [tex]3x^2 + 4x - 2 = 0[/tex]. Therefore, the discriminant of the equation is:
b² - 4ac = (4)² - 4(3)(-2)

             = 16 - (-24)

             = 40

Since the discriminant, 40, is greater than zero, the quadratic equation has 2 rational solutions.

Answer: 29%

Step-by-step explanation:

To find the percent of decrease, you need to first calculate the difference between the original cost and the current cost of the TV. You can do this by subtracting the current cost from the original cost: $700 - $500 = $200.

Next, divide the difference by the original cost and multiply by 100% to express the result as a percentage: ($200 / $700) * 100% = 28.57%.

Rounding this result to the nearest whole percent, we get that the percent of decrease is 29%.

Rounded to the nearest whole percent, the answer is 29%.

The equation that represents the number of pages Ben can read per minute is p = (3/4)m.

The two quantities are said to be in a directly proportionate relation when the connection between them is such that if we increase one, the other will also increase, and if we reduce one, the other quantity will also drop.

If x and y are in direct proportion then

=>  x ∝ y

=>  x = ky  [ where k is constant ]

Here we have,

Ben reads 6 pages in 8 minutes

9 pages can be read in 12 minutes

30 pages can be read in 40 minutes

And the number of minutes = m

Number of pages = p

If observe the given data,

When the number of pages increases, the number of minutes are also increasing, So here we can conclude that the number of minutes is directly proportional to the number of pages

=> p ∝ m

=> p = km --- (1)  

[ where k is constant ]  

From the given data,

At p = 6 pages, m = 8 minutes

=> 6 = k(8)

=> k = 6/8 = 3/4

From (1)

=> p = (3/4)m

Therefore,

The equation that represents the number of pages Ben can read per minute is p = (3/4)m

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Answer:

3x2a2-15xa+10

Step-by-step explanation:

The solution to the equation are x=a

The given equation is sin (2x) = a and 0 < x < pi/2

Sin(2x) = sin x, 0≤x≤2п  ........................... (eq. 1)

Using the trigonometrical formula,

sin(2x) = sin xcosx

Let us subtract the formula from equation 1

2sinxcosx = sinx

Therefore, 2sinxcosx-sinx = 0

Let us remove common terms to get

sinx(2cox-1)=0

Now, sinx=0

x= 0, [tex]\pi[/tex], [tex]2\pi[/tex]

Also, 2cos x =1

This means that cos x = 1/2

By implication, x=cos⁻¹(1/2)

That is to say that x= [tex]\frac{\pi }{3} , \frac{5\pi }{3}[/tex]

In conclusion, the value of [tex]\pi[/tex] is a as a single integer

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Answer:

Plan A is a better deal than Plan B when you use more than 10.4 GB of data in a month. For any usage lower than that, Plan B would be the cheaper option.

Step-by-step explanation:

To determine at which point Plan A is a better deal than Plan B, we need to compare the total cost of each plan for a given amount of data usage.

The total cost of Plan A for 3GB of data is $52 per month. For every additional GB of data, the cost is $3, so if we use x GB of data beyond the included 3GB, the total cost of Plan A would be $52 + $3x.

The total cost of Plan B for 5GB of data is $65 per month. For every additional GB of data, the cost is $1.75, so if we use x GB of data beyond the included 5GB, the total cost of Plan B would be $65 + $1.75x.

To determine at which point the total cost of Plan A is less than the total cost of Plan B, we can set the two equations equal to each other and solve for x:

$52 + $3x = $65 + $1.75x

$1.25x = $13

x = $13 / $1.25

x = 10.4

Therefore, Plan A is a better deal than Plan B when you use more than 10.4 GB of data in a month. For any usage lower than that, Plan B would be the cheaper option.

Let a be the area of smaller pentagon. Then area of the smaller pentagon is a=8 [tex]in^{2}[/tex] .

A pentagon is a 2D polygon with five sides and five angles. The word "pentagon" is created by combining the Greek words "penta" (which means "five") and "gon," which means "angles."

The President and the Secretary of Defense have exercised global command and control over the nation's armed forces from the Pentagon. Since its construction, the Pentagon has served as a national and international emblem. It is, above all, a metaphor for American strength and influence, with all the positive and negative connotations that entails.

Similar figures' surfaces have an area that is proportional to the square of their sides.

The ratio of the sides is on the left, and the ratio of their areas is on the right, therefore we may write this as a proportion.

Keep in mind that the ratio of the sides is squared because we are working with areas.

[tex]\frac{side_{1} ^{2} }{side_{2} ^{2} } =\frac{area_{1} }{area_{2} }[/tex]

Let area a smaller pentagon is a

[tex]\frac{7^{2} }{2^{2} }=\frac{98}{a}[/tex]

a=[tex]\frac{98*4}{49}[/tex]

a= 8 [tex]in^{2}[/tex]

So the area of the smaller pentagon is 8 [tex]in^{2}[/tex]

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Answer:

533

Step-by-step explanation:

3 hours = 180 minutes

2400 : 180 = x : 40

x = 2400 * 40 / 180

x = 2400 * 4 / 18

x = 2400 * 2 /9

x = 800 * 2 / 3

x = 1600/3

x = 533.333333

x = 533

The probability that Steph Curry makes the first 2 free throws and misses the last throw is 81/1000

Let A be the event that Steph Curry makes the free throw.

Let B be the event that Stech Curry does not make the free throw.

According to the problem,

P(A) = 90%

= 9/10

Since B is the complement of A,

P(B) = 1 - P(A)

= 1/10

Hee, Steph Curry gets 3 free throws. Hence, the probability that he makes the first 2 throws while he misses the third one is

P(A) X P(A) X P(B)

= 9/10 X 9/10 X 1/10

= 81/1000

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Answer:

x = 2

Step-by-step explanation:

6 : 4 = 3 : x

x = 4 * 3 / 6

x = 4/2

x = 2

The value of x in the given figure is 2

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.

Given that, Triangle ABC is dilated into A'B'C'

We know that dilated triangles are similar

Hence, their corresponding sides are in equal ratio,

BC : B'C' = AC : A'C'

6 : 4 = 3 : x

x = 4 × 3 / 6

x = 4/2

x = 2

Hence, The value of x in the given figure is 2

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The graph that shows the function with the determined behavior is the last graph, circled on the image given at the end of the answer.

The graph of a function is classified as either increasing, decreasing or constant, as follows:

Hence the fourth graph on the image given at the end of the answer is the one with the desired behavior on each interval.

The graphs are given by the image shown at the end of the answer.

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1) The probability of F2 seed chosen at random will be yellow is the same as asking about the probability of forming a yellow seed in that generation. The answer is 3/4 (75%) because 1/4 = 25% GG is homozygous dominant and the rest 2/4 = 50% Gg are heterozygous.

2) In the F2 generation there are two genotypes that will breed true, which is homozygotic genotypes: GG and gg. But of these two, only one of them is yellow. The answer is 1/3 because from all the yellow seeds that resulted (GG, Gg and gG) only one has the genotype for true breeding.

3) The probability of taking out three seeds in which a least one is yellow can be calculated by subtracting the only  probability that doesn't fit the criterion, which is taking out a green seed 3 times:   = 1/64.

Then subtract that to 1  =  63/64

4) there are three possible groupings in which the green is taken once and the yellow seeds taken twice. The first possibility (follow the example) is the green being the first to come out, another possibility is being the second and the last possibility is being taken in the third time.

For example, Green yellow yellow- probability :

= 9/64

This is one possibily, but since there are 3, multiply it by 3 and you obtain the final answer:27/64.

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The number of applicants that were not accepted are calculated to be 1260.

The number of applicants that were not accepted can be determined as follows;

Since 2 out of every 9 applicants are accepted; therefore the total number of applicants out of which 360 applicants were accepted can be calculated as follows;

360 × 9 / 2 = 3240 / 2 = 1620

Therefore the total number of applicants is calculated to be 1620, out of these 1620 applicants, 360 were accepted therefore the number of applicants that were not accepted can be determined by subtraction.

The number of applicants that were not accepted can be determined by subtracting the accepted applicants from the total number of applicants as follows;

Applicants not accepted = 1620 - 360

Applicants not accepted = 1260

Therefore 1260 applicants were not accepted by the program.

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∫[tex]r(t)dt=[/tex][tex](0,t,\frac{t^2}{2} )+c[/tex] is accurate in its statement.

A definite integral whose limits are functions of the differential variable can be differentiated using Newton Leibniz Theorem's formula. Differentiation under the integral sign is another name for this. When limits are functions of the differential variable, the Newton Leibniz Theorem makes it simple to handle problems involving the differentiation of a definite integral.

Suppose that F(x) is a function whose derivative is f(x). Consequently, abf(x) dx = F(b) - F (a).

The Newton Leibniz Theorem can be used to determine the derivative of a definite integral when the limits of a definite integral are functions of t and the integrands are functions of x or vice versa.

As a result, statement C is the appropriate response.

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