SOLVING WORD PROBLEMS INVOLVING QUADRATIC INEQUALITIES:
As an architect, your job is to fulfill the requirements of the client. You are demanded by your client to have a plan or sketch in planting a garden and surrounding it with decorative stones. The desired length of the lot is 15 meters longer than its width. The area of the rectangular plot should not be more than 126 m^2.

Solution:

Answer: 15

Step-by-step explanation:

slow eater lol.

in one fifth of a minute, they ate 3 pieces. so add the other four fifths, 3 + 3 + 3 + 3 + 3, and youll get 15. easier to just multiply tho, 1/5 is 3, so 5/5 would be 3(5) = 15. hope this helps

Answer:

y = 554.55 minutes

Step-by-step explanation:

y = 5.5/10 x

y = 5.5/10 x 305

y = (5.5 x 305) / 10

y = 1677.5 / 10

y = 554.55 minutes

Answer:

It is given that:

The equation is:

y = (5.5/10)x

Here y represents the total time in minutes and x represents the number of pages read.

Plug x = 305

y = (5.5/10)(305)

y = 167.75 minutes

Thus, it will take 167.75 minutes to read a book that has 305 pages.

Answer:

y = -2/3x + 13/3

Step-by-step explanation:

y = mx + c

m = -2/3

y = -2/3x + c

Put in your point (2,3):

3 = -2/3 (2) + c

3 = -4/3 + c

3 + 4/3 = c

13/3 = c

so

y = -2/3x + 13/3

The equation of the least-squares line when y is expressed in kilograms is y = 2114.20 + 18.96x.

What is the linear system?

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more two variables.

The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for five different spot welds on steel. A scatterplot shows a pronounced linear pattern.

Given the least square regression model equation:

y hat = -959.00 + 8.60x

weld diameter x ; shear strength y (in pounds)

1 lb = 0.4536 kg

To express shear strength y in kilogram:

y is multiplied by 0.4536

(y hat × 0.4536) = -959.00 + 8.60x

Divide both sides by 0.4536

(y hat × 0.4536) / 0.4536= (-959.00 + 8.60x) / 0.4536

y hat = 2114.1975 + 18.959435x

y hat = 2114.20 + 18.96x

The equation of the least-squares line when y is expressed in kilograms is y = 2114.20 + 18.96x.

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Disclaimer

The question given by you is incomplete, the above answer is done as per a similar question

The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for five different spot welds on steel. A scatterplot shows a pronounced linear pattern. The least-squares line is y hat = -959.00 + 8.60x. Because 1 lb = 0.4536 kg, strength observations can be re-expressed in kilograms through multiplication by this conversion factor: new y = 0.4536(old y). What is the equation of the least-squares line when y is expressed in kilograms? (Give the answer to two decimal places.)

Answer:

b

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180° , that is

∠ 1 + 92° + 30° = 180°

∠ 1 + 122° = 180° ( subtract 122° from both sides )

∠ 1 = 58°

Answer:

[tex]\huge\boxed{\sf < 1 = 58\°}[/tex]

Step-by-step explanation:

So,

30 + 92 + ∠1 = 180

122 + ∠1 = 180

Subtract 122 to both sides

∠1 = 180 - 122

[tex]\rule[225]{225}{2}[/tex]

By the use of a mirror, the school is 19.38 meters tall

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

From the above parameters, we have the following equivalent ratio

Distance walked from the school : Height of the school = Distance walked to the other side : Distance from her eyes to the ground

Substitute the known values in the above equation, so, we have the following representation

11.25 : Height of the school = 0.9 : 1.55

Express as fraction

Height of the school/11.25 = 1.55/0.9

So, we have

Height of the school = 11.25 * 1.55/0.9

Evaluate

Height of the school = 19.38

Hence, the height of the school is 19.38 meters

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The probability of getting at least one even number and at least one odd number is (3/4).

What is the probability of getting an even number in a single-dice throw?

If we throw a die, we have six possible outcomes: {1,2,3,4,5,6}. Now:

P(E) = Favourable outcomes / Total outcomes

     = 3/6

     = 1/2

As per the question, we need at least one even number and one odd number in three throws. We know that for independent events:

P(A∩B∩C) = P(A)*P(B)*P(C)

Let A be the event of getting an even number and B be the event of getting an odd number on the dice.

P(A) = P(B) =  1/2

So, we need to have events occur like:

ABA or ABB (with all their possible combinations)

So, P(A∩B∩A) = (1/2)*(1/2)*(1/2) = 1/8

P(A∩B∩B) = (1/2)*(1/2)*(1/2) = 1/8

Possible number of combinations of ABA = 3

Possible number of combinations of ABB = 3

So, required probability = 3*(1/8) + 3*(1/8)

= 6/8

= 3/4                          

So, the Required probability is (3/4)

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By using multiplication, it can be calculated that

3 [tex]\times[/tex] 9423 = 28269

What is multiplication of integers?

At first it is important to know about integers

Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.

Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.

Here the given multiplication is 3 [tex]\times[/tex] 9423

3 [tex]\times[/tex] 9423 = 28269

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Answer:i dont now

Step-by-step explanation:

I SAID I DONT NOW

Answer:

39.2

Step-by-step explanation:

Avg ROC = [tex]\frac{f(b) - f(a)}{b-a} \\[/tex]

Thus

a = 0

b = 2.5

Avg ROC = [tex]\frac{98 - 0}{2.5-0} \\[/tex]

Avg ROC = 39.2

The snail travels at rate 0.528 in/sec.

What is rate?

A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities and it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

Given that,

A snail travels at a rate of 31.68 in./min.

This means

In 60 sec the snail travels 31.68 in.

In 1 sec the snail travels (31.68/60) in = 0.528 in.

This implies that the snail travels at rate 0.528 in/sec

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Answer:

[tex] x = \dfrac{9}{8} \pm \dfrac{\sqrt{241}}{8} [/tex]

Step-by-step explanation:

[tex] x^2 + \dfrac{9}{-4}x + \dfrac{81}{64}= \dfrac{5}{2} + \dfrac{81}{64} [/tex]

[tex] \dfrac{-4x^2}{-4} + \dfrac{9x}{-4} = \dfrac{-10}{-4} [/tex]

[tex] x^2 + \dfrac{9}{-4}x + \dfrac{81}{64} = \dfrac{5}{2} + \dfrac{81}{64} [/tex]

[tex] (x - \dfrac{9}{8})^2 = \dfrac{241}{64} [/tex]

[tex] x - \dfrac{9}{8} = \pm\sqrt{\frac{241}{64}} [/tex]

[tex] x = \dfrac{9}{8} \pm \dfrac{\sqrt{241}}{8} [/tex]

The Probability of selecting a Vowel is 21/50

What is Probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Solution:

Adding the total number of Vowels = 9 + 12 + 9 + 8 + 4 = 42

Total Number of Letters = 100

Probability of getting a Vowel = 42/100

Probability = 21/50

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As per the set theory, the number of student who take math course is 800

Set:

In math, set means an organized collection of objects and can be represented in set-builder form or roster form.

Given,

Here we know that suppose that all of the 1000 first-year students at a certain college are enrolled in a math or an English course. suppose 400 are taking both math and English and 600 are taking English.

Now, we need to find the number of students who take math course.

While looking into the given question we have identified that,

Total Number of students = 1000

Number of students in both course = 400

Number of students taking English = 600

Then the number of students who take math course is calculated as

=> 1000 - 600 + 400

=> 800

Therefore, the resulting number of students is 800.

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The number of cups of strawberries that will be needed is 10/3

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

Ratio = 3 : 2

This ratio means that

Ratio = blueberries : strawberries

Substitute the known values in the above equation, so, we have the following representation

blueberries : strawberries = 3 : 2

Also, from the question, we have

blueberries = 5

This means that

5 : strawberries = 3 : 2

So, we have

strawberries/5 = 2/3

Multiply both sides by 5

strawberries = 10/3

Hence. strawberries will be 10/3 cups

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C.( $100.00) is the correct answer.

If you want to know how to get that answer, simply add all of the Cash and Checks together.

Answer:

θ = 35°

tanθ = 1

Step--step explanation:

using SOH CAH TOA

Hypotenuse = 7

opposite = 4

adjacent = needs to be found

θ = needs to be found

According to Pythagoras theorem

Hyp² = opp² – Adj²

7² = 4² – Adj²

Adj² = 49 – 16

Adj ² = 33

Adj = 5.7

what connects Hypotenuse and opposite os SOH

sinθ = opposite/Hypotenuse

sin θ = 4/7

sinθ= 0.57

divide bith sides by sin

θ = sin-¹ 0.57

θ = 34.75°

to find Tan θ TOA

Tanθ = opposite / adjacent

Tanθ = 4/5.7

Tan θ= 0.7018

Tanθ = 1

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Answer:

Yes, 78 is a multiple of 2. A multiple of a number is a number that can be evenly divided by that number, and 78 can be evenly divided by 2. To prove this, we can perform the division: 78 / 2 = 39. Since there is no remainder when we divide 78 by 2, this means that 78 is a multiple of 2.

After solving the given expression → F = - m + B/q³  for  [B], we get -

B = q³(F + M).

We have the following equation -

F = - m + B/q³

We have the following equation -

F = - m + B/q³

On solving for [B], we get -

F + M = B/q³

B = q³(F + M)

Therefore, the given expression after solving for [B], we get -

B = q³(F + M).

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The shape of the cross section is a triangle. It is always triangle if the triangular pyramid sliced from any side perpendicularly to its base. See the picture in the attachment!

A pyramid is a polyhedron that has one base and lateral faces with the vertex at the top of the pyramid. The shape of lateral faces is always a triangle. While, the shape of the base varies and is used to name the pyramid.

A triangular pyramid is a pyramid with a triangular base. It has three lateral faces.

If a triangular pyramid is sliced by a plane from any side that is perpendicular to its base, the cross section formed will be a triangle. One line is at the base and two lines are at the lateral faces. See the picture in the attachment!

Hence, the cross section formed by the slicing is a triangle.

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After 7 days, people will stop watching the video.

What is Substitution ?

The algebraic approach to solving simultaneous linear equations is known as substitution technique. In this process, the value of one variable from one equation is substituted in the second equation, as the name indicates.

We'll use the idea of substitution in this case.

The given equation is:-

y = -0.625x² + 5x

where x = number of days

y = number of views per day in thousands

Let's check, number of views on day 1

x=1

y = (-0.625×1²) + (5×1) = 4.375 => 4375 views

For day 2

x=2

y=(-0.625×2²)+(5×2) = 7.5 => 7500 views

For day 3

x=3

y=(-0.625×3²)+(5×3) = 9.375  => 9375 views

For day 4

x=4

y=(-0.625×4²)+(5×4) = 10  => 10000 views

For day 5

x=5

y=(-0.625×5²)+(5×5) = 9.375  => 9375 views

For day 6

x=6

y=(-0.625×6²)+(5×6) = 7.5 => 7500 views  

For day 7

x=7

y = (-0.625×7²) + (5×7) = 4.375 => 4375 views

For day 8

x=8

y=(-0.625×8²)+(5×8) = 0  => 0 views

So, on day 8 there are 0 views, which means people will stop watching video after 7 days.

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From 8th day people will stop watching the video.

given:

y = -0.625x² + 5x

where x represents the number of days

y represents the no. of views per day.

solution:

for x=1

y = (-0.625) + (5)

= 4375

for x=2

y = (-0.62 5× 2² )+ (5 × 2 )

= 7500

for x=3

y=(-0.625 × 3² ) + ( 5 × 3 )

= 9375

for x=4

y=(-0.625 × 4² ) + ( 5 × 4 )

= 10000

for x=5

y=(-0.625 × 5² ) + ( 5 × 5 )

= 9375

For x=6

y=(-0.625 × 6² ) + ( 5 × 6 )

= 7500  

For x=7

y = (-0.625 × 7² ) + ( 5 × 7 )

= 4375

For x=8

y=(-0.625 × 8²)+ ( 5 × 8 )

= 0

therefore from 8th day there will be 0 views on the video.

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According to the given statement 15600 possible options to a unique code.

A digit is a numerical unit of measurement and labeling in mathematics. The real numbers 1, 2, 3, 4, and so on constitute the first instances.

For the first password, we can choose any of the 26 numbers that are able, right? So for the first, we have 26 possible options.

For the second, we have 26 possible options minus 1 option which is already in use in the first password, so we have 26 -1 = 25 possible options here.

For the third, we also have 26 options, but we have to consider 2 unavailable options (1 in the first and 1 in the second), so we have 26 -2 = 24 options.

To finish it, we just have to multiply the possibilities of each lock:

26 * 25 * 24 = 15600 possible options to a unique code.

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The slopes of both equations are different. Then the lines are neither parallel nor perpendicular. Then the correct option is A.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equations of the line are given as,

y - (2/5)x = 1

y = (2/5)x + 1

25y + 10x = 50

y = -(2/5)x + 2

The slopes of both equations are different. Then the lines are neither parallel nor perpendicular. Then the correct option is A.

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The solution to the system of equations is ( 160/11 , -100/37 )

The value of x = 160/111

The value of y = -100/37

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

y = 15x + 9y   be equation (1)

y = 12x - 20   be equation (2)

Now , on simplifying the equations , we get

From equation (1) , we get

y = 15x + 9y

Subtracting y on both sides of the equations , we get

15x + 8y = 0

Subtracting 15x on both sides of the equations , we get

8y = -15x

Divide by 8 on both sides , we get

y = -15x/8   be equation (3)

Substitute the value of y from equation (3) in equation (2) , we get

12x - 20 = -15x/8

Multiply by 8 on both sides of the equation , we get

96x - 160 = -15x

Adding 15x on both sides of the equation , we get

111x - 160 = 0

Adding 160 on both sides , we get

111x = 160

Divide by 111 on both sides , we get

x = 160/111

Now , substitute the value of x in equation (3) , we get

y = -15x/8

y = ( -15 x 160 ) / ( 111 x 8 )

y = -100/37

Therefore , the value of x is 160/111 and value of y is -100/37

Hence , The solution to the system of equations is ( 160/11 , -100/37 )

The value of x = 160/111

The value of y = -100/37

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There are 16 different truth tables of compound propositions are there that involve the propositional variables p and q

What do you mean by compound proposition?

A truth table for compound propositions reveals the conditions under which the compound assertion is true. This uses more than one of the logical operators "and," "or," "negation," etc., but otherwise is identical to basic truth tables for these logical operators.

The variety of truth tables indicates the range of p and q-based functions that are possible.

Now that there are two propositions for which we are creating truth tables, p and q, any truth table will have four rows.

Each of these four rows can have a value of 0 or 1, hence there are a total of [tex]2^{4}[/tex]=16 possible ways in which these four rows can be given values.

Therefore, there are 16 different truth tables of compound propositions are there that involve the propositional variables p and q

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Therefore , the upper bound of the confidence interval is  - 8.82 .

A confidence interval in frequentist statistics is a range of estimates for an unobserved parameter. The most common confidence level for computing confidence intervals is 95%, however other levels, including 90% or 99%, are sporadically employed.

Here,

n1 = 17 ; X1' = 78.4 ; s1² = 90.3

n2 = 13 ; X2' = 92 ; s2² = 107.8

Confidence interval :

(x1 - x2) ± Tcritical * [tex]\sqrt{[(sp^{2} /n1 + sp^{2}/n2)]}[/tex]

Pooled variance = Sp²

=> Sp² = (df1*s1² + df2*s2²) / (n1 + n2 - 2)

df = n - 1

Sp² = (16*90.3 + 12*107.8) / 28

Sp² = 97.8

Tcritical, 90%, df = n1 + n2 - 2 = 28 (1 - tail)

Tcritical = 1.313

(78.4-92)±1.313*sqrt[(sp²/n1 + sp²/n2)]

Margin of Error = Tcritical *[tex]\sqrt{[(sp^{2} /n1 + sp^{2}/n2)]}[/tex]

Margin of Error = (1.313 * √(97.8/17 + 97.8/13)) = 4.7771473

Upper boundary :

(78.4-92) + 4.7771473

-13.6 + 4.7771473

= -8.8228527

= - 8.82

Therefore , the upper bound of the confidence interval is  - 8.82 .

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Answer:

Infinitives are a special form of verbs that can be used as a noun, adjective, or adverb. They are usually made by adding the word to before the base verb, and they can be useful when discussing actions without actually doing the action, such as “I want to go home,” or “To err is human.”

Step-by-step explanation:

The purpose of infinitives is to discuss an action in general instead of a specific instance of the action being done. For example, take a look at these two sentences:

I need to win.

Today, we win.

The first sentence uses the infinitive form of the verb win as a noun; the main verb of the sentence is actually “need.” The second sentence uses the standard form of win as an actionable verb. In the first sentence with the infinitive, the action of “winning” is not actually done; the sentence simply discusses the idea of winning.  The second sentence, however, describes the action of winning.

The equation should she use was k = 2p/x²

Potential energy is the power that an object can store due to its position in relation to other things, internal tensions, electric charge, or other circumstances.

Common kinds of potential energy include the gravitational potential energy of an object, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field. The joule, denoted by the letter J, is the energy unit in the International System of Units (SI).

p=1/2kx²

To get the equivalent formula, we make k the subject

p=1/2kx²

Multiply both sides by 2

2p = kx²

Divide both sides by x²

2p/x² = k

∴ the equivalent formula is;

k = 2p/x² .

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Answer: The equation that has infinitely many solutions is -6x + 35 = -6x + 35

How to determine the equation?

An equation that has infinitely many solutions is represented as:

ax + b = ax + b

The above means that both sides of the  equations are the same

From the list of options, we have:

-6x + 35 = -6x + 35

Both sides of the  equations are the same

Hence, the equation that has infinitely many solutions is -6x + 35 = -6x + 35

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Step-by-step explanation: