Tran bought 25 marbles and put them in his pocket with 10 other marbles. He had a hole in his pocket and lost 6 marbl
Which number sentence tells the story of how many marbles he had left ?

The points where the graph intercepts the x-axis is the root of the function.

from the graph the points are 3.9 and 6.1

The vertex v is at v ( 5, -4 ) this is equivalent to v ( h, k )

the equation of parabola in vertex form is y = a ( x- h )^2 + k

y = a ( x - 5 )^2 + {-4)

substituting point ( 4, -1 ) from the graph we have:

-1 = a ( 4 - 5 )^2 - 4

-1 = a - 4

a = 3

substituting the known values to y = a ( x- h ) + k

y = 3 ( x - 5 )^2 - 4

y = 3 ( x - 5) ( x - 5 ) - 4

y = 3 ( x - 5) ( x - 5 ) - 4

y = 3 ( x^2 - 10x + 25 ) - 4

y = 3x^2 - 30x + 75 - 4

y = 3x^2 - 30x + 71

The points where the graph intercepts the x-axis is the root of the function.

from the graph the points are 2 and 4

The vertex v is at v ( 3, 2 ) this is equivalent to v ( h, k )

the equation of parabola in vertex form is y = a ( x- h )^2 + k

y = a ( x - 3 )^2 + 2

substituting point ( 0, -16 ) from the graph we have:

-16 = a ( 0 - 3 )^2 + 2

-16 = a - 9 + 2

-16 = a - 7

a = -9

substituting the known values to y = a ( x- h ) + k

y = -9 ( x - 3 )^2 + 2

y = -9 ( x - 3) ( x - 3 ) + 2

y = -9 ( x - 3) ( x - 3 ) + 2

y = -9 ( x^2 - 6x + 9 ) - 4

y = 3x^2 - 54x - 81 - 4

y = 3x^2 - 54x - 85

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Answer:  m 21=

I got it right on test!

Step-by-step explanation:

An infant may have had birthing complications that reduced the amount of oxygen in her blood if her Apgar score ranges from 7 at 1 minute to 9 at 5 minutes. In this situation, the hospital nurses will most likely vigorously dry her with a towel while holding oxygen under her nose.

The Apgar score is a recognized and practical way to report on the newborn baby's condition right after birth and their reaction to resuscitation, if necessary. One's particular neonatal mortality or neurologic prognosis cannot be predicted by the Apgar score alone, nor can it be regarded as a result of suffocation. It should also not be utilized to do so. An infant's spontaneous breathing score and the Apgar score given after resuscitation are not the same thing. An enhanced Apgar score reporting form that takes into account concurrent resuscitative treatments is encouraged by both the American Academy of Pediatrics and the American College of Obstetricians and Gynecologists.

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1 hour & 45 minutes is the distance between his home and school.

What is distance short answer?

d=rt

distance = rate of speed times time

d= 33X = 44(7/4-X)

33X = 77- 44X

77X = 77

X = 1 hour

33X = 33 miles

44(7/4 - 4/4) = 33 miles each way

1 hour & 45 minutes = 1 3/4 hours or 7/4 hours

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The the value of constant proportionality k is 3 and the value of y is 42 when the value of x is 14.

Constant proportionality:

Constant proportionality means the ratio of two proportional values at a constant value.

Directly Proportional:

In direct proportion, if one quantity is increased or decreased then the other quantity increases or decreases, respectively.

Given,

Suppose that y is directly proportional to x.

And y = kx.

Here we need to find the value of k when the value of x = 10 and the value of y = 30.

And we also need to find the value of y when the value of x = 14.

First, we have to find the value of k by apply the given value of the equation,

=> 30 = k x 10

=> 30 /10 = k

=> k = 3

Now the value of y when the value of x = 14 and the value of k = 3,

Then

=> y = 3 x 14

=> y = 42.

Therefore, the value of constant proportionality k is 3 and the value of y is 42 when the value of x is 14.

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The answer is m∠1 = 84°

Step-by-step explanation:

m∠4 = m∠2 so m∠2 = 96°

m∠1 + m∠2 = 360 - m∠4 - m∠2

m∠1 + m∠2 = 360 - 96 - 96

m∠1 + m∠2 = 168

m∠1 = 168/2

m∠1 = 84°

The objective of Exploratory Research research is to gather preliminary information that will help define the problem and suggest hypotheses.

Exploratory Research is a methodology approach that explores research

question that have not previously been studied in depth.

The nature of experimental studies is generally frequently qualitative. However, an investigation with a big sample size might also be quantitative. Due to its open-mindedness and flexibility, it is additionally commonly referred to as interpretivism or a grounded theory method.

It is commonly employed when the subject you're examining is new, or perhaps the data collection method is challenging in certain way.

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Answer:

(4), -5/6

Step-by-step explanation:

[tex]13-36x^2-13=-12-13\\-36x^2=-25\\\frac{-36x^2}{-36}=\frac{-25}{-36}\\x^2=\frac{25}{36}\\x=\sqrt{\frac{25}{36}},\:x=-\sqrt{\frac{25}{36}}[/tex]For x^2 = f(a), x = f(a), -f(a)

[tex]x=\sqrt{\frac{25}{36}},\:x=-\sqrt{\frac{25}{36}}\\\sqrt{\frac{25}{36}}\\\sqrt{25}\\\sqrt{5^2}=5\\=\frac{5}{\sqrt{36}}\\\sqrt{36}\\=\sqrt{6^2}=6\\=\frac{5}{6}[/tex]

Reverse the same equation from the negative side

[tex]=-\frac{\sqrt{25}}{\sqrt{36}}\\\sqrt{25}\\=\sqrt{5^2}\\=5\\=-\frac{5}{\sqrt{36}}\\\sqrt{36}\\=\sqrt{6^2}\\=6\\=-\frac{5}{6}[/tex]

Therefore,

[tex]x=\pm\frac{5}{6}[/tex]

Answer:

n = 3p

Step-by-step explanation:

12n + 7p - 6n = 25p

12n - 6n +7p = 25p

12n - 6n = 25p - 7p

6n = 18p

[tex]n=\frac{18p}{6}[/tex]

n = 3p

The price of carrots per ounce is $0.24 .

Ounce is an unit of mass in the Imperial System. It is widely used throughout the world and is one of the oldest units of measurement to still exist. The unit ounce is derived from uncia, a unit of measurement in roman times.

The ounce(abbreviated oz) is equal to approximately 28.35 grams and 16 ounces make up a pound.

Now it is given that a 2-pound bag of carrots cost $7.68 .

Therefore price per pound of carrots=$7.68÷2

Price per pound=$ 3.84 .

Now we know that 16 ounces make up a pound.

Price of carrots per ounce=  $3.84 ÷16

Price per ounce=  $ 0.24

Therefore the price of carrots per ounce is $0.24

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The  entire area under the standard normal distribution curve is always positive even if the z value is negative.

The normal distribution, it's useful to think of the standard deviation as being steps away from the mean. One step to the right or one step to the left is considered one standard deviation away from the mean. Two steps to the left or two steps to the right are considered two standard deviations away from the mean. Likewise, three steps to the left or three steps to the right are considered three standard deviations from the mean.

The probability of the outcome of an experiment is never negative, although a quasi probability distribution allows a negative probability, or quasi probability for some events. These distributions may apply to unobservable events or conditional probabilities.

Therefore,

The value can be negative can be any positive value can be any positive value larger than 1.

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Answer:

[tex]\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{16}{x}-\dfrac{11}{(x+1)}-\dfrac{1}{(x+1)^2}[/tex]

Step-by-step explanation:

When writing an algebraic fraction as an identity, if its denominator has repeated linear factors, the power of the repeated factor indicates how many times that factor should appear in the partial fractions.

Write out the fraction as an identity:

[tex]\begin{aligned}\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{A}{x}+\dfrac{B}{(x+1)}+\dfrac{C}{(x+1)^2}\\\\\implies \dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{A(x+1)^2}{x(x+1)^2}+\dfrac{Bx(x+1)}{x(x+1)^2}+\dfrac{Cx}{x(x+1)^2}\\\\\implies 5x^2+20x+16 & \equiv A(x+1)^2+Bx(x+1)+Cx\end{aligned}[/tex]

Calculate the values of A and C using substitution:

[tex]\begin{aligned}\textsf{When }x=0 \implies 16 & =A(1)+B(0)+C(0) \implies A=16\\\\\textsf{When }x=-1 \implies 1 & =A(0)+B(0)+C(-1) \implies C=-1\end{aligned}[/tex]

Substitute the found values of A and C and expand the identity:

[tex]\begin{aligned}\implies 5x^2+20x+16 & \equiv 16(x+1)^2+Bx(x+1)-x\\& \equiv 16x^2+32x+16+Bx^2+Bx-x\\& \equiv (16+B)x^2+(31+B)x+16\\\end{aligned}[/tex]

Compare the coefficients of the x² term to find B:

[tex]x^2 \textsf{ term } \implies 16+B =5\implies B & =-11[/tex]

Replace the found values of A, B and C in the original identity:

[tex]\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{16}{x}-\dfrac{11}{(x+1)}-\dfrac{1}{(x+1)^2}[/tex]

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Yes, it is not possible to have an absolute maximum or absolute minimum.

Here,

We are examining a function over an interval ( a , b ) , for a and b finite,

We have to find,  is it possible not to have an absolute maximum or absolute minimum.

What theorem indicates the existence of absolute maxima or absolute minima of a function?

If f is continuous on a closed interval [a, b] (that is: on a closed and bounded interval), then, the Extreme Value Theorem indicates the existence of an absolute maximum or minimum value of f on the interval [a, b].

Now,

The function is define over an interval (a, b).

Hence, the function is define on open interval.

So, it is not possible to have an absolute maximum or absolute minimum.

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The mathematical expression can be written as [tex]5(x+7)-4^3[/tex]

Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression). Let's use the equation 5x + 7 as an example. Thus, 5x + 7 is an illustration of an algebraic expression.

We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value.

The algebraic properties most frequently utilized to simplify algebraic statements are associative, commutative, and distributive.

Here the quantity x is increased by 7 and the sum is multiplied by 5.

so we get 5(x+7).

Now 4 cubed is subtracted from the resulting expression.

Therefore the expression looks like [tex]5(x+7)-4^{3}[/tex] .

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Answer: -17

Step-by-step explanation:

-3^2 + -5^2/ -3 - (-5)

-34 / -3 - (-5)

-34/2

-17

Answer:

-5,-1

Step-by-step explanation:

add 4 to get the next number

The hypothesis of extinction by the violence between them does not seem true as this is the common nature of the species to fight and this would not be a reason for their extinction.

What is a hypothetical illustration?

How should a hypothetical example be written?

The words or abbreviations "for instance," "for example," "i.e." or "e.g." are frequently used after a hypothetical example, albeit the latter two, as you are probably aware, will only come after a comma and won't initiate a new sentence like "for instance" or "for example."

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The solution for the expression {8 ( 29 - 7 * 4 ) / ( 7 + 4 - 8 + 1 } - 3 ( 2 ) / 6 will be 1.

We are given the expression:

{8 ( 29 - 7 * 4 ) / ( 7 + 4 - 8 + 1 } - 3 ( 2 ) / 6

We will solve this expression by using the property of PEMDAS:

Solving the expression , we get

{8 (29 - 28) / 11 - 8 + 1} - 3 (2) / 6

= (8 × 1) / 4  -( 6 / 6)

= 2 - 1

= 1

Therefore, the solution for the expression {8 ( 29 - 7 * 4 ) / ( 7 + 4 - 8 + 1 } - 3 ( 2 ) / 6 will be 1.

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answer: 180

first I multiplied -4 with 45, which gave me -180, then I made 180 positive by multiplying it with -1

Answer:

If real GDP in a particular year is $80 billion and nominal GDP is $240 billion, the GDP price index for that year is: 300.

Step-by-step explanation:

[tex] \large \bf \implies{15}[/tex]

[tex]\bf \longrightarrow((2 + 4 \times 2) - 5) \times 3[/tex]

Step 1) ; Calculate the product or quotient

[tex]\bf \longrightarrow((2 + 8) - 5) \times 3[/tex]

Step 2) ; Calculate the sum or difference

[tex]\bf \longrightarrow(10 - 5) \times 3[/tex]

Step 3) : Calculate the sum or difference

[tex]\bf \longrightarrow5 \times 3[/tex]

Step 4) : Calculate the product or quotient

[tex]\bf \longrightarrow15[/tex]

Three principles of experimental design: Control, Random, Enough.

What is the principle of an experiment?

The guiding principles of experimental designs are randomization, replication, and local control. These recommendations offer a valid test of significance.

What are the three experimental design principles, and can you briefly describe how each one reduces experimental error?

How many experimental design principles are there?

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The explicit formula, for the arithmetic sequence 3, 7, 11, 15,... is an = 4n - 1

An ordered group of integers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.

For the arithmetic sequence,

3, 7, 11, 15,...

a = 3,

d = 7 - 3 = 4

So, an = a + (n - 1)d

an = 3 + (n - 1)4

an = 4n - 1

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Applying the angle relationship, the measures of the angles are:

m<a = 126°

m<b = 54°

m<c = 126°

m<d = 54°

m<e = 126°

m<f = 54°

m<g = 126°

The diagram shows different angles that are formed when a transversal crosses two parallel lines. To find the measure of the missing angles, we would apply the angle relationship.

m<a = 180 - 54 [linear pair]

m<a = 126°

m<b = 54° [vertical angles pair]

m<c = m<a [vertical angles pair]

m<c = 126°

m<d = 54° [corresponding angles]

m<e = m<a [corresponding angles]

m<e = 126°

m<f = m<d [vertical angles pair]

m<f = 54°

m<g = m<e [vertical angles pair]

m<g = 126°

Therefore, applying the angle relationship, the measures of the angles are:

m<a = 126°

m<b = 54°

m<c = 126°

m<d = 54°

m<e = 126°

m<f = 54°

m<g = 126°

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The range of allowable values based on 44 vary by 4.2% is 42.1 to 45.9.

As given in the question,

Value 44 vary by 4.2%  is equal to

4.2% of 44

= ( 4.2 / 100) × 44

= 184.8 /100

= 1.848

≈ 1.9 (nearest tenth)

Range of allowable values based on 44 vary by 4.2% is given by

Lower limit = 44 - 1.9

                 = 42.1

Upper limit = 44+ 1.9

                 = 45.9

Therefore, the range of allowable values based on 44 vary by 4.2% is 42.1 to 45.9.

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A new apple orchard is being planted by Aaron's uncle. They plant 12 trees after picking up a truckload of them. They still need to plant 40 trees the following day.

The letter (N) is the symbol used to represent natural numbers. Natural numbers are also known as counting numbers, and they begin with the number 1 and continue to infinity (never ending), which is represented by three dots (...)

900n - 9[tex]n^2[/tex] = A(n) = n(900 - 9n)

For the highest A(n), A'(n) = 0, A'(n) = 900 - 18n = 0, 18n = 900, and n = 900/18 = 50.

50 trees should be planted per acre to produce the most apples possible

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Answer:

v = 5(a - gt) or

v = 5a - 5gt  These both mean the same thing

Step-by-step explanation:

1/5 v + gt = a  Subtract gt from both sides of the equation.

1/5 v = a - gt  Multiply both sides by 5

v = 5(a - gt)

The value of g(-4) is 8.

A set of inputs and outputs that are connected to one another in some way is referred to as a relation. We refer to the relations as a function when each input results in a single output. However, you must be certain that no input leads to more than one output in order to determine if a relation is a function or not.

Only when each element of a nonempty set M has a single range to a nonempty set N is a function a relation.

g(x) = ax^2 + 24

⇒ g(4) = a (4)^2 + 24

⇒ 8 = 16a + 24

⇒ 8 − 24 = 16a

⇒ −16 = 16a

⇒ a = −1

Since, g(−4) = a(−4) ^2 + 24

∴ g(−4) = 16(−1) + 24

⇒ g(−4) = 8

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