the ratio of pencils to erasers is 4 to 9. if there are 25 more erasers than pencils, how many pencils are there? how many erasers are there? How many total writing utensils are there

By the concepts of trigonometric ratios, the value of x in the right angle triangle is 1.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

If we take the reference angle of 60°, Then the hypotenuse is x and the adjacent is 2.

We know, cos = adjacent/hypotenuse.

Therefore,

cos60° = 2/x.

x = 2cos60°.

x = 2×1/2.

x = 1.

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Answer:

- 8

Step-by-step explanation:

x = - 10

y = 2

I x I

= I - 10 I

= 10

y - I x I

= 2 - 10

= - 8

Answer:

11(2) - |-10|

= 22 - |-10|

=32

x and x⁴-16x²+56 are the resulting composite functions respectively.

Given the following functions below

f(x) = 7/x

g(x) = x² - 8

We need to determine the composite functions (fof)(x) and (gog)(x)

(fof)(x) = f(f(x))

f(f(x)) = f(7/x)

Replace x with 7/x

f(7/x) = 7/(7/x)

f(7/x) = 7 * x/7

f(7/x) = x

Similarly:

(gog)(x) = g(g(x))

g(g(x)) = (x² - 8)² - 8

g(g(x)) = x⁴-16x²+64 - 8

g(g(x)) = = x⁴-16x²+56

Hence the resulting composite functions of f(f(x) and g(g(x)) are x and x⁴-16x²+56

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Answer:

See below

Step-by-step explanation:

All other parabolas are transformations of \(y=x^2\)

Transformations include:

Answer:

The number is 1.2 and the algebraic equation is 10x=12

Step-by-step explanation:

Since the product of a number and ten is 12, we can express it as the algebraic equation x*10=12, where x is any number.

x*10=12

10x=12

x=12/10

x=1.2

Therefore, The number is 1.2

The Answer:the answer is D

Step-by-step explanation:

Answer:

No, because if x=? then itś, not a true equation, a true equation is when you have infinite solutions, in this case, if the problem is asking for 1 solution then yes, if it's asking for a true statement no.

Answer:

Yes, Brianna is correct because when you solve for x you get 5 and when you substitute you get 20.

Step-by-step explanation:

combine like terms 4x-3x=x

5=x

substitute x with 5

3(5)+5=4(5)

distribute

15+5=20

If p and q vary inversely and p is 5 when q is 4, the value of q when p is equal to 10 is 2.

An inverse variation can be defined as a type of proportionality which shows the relationship that exist between two (2) distinct variables, wherein, as the value of one variable increases, the value of the other variable decreases and vice-versa.

Mathematically, an inverse variation can be modeled or represented by this expression:

p ∝ 1/q

p = k/q

Where:

Next, we would determine the constant of proportionality (k) by substituting the value of the given variable as follows:

k = pq

k = 5(4)

k = 20

Now, we can determine the value of q:

q = k/p

q = 20/10

q = 2.

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The factor of the polynomial is option (D) (2x+5)^2 is the correct answer.

In this question,

Factorization is the breaking or decomposition of an entity (i.e.,) a number, a matrix, or a polynomial into a product of another entity, or factors, which when multiplied together give the original number. Factorize an expression involves take out the greatest common factor (GCF) of all the terms.

The polynomial is \(4x^{2} +20x+25\)

The above polynomial can be factored as

⇒ \(4x^{2} +20x+25=0\)

⇒ \((2x)^{2}+2(2x)(5)+5^{2}\)

⇒ \((2x+5)^{2}\)

Hence we can conclude that the factor of the polynomial is option (D)(2x+5)^2 is the correct answer.

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Answer:

5B; 7B; 1,024; see answer

Step-by-step explanation:

5.

We can see from the table that

a1 = 5

a2= 5·2 = 10

a3= 5·2·2 = 5·2² = 20

a4 = 5·2·2·2 = 5·2³ = 40

...

\(a_{n} = 5*2^{n-1}\)

7.

Is given that the filter removes 90% of contaminated air

after run 1 :

100% air

90% contamination removed for 100% air

100% is 10%+10%+10%+10%+10%+10%+10%+10%+10%+10%

10% is still contaminated air

after run 2:

10% air

90% contamination removed for 10% air

10% is 1%+1%+1%+1%+1%+1%+1%+1%+1%+1%

1% is still contaminated air

after run 3:

1% air

90% contamination removed for 1% air

1% is .1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%

.1% is still contaminated air

11.

Figure 1 = 1 piece

Figure 2 = 4 pieces

Figure 3 = 4² = 16

...

\(Figure 6 = 4^{(6-1)} = 4^{5} = 1024\)

12.

\((c+d)^{6} \\\)

-we know that the coefficients should be 1, 6, 15, 20, 15, 6, 1

-we start with c to the lowest power 0 and d to the highest power 6  and end with  d to the lowest power 0 and c to the highest power 6

\((c+d)^{6} = 1*c^{0} d^{6} +6*c^{1} d^{5} +15*c^{2} d^{4} +20*c^{3} d^{3} +15*c^{4} d^{2} +6*c^{5} d^{1} +1*c^{6} d^{0}\)

-we simplify to have the final answer:

\((c+d)^{6 } = d^{6} +6cd^{5} +15c^{2} d^{4} +20c^{3} d^{3} +15c^{4} d^{2} +6c^{5} d+c^{6}\)

Answer:

€3,551.05

Step-by-step explanation:

31*29=899

899*3.65=€3,551.05

the school will get an estimate of €3,551.05

Answer:

D

Step-by-step explanation:

Answer:

D would be the answer:) hope this helps

The correct answer to express the number "4.1.30E+08" in standard notation is option D: 413,000,000.

In scientific notation, the number "4.1.30E+08" represents a value multiplied by 10 raised to the power of 8. The "E+08" notation indicates that we move the decimal point 8 places to the right. Therefore, the number can be expressed as 413,000,000 in standard notation.

Options A and B are incorrect because they involve multiplying by a factor of 10 raised to a different power. Option C, 41,300,000, does not account for the correct number of zeros. The correct representation is option D, 413,000,000, which reflects the value indicated in scientific notation.

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The floor function of a number is taken out to get the greatest integer that is less than or equal to the number.

To get the floor of any number assume the y-axis of the graph and on that axis plot the number, when you plot the number, the integer just below that point is known as the floor for that number.

function,  \(f(x)=\lfloor{x}\rfloor\)

a.)  for f(2),

\(f(x)=\lfloor{x}\rfloor\\f(2)=\lfloor{2}\rfloor\)

for a whole number, the number itself is the floor of the number. thus, the function will return the value as 2.

b.)  for f(6.8),

\(f(x)=\lfloor{x}\rfloor\\f(6.8)=\lfloor{6.8}\rfloor\\f(6.8)=6\)

for the number 6.8, the ceiling will be 6 as 6 is the greatest integer that is less than 6.8.

c.)  for f(-3.3),

\(f(x)=\lfloor{x}\rfloor\\f(-3.3)=\lfloor{-3.3}\rfloor\\f(-3.3)=-4\)

for the number -3.3, the ceiling will be -4 as -4 is the integer that will be on the floor when seen on the negative number line.

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Answer:

Step-by-step explanation:

Let n represent the unknown number.

1) The sum of a number and 5 is less than 7 becomes n + 5 < 7

2) The product of a number and 8 is at least 25 becomes 8n ≥ 25

3) Six less than a number is greater than 54 becomes n - 6 > 54

4) the quotient of a number and 12 is no more than 6 becomes n/12 ≤ 6

The statement "An integer multiplied by an integer is an integer" is true.

An integer is a whole number that can be positive, negative, or zero. When you multiply two integers, the result is also an integer. For example, if you multiply 3 and 4, you get 12, which is an integer.

This property is one of the defining characteristics of the integers. It means that the integers form a closed set under multiplication. In other words, when you multiply any two integers, you always get another integer. This is not true for all numbers, such as fractions or decimals.

The whole numbers are the numbers without fractions and it is a collection of positive integers and zero. It is represented by the symbol “W” and the set of numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………}.

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Answer:

Step-by-step explanation:

9x - 7y = 24

3x + y = -2

9x - 7y = 24

-9x - 3y = 6

-10y = 30

y = -3

3x - 3 = -2

3x = 1

x = 1/3

(1/3, -3)

The lines 9x – 7y = 24 and 3x + y = -2 intersect at (\(\frac{1}{3}\), -3).

That is the common point, from where both the lines passes through at the same time.

Given lines:

9x – 7y = 24 (say eq. 1)

and 3x + y = -2 (say eq. 2)

Multiply eq. 2 with 3 and then subtract from eq. 1 :

Multiply eq. 2 with 3

⇒ 3 x (3x + y = -2 ) = 9x + 3y = -6

subtract eq. 2 from eq. 1:

9x – 7y = 24

- (9x + 3y = -6 )

= -10y = 30

or y = 3

put y = 3 in eq. 1, we get:

9x -7 (3) = 24

9x = 24 - 21 = 3

x = \(\frac{1}{3}\)

Hence the intersection point of both lines is (\(\frac{1}{3}\), -3).

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Answer:

Ration is an ordered pair of numbers that show a comparison between two things.

Answer:

Step-by-step explanation:

Number 1 FALSE

9 * 9 * 3 = 81 * 3 = 243

Number 2 TRUE

7 + 7 + 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3

7 * 3 = 3 * 7

21 = 21

Number 3 FALSE

17 * 17 * 17 = 4913

Number 4 FALSE

4 * 1 = 4

Number 5 FALSE

6 + 6 + 6 = 18

Answer: A 4 91/100

Step-by-step explanation:  its 491/100  because the 100  is 1 and 4 is the number 4 and 91/100 is .91

E(U) = 4, which is an integer.

What is Linearity of expectation?

Linearity of expectation is a fundamental property of expected value that states that the expected value of a sum or difference of random variables is equal to the sum or difference of their individual expected values.

To find E(U), where U = 2X - Y - 4, we can use the properties of expected value.

First, let's find the expected values of 2X, Y, and 4 separately using the linearity of expectation:

E(2X) = 2E(X) = 2 * 6 = 12

E(Y) = 4 (given)

E(4) = 4

Now, let's calculate the expected value of U:

E(U) = E(2X - Y - 4)

Since expected value is a linear operator, we can rearrange and simplify the expression:

E(U) = E(2X) - E(Y) - E(4)

= 12 - 4 - 4

= 4

Therefore, E(U) = 4, which is an integer.

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The option that is correct about the central limit theorem is D (II only).

According to the central limit theorem, if you have a population with a mean and standard deviation and take sufficiently large random samples from it with replacement, the distribution of the sample means will be nearly normally distributed.

As we know about the central limit theorem, the distribution of the sample means is approximately normal. Therefore, the option that is correct about the central limit theorem is D (II only).

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Answer:

x1 = s

x2 = t

x3 = -2s - 2t

x4 = 2s + t

Step-by-step explanation:

We can arrive at this solution by the following steps:

We are given two equations:

x1 + 2x2 + 2x3 + x4 = 0

2x1 + 4x2 + 2x3 - x4 = 1

To solve for x1 and x2 in terms of s and t, we choose two of the variables to be the parameters s and t. Let's choose:

x1 = s

x2 = t

Now, we can substitute x1 = s and x2 = t into the first equation:

s + 2t + 2x3 + x4 = 0

Solving for x3:

2x3 = -s - 2t

x3 = -2s - 2t

Substitute into the second equation:

2s + 4t + 2(-2s - 2t) - x4 = 1

2s + 4t - 4s - 4t - x4 = 1

-2s - x4 = 1

x4 = 2s + 1

So the general solution can be written as the 4 equations:

x1 = s

x2 = t

x3 = -2s - 2t

x4 = 2s + t

Answer:

the first one

Step-by-step explanation:

the other 3 are correct if you was to convert them into fractions

Yellow = 8/17

Orange = 3/17

Red = 6/17

2nd statement: Y > R which is correct

3rd statement: R = 2×O which is correct

4th statement: 1/2×R=O which is correct

Answer: It is likely that the pinnies will be orange

Step-by-step explanation:

Because there are a total of 17 pinnies and only 3 of them are orange so there is a 3/17 chance you get the orange. which is the least likely to happen

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:

where is the paragraph can show it

The Gaussian Function in statistical method is defined as follows:

f(x) = (1 / σ√(2π)) e^(-0.5((x-μ)/σ)²)

In which the parameters are listed as follows:

The Gaussian function is a widely used probability density function in statistics, also known as the normal distribution or bell curve, and has the equation defined at the beginning of the answer.

The curve is symmetrical around the mean (μ) of the distribution. The standard deviation (σ) of the distribution determines the width of the curve, with smaller standard deviations resulting in narrower curves and larger standard deviations resulting in wider curves.

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