Anita brings 7 dolls to her grandma’s house. These dolls represent 20% of Anita’s doll collection. What is the total number of dolls in the collection? And WHY?

if we take 32(origin amount) to be the 100%, what's 7.1 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 32 & 100\\ 7.1& x \end{array} \implies \cfrac{32}{7.1}~~=~~\cfrac{100}{x} \\\\\\ 32x=710\implies x=\cfrac{710}{32}\implies x\approx 22.19[/tex]

The point of intersection of the two lines is the fixed point or center of the point reflection.

A point reflection is a geometric transformation that maps a point across a fixed point called the center of reflection. The transformation involves reflecting the point across two intersecting lines that pass through the center of reflection. The point reflection can be thought of as a composite of two reflections, one across each line of reflection. The result is a mirror image of the original point that is equidistant from the center of reflection. The concept of point reflection is used in geometry to construct symmetrical figures and in crystallography to describe the symmetry of crystals.

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arctan(4/7) + arctan(7/4) is 90 degrees

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the functions that describe those relationships. It has applications in fields such as engineering, physics, astronomy, and navigation.

We can use the following trigonometric identity to simplify the expression:

arctan(x) + arctan(1/x) = pi/2

where x is a positive number.

In this case, we can set x = 4/7, which is a positive number, and apply the identity to get:

arctan(4/7) + arctan(7/4) = pi/2

Therefore, the sum of the two arctan terms simplifies to pi/2.

So, the simplified expression is:

arctan(4/7) + arctan(7/4) = 90 degrees (rounded to the nearest degree).

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Brooklyn has 7 brain teasers and total of 15 brain teasers, then Lincoln has 8 brain teasers.

Linear equations are equations that can be written in the form ax + b = 0, where a and b are constants and x is a variable. Linear equations represent straight lines when graphed on a coordinate plane.

We can solve the Linear equation x + 7 = 15 to determine how many brain teasers Lincoln has.

First, we want to isolate the variable x on one side of the equation. To do this, we can subtract 7 from both sides of the equation:

x + 7 - 7 = 15 - 7

Simplifying the equation gives us:

x = 8

Therefore, Lincoln has 8 brain teasers.

In conclusion, if Brooklyn has 7 brain teasers and together they have 15 brain teasers, then Lincoln has 8 brain teasers.

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The equation x · 1 = x is true for all real numbers. This is because any number multiplied by 1 is equal to itself.

For example, if x = 2, then 2 · 1 = 2. If x = 5, then 5 · 1 = 5. This is true for any value of x, so the equation is true for all real numbers.

In mathematical terms, 1 is known as the multiplicative identity because it does not change the value of a number when it is multiplied by it. Therefore, the equation x · 1 = x is always true for any real number x.

In conclusion, the equation x · 1 = x is true for all real numbers.

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The given function evaluates to [tex]\frac{x^2(1-x)}{x^2 + 1}[/tex].

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837: A variable y is said to be a function of the independent variable x if there is a relationship between them such that whenever a numerical value is assigned to x, there is a rule that determines a specific value of y.

As per the given data:

The function is [tex]f(x) = \frac{2}{x^2 + 1}[/tex]

To determine the function: [tex]f(\frac{1}{x}) - x^2f(-1)[/tex]

Substituting (1/x) and (-1) respectively:

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

[tex]= \frac{2x^2}{x^2 + 1} - x^2\frac{2}{2}[/tex]

[tex]= \frac{2x^2}{x^2 + 1} - x^2[/tex]

Taking the LCM:

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

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

Hence, the given function evaluates to [tex]\frac{x^2(1-x)}{x^2 + 1}[/tex]

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The dimensions of the rectangle is 3.33 by 5.33

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

Using the above as a guide, we have the following:

Third side of triangle, w = 12 - 5 - 1/2l

The perimeter of the rectangle is then calculated a

2 * (1/2l + 1/2l + 12 - 5 - 1/2l) = 22

So, we have

(1/2l + 1/2l + 12 - 5 - 1/2l) = 11

Evaluate

1 1/2l + 7 = 11

This gives

3/2l = 5

Evaluate

l = 10/3

The dimension is then represented as

l by 12 - 5 - 1/2l

This gives

10/3 by 12 - 5 - 1/2 * 10/3

Evaluate

3.33 by 5.33

Hence, the dimension is 3.33 by 5.33

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The solution to the equation (-3/4)(-16 + 8x) by applying the distributive property is 12 - 6x

An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.

The distributive property states that for three variables a, b and c, the following rule apply:

a(b + c) = ab + ac

Given that:

(-3/4)(-16 + 8x)

Applying the distributive property:

= (-3/4)(-16) + (-3/4)(8x)

= 12 - 6x

The solution is 12 - 6x

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The linear equation that shows the interest earned from each investment is (d): "4a + 6b + 5c = 950"

Investment refers to the act of allocating money or other resources to an asset or venture with the expectation of generating a profit or some other form of return over a period of time.  The primary goal of investing is to use the available resources to generate a return that is greater than the initial investment, thus growing wealth over time.

A linear equation is an algebraic equation in which the highest power of the variable is one. In other words, a linear equation is a polynomial of degree one. It represents a straight line when plotted on a graph. The general form of a linear equation with one variable, x, is:

ax + b = 0

In the given question,

Let's assume that Mr. Silverstone invested a dollars in the first annuity with an interest rate of 2%, b dollars in the second annuity with an interest rate of 4%, and c dollars in the bond with an interest rate of 5%. The interest earned from each investment can be calculated as follows:

Interest earned from the first annuity = 0.02a

Interest earned from the second annuity = 0.04b

Interest earned from the bond = 0.05c

The total interest earned from all three investments together is given as $950. Therefore, we can write the equation:

0.02a + 0.04b + 0.05c = 950

This is the same as option (c) given in the question: "0.04a + 0.06b + 0.05c = 950". However, option (c) has some errors in the coefficients, as the interest rates for the annuities were given as 2% and 4%, not 4% and 6%.

Therefore, the linear equation that shows the interest earned from each investment if the total was $950 is:

0.02a + 0.04b + 0.05c = 950

This can also be simplified as:

2a + 4b + 5c = 95000 (by multiplying both sides by 100 to remove the decimals)

So, the correct option is (d): "4a + 6b + 5c = 950".

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a)f(x) = { 0, if x < 0 \\ 4x, if 0 ≤ x < 4 \\ 0, if x ≥ 4 }

b)P(X=-1) = 0

c)P(X ≤ 3) = 4 * 3 = 12

a) The pdf (probability density function) of the variable X is given by
f(x) =
{
   0, if x < 0 \\
   4x, if 0 ≤ x < 4 \\
   0, if x ≥ 4
}

b) P(X=-1) = 0, since x < 0

c) P(X ≤ 3) = 4 * 3 = 12

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Therefore , the solution of the given problem of unitary method comes out to be Mr. Tan makes a total of $30 Plus $18 = $48.

To finish the job using the unitary technique, the equation from this nano section should be multiplied by two. In essence, when a wanted object is present, both the characterised by either a group and the pigment sections are omitted from the unit method. A variable fee of Inr ($1.01), for instance, would be paid for 40 pens. It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

Let's name the CDs' pre-tax cost "x" for simplicity. The overall cost of the CDs before tax is two times because Lena purchased two of them for the same price. The cost of the Discs, with the addition of the $1.80 sales tax, is:

=> 2x + $1.80

Given that we know the final price, including tax, was $23.40, we can create the following equation:

=> 2x + $1.80 = $23.40

By deducting $1.80 from each half, we arrive at:

=> 2x = $21.60

When you divide both parts by 2, you get:

=> x = $10.80

As a result, each Disc cost $10.80 before taxes.

We can create another equation now that we know his revenues from selling apple juice are $12 higher than his profits from selling lemon juice:

=> 30n - 18n = 12

=> 12n = 12

=> n = 1

As a result, Mr. Tan sells 2n + 5n = 7n = 7 glasses of juice, for a total profit of 30n = $30 from the sale of apple juice and 18n = $18 from the sale of lemon juice.

Therefore, Mr. Tan makes a total of $30 Plus $18 = $48.

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Answer:

y=2x+3

Step-by-step explanation:

Using the point-slope form of the equation of a line, we can write:

y - 9 = 2(x - 3)

Simplifying, we get:

y - 9 = 2x - 6

y = 2x + 3

Therefore, the equation of the line that is parallel to y=2x+1 and goes through the point (3,9) is y=2x+3.

parallel → the same slope

slope: y = 2x +1 → m = 2

y=2x+3 ⇔ 2(3)+3=6+3=9

y=2x+9 ⇔ 2(3)+9=6+9=15≠9

⇒ answer: y=2x+3

Answer:

Step-by-step explanation:

When calculating this equation you simply insert the x value into the equation given, in this case (x-2)^2

for example you are given 4 to 4 which is achieved by the method previously described, like this (4-2)^2 = (2)^2 = 4

so the answers would be

6 -> 16 (6 - 2 = 4 and 4^2 is 16)

10 -> 64 (10 - 2 = 8 and 8^2 is 64)

The volume is 3x³ + 16x² + 3x - 10, while when the height is reduced by 50%, the new volume is (1/2)(3x³ + 16x² + 3x - 10)

An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.

The volume of the triangular prism is:

Volume = area of base * height

Substituting:

Base area = (1/2) * (2x + 2) * (x + 5) = x² + 6x + 5; height = 3x - 2

Volume = area of base * height = (x² + 6x + 5)(3x - 2)

Volume = 3x³ + 18x² + 15x - 2x² - 12x - 10 = 3x³ + 16x² + 3x - 10

The volume is 3x³ + 16x² + 3x - 10

If the height is reduced by 50%, new height =  (1/2)(3x - 2)

Volume = area of base * height = (x² + 6x + 5) * (1/2)(3x - 2)

Volume = (1/2)(3x³ + 16x² + 3x - 10)

The new volume is (1/2)(3x³ + 16x² + 3x - 10)

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The triangle with measure of the angle is 30°, 60°, and 90° proves that it is right angled triangle.

Let us consider 'x' be the measure of the angles in a triangle.

Ratio of the angles in a triangle is 1 : 2 : 3

Measure of angle 1 = 1x

Measure of angle 2 = 2x

Measure of angle 3 = 3x

Sum of all the interior angles in a triangle = 180°

Substitute the value of the measure of the angles we get,

⇒ 1x + 2x + 3x = 180°

⇒ 6x = 180°

⇒ x = 180° / 6

⇒ x = 30°

Measure of angle 1 = 30°

Measure of angle 2 = 2× 30°

                                 = 60°

Measure of angle 3 = 3× 30°

                                 = 90°

Therefore, as measure of one of the interior angle is 90 degree this implies it is a right angled triangle.

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Landon would make a salary of $96,000 in his 23rd year working at this job.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

If Landon starts with a salary of $30,000 and gets a raise of $3,000 every year going forward, then his salary in the 23rd year can be calculated as follows:

Salary in 2nd year = $30,000 + $3,000 = $33,000

Salary in 3rd year = $33,000 + $3,000 = $36,000

Salary in 4th year = $36,000 + $3,000 = $39,000

and so on...

So, we can see that Landon's salary increases by $3,000 every year.

His salary in the 23rd year would be:

Salary in 23rd year = $30,000 + ($3,000 x 22) = $30,000 + $66,000 = $96,000

Therefore, Landon would make a salary of $96,000 in his 23rd year working at this job.

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Answer:

Let's say that the class has a total of 7x students, where 2x wear glasses and 5x don't.

After 5 of the students who didn't wear glasses now do, the number of students who don't wear glasses becomes 5x - 5.

So, the new ratio of students who wear glasses to those who don't wear glasses is:

2x : (5x - 5)

We can simplify this ratio by dividing both terms by the greatest common factor, which is x:

2 : (5 - 5/x)

We can't simplify this any further, but we can see that the ratio is not fixed and depends on the value of x.

The exponential decay model for this situation is P(t) = 200,000 * (1 - 0.03)^t

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

We are given that;

Population in 1992=200000

Time=6years

Rate=3%

To write an exponential decay model to represent this situation, we can use the formula:

P(t) = P * (1 - r)ᵗ

where P(t) is the population after t years, P is the initial population, r is the annual rate of decline as a decimal, and t is the number of years. In this case, the initial population P is 200,000, the annual rate of decline r is 0.03 (since the population declines by 3% each year), and t is the number of years from 1992, so t = 0 corresponds to 1992 and t = 6 corresponds to 1998.

P(t) = 200,000 * (1 - 0.03)^t

where t is the number of years from 1992 to 1998.

Therefore, by the given percent answer will be P(t) = 200,000 x (1 - 0.03)^t

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The situation in which the quantities combine to make 0 is D.

What is a combination of quantities?

In mathematics, a combination of quantities usually means taking a group of items or values and selecting some of them without regard to their order. A combination is different from a permutation in that order does not matter in a combination, whereas it does matter in a permutation.

For example, if you have three objects labeled A, B, and C, then the possible combinations of two objects are AB, AC, and BC. These combinations are different from the permutations of two objects, which include AB and BA, AC and CA, and BC and CB.

Combinations are often used in probability, statistics, and combinatorics to calculate the number of ways that objects or values can be selected from a set, without regard to their order.

The situation in which the quantities combine to make 0 is:

D. In the morning, the temperature rises 30 degrees. In the evening, it falls by 30 degrees.

In situation D, the temperature rises by 30 degrees in the morning and then falls by 30 degrees in the evening, which means that the overall change in temperature is 0. In situations A, B, and C, the quantities do not combine to make 0. In situation A, the hot air balloon rises a total of 80 feet, which is not 0. In situation B, Kathy has $10 left after giving half to her friend, which is not 0. In situation C, the player earns a total of 8 points, which is not 0.

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The depth of water is fount to be 2.0 fathom when its was 12 feet.

Given:

Conversion unit:

1 foot = 0.167 fathom

Then,

12 feet = 0.167*12 fathom

12 feet = 2.004 fathom

12 feet = 2.0 fathom

Thus, the depth of the water is fount to be 2.0 fathom when its was 12 feet.

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To input the given commands and find the Z-scores for the different heights, you will need to use the following steps:

1. Convert the heights from feet and inches to inches. For example, 6'4" would be 76 inches, 5'8" would be 68 inches, and 5'2" would be 62 inches.

2. Use the formula Z = (X - mean) / standard deviation to find the Z-scores for each height. For example, for the height of 6'4", you would use the formula Z = (76 - height.xbar) / height.s.

3. Use the pnorm command to find the percentiles for each Z-score. For example, for the Z-score of the height 6'4", you would use the command pnorm(Z).

4. Use the pnorm command with the lower.tail = FALSE argument to find the portion of people taller than a given height. For example, for the height of 6'4", you would use the command pnorm(Z, lower.tail = FALSE).

5. Use the pnorm command with the lower and upper limits to find the portion of people between two heights. For example, for the heights of 5'2" and 5'8", you would use the command pnorm(upper limit) - pnorm(lower limit).

Using these steps, you can input the given commands and find the Z-scores and percentiles for the different heights. Remember to use the variable names height.xbar and height.s for the mean and standard deviation of the height variable, and to use the number, variable, and height terms in your answer.

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Step-by-step explanation:

it is a quadrilateral.

the sum of all angles in a quadrilateral is always 360°.

so,

360 = x + x + 2x + 7 + 2x + 5 = 6x + 12

348 = 6x

x = 348/6 = 58°

that's it.

Using the gratuity percentages, we found that the amount of meal is $32.6 and the amount to be paid is $41.89

What is meant by percentage?

A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.

Given,

Gratuity guide :

15% would be $4.89

18% would be $5.87

20% would be $6.52

1) The tip percentages are given above.

If the cost of the meal is x.

15% of x = 4.89

18% of x = 5.87

0.15x = 4.89

x = 32.6

0.18x = 5.87

x = 32.6

So the cost of the meal is $32.6.

2)The family choose a 20% tip.

   The tax percentage is 8.5% of 32.6.

Tip = 6.52 ( from gratuity guide)

Tax  =  8.5 % of 32.6

    = 0.085 * 32.6 = $2.77

Total amount to be paid = 32.6 + 6.52 + 2.77 = $41.89

Therefore using the gratuity percentages, we found that the amount of meal is $32.6 and the amount to be paid is $41.89.

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Answer:$20.40

Step-by-step explanation:

 20% off means that the new price of the skirt will be 80% of the original price:

$30(100%  – 20%) = $30(80%)

Converting the percent to a decimal gives:

$30(0.8) = $24.00

There is an additional 15% off the sale price of $24.00, so the final price is 85% of the sale price:

$24(100%  – 15%) = $24(85%)

Again converting the percent to a decimal gives:

$24(0.85) = $20.40

The simplified form of the given expression by the laws of indices is; x^(-3/10).

As evident in the task content; the given expression is;

1 / ⁵√√x³

Therefore, we have that;

By the laws of indices we have that;

= 1 / ⁵√x^(3/2)

= 1 / x^(3/10)

On this note, the simplified form of the expression as required is; x^(-3/10).

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The zeros of the function c(x) = 6x^3 + 3x^2 - 3x are x = 0, 1/2, and -1, all with a multiplicity of 1.

To find the zeros of the function c(x) = 6x^3 + 3x^2 - 3x, we need to factor the equation and set it equal to zero.

First, we can factor out a common factor of 3x from all of the terms:
c(x) = 3x(2x^2 + x - 1)

Next, we can use the quadratic formula to find the zeros of the remaining quadratic equation:
2x^2 + x - 1 = 0

x = (-1 ± √(1^2 - 4(2)(-1)))/(2(2))
x = (-1 ± √(1 + 8))/4
x = (-1 ± √9)/4
x = (-1 ± 3)/4

So, the two zeros of the quadratic equation are:
x = (-1 + 3)/4 = 1/2
x = (-1 - 3)/4 = -1

Finally, we can combine the zero from the factored term with the zeros from the quadratic equation to find all of the zeros of the function:
x = 0, 1/2, -1

The multiplicities of these zeros are:
x = 0 has a multiplicity of 1
x = 1/2 has a multiplicity of 1
x = -1 has a multiplicity of 1

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Answer:

i need more details i cant answer.

Answer:

Let's call the length of the rectangle "L" and the width "W".

From the problem, we know that:

W = L - 4

And

Area = Length x Width

Substituting the first equation into the second equation, we get:

Area = L x (L - 4)

We also know that the area is 21 square units, so we can set up the following equation:

21 = L x (L - 4)

Expanding the right side of the equation:

21 = L^2 - 4L

Rearranging the terms:

L^2 - 4L - 21 = 0

Now we can solve for L using the quadratic formula:

L = (-b ± sqrt(b^2 - 4ac)) / 2a

Where a = 1, b = -4, and c = -21

L = (-(-4) ± sqrt((-4)^2 - 4(1)(-21))) / 2(1)

L = (4 ± sqrt(100)) / 2

L = (4 ± 10) / 2

L = 7 or L = -3

Since the length cannot be negative, we choose L = 7.

Therefore, the length of the rectangle is 7 units.

Therefore, teachers should anticipate the greatest increase in spring fever during the 4th week.

Week New Cases Total Cases So Far Individual at Risk at Start of Week Weekly Incidence Prevalence

1 105 105 920 0.102 0.102

2 180 285 740 0.196 0.278

3 390 675 350 0.527 0.659

4 325 1000 25 0.929 0.976

B) Spring Fever: Incidence and Prevalence per 100

Week Weekly Incidence per 100 Prevalence per 100

1 10.2 per 100 10.2 per 100

2 19.6 per 100 27.8 per 100

3 52.7 per 100 65.9 per 100

4 92.9 per 100 97.6 per 100

C) The 4th-week incidence is much higher, indicating an increase from 0.527 in the 3rd week to 0.929 in the 4th week.

Therefore, teachers should anticipate the greatest increase in spring fever during the 4th week.

Incidence= Number of new cases at particular week/total number of cases in that week

Prevalence= Total number of cases diagnosed/total number of subjects

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