The ratio of yellow shirts to green shirts in Ms. Grayson’s closet is 5:2. She has a total of 21 yellow and green shirts combined. How many yellow shirts are in Ms. Grayson’s closest?

Answer:

no, because both muffins are different sizes, meaning that if a friend ate 2/3 of a small muffin than that would be different

The logarithm of 64 to the base 0.25 is -2: log₀.²⁵ 64 = -2

In mathematics, a logarithm is an operation that involves determining the power to which a given number, called the base, must be raised to produce a certain value.

According to question:

The logarithm of 64 to the base 0.25 can be written as:

log₀.²⁵ 64

We need to find the exponent to which we raise the base 0.25 to get 64. In other words, we need to solve for x in the following equation:

0.25ˣ = 64

We can rewrite 64 as a power of 0.25, using the fact that 64 = 0.25⁻² :

Now, we can equate the exponents on both sides:

0.25ˣ  = 0.25⁻²

x = -2

Therefore, the logarithm of 64 to the base 0.25 is -2:

log₀.²⁵ 64 = -2

For example, if we know that 2 raised to the power of 3 is equal to 8 (i.e., 2³ = 8), then we can say that the logarithm of 8 with base 2 is 3, denoted as log₂ 8 = 3.

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Step-by-step explanation:

please mark me as brainlest

Answer:

135

Step-by-step explanation:

2x²/x + x(100 - 15x)

If x = 5 ;

2(5)²/5 + 5(100 - 15×5)

= 2×25/5 + 5(100 - 75)

= 2 × 5 + 5 × 25

= 10 + 125

= 135

Answer:

The number is 24

Step-by-step explanation:

Let the two digits number be ab

In real terms, this is 10a + b

So, we have that the sum of the digits subtracted from 10a + b is 18

Mathematically, we have this as;

10a + b - (a + b) = 18

10a + b - a - b = 18

9a = 18

a = 18/9

a = 2

We are also told that the digit at the units place b is double the digit at the ten’s place a

That means b = 2a

b = 2 * 2 = 4

The perimeter of the nonagon attached is

124.5

The formula for the perimeter of a nonagon (a polygon with nine sides):

Perimeter = 9 * side length

side length = 2 * apothem * tan(π/9)

= 2 * 19 * tan(π/9)

= 13.831

The perimeter

Perimeter = 9 * side length

Perimeter = 9 * 13.81

Perimeter = 124.5

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Answer:

4%

Step-by-step explanation:

to find percentage do 37 divided by 925 helps it helps :)

To determine the number and type of solutions for a specific equation, we need to consider the degree of the polynomial and use other mathematical techniques.

1. Linear Equation (degree 1):

A linear equation in one variable has exactly one solution, regardless of whether the coefficients are real or complex.

2. Quadratic Equation (degree 2):

A quadratic equation in one variable can have zero, one, or two solutions. The nature of the solutions depends on the discriminant (b² - 4ac), where a, b, and c are the coefficients of the equation.

- If the discriminant is positive, the equation has two distinct real solutions.

- If the discriminant is zero, the equation has one real solution (a double root).

- If the discriminant is negative, the equation has two complex solutions.

3. Cubic Equation (degree 3):

  A cubic equation in one variable can have one, two, or three solutions. To determine the nature of the solutions, it often requires advanced algebraic techniques, such as factoring, the Rational Root Theorem, or Cardano's method.

4. Higher-Degree Equations (degree 4 or higher):

Equations of higher degree can have varying numbers of solutions, but there is no general formula to determine them. Instead, various numerical methods, such as numerical approximation or graphing techniques, are commonly used to estimate the solutions.

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Answer:

3240

Step-by-step explanation:

25% of 1620 is 405

Initial chocolate number is multiple 405 by 4 then add into 1620

405 *4 =1620

1620+1620 =3240

The number of chocolates that Tarquin had initially is 3240 and the calculation is below,

Tarquin ate 25% of his chocolate each day, so after 4 days, he had eaten 25% * 4 days = 100% of his chocolate.

Since he had 1620 chocolates left, this means that he initially had 1620 * 100% = 3240 chocolates.

Therefore, the answer is 3240.

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Answer:

\(14 \times 0.5 = 70 \\ 70\)

The value of the profitability index of the project is 2.381.

We know that the growth rate is 4% and the cash flow is $3.7 million, so we can calculate the present value of all future cash flows as follows;

PV of all subsequent cash flows = 3.7 million * (1 + 0.04) / (0.11 - 0.04) = $68.1333 million

Total PV = PV of first-year cash flow + PV of all subsequent cash flows = $3.3154 million + $68.1333 million = $71.4487 million

Finally, we can calculate the profitability index as;

Profitability index = PV of future cash flows / Initial investment = $71.4487 million / $30 million = 2.381

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Answer:

djdjdjdjdhdhdhdhdhdh

£5:50

y=10x+235 is the equation of the least squares regression line.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We need to find the equation of the least squares regression line.

The value of the slope of the regression line can be find by using any two points from the table.

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

(58, 335) and (70, 450)

Slope of line = 450-335/70-58

=115/12

=10

The equation of line is y=10x+b

335=10(10)+b

335=100+b

335-100=b

235=b

Hence, the equation of the least squares regression line is y=10x+235.

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Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

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Let's start solving the expression using the product to sum formulae.

Here's the given expression,

\[\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3}\]

Using the product-to-sum formula,

\[\sin A \cos B=\frac{1}{2}[\sin (A+B)+\sin (A-B)]\]

Applying the above formula in the first term,

\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3} &= \frac{1}{2} \left[\sin \left(\frac{x}{3}+\frac{2 x}{3}\right)+\sin \left(\frac{x}{3}-\frac{2 x}{3}\right)\right] \\&= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]\end{aligned}\]

Using the product-to-sum formula,

\[\cos A \sin B=\frac{1}{2}[\sin (A+B)-\sin (A-B)]\]

Applying the above formula in the second term,

\[\begin{aligned}\cos \frac{x}{3} \sin \frac{2 x}{3}&= \frac{1}{2} \left[\sin \left(\frac{2 x}{3}+\frac{x}{3}\right)-\sin \left(\frac{2 x}{3}-\frac{x}{3}\right)\right] \\ &= \frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right]\end{aligned}\]

Substituting these expressions back into the original expression,

we have\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} &= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]+\frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right] \\ &=\frac{1}{2} \sin x + \frac{1}{2} \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\\ &= \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\end{aligned}\]

Therefore, the given expression can be written in terms of a single trigonometric function as:

\boxed{\sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)}

Hence, the required expression is \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right). The solution is complete.

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Reasoning: Complementary angles always add to 90 degrees.

If angle 2 was x, then x+83 = 90 solves to x = 7

The measure of m∠2 is 7° due to the pair of angles being complementary.

The complementary angles are defined as when pairing of angles addition to 90° then they are called complementary angles. There are two types of supplementary angles.

Adjacent angles: Adjacent angles are the type of supplementary angles. Adjacent angles have a common side and vertex, for example, a corner point. Their points do not overlap in any way. In other terms, adjacent angles are pairs of two angles next to each other.

We have been given that the pair of angles as

m∠1 = 83°  and m∠2 = x

Here, the pairing of angles sums up to 90° then they are called complementary angles.

So x + 83 = 90°

⇒ x = 90° - 83°

⇒ x = 7°

Therefore, the value of m∠2 is 7°.

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Answer:

true

Step-by-step explanation:

The statement that describes when the plans are based on the same number of aerobic exercise sessions is:

The number of strength-training exercises and aerobic exercises per week is calculated as follows:

Let a be the number of strength-training exercises and b be the number of aerobic exercises per week respectively.

For the beginner plan:

15a + 20b = 90  eqn. (1)

For the advanced plan:

20a + 30b = 130 eqn. (2)

Solving the simultaneous equation by elimination method:

Multiply eqn. (1) by 3 and eqn. (2) by 2

45a + 60b = 270 eqn. (3)

40a + 60b = 260 eqn. (4)

Subtract eqn. (4) from eqn. (3)

5a = 10

a = 2

Substitute a = 2 in eqn (2)

b = 3

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Complete question:

A personal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. A beginner plan has 15 minutes per session of strength training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. An advanced plan has 20 minutes per session of strength training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week.

Which statement describes when the plans are based on the same number of aerobic exercise sessions?

Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.

Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.

Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.

Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.

The domain of the function f(x, y, z) = ln(144 − 9x² − 16y² − z²) is x ∈ (-4, 4), y ∈ (-3, 3) and z ∈ (-12, 12). It forms an ellipsoid.

Domain of a function is the set of all values possible for the input parameters for real output parameter or output parameter in given range.

f(x, y, z) = ln(144 − 9x² − 16y² − z²)

For f(x, y, z) to be real, 144 − 9x² − 16y² − z² should be greater than 0. So,

144 − 9x² − 16y² − z² > 0

9x² + 16y² + z² < 144

x²/ 4² + y²/ 3² + z²/ 12² < 1

So the domain is an ellipsoid.

Therefore x ∈ (-4, 4)

y ∈ (-3, 3)

z ∈ (-12, 12)

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Mahelet's age is found to be 14 years by solving the simultaneous equations using the given data.

A collection of two or more equations, each having two or more variables, whose values can concurrently fulfil one, more, or all of the equations in the collection, with the number of variables being equal to or fewer than the collection's equations.

Given: Mahelet is four times older than Mr. Jones, who is three years older than Mahelet. The total of their ages is 73.

Let, x =  Mahelet's age

      y =  Mr. Jones's age

We know that,

y = 4x +3

x + y = 73

Solving these equations simultaneously we get,

y = 4(73-y) +3

y = 292 - 4y + 3

5y = 295

y = 59

x = 73 - y = 73 - 59 = 14

Therefore, Mahelet's age is found to be 14 years by solving the simultaneous equations.

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Answer:

\(d=\sqrt{73}\approx8.54\)

Step-by-step explanation:

So we have the two points (10,-4) and (2,-7).

And we want to find the distance between them using the Distance Formula and the Pythagorean Theorem. Let's do each one individually.

1) Distance Formula.

The distance formula is:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

Let's let (10,-4) be (x₁, y₁) and let's let (2,-7) be (x₂, y₂). So:

\(d=\sqrt{((2)-(10))+((-7)-(-4))^2\)

Simplify:

\(d=\sqrt{(2-10)^2+(-7+4)^2\)

Subtract:

\(d=\sqrt{(-8)^2+(-3)^2\)

Square:

\(d=\sqrt{64+9}\)

Add:

\(d=\sqrt{73}\)

Approximate:

\(d\approx8.54\)

So, the distance between (10,-4) and (2,-7) is approximately 8.54 units.

2) Pythagorean Theorem

Please refer to the graph.

So, we want to find the distance. This will be the length of the red line, or the hypotenuse.

First, let's find the length of the two legs.

The longer leg will be the difference between the two x-coordinates. So, the length of the longer leg is:

\((10-2)=8\)

Note: It doesn't matter if we do 2-10, which gives -8, since we are going to square anyways. Also, distance is always positive, so 8 would be our answer.

And the shorter leg is the difference between the two y-coordinates. Namely:

\((-7-(-4))=-3=3\)

So, the shorter leg is 3 units.

So now, we can use the Pythagorean Theorem, which is:

\(a^2+b^2=c^2\)

Substitute 8 for a and 3 for b. So:

\((8)^2+(3)^2=c^2\)

Square:

\(64+9=c^2\)

Add:

\(c^2=73\)

Take the square root:

\(c=\sqrt{73}\approx8.54\)

This is the same as our previous answer, so we can confirm that it's correct.

So, using both the distance formula and the Pythagorean Theorem, the distance between the two points is approximately 8.54.

And we're done!

Distance formula: d = √(x2-x1)²+(y2-y1)²

= √(2-10)²+(-7-(-4))²

= √-8²+(-3)²

= √64+9

= √73

≈ 8.54

Best of Luck!

Answer:

X=2

Step-by-step explanation:

first combine like terms

subtract the x

add 5

lastly divide by 7

The material remained for the blanket after trimming off by Keith is 2.5 yards.

Simple subtraction and multiplication can provide the result. Beginning will be by the multiplication. Firstly finding the exact amount of material trimmed = 3×1/6

Performing multiplication and division on Right Hand Side of the equation

Trimmed material = 1/2 or 0.5

Now, we need to subtract the trimmed material from overall amount of material

Remaining material = 3 - 0.5

Performing subtraction on Right Hand Side of the equation

Remaining material = 2.5 yards

Hence, 2.5 yards of material remained.

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Answer:

man you still have to use IXL

Step-by-step explanation:

The height of the recycling bin is approximately 6.71 feet.

To find the height of the rectangular recycling bin, we'll use the given information of its length, width, and surface area.

Let's assume the height of the box is denoted by "h" (in feet).

The formula for the surface area of a rectangular box is given by:

Surface Area = 2lw + 2lh + 2wh

In this case, we have the following information:

Length (l) = 20 ft

Width (w) = 8 ft

Surface Area = 712 ft²

Plugging in these values into the surface area formula:

712 = 2(20)(8) + 2(20)h + 2(8)h

712 = 320 + 40h + 16h

712 = 336 + 56h

712 - 336 = 56h

376 = 56h

Dividing both sides by 56:

h = 376/56

h = 6.71 ft (rounded to two decimal places)

Therefore, the height of the recycling bin is approximately 6.71 feet.

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The question seems incomplete, the correct question is as follows:

A recycling bin is in the shape of a rectangular box find the height of the box if its length is 20 ft its width is 8 feet and its surface area is 712 ft squared.

Answer:

4

Step-by-step explanation:

32 divided by 8

The aspect ratio is a potential source of deception if it is not approximately 1.67.

The aspect ratio refers to the ratio of the width to the height of a visual or graphical display. It is commonly used in the context of images, videos, and screen displays. An aspect ratio of approximately 1.67 (or 5:3) is often considered to be aesthetically pleasing and visually balanced.

If the aspect ratio deviates significantly from 1.67, it can distort the appearance of the content and lead to visual deception. For example, if the aspect ratio is too wide, it can stretch or elongate the images, making them appear unnatural or disproportionate. On the other hand, if the aspect ratio is too narrow, it can compress or squish the images, causing distortion or loss of detail.

Therefore, when creating or presenting visual materials, it is important to consider the aspect ratio and aim for a value close to 1.67 to maintain visual accuracy and avoid potential sources of deception.

The other options mentioned, such as the bin frequency divided by the sample size, the skewness divided by the kurtosis, and the center divided by the variability, are not directly related to the concept of aspect ratio. They involve different statistical measures and calculations that are used to analyze and describe data distributions, asymmetry, and variability. These measures provide insights into the shape and characteristics of the data, but they do not pertain to the aspect ratio of visual displays.

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Answer:

g(f(x)) = 9x² + 12x + 5

Step-by-step explanation:

g(f(x))

= g(3x + 2) ← substitute x = 3x + 2 into g(x)

= (3x + 2)² + 1

to expand (3x + 2)² = (3x + 2)(3x + 2)

each term in the second factor is multiplied by each term in the first factor

3x(3x + 2) + 2(3x + 2) ← distribute both parenthesis

= 9x² + 6x + 6x + 4 ← collect like terms

= 9x² + 12x + 4

then

g(f(x)) = (3x + 2)² + 1 = 9x² + 12x + 4 + 1 = 9x² + 12x + 5

Answer:

Donno dont care answer is 5

Step-by-step explanation:

Answer:

The answer is -7s

Step-by-step explanation:

Combine like terms

Hoped this helped!

Brainly, please?

The value of u is 2.5 miles.

A rectangle is a 2-D shape with length and width.

The length and width are different.

If the length and width are not different then it becomes a square.

The area of a rectangle is given as:

Area = Length x width

We have,

Rectangle:

Perimeter = 17 miles

Length = 6 miles

Width = u

Now,

The perimeter = 2 (Length + Width)

17 = 2 ( 6 + u)

17 = 12 + 2u

17 - 12 = 2u

2u = 5

u = 5/2

u = 2.5 miles

Thus,

The value of u is 2.5 miles.

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The complete question.

Find the value of the width u.

where the rectangle has a length of 6mi and a Perimeter of 17 miles.