PLS HELP!!
Which expressions are equivalent to log4 (1/4x^2)?

The total miles drive by Suzy in 18 hours when she can drive 53 miles in 1 hour is equal to 954 miles.

If Suzy can drive 53 miles in 1 hour,

Using the formula of speed based on distance and time we have,

Speed = Distance / Time

Substitute the values in the formula we get,

⇒ Speed = 53 miles / 1 hour

⇒ Speed  = 53 miles/hour

Use this information to find out how far Suzy can drive in 18 hours we get,

Now, Speed =  53 miles/hour

Time = 18 hours

Distance = Speed x Time

Substitute the value of speed and time we get,

⇒ Distance  = 53 miles/hour x 18 hours

⇒ Distance = 954 miles

Therefore, Suzy can drive 954 miles in 18 hours.

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Here, we want to get the final volume

From the general gas equation, we have it that:

[tex]\dfrac{P_1V_1}{T_1} =\dfrac{P_2V_2}{T_2}[/tex]

From the question, we have it that:

P1 is the initial pressure which is 475 torr

V1 is the initial volume which is 296 mL

T1 is the initial temperature which we have to convert to absolute value by adding 273.15 K ([tex]68 + 273.15 = 341.15 \ \text{K}[/tex])

P2 is the final pressure that is the same as the initial which is 475 torr

V2 is the final volume that we want to calculate

T2 is the final temperature which is 273.15 K (0 degrees Celsius is 273.15 K)

Substituting the values, we have:

            [tex]\dfrac{475\times296}{341.15}=\dfrac{475\times V_2}{273.15}[/tex]

[tex]V_2=\cfrac{475\times296\times273.15}{341.15\times475} =\boxed{\bold{237 \ mL}}[/tex]

We could have solved this by using Charles' law that relates temperature to volume (volume is directly proportional to temperature)

Using Integration,  Area of the curve is 16/3 unit² and the maximum height of the curve is 2 unit.

What exactly is integration?

Integration is a fundamental concept in calculus, which is a branch of mathematics that deals with rates of change and accumulated quantities. Integration is the process of finding the integral of a function, which is the inverse of differentiation.

Now,

For the maximum height that the curve has we have to

put dy/dx=0

d(4x-2x²)/dx=0

4-4x=0

x=4/4

x=1

and when x=1 then y=4*1-2*1²

=4-2

=2

So, the maximum height of the curve is 2 unit.

and for the area

we need to find y.dx for the curve

So,

y.dx=(4x-2x²).dx

=4x+2x²-2x³-2x³/3 for x=0 to x=2

=8+8-16-16/3

=16/3 unit²

Hence, Area of the curve is 16/3 unit².

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Answer:

y intercept when x is 0, so the answer is 3

Hence, 7, 22, 37, and 52 are the first four terms in the arithmetic series with initial term 7 and common difference 15.

Algebraic progression is a series of numbers where each term following the first is derived by multiplying the previous president by a constant known as the common difference (d). An arithmetic progression often takes the form: A, A+D, A+2D, A+3D,... where "a" stands for the initial keyword and "d" for the common distinction.

given

The sequence's initial term is 7, and the shared discrepancy is 15. We can continuously add 15 to the preceding word to find the next terms.

As a result, the arithmetic sequence's first four terms are:

Initial term = 7

Term two: 7 plus 15 equals 22

Third term = 22 plus 15 equals 37

Fourth term: 37 plus 15 equals 52

Hence, 7, 22, 37, and 52 are the first four terms in the arithmetic series with initial term 7 and common difference 15.

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The value of y that makes the hanger balance is 3.

The value of y can be solved considering linear equation method.

A linear equation is an algebraic equation in which the highest power of the variable(s) is always 1. It represents a straight line when graphed on a Cartesian coordinate plane. A linear equation can have one or more variables.

To solve for y in the equation 5 + y = 8, you can follow these steps:

Step 1: Subtract 5 from both sides of the equation to isolate the term with y on one side.

5 + y - 5 = 8 - 5

This simplifies to:

y = 3

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Answer:

x = 16°

Step-by-step explanation:

What we know:

∠JML = 47°

∠JKL = (7x + 21)°

∠JML is an inscribed angle

∠JKL is an inscribed angle

Inscribed angles are half of the value of their intercepted arc

So if m∠JML = 47° then mArc JL is double that or 94°

And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so

mArc JL + Arc JML = 360°

94 + Arc JML = 360

Subtract 94 from both sides to isolate Arc JML

Arc JML = 266°

So if Arc JML = 266° then it's intercepted inscribed angle is half of that.

Arc JML ÷ 2 = ∠JKL

266 ÷ 2 = ∠JKL

133 °= ∠JKL

Now we can use this value and set it equal to the expression to find the value of x

(7x + 21) = 133

Subtract 21 from both sides to isolate the x

7x = 112

Divide both sides by 7

x = 16

The value of x is given as follows:

x = 4.2 cm.

The value of x is obtained applying the proportions in the context of the problem.

The ratio between the volumes is given as follows:

3375/512 = 6.59

The side lengths are measured in units, while the volume is measured in cubic units, hence the proportion to obtain the value of x is given as follows:

8/x = cubic root of 6.59

8/x = 1.9

x = 8/1.9

x = 4.2 cm.

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Answer:

PMT = $52,023.26

Step-by-step explanation:

To calculate how much Fiona must deposit into her retirement account each year, we can use the formula for annuity payments:

PMT = PV x (r / (1 - (1 + r)^(-n)))

Where:

PMT is the periodic payment

PV is the present value (or desired future value) of the annuity

r is the interest rate per period (in this case, the annual yield of 6% divided by the number of periods per year, which is 1)

n is the total number of periods (in this case, 20 years)

We know that Fiona wants to have a total of $600,000 in her retirement account by the time she retires, so PV = $600,000. We also know that the interest rate per period is 6% / 1 = 0.06, and the total number of periods is 20.

Plugging these values into the formula, we get:

PMT = $600,000 x (0.06 / (1 - (1 + 0.06)^(-20)))

PMT = $600,000 x (0.06 / (1 - 0.312))

PMT = $600,000 x (0.06 / 0.688)

PMT = $52,023.26

Therefore, Fiona would need to deposit approximately $52,023.26 into her retirement account each year for the next 20 years to have a total of $600,000 by the time she retires, assuming the annual yield remains constant at 6%.

Answer:

B

Step-by-step explanation:

Pretty sure this is B. The height of your parents is the clearest way to determine how tall someone you'll be, and usually, your shoe size depends on your height. You can see this in real life. Shaq has huge feet because he's a huge guy.

A makes no sense. C might, but this will only apply to really small children. And D makes no sense either. So B is the best choice.

Answer:

C. age of the student is likely to be the answer

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 50000\\ P=\textit{original amount deposited}\dotfill &\$23000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]

[tex]50000 = 23000\left(1+\frac{ ~~ \frac{r}{100} ~~ }{4}\right)^{4\cdot 7} \implies \cfrac{50000}{23000}=\left( 1+\cfrac{r}{400} \right)^{28} \\\\\\ \cfrac{50}{23}=\left( \cfrac{400+r}{400} \right)^{28}\implies \sqrt[28]{\cfrac{50}{23}}=\cfrac{400+r}{400} \\\\\\ 400\sqrt[28]{\cfrac{50}{23}}=400+r\implies 400\sqrt[28]{\cfrac{50}{23}}-400=r\implies \stackrel{ \% }{11.25}\approx r[/tex]

The blanks when completed are

In a scale drawing, the scale factor represents the ratio of the size of an object in the drawing to the size of the corresponding object in real life.

In the given scale drawing, we have

Longest side in B = 12

So, the scale factor is

scale factor = size of object in drawing / size of corresponding object

This gives

scale factor = 12 / 4

scale factor = 3

This means that

Every side length in A grew by a factor of 3

Using the scale ratio formula, we have

A length in B/A corresponding length in A = 3

Lastly, the size of the angles remain unchanged

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Answer: The primary rectangle contains a length of 2a units (since it is labeled as "2a" within the diagram), so its zone is 2a x a = 2a^2 square units.

The moment rectangle contains a length of 3a units (since it is labeled as "3a" within the diagram), so its range is 3a x a = 3a^2 square units.

The third rectangle contains a length of 4a units (since it is labeled as "4a" within the graph), so its range is 4a x a = 4a^2 square units.

To discover the overall region of the expansive rectangle, able to include the zones of these three rectangles:

Add up to zone = 2a^2 + 3a^2 + 4a^2

Disentangling this expression, we are able combine the like terms (2a^2, 3a^2, and 4a^2) to urge:

Add up to range = (2 + 3 + 4) a^2

Step-by-step explanation:

The volume of the complete prism is  1625 cubic in

The volume of the figure is solved by dividing the figure into two sections and solving for each volume then adding the individual volume together.

The divisions are section 1 and section 2

section 1 has dimensions: 20 x 15 x 5

volume = 20 x 15 x 5 = 1500 cubic in

section 2 has dimensions: 5 x 5 x 5

volume = 5 x 5 x 5 = 125 cubic in

Volume of the complete figure

section 1  + section 2

= 1500 cubic in + 125 cubic in

= 1625 cubic in

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The field's length is therefore three times its breadth, or 3(50), or 150 yards, and its width is 50 yards.

A this double shape's perimeter is the space encircling its outside edge. It is the length of the object's sides. As an illustration, the perimeter of a rectangle is equivalent to the total of its four sides' lengths.

given

Assume that the rectangular field has a width of "x" yards.

The problem states that the field's length is three times its breadth, or three times yards.

The lengths of all the sides make up the rectangle's perimeter, therefore we can write:

[tex]Perimeter = 2 (length + width).[/tex]

In place of the values we hold:

[tex]400 = 2(3x + x)\\400 = 2(4x) (4x)\\400 = 8x\\x = 50[/tex]

The field's length is therefore three times its breadth, or 3(50), or 150 yards, and its width is 50 yards.

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Using the given angle of depression the equation (D) cos(24) = x/45 will be used to find the answer.

The angle of depression is the angle formed by the horizontal line and the horizontal line's observation of the item.

When we know the angles and the distance of an object from the ground, it is primarily utilized to find the distance between the two objects.

The angle from the horizontal downward to an item is referred to as the "angle of depression."

The line of sight of an observer would be below the horizontal.

So, in the given situation:
We will find the base which is the distance of the boat from the land.

Which means:
hypotenuse/Base

Which is represented by Cosx.

The angle is 24°.

Then, the equation for a solution would be:

cos(24) = x/45

Therefore, using the given angle of depression the equation (D) cos(24) = x/45 will be used to find the answer.

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Explanation:

We have 5 green in the 1st row and 4 green in the 2nd row.

The LCM is 5*4 = 20.

The ratio [tex]6 \text{ yellow} = 5 \text{ green}[/tex] scales up to [tex]24 \text{ yellow} = 20 \text{ green}[/tex] after multiplying both sides by 4.

The ratio [tex]4 \text{ green} = 3 \text{ purple}[/tex] scales up to [tex]20 \text{ green} = 15 \text{ purple}[/tex] after multiplying both sides by 5.

--------------

These set of ratios

[tex]6 \text{ yellow} = 5 \text{ green}\\\\4 \text{ green} = 3 \text{ purple}\\\\[/tex]

scale up to

[tex]24 \text{ yellow} = 20 \text{ green}\\\\20 \text{ green} = 15 \text{ purple}\\\\[/tex]

The key is the "20 green" on each line. This leads to the ratios linking up.

If A = B and B = C, then A = C (transitive property).

So we can say [tex]24 \text{ yellow} = 20 \text{ green} = 15 \text{ purple}\\\\[/tex]

That simplifies to [tex]24 \text{ yellow} = 15 \text{ purple}\\\\[/tex]

We can divide both sides by 3 to get [tex]8 \text{ yellow} = 5 \text{ purple}\\\\[/tex]

--------------

We now have these set of ratios

[tex]8 \text{ yellow} = 5 \text{ purple}\\\\5 \text{ purple} = 2 \text{ red}\\\\[/tex]

Connect those two equations together to get

[tex]8 \text{ yellow} = 2 \text{ red}\\\\[/tex]

Lastly, divide both sides by 4

[tex]4 \text{ yellow} = 1 \text{ red}\\\\[/tex]

The areas of the region between the curves is -40/3square units.

We must first graph the curves in order to identify which one is on top in order to calculate the area of the region bounded by the curves for x in [0, 3]. y = x²− 4x + 1 and y = −x²+ 4x − 5

The vertex of the graph of y = x²− 4x + 1is at (2, -3), and it opens upward. The vertex of the graph of y =−x²+ 4x − 5 is at (2, -1), and it opens downward.

Thus, the curve y = x²− 4x + 1 is on top for x in [0, 1], and the curve y = −x²+ 4x − 5 is on top for x in [1, 3].

To determine which curve is on top, we can set them equal to each other and solve for x:

x²− 4x + 1 = −x²+ 4x − 5

2x² - 8x + 6 = 0

x² - 4x + 3 = 0

(x - 3)(x - 1) = 0

x = 1 or x = 3

Thus, the curves cross at x = 1 and x = 3. To find which curve is on top between these two points, we can test a point in between, such as x = 2:

y = x²− 4x + 1 = 1

y = −x²+ 4x − 5 = -1

Using integration, we can find the area of the region:

∫[0,1] (x²− 4x + 1) dx + ∫[1,3] (−x²+ 4x − 5) dx

= [(1/3)x³ - 2x² + x] from 0 to 1 + [(-1/3)x³ + 2x² - 5x] from 1 to 3

=[1/3-2+1]+[{-9+8-15}-{-1/3+2-5}]

=-2/3+-38/3

=-40/3 square units.

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10 x 8 face as the base for prism 1

10 x 3 face as the base for prism 2

To find the area of the base, you simply multiply the length and width:

Base area = length x width = lw

Therefore, for rectangular prism 1 we get:

10 x 8

For rectangular prism 2 we get:

10 x 3

Similarly, if the base of the prism is a triangle, you would need to use the formula for the area of a triangle, which is:

Base area = 1/2 x base x height

where base and height are the base and height of the triangle respectively.

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the total number of boxes with at least 20 but fewer than 60 broken crayons is  33.To answer this question, we need to use the stem-and-leaf plot to count the number of boxes with at least 20

what is at least ?

"At least" is a phrase that is used to indicate a minimum quantity or degree of something. It means that the stated quantity or degree is the smallest amount that is acceptable or possible. For example, if someone says "I need at least 10 dollars,"

In the given question,

To answer this question, we need to use the stem-and-leaf plot to count the number of boxes with at least 20 but fewer than 60 broken crayons.

From the stem-and-leaf plot, we can see that the stems 2, 3, 4, and 5 have leaves that add up to at least 20 but fewer than 60:

Stem 2 has leaves 3 and 8, which add up to 11.

Stem 3 has leaf 3, which adds up to 3.

Stem 4 has leaves 0 and 9, which add up to 9.

Stem 5 has leaves 1 and 9, which add up to 10.

Therefore, the total number of boxes with at least 20 but fewer than 60 broken crayons is 11 + 3 + 9 + 10 = 33.

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Answer:

b. parallelogram

Step-by-step explanation:

The figure cannot be square because a square has four congruent sides and four right angles, and this figure does not have either of those properties.

The figure cannot be a triangle because a triangle has only three vertices, and this figure has four vertices.

The figure cannot be a trapezoid because a trapezoid has at least one pair of parallel sides, and it is not clear from the given information whether any of the sides are parallel.

The figure could be a parallelogram, which is a quadrilateral with opposite sides parallel. To determine whether this is the case, we can check whether the slopes of opposite sides are equal. Here are the slopes of the sides:

AB: (4-1)/(1-(-4)) = 3/5

BC: (-1-4)/(6-1) = -5/5 = -1

CD: (-4-(-1))/(1-6) = 3/5

DA: (1-(-4))/(-4-1) = -5/5 = -1

We can see that the slopes of opposite sides AB and CD are equal, and the slopes of opposite sides BC and DA are equal. Therefore, the figure is a parallelogram.

The figure cannot be a kite because a kite is a quadrilateral with two pairs of adjacent congruent sides, and this figure does not have that property.

So the answer is: b. parallelogram.

Since 260 is close to 264, our answer of 264 is reasonable.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

The sum of 401-137 can be found by subtracting 137 from 401:

401 - 137 = 264

Therefore, the sum of 401-137 is 264.

To estimate whether this answer is reasonable, we can use rounding. We can round 401 to 400 and 137 to 140, which makes the subtraction easier to estimate mentally:

400 - 140 ≈ 260

Since 260 is close to 264, our answer of 264 is reasonable.

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The standard deviation of the sampling distribution is approximately 0.3292.

The behaviour of the sampling distribution of the mean is described by the central limit theorem, a key conclusion in statistics. It asserts that regardless of how the population distribution is shaped, if a random sample of size n is taken from a population with mean and standard deviation, the distribution of sample means will tend towards a normal distribution as n increases.

Because it enables us to utilise the normal distribution to draw conclusions about the population mean based on sample means, the central limit theorem has significant practical ramifications. Additionally, it offers a foundation for confidence interval estimation and statistical hypothesis testing.

The standard deviation is given by the formula:

SD = σ/√(n)

Now, substituting the value of σ = 40, n = 147,400 we have:

SD = σ/√(n) = 40/√(147400) ≈ 0.3292

Hence, the standard deviation of the sampling distribution is approximately 0.3292.

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The correct option is (D) A, B, C, E, G, I

What is the cube?

A cube is a three-dimensional solid shape that has six square faces of equal size. It has twelve edges and eight vertices, and all angles between the faces are right angles. The cube is a regular polyhedron, which means that all its faces are congruent and all its edges have the same length.

The net of a cube is the one that has the faces arranged in such a way that it makes a complete cubic structure

A) In the given figure, the net cannot be folded into a cube by folding the six faces of the net. Therefore, it is not a cube net.

B)  In the given figure, the net cannot be folded into a cube by folding the six faces of the net. Therefore, it is not a cube net.

C) In the given figure, the net cannot be folded into a cube by folding the six faces of the net. Therefore, it is not a cube net.

D) In the given figure, the net can be folded into a cube when its faces are folded one over the other. Therefore, it is a cube net.

Hence, The correct option is (D) A, B, C, E, G, I.

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Answer:

3 (x + y) (x - y)

Step-by-step explanation:

3x²-3y²​

GCF is 3

3(x² - y²)

Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = (a+b) (a−b) where a = x  and b = y.

So, the answer is 3 (x + y) (x - y)

Answer:

no

Step-by-step explanation:

to check if (-1,-10) is a solution to the system of equations y = -8x + 7 and y = 6x + 5, we substitute x=-1 and y=-10 into both equations and check if both equations hold true.

y = -8x + 7 -10 = -8(-1) + 7 -10 = 8 + 7 -10 ≠ 15

y = 6x + 5 -10 = 6(-1) + 5 -10 = -1

Since (-1,-10) does not satisfy both equations simultaneously, it is not a solution to the system of equations.