12 ÷ (4 − (6 × 2 − ((3 + 3) × 2 − 1)))

a) To evaluate loga 15, we can use the property of logarithms that states logab = loga + logb. Since 15 = 3 * 5, we can use this property to find that loga 15 = loga 3 + loga 5. Since loga 3 = 0.56 and loga 5 = 0.83, we can add these values to find that loga 15 = 0.56 + 0.83 = 1.39.

The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to express enormous numbers is this manner.

Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms may also be represented as multiplication and division of logarithms.

b) To evaluate loga(2/5), we can use the property of logarithms that states log(a/b) = loga - logb. Since 2/5 = 2*(1/5) we can use this property to find that loga(2/5) = loga2 - loga(1/5). Since loga2 = 0.36 and loga(1/5) = -loga5, we can subtract these values to find that loga(2/5) = 0.36 - 0.83 = -0.47

c) To evaluate loga (8a^4), we can use the property of logarithms that states log (a^n) = nloga. We get, loga (8a^4)=loga 8 + log (a^4)

=> loga 8 + loga (a^4)

=>3loga 2 + 4 loga a

=>3loga 2 + 4

=>3 * 0.36 + 4

=5.08

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Therefore , the solution of the given problem of graph comes out to be

x = 0 , y =22 and  x= 1 , y=23.

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

Here,

Given :

=> h(x) = g(x+3) - 6

g(x) = x+ 25

So,

=> g(x+3) = x +3 + 25 = x+28

and

=> h(x) = x + 28 -6

=>y= h(x) = x+ 22

Thus,

y= x+22

the points which can be graph area:

=> x = 0 , y =22

=> x= 1 , y=23

Therefore , the solution of the given problem of graph comes out to be

x = 0 , y =22 and  x= 1 , y=23.

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Answer: 25

Step-by-step explanation:

simple math

Answer:

25 cookies

Step-by-step explanation:

After she gives away 5 of her 10 cookies she is left with 5 cookies. Then she bakes 20 more. So you add 5 cookies to 20 cookies, and you get 25 cookies.

Or in total with all of the cookies she had before she gave away 5 of the 10, and the newly baked 20 cookies she has 30 cookies.

-Hope this helped

The truth of z scores that fall below the mean is - they are negative. Option(b) is the correct answer.

A z-score called a standard score gives an idea of how far from the mean a data point is. But technically it is a calculation of how many standard deviations below or above the population mean a raw score is.

A z-score can place on a normal distribution curve. Z-score ranges from -3 standard deviations up to +3 standard deviations.

A z-score is equal to 0 means that it is on the mean. A positive z-score shows the score is higher than the mean average.

A negative z-score reveals the score is below the mean average.

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The best estimate willl 20

Step-by-step explanation:I

Answer:

x intercepts (-2,0) and (-4,0)

y intercept: (0,8)

Vertex: (-3,-1)

Axis of symmetry x = -3

Step-by-step explanation:

Answer:

  a)  93 cm²

  b)  98 cm²

Step-by-step explanation:

You want the areas of the squares shown in each of the figures.

The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the other two sides of a right triangle.

The square of the hypotenuse is 17² = 289.

The sum of the squares of the other two sides is ...

  shaded square + (14)² = 17²

  shaded square + 196 = 289

  shaded square = 289 -196 = 93 . . . . cm²

Sabcd = 93 cm².

The square of the diagonal is the sum of the squares of the sides. Each of those squares is the area of interest:

  14² = (shaded square) + (shaded square)

  196 = 2(shaded square)

  98 = shaded square

Sabcd = 98 cm².

__

Additional comment

Perhaps you have seen the attached figure. It is intended to show the squares on each of the legs of the right triangle, and to illustrate that the sum of the areas of the green and purple squares is the area of the red square. This figure compares to the one for part (a) of the problem.

  a² +b² = c²   ⇒   a² = c² -b²

The the average age of the remaining 4 students is 9.5 years.

The average may be calculated by dividing the total number of values by the sum of all the numbers. An average of the values in a sample of data may be used to determine a mean. In other words, the arithmetic mean is another name for an average. A mean is a term used to describe the average.

The average age of 5 students is 10 years.

∴  Sum of age of 6 students =5 × 10 = 66

⇒  When two more students of age 5 and 1 added to 4 students then, total students will become 8

⇒  Sum of age of 6 students =66 + 6 + 4 = 76

∴  Required average =

76 / 8  = 9.5

=9.5 years

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In the graphic below, assuming the lines are parallel, the value of x is 15.

Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance. Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. Parallel lines can be found in everyday life, such as zebra crossings, notepad lines, and railway tracks.

Here,

6x+3=7x-12

x=15

The value of x in the figure below assuming that the lines are parallel is 15.

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Joe made a mistake in his calculations by multiplying 28 quarts by 4.

To know the mistake that Joe made and the possible correction, we shall convert 28 quart to gallon.

Recall that 4 quart = 1 gallon

Therefore, 28 quart will be:

= 28 quart × 1 gallon / 4 quart

28 quart = 7 gallon

Therefore, 28 quarts is equivalent to 7 gallons.

Hence, Joe made a mistake in his calculations by multiplying 28 quarts by 4 instead of dividing 28 quart by 4.

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x2 = 3/5, x1 = 9/4, and x3 = 2/3 of the row-echelon form of the augmented matrix are the answers to the equations.

The unit technique is a method of problem-solving where you first calculate the value of a single unit, then multiply that value to get the answer. Simply expressed, a single unit value is extracted from a specified multiple using the unit method. For instance, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and reciprocal are equivalent. (Linear Algebra, Mathematical Analysis, Mathematics of Matrix or Operators)

given

Replace the variable in the equation with the given integer.

Check to see if the resulting equation is correct. The number is not a solution if it is false.

x2 = 3/5, x1 = 9/4, and x3 = 2/3 of the row-echelon form of the augmented matrix are the answers to the equations.

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The value of X is 7.625 while the two sides are 38.125 and 27.875.

Perimeter = 2(L+B)

112 = 2(5x + 3x + 5)

112 = 2(8x + 5)

Dividing both sides by 2

56 = 8x + 5

56 + 5 = 8x

61 = 8x

x = 61/8

x = 7.625

The sides are;

5x = 5(7.625)

5x = 38.125

3x + 5 = 3(7.625) + 5

3x + 5 = 22.875 + 5

3x + 5 = 27.875

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So on solving the provided question we can say that - Area of prism,

Area, A = 2(wl+hl+hw) = 180 sq units

The definition of a prism in geometry is a polyhedron with an n-sided polygonal base, a second base that is a shifted copy of the first base, and n additional faces (necessarily all parallelograms), with two Connect the corresponding sides of the base. Translations of the base are all cross sections that are parallel to it. A prism is a two-sided, solid, three-dimensional object. It consists of equal cross-sections, flat sides, and identical bases. A prism has faces that are parallelograms or rectangles without bases. A prism is a homogenous, solid, transparent, refracting object enclosed by two planes that are obliquely angled to one another. Two triangular faces and three parallel rectangular faces make up a typical prism. They are constructed of either glass.

Area, A = 2(wl+hl+hw)

A = 2(20 + 40 + 30)

A = 2(90)

A = 180sq units

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Answer:

See below

Step-by-step explanation:

You could say "2 times the difference between n and 7 is equal to -14"

Answer:

159

Step-by-step explanation:

Median = When ordered least to greatest, the number in the middle

140, 141, 146, 148, 151, 156, 159, 159, 160, 167, 170, 173, 174

Answer:

a)  See below.

b)  Geometric sequence

[tex]\textsf{c)} \quad a_n=7.5(0.5)^{n-1}[/tex]

Step-by-step explanation:

From inspection of the given table, t(n) halves each time n increases by 1.

Therefore:

[tex]\implies a_4=1.875 \div 2 = 0.9375[/tex]

[tex]\implies a_5=0.9375 \div 2 =0.46875[/tex]

Completed table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&t(n) \\\cline{1-2} \vphantom{\dfrac12} 1& 7.5\\\cline{1-2} \vphantom{\dfrac12} 2& 3.75\\\cline{1-2} \vphantom{\dfrac12} 3&1.875 \\\cline{1-2} \vphantom{\dfrac12} 4& 0.9375\\\cline{1-2} \vphantom{\dfrac12} 5& 0.46875\\\cline{1-2} \end{array}[/tex]

As the given sequence has a constant ratio of 0.5, it is a geometric sequence.

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

The first term of the sequence is 7.5.  Therefore,:

The common ratio is 0.5. Therefore:

Therefore, to write an equation for the given geometric sequence, substitute the found values of a and r into the formula:

The possibility that someone randomly guesses the correct combination in five attempts is 1/200

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

Given;

There are three wheels

Each numbered from 0 to 9

For the first wheel, you have 10 possible digits.

For the second wheel, you have 10 possible digits.

For the third wheel, you have 10 possible digits.

10 x 10 x 10 = 1000

For 5 attempts= 5/1000

=1/200

Therefore, the probability will be 1/200

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Answer:

To find how far a zebra can run in 30 minutes, we need to multiply its speed by the amount of time it runs.

Distance = speed x time

In this case, the speed of the zebra is 0.6 miles per minute and the time it runs is 30 minutes.

Distance = 0.6 miles/min x 30 min = 18 miles

So, a zebra can run 18 miles in 30 minutes at a constant speed of 0.6 miles per minute.

Answer:

18 miles

Step-by-step explanation:

0.6 -----> 1

x -----> 30

30×0.6= 18

=======================================================

Explanation:

Use the two given angle measures (Y and Z) to find angle X.

X+Y+Z = 180

X+141+25 = 180

X+166 = 180

X = 180-166

X = 14

Angle X is 14 degrees.

-----------

Now use the law of sines to determine side length z.

Make sure your calculator is in degree mode.

z/sin(Z) = x/sin(X)

z/sin(25) = 830/sin(14)

z = sin(25)*830/sin(14)

z = 1449.9438

z = 1449.9 cm is the final answer.

The solution is : the length of z, to the nearest 10th of a centimeter is, 1449.9 cm.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Explanation:

Use the two given angle measures (Y and Z) to find angle X.

X+Y+Z = 180

X+141+25 = 180

X+166 = 180

X = 180-166

X = 14

Angle X is 14 degrees.

Now use the law of sines to determine side length z.

z/sin(Z) = x/sin(X)

z/sin(25) = 830/sin(14)

z = sin(25)*830/sin(14)

z = 1449.9438

z = 1449.9 cm is the final answer.

Hence, The solution is : the length of z, to the nearest 10th of a centimeter is, 1449.9 cm.

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Luis genera $13680 al mess, sir se incremental un 14% ell valor de sub seldom actual.

De actedron con las condictiones dadas, planter=12000*(14% + 1)

Calculary loss dos primero's terminus =12000*1.14

Calculary loss dos primero's terminus =13680

get the result=13680

Explication paso a paso:

multiplicate ell 14% de 12.000= 1.680

le sulfas ese 1.680 a 12.000 y tee da ell resulted de 13.680

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In linear equation, 16 is represent The speed at which Serena is cycling from the dance class to her home

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

6x + y = 16

6x = 16 - y

x = 8/3 - y/6

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Answer:1111

Step-by-step explanation:1111

Therefore , the solution of the given problem of expression comes out to be 4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.

Verifying an algebraic expression requires substituting a number for each variable and performing arithmetic operations. Given that 6 + 6 equals 12, the answer variable in the example above is equivalent to 6. If we are aware of the values of the variables, we can substitute those values for the original ones, which will allow us to evaluate the expression.

Here,

It is important to note that now the ratio of a coefficient of the terms 

The coefficient ratio of the words

8x³ and 2x is 8:2 = 4:1, and the coefficient ratio of the phrases 12x² and 3 is 12:3 = 4:1.

This suggests that we should categorize the original statement as follows: 

This suggests that we should combine the original expression, which is written as

=> (8x³+2x)(12x²+3)=2x(4x²+1))3(4x²+1),

before determining the common component (4x2+1)=(2x³)(4x2+1).

The fact that 4x²≥0 for x ∈ R means that

4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.

Therefore , the solution of the given problem of expression comes out to be 4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.

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Answer:

5%

Step-by-step explanation:

105=100

110=x

*cross multiply*

=100x110/105

=104.76

=100-105

=5%

subtract the answer gotten with the 100 %

Brooke's yard is a square with a side length of 22 meters.

Perimeter is the total distance around the outside edge of a two-dimensional shape. Perimeter is a measure of the length of the boundary of a shape and is typically expressed in units of length, such as feet or meters. Calculating the perimeter of a shape can help you measure the size of a yard, garden, or other outdoor area.

Since the perimeter of the part covered in gravel is 22 meters, we can use the formula for the perimeter of a square (4s) to find the length of one side of the square. Therefore, the side length of the part covered in grass is 4s = 22, or s = 5.5 meters.

Using the formula for the area of a square (A = s²), we can calculate the area of the grass section of Brooke's yard. The area of the grass section of Brooke's yard is A = s²= 5.5²= 30.25 square meters.

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The measure of angle L is 66 degrees, which is found using the sum of the internal angle of a triangle. The length is 3.56 units.

A polygon's interior angle is the angle created between its two adjacent sides. Alternately, we may state that the internal angle of a polygon refers to the angle measured at the interior portion of a polygon.

Given that the measure of angle M is 24 degrees and angle K is 90 degrees.

The sum of internal angles of a triangle is 180 degrees, thus:

[tex]\angle M + \angle K + \angle L = 180\\\\24 + 90 + \angle L = 180 \\\\\angle L = 66[/tex]

The length of side LK can be found as follows:

tan 24 = LK / MK

tan 24 = LK / 8

0.44 * 8 = LK

LK = 3.56 units.

The length of LM can be found by applying the Pythagorean theorem.

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