What is another word for logarithm?

Answer:

45 acres of wheat

Step-by-step explanation:

let w represent wheat then corn is 3w , so

w + 3w = 180

4w = 180 ( divide both sides by 4 )

w = 45

3w = 3 × 45 = 135

that is

135 acres of corn and 45 acres of wheat

The correct statement is "only a and c are correct"  so option g is the answer.

The statement that is true in a normal distribution is "approximately 70% of the values are within one standard deviation from the mean" (a), and "2.1% of the values are between -2 and -3 standard deviations from the mean" (c).

These statements are true because of the properties of a normal distribution, also known as a Gaussian distribution or bell curve. In a normal distribution, the majority of values cluster around the mean, with fewer and fewer values as you move further away from the mean.

The statement "twenty-seven percent of the values are between one and two standard deviations from the mean" (b) is not true, as the correct percentage is approximately 27.7% (68-95-99.7 rule).

The statement "0.1% of the values are 3 or higher standard deviations from the mean" (d) is also not true, as the correct percentage is approximately 0.3%.

Therefore, the correct statement is "only a and c are correct".

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The answer is in the image attached below. Sorry for the goofy looking arrow.

The value of the expression given is undefined when x equals 2 and -2.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given expression is,

(14+x)/(x^(2)-4)

This can be written as,

[tex]\frac{14+x}{x^{2} -4}[/tex]

The value of the expression is undefined when the denominator equals 0.

Denominator is [tex]x^{2} -4[/tex].

[tex]x^{2} -4[/tex] = 0

[tex]x^{2}[/tex] = 4

x = √4

x = ± 2

Hence when the value of x is +2 or -2, the expression is undefined.

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Answer:

Step-by-step explanation:

Answer:

Horizontal line on the "2" line of the y axis.

Step-by-step explanation:

y=2 means y is constantly at 2, so it would be a horizontal line there.

The number of child tickets sold on Saturday is 5.

We know that at the city museum, the child admission is $5.20 and adult admission is $9.10. We also know that on Saturday 162 tickets were sold for a total sales of $1491.60.

We can use this information to find the number of child tickets sold on Saturday. We can set up an equation with the total sales and the price of the tickets.

Let x be the number of child tickets sold.

x(5.2) + (162-x)(9.10) = 1491.60

The equation represents the total sales by the number of child tickets sold multiplied by the price of child admission, and the number of adult tickets sold multiplied by the price of adult admission.

We can solve for x by isolating it and substituting the given values:

x(5.2) + (162-x)(9.10) = 1491.60

x*5.2 + (162-x)*9.10 = 1491.60

5.2x + 1472.20 - 9.10x = 1491.60

-3.9x = -19.40

x = 19.40/-3.9

x = 5

So, the number of child tickets sold on Saturday is 5.

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Answer:

Step-by-step explanation:

The expression is (4 x 1,000) + (3 x 100) + (6 x 1 / 100) + (7 x 1 / 1000) in simplified as the decimal number = 4,300.067

The roots of the quadratic equation 3x² + 5x - 2 = 0 are the two values of x that make the equation true. In this case, they are x = -2 and x = 0.

Step 1: Move all terms with an x to one side of the equation and all terms without an x to the other side:

3x² + 5x - 2 = 0

3x² + 5x = 2

Step 2: Divide both sides of the equation by the coefficient of the x² term (3):

(3x² + 5x)/3 = 2/3

x² + (5/3)x = 2/3

Step 3: Use the quadratic formula to calculate the roots of the equation:

x = [-b ± √(b² - 4ac)]/2a

x = [-(5/3) ± √((5/3)² - 4(1)(2/3))]/2(1)

x = [-(5/3) ± √(25/9 - 8/3)]/2

x = [-(5/3) ± √(7/9)]/2

Step 4: Calculate the values of x that make the equation true:

x = [-(5/3) + √(7/9)]/2

x = [-(5/3) - √(7/9)]/2

x = [-2]

x = [0]

Therefore, the roots of 3x² + 5x - 2 = 0 are x = -2 and x = 0.

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Step-by-step explanation:

see attachment

hope this helps!

-Rishabh

Answer:

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

Add up the mixed numbers in below steps:

A. Def. of Complementary Angles states the measure of the sum of two angles is 90°.

Complementary angles are two angles whose measures add up to 90 degrees. The definition states that if two angles are complementary, their measures will sum up to 90 degrees. The concept of complementary angles is important in trigonometry, where the complementary angles are used in the relationship between the sine, cosine, and tangent of an angle.

For example, if angle A is complementary to angle B, then we can write:

Angle A + Angle B = 90 degrees

It is important to note that complementary angles do not have to be adjacent or next to each other, but they must always add up to 90 degrees when measured in degrees.

Therefore, option A. Def. of Complementary Angles is the correct answer.

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The sum of all 3-digit multiples of 10 is 49500.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

The first 3-digit number divisible by 10 is 100, and the last 3-digit number divisible by 10 is 990.

The total number of such digits are,

= (990 - 10)/10 + 1.

= 980/10 + 1.

= 98 + 1.

= 99.

We know sum of an arithmetic series when the first term and the last term is given is,

= [n(a + l)/]2.

= [99(10 + 990)]/2.

= (990 + 98,010)/2.

= 49500.

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The graph is a horizontal line where all values for y are -2.

Now, According to the question:

What is called graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

Generally, graphs show a function, for example,

y = x −3. In that case, one would draw a graph by substituting an x value into the equation and connecting the points.

In this case, however, there are no x values in the equation. Therefore, regardless of the number on the x-axis, the y value will remain the same (−2). Therefore, the line will be a horizontal line with a slope of zero and a y-intercept of −2.

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Answer: y-axis

Step-by-step explanation:

The y-axis determines the "height" of the graph, so 2 units higher would mean 2 units higher on the y-axis.

You know the difference in the distance the boys ran, so this is an subtraction problem. The correct expression is s - 2.3=6.8

Length is measured in distance. For instance, the length of a road equals its distance.

The most popular units of measurement for distance in the metric system are millimeters, centimeters, meters, and kilometers.

A scalar quantity known as distance measures "how much ground an object has traversed" while moving. An object's total change in position is referred to as displacement, a vector variable that measures "how far out of place an object is."

Step1:

Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km

Distance run by dean = 6.8 km

Distance run by dean = 2.3 fewer kilometers than Sam.

Let us assume that, distance run by same is s km

Step2:

Distance run by dean = s - 2.3

therefore,

s - 2.3 = 6.8

s = 6.8 + 2.3

s = 9.1 km .

Hence, The correct equation is s – 2.3 = 6.8 .

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The meaning of substitution originates from Latin with the basic meaning of "in place of." The meaning of substitution in math is an absolute, 100% replacement in value.

Mathematics properties are statements that have been tested and proven to be true. These properties are used always throughout math. The substitution property of equality, just like the others, is particularly useful.

The substitution property of equality describes that one value can replace another value in an expression or equation and the value will stay the same. For instance, if the values of y and z are equal, then they are interchangeable.

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$87.50is the total cost of the materials.

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the diameter is multiple by two of the radius

Answer:

f(- 2) = 5

Step-by-step explanation:

f(- 2) with x = - 2 in the interval x < 2, then f(x) = 3 - x , that is

f(- 2) = 3 - (- 2) = 3 + 2 = 5

Answer:

Perimeter of rectangle is larger by 6 cm

Step-by-step explanation:

area of rectangle = 48 * 27 = 1296

√1296 =  36

length of square = 36 cm

Perimeter of square = 36 + 36 + 36 + 36 = 144

Perimeter of rectangle = 48 + 48 + 27 +27 = 150

Perimeter of rectangle is larger by 6 cm

The greatest common factor (GCF) of two or more numbers is the largest number that divides evenly into each of the numbers without leaving a remainder. To find the GCF of 24, 30 and 50, we can use the prime factorization method. The prime factorization of 24 is 2^3 * 3^1, the prime factorization of 30 is 2 * 3^1 * 5^1, and the prime factorization of 50 is 2 * 5^2. We can see that the GCF of these numbers is 2 * 3^1 = 6, since 6 is the highest power of 2 and 3 that divides all three numbers evenly. So, the GCF of 24, 30 and 50 is 6.

I hope this helps :)

Answer:

2

Step-by-step explanation:

I did the work.

The length of the ball from the center green using the cosine rule is;  84.4 yards

In trigonometry, the Cosine Rule is a rule that states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle that is included between them.

This can be expressed as;

c = √(a² + b² - 2ab cos C)

In this question, the length of the length of the ball from the center green is c and as such using the cosine rule, we have;

c = √(110² + 45² - 2(110 * 45)cos 45)

c = √(14125 - 7000.36)

c = 84.4 yards

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The length of top enclose r s end enclose = √(4² + 5²) = √(16 + 25) = √(41) = approximately 6.4 inches.

The length of top enclose r s end enclose can be determined using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Since top enclose p s end enclose is a diameter of the circle, it is the hypotenuse of a right triangle formed by top enclose p s end enclose, top enclose p q end enclose and top enclose p r end enclose. Thus, the length of top enclose r s end enclose is the square root of the sum of the squares of the lengths of the other two sides, which are 4 inches and 5 inches.

In other words, the length of top enclose r s end enclose = √(4² + 5²) = √(16 + 25) = √(41) = approximately 6.4 inches.

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The length of the guy wire, to the nearest foot is: 207 ft.

What is Pythagorean theorem ?

Pythagorean theorem can be defined as the square of hypothenuse is equal to sum of squares of base and adjacent

Given ,

The length of the guy wire, to the nearest foot is: 207 ft.

After sketching the information given, we have two similar right triangles, ΔABE and ΔCDE.

CD = 11 ft

DE = 2 ft

BD = 35 ft

Required:

Length of the guy wire (AE)

First, find AB:

Since ΔABE ~ ΔCDE, therefore,

AB/CD = BE/DE (proportional sides)

Plug in the values

AB/11 = (35 + 2)/2

AB/11 = 37/2

Cross multiply

AB = (37 × 11)/2

AB = 203.5 ft

Apply Pythagarean Theorem to find AE:

AE = √(AB² + BE²)

AE = √(203.5² + 37²)

AE = 207 ft (nearest foot)

Therefore, the length of the guy wire, to the nearest foot is: 207 ft.

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The space left for the sand is  [tex]5\frac{3}{10}[/tex] square yards.

In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows:

Operands: An operation uses operands, which are numbers. Depending on the type of operation, different terms are applied to the operands.

Given the total space for beach play = [tex]8\frac{2}{5}[/tex] square yards

 [tex]8\frac{2}{5}[/tex] square yards = 42/5 square yards

and space for water = [tex]3\frac{1}{10}[/tex] square yards

[tex]3\frac{1}{10}[/tex] square yards = 31/10 square yards

let us assume the rest of the area for the sand

area of sand = total area - space for water

area of sand = 42/5 - 31/10

area of sand = (42(2) - 31)/0

area of sand = (84 - 31)/10

area of sand = 53/10

area of sand = [tex]5\frac{3}{10}[/tex] square yards

Hence the space left is  [tex]5\frac{3}{10}[/tex] square yards.

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Answer:

a) To calculate the remaining balance on the loan at the end of the first year, you need to first calculate the interest that has accumulated on the loan. This can be done using the formula:

Interest = Principal x Rate x Time

In this case, the interest for the first year would be:

Interest = 150000 x (10/100) x 1 = 15000

So the total amount owed at the end of the first year, including interest, would be:

Total = Principal + Interest = 150000 + 15000 = 165000

Now, after paying Rs 85000 at the end of the first year, the remaining balance on the loan would be:

Remaining Balance = Total - Payment = 165000 - 85000 = 80000

To calculate the amount that needs to be paid at the end of the second year, you need to calculate the interest that has accumulated on the remaining balance of the loan. This can be done using the same formula as before:

Interest = Remaining Balance x Rate x Time = 80000 x (10/100) x 1 = 8000

So the total amount that needs to be paid at the end of the second year would be:

Total = Remaining Balance + Interest = 80000 + 8000 = 88000

b) If he had paid the loan only at the end of second year, the interest would have been:

Interest = Principal x Rate x Time = 150000 x (10/100) x 2 = 30000

Thus, he would have paid 30,000 more than he paid by paying partly at the end of first year.

Step-by-step explanation:

Answer:

I believe the answer to be 1 : 8

On graphing function A: 3x - 21 and function B: y = 2x - 3, it is known that both are linear as they both form a straight line.

What is a linear function?

A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nevertheless, calculus and linear algebra are also used to represent linear functions.

The function A is given as 3x - 21.

The function B can be written in slope intercept form -

y = mx + b

where m is the slope and b is the y-intercept.

m = (y2-y1)/(x2-x1)

m = [1-(-1)]/(2-1)

m = 2/1

m = 2

To find y-intercept substitute x = 1 and y = -1.

y = mx + b

-1 = 2(1) + b

-1 = 2 + b

b = -1 - 2

b = -3

Hence the equation for function B is y = 2x - 3.

Therefore, on graphing function A and B it can be seen that both are linear.

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