Solve for x. Round to the nearest hundredth.12.1sin 24°---x= 31.64x=4.92x = 29.75x = 28.52

The circumference of the circle with the measure of diameter as 28 cm is 87.92 cm.

Given a circle.

Also given that,

Diameter of the circle = 28 cm

We know that, radius of a circle is half the measure of the diameter of the circle.

Radius of the circle = 28 / 2 = 14 cm

The formula to find the circumference of the circle is,

Circumference = 2 πr

Here r is the radius of the circle.

Substituting the given,

Circumference = 2 π (14)

                         = 28π

                         = 28 × 3.14

                         = 87.92 cm

Hence the circumference is 87.92 cm.

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A: partial variation

B: Direct variation

C: Direct variation

D: Partial variation

The quotient using compatible numbers for 2252 divided by 7 is 321 remainder 5.

Compatible numbers are those that are simple to mentally add, subtract, multiply, or divide. Compatible numbers are close in value to the actual numbers, making it easy to estimate the answer and solve problems.

The following steps are required:

Step 1: Take the dividend's first digit from the left.

Step 2: Next, divide it by the divisor and write the result as the quotient on top.

Step 3: Subtract the result from the digit and record the difference.

Step 4: Subtract the dividend's next digit (if present).

Step 5: Write the value gotten.

A quotient is a quantity created by the division of two numbers in mathematics. The quotient is widely used in mathematics and is also known as the integer component of a division, a fraction, or a ratio. In this case, the value gotten after the division is 321 remainder 5.

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Answer:

Step-by-step explanation:

You want the solutions to the trig equation csc(θ)² = 6csc(θ) +7 on the interval [0°, 360°].

We can write this equation in standard form, then factor it:

  csc(θ)² -6csc(θ) -7 = 0

  (csc(θ) -7)(csc(θ) +1) = 0

  csc(θ) = 7  or  -1

  sin(θ) = 1/csc(θ) = 1/7  or  -1

There are two values of θ in the range that have a sine of 1/7: 8.2° and 171.8°.

There is one value of θ such that sin(θ) = -1: θ = 270°.

The solutions are 8.2°, 171.8°, and 270°.

__

Additional comment

Some calculators may be able to tell you the value of csc^-1(x) directly, without converting to sin^-1(1/x).

The second attachment shows a graphing calculator solution for csc(θ)² -6csc(θ) -7 = 0. (horizontal axis is degrees)

<95141404393>

The work W done in pulling the toboggan 100 feet is given as follows:

2,318.96 ft - lb.

The equation for the work is given as follows:

W = Fdcos(a).

In which the parameters are given as follows:

The parameters values for this problem are given as follows:

F = 25, d = 100, a = 22º.

Hence the work is obtained as follows:

W = 25 x 100 x cosine of 22 degrees

W = 2,318.96 ft - lb.

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Answer:

Step-by-step explanation:

1. j

2. k

3. L

4. Lj

5. kL

6. jk

The binomials (x - 3) and (x - 10) are factors of the trinomial x² - 13x + 30.

To determine which binomial is a factor of the trinomial x² - 13x + 30, we need to factorize the trinomial completely.

In this case, we need to find two binomials in the form (x - a)(x - b) that satisfy the equation:

(x - a)(x - b) = x² - 13x + 30

So, (x - 3)(x - 10) = x² - 13x + 30.

Therefore, the binomials (x - 3) and (x - 10) are factors of the trinomial x² - 13x + 30.

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Answer:

uhmm i don't know sorry I am just kind of doing this so I get the credit for answering a question:)

Answer:

D. \(y = 5\cdot \Sigma_{i=0}^{4} \left(\frac{1}{3} \right)^{i}\)

Step-by-step explanation:

Let be \(y = \Sigma_{i = 0}^{4} \left[5\cdot \left(\frac{1}{3} \right)^{i}\right]\). To find the equivalent expression we must use the following property:

\(y = c\cdot \Sigma_{i = 0}^{n} p(x) = \Sigma_{i=0}^{n} [c\cdot p(x)]\) (1)

Based on this fact, we find the following equivalence:

\(y = 5\cdot \Sigma_{i=0}^{4} \left(\frac{1}{3} \right)^{i}\)

Hence, the correct answer is D.

let's keep in mind that arc's get their angle value from the central angle they cover, so in this case whatever angle value the arcAFB has, will also be the same for the ∡AFB.

Check the picture below.

The volume of the tower is 224 in³, which is not listed among the given options.

To find the volume of the rectangular block, we need to multiply its length, width, and height. Therefore, the volume of the single block is:
8 x 3.5 x 2 = 56 cubic inches.
Since we are stacking four blocks to create a tower, we need to multiply the volume of a single block by 4.

Thus, the volume of the tower is:
56 x 4 = 224 cubic inches.
The volume of a rectangular block can be found using the formula,

V = length × width × height.

In this case, the length is 8 inches, the width is 3.5 inches, and the height is 2 inches.

V = 8 × 3.5 × 2 V

= 28 × 2 V

= 56 in³

Now that we know the volume of one block, we can find the volume of the tower created by stacking four blocks. Tower volume = block volume × number of blocks Tower volume = 56 in³ × 4 Tower volume = 224 in³

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The correct option is A {-5, 0, 3, 4}.

In mathematics, the domain of a function is the set of all possible input values (independent variable) for which the function is defined. In other words, the domain is the set of values that we can substitute for the independent variable in a function to produce a meaningful output.

For example, consider the function f(x) = 2x. Here, we can substitute any real number for x and get a meaningful output. Therefore, the domain of this function is all real numbers, or (-∞, ∞). However, if we consider the function g(x) = 1/x, we can see that we cannot substitute 0 for x because division by 0 is undefined. Therefore, the domain of this function is all real numbers except 0, or (-∞, 0) U (0, ∞).

The domain of a relation is the set of all possible values for the independent variable (x) for which there exists a corresponding value of the dependent variable (y). In this case, the given coordinates are (1,3), (4,1), and (-5,-4).

The domain of the relation would be the set of x-values that correspond to the given coordinates. So, the domain of this relation is {-5, 1, 4}.

Therefore, the correct answer is A: {-5, 0, 3, 4}.

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The dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ration.

To determine the amounts of the 70% protein supplement and the 20% protein ratio needed to make a 1900-pound high-grade 55% protein ration, we can set up a system of equations.

Let's assume x represents the pounds of the 70% protein supplement and y represents the pounds of the 20% protein ratio.

The total weight equation is given by:

x + y = 1900

The protein content equation is given by:

(0.70x + 0.20y) / 1900 = 0.55

Simplifying the second equation, we get:

0.70x + 0.20y = 0.55 × 1900

0.70x + 0.20y = 1045

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

Rearrange the first equation to solve for x:

x = 1900 - y

Substitute this expression for x in the second equation:

0.70(1900 - y) + 0.20y = 1045

1330 - 0.70y + 0.20y = 1045

1330 - 0.50y = 1045

-0.50y = 1045 - 1330

-0.50y = -285

y = -285 / -0.50

y = 570

Now substitute this value of y back into the first equation to find x:

x + 570 = 1900

x = 1900 - 570

x = 1330

Therefore, the dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ratio.

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The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.

Given that,

Finding the expression that can be utilised to find

20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98.

From the Latin word "per centum," which means "by the hundred," the word "percentage" was borrowed. The denominator of percents is 100, making them fractions. In other words, it is the relationship between a part and a whole in which the value of the whole is consistently set to 100.

Take

20% of 92

Multiply 20%×92

=18.4

45% of 76

Multiply 45% ×76

=34.2

50% of 62

Multiply 50%×62

=31

60% of 92

Multiply 60%×92

=55.2

12% of 98

Multiply 12%×98

=11.76

Therefore,

The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.

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Let's write this verbal phrase as an inequality.

First of all, let the number be n.

"three times n" can be written like so:-

\(\pmb{3n}\)

Now, 18 is greater than 3n:-

\(\pmb{18 > 3n}\)

Which means 3n is less than 18:-

\(\bigstar{\boxed{\pmb{3n < 18}}}\)

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)

The surface area of the similar model is 15.9 square meters (Rounded to the nearest tenth).

We need to use the fact that the surface area of similar shapes is proportional to the square of the scale factor.

Let SA be the surface area of the original skyscraper, and SA' be the surface area of the similar model. The scale factor is 1/300, which means that the dimensions of the similar model are 1/300 times the dimensions of the original. Therefore, the surface area of the similar model can be found using the formula:SA' = (1/300)^2 * SA

Substituting the given values, we get:SA' = (1/300)^2 * 1,429,000

SA' = 15.879 m^2 (rounded to the nearest tenth)

Therefore, the surface area of the similar model is 15.9 square meters (rounded to the nearest tenth).

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Answer:

Step-by-step explanation:

A fraction represents a part of a whole number. A fraction is a ratio between the upper number (the numerator) and the lower number (the denominator). The numbers are stacked vertically and separated with a bar.

is that decimals and fractions are different ways of representing the same thing—a number that is not whole.

1.) By Using a Calculator

The easiest way to convert a fraction to a decimal is to divide the numerator (the top of the fraction) by the denominator (the bottom of the fraction) by using a calculator.  The resulting answer will be the value of the fraction expressed as a decimal number.

For example, to convert the fraction 7/8 to a decimal using a calculator, simply perform 7 divided by 8 and press enter. The resulting decimal would be 0.875.

Therefore, you can say that 7/8 expressed as a decimal is 0.875

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Answer:

hello ok I will share u the link where u can find step by step answers

Answer:

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.

A Let tower be AB

Let point be C

Distance of point C from foot of tower = 30m Hence,

BC = 30m

Angle of elevation = 30°

So < ACB = 30°

Since tower is vertical,

< ABC = 90°

The value of \(log_35 \times log_{25}9\) is 1.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

\(log_35 \times log_{25}9\)

\(log_ab = \frac{logb}{loga}\)

So,

= log 5 / log 3 x log 9 / log 25

= log 5 / log 3 x log 3² / log 5²

\(logm^n = n~logm\)

So,

= log 5 / log 3 x log 3² / log 5²

= (log 5 / log 3) x (2 log 3 / 2 log 5)

= (log 5 / log 3) x (log 3 / log 5)

= 1

Thus,

1 is the value.

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Thus, the inequality y > -4 on a number line will have values from -4 till infinity will be taken, in which -4 is not taken.

The values just on number line that satisfy each individual inequality in the compound inequality should be shaded in -

Given  inequality:

y > -4

As, the value of y is greater than -4, y is not taken on number line.

All the value greater than -4 till infinity will be taken.

Thus, the inequality  y > -4 on a number line will have values from -4 till infinity will be taken, in which -4 is not taken.

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The product of the expression 1 1/6 x 7/8  is 49/48

Fractions are defined as parts of a whole number.

The different types of fractions are;

From the information given, we have the fractions;

1 1/6 x 7/8

convert the mixed fraction to improper fractions, we have;

7/6 × 7/8

Now, multiply both the numerators and denominators, we get;

49/48

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Answer:

A

Step-by-step explanation:

The required range of drivers who own 8 years car is 23years.

Given that,

The scatter plot shows the ages of drivers who attended a car show and the ages of their cars.

We have to determine,

The age range of drivers who own an 8-year-old car.

According to the question,

The Range is the difference between the lowest and highest values.

Therefore,

The age range of drivers who own 8 years old car is 17,25 and 40 years.

Then,

Range of drivers who own 8 years car = highest value of range - lowest value of age.

Range of age of drivers who own 8 years car = 40 - 17 = 23years

Hence, The required range of drivers who own 8 years car is 23years.

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Answer:

You to it right, 18

Step-by-step explanation:

Answer:

27 ft I think

Step-by-step explanation:

The answer is 27

The fractions arranged from greatest to least are- 13/15, 4/5, 7/9, 30/45

Here, we are given 4 fractions- 4/5, 2/3, 13/15, 7/9

In order to compare them, let us equalize their denominators.

The denominators are- 5, 3, 15 and 9

The LCM of 5, 3, 15 and 9 is 45

Thus, we can write the fractions as-

4/5 = (9*4)/(5*9) = 36/45

2/3 = (2*15)/(3*15) = 30/45

13/15 = (13*3)/(15*3) = 39/45

7/9 = (7*5)/(9*5) = 35/45

Now, we can easily compare the fractions by comparing their numerators.

We see that-

39 > 36 > 35 > 30

Thus, 13/15 > 4/5 > 7/9 > 30/45

Hence, the fractions arranged from greatest to least are- 13/15, 4/5, 7/9, 30/45

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After considering the given data we conclude that the perimeter of the given swimming pool is 23 meters which is Option A.

The perimeter of a rectangle is evaluated by adding up all its sides. For the given case, we possess a rectangle with sides
a = 5m,
b = 8m,
c = 8m and
d = 2m.
Perimeter regarding the swimming pool is evaluated as
a + b + c + d
= 5m + 8m + 8m + 2m
= 23 meters
Hence the option regarding the question which satisfy the perimeter is Option A.
Perimeter the counted  measurement regarding the distance around the outside of a two-dimensional shape. In this system  the length of the outline or boundary of any two-dimensional geometric shape is defined as perimeter .
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The complete question is
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
A.23 m
B. 32 m
C.29 m
D.34 m

Answer:

positive and odd

Step-by-step explanation:

If a is a negative odd number, then a² can't be negative, because a number squared is always positive.

I'll illustrate this with an example.

Let's choose -7 as an example. Instead of a.

-7² = 49

So we see that the result is positive & odd.

So the words that describe a^2 are positive and odd.

Answer: A. $16.13

Step-by-step explanation:

Total students = 82+74+96+99 =351

Sum of earnings of 82 seniors  = $26.75  x 82= $2193.5

Sum of earnings of 74 juniors  = $12.25 x 74 = $906.5

Sum of earnings of 96 sophomores  = $15.50  x 96 = $1488

Sum of earnings of 99 freshmen  =  $10.85 x 99 = $1074.15

Total earnings =  $2193.5  + $906.5+  $1488 +$1074.15

= $5662.15

(Total earnings) ÷ (Total students )

= $5662.15÷ 351

= $16.13