Absolute value equations and inequalities.

The measure of ∠Z is 165 degrees to the nearest degree.

In a triangle, the measure of each angle is equal to the sum of the measures of the other two angles subtracted from 180 degrees. This is known as the Triangle Sum Theorem.

Given that x = 5.2 inches, y = 9.8 inches, and z = 7.1 inches in triangle XYZ, we can use the theorem to find the measure of angle Z.

∠Z = 180 - (x+y)

∠Z = 180 - (5.2+9.8)

∠Z = 180 - 15

∠Z = 165

So the measure of ∠Z is 165 degrees to the nearest degree.

Therefore, The measure of ∠Z is 165 degrees to the nearest degree.

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The light cream milk product have approximately 15.36 grams of milk fat in an 80-gram serving.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Let n be the percentage of milk product to have approximately 15.36 grams of milk fat in an 80-gram serving.

Using percentage formula,

15.36 = n x 80 / 100

n = 1536 / 80

n = 19.2%

Therefore, the product is light cream milk.

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Answer: its D

Step-by-step explanation: 3 yard is bigger then 6 feet because 3 yards equals 9 feet hope this helps

Answer:

28

Step-by-step explanation:

1 + 2 + 3 + 4 + 5 + 6 + 7

Answer:

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

a1 = 85 = first term

d = -4 = common difference

an = a1 + d(n-1)

an = 85 - 4(n-1)

an = 85 - 4n + 4

an = -4n+89

a10 = -4*10+89

a10 = 49 is the tenth term

The positive value of the distance between the two objects

is  [tex]r = + \sqrt\frac{GM_1M_2}{F_g}[/tex]

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Considering the equation for determining the gravitational pull between two items [tex]F_g = \frac{GM_1M_2}{r^2}[/tex], where r is the distance between the objects M is the individual masses and G is the gravitational constant.

The answer to the r in the problem has two values. Since distance cannot be negative, there can only be one positive value, hence we want the positive value.

[tex]F_g = \frac{GM_1M_2}{r^2}[/tex]

[tex]r^2 = \frac{GM_1M_2}{F_g}[/tex].

[tex]r = \pm\sqrt\frac{GM_1M_2}{F_g}[/tex]

[tex]r = +\sqrt\frac{GM_1M_2}{F_g}[/tex].

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Answer:

A - $360

Step-by-step explanation:

Length times width equals area.

12 × 10 = 120

His office has 120 sq ft of space. If each sq ft costs $3

120 × 3 = $360

A

Answer:

A ($360)

Step-by-step explanation:

imagine a rectangle with one side 12ft and one side 10ft

multiply the length and the width to find the square footage:

12*10=120ft^2

each square foot is $3 so multiply 3 by 120

$3*120ft^2= $360

oops didn't realize someone already answered sorry

The deposit to be made to save $10,000 in 5 years is $8189.67 when compounded monthly.

Compound interest is interest on a loan or deposit that is calculated on both the principal amount and the interest accumulated in previous periods. It differs from simple interest, which is calculated on the principal only. Compound interest can be more favorable to the lender and more expensive to the borrower. The frequency of compounding (annual, quarterly, monthly, etc.) also affects the total amount of interest earned or paid.

Given that:

A = $10,000

r = 4% = 0.04

t = 5 years

n = 12 (since the compounding is monthly)

P = ?

The compound interest is given as follows:

[tex]A= P(1+\frac{r}{n} )^{nt}[/tex]

Substituting the values in the formula we have:

[tex]10000= P(1+\frac{0.04}{12} )^{(12)(5)}\\\\10000= P(1+0.0033 )^{(60)}\\\\10000= P(1.0033 )^{(60)}\\\\10000= P(1.2185)\\\\P= \frac{10000}{1.2185} \\\\P=8189.67[/tex]

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The expected number of ball pens of a student is 2.4.

What is the expected number?

In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values.

The expected number of ball pens of a student can be calculated by taking a weighted average of the number of ball pens that each group of students has.

The weight for each group is the percentage of students that are in that group.

So, we can calculate the expected number of ball pens of a student by:

(10% * 7) + (30% * 3) + (40% * 2) + (20% * 1)

0.7 + 0.9 + 0.8 + 0.2

The expected value is also known as the population means and it can be calculated by summing the product of each outcome’s probability and its corresponding value.

Here, the outcome is the number of ball pens.

Hence, the expected number of ball pens of a student is 2.4.

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The equation to find the root of the statement given in the question is , 12x = 2x - 24.

Let the number of tamp which Ritu have be x

Then the number of tamp which Raj have be 2x = 24

Now as Ritu has 6 times more than Raj , 6( 2x) = 24 x 6

Therefore, the required equation becomes,

12x = 2x - 24

=> 10x = 24

=> x = 2.4 answer.

An equation is a mathematical statement which is made up of constants , variables and operators. There are two parts of an equation which are equated using the equal sign . The right hand and the left hand side of the equation.

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Bar charts display categorical variables, whereas histograms display numerical or quantitative data.

The frequency distribution of a few data points for one variable is represented graphically by a histogram. Heterogeneous "bins" or "range groups" are frequently used in histograms in order to categorize data and count the number of data points that are part of each bin.

Among graphing tools, the histogram is widely used. It is utilized to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.

Histograms show numerical or quantitative data, whereas bar charts show categorical factors. The numerical data in a histogram will typically be continuous in most cases (having infinite values). It would be ridiculous to attempt to plot an axis that included every potential value for a continuous variable.

Therefore, the correct answer is option C. 6 or fewer.

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The number of installations in September were forty that lead to John and Wesley earning same amount of money.

Let the number of installations be x. The equation of be formed for each paycheck will be -

Total paycheck = base pay + number of installations × comission on each installation

The total paycheck and number of installations is same. So equating the equations by keeping x.

2000 + 65.25x = 380 + 105.75x

Rewriting the equation -

105.75x - 65.25x = 2000 - 380

Performing subtraction on each side of the equation

40.5x = 1620

x = 1620/40.5

Performing division on Right Hand Side of the equation

x = 40

There were 40 installations.

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The potential instances of sample distribution are options C and E.

Option E. Average male height based on samples of size 30.

Option C. Mean trout lengths based on samples of size 5.

The sampling distribution of the mean is the distribution of the variable x (all feasible sample means of size n) for a variable x and a given sample size n.

The mean is the most typical kind of sample distribution. Plotting the data points and computing the means of each sample group drawn from the population are its main goals.

This idea, which is a form of the probability distribution, is frequently used to gather precise data from a sizable population that is divided into a number of randomly chosen samples. This idea is further divided into three categories: T-Sampling, proportional sampling, and the sampling distribution of the mean.

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The correct questions should be like this:

Which of the following are possible examples of sampling distributions? (Select all that apply.) average SAT score of a sample of high school students

all mean trout lengths in a sampled lake

mean trout lengths based on samples of size 5

heights of college students at a sampled university

average male height based on samples of size 30

The gradient of the linear equation 2x + 3y + 6 is (3/2).

The gradient of a linear equation in the form of y = mx + c is m, which represents the slope of the line. The slope is defined as the ratio of the change in y to the change in x. It represents the steepness of the line.

The equation 2x + 3y + 6 is not in the form of y = mx + c. It is in the form of Ax + By + C = 0, which is the general form of a linear equation. To find the gradient of such an equation we need to divide -A/B. In this case, the gradient of the line is -2/3.

The gradient of a line gives us the direction of the line, it is the slope of the line. It tells us how steep the line is and if it is going up or down. A positive gradient means the line is going up and a negative gradient means the line is going down.

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After 0.6412 years the average for mobile device and television usage will coincide.

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here the equations as  y=-9.11x+280x and  y=12.34x + 169.9 the period for which the averages are equal will be given by

9.11x+280x=12.34x + 169.9

       x   = 0.6412 years

Again, after 7 years in 2021 the respective averages will be                  9.11 ×7+280×7 = 2023.77 and similarly for mobile device the time spent would be 256.28 minutes

Hence, the answers are After 0.6412 years the average for mobile device and television usage will coincide.

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The product for the given polynomial is [tex]8y^5 + 6y^4 + 20y^3.[/tex]

When multiplying two polynomials, it is important to keep track of the exponents of each term. The exponents will determine the degree of the resulting polynomial. To find the product, you multiply each term of the first polynomial by each term of the second polynomial, then combine like terms.

In this case, the first polynomial is 4y^3 and the second polynomial is 2y^2 3y 5. To find the product, you would multiply 4y^3 by 2y^2, 4y^3 by 3y, and 4y^3 by 5. This would give you 8y^5, 12y^4, and 20y^3. Since these are the only terms in the product, you simply add them together to get the final answer of [tex]8y^5 + 6y^4 + 20y^3.[/tex]

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The degree of polynomial 7x³ + 4x² is 3 as the highest power is 3.

One of the fundamental ideas in mathematics is the degree of polynomials, which determines the maximum number of solutions a function can have and how frequently a function will cross the x-axis on a graph.

Polynomials are also useful in understanding how functions can be represented mathematically. It has the highest exponential power in the polynomial equation.

The greatest power of a variable in a polynomial equation is its degree. When calculating the degree of a polynomial function, only terms with variables are considered. The degree of the polynomial can be determined by looking at the variable term with the highest exponential power.

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The x-coordinate of the solution of the system of equations is x = 20/3

Here we have a system of equations below:

3x - y = 6

3x + y = 34

And we want to find the x-cordinate of the solution, so we need to solve this for x.

We can use the elimination method, you can see that if we add both equations we will get:

(3x - y) + (3x + y) = 6 + 34

6x = 40

x = 40/6

We can simplify that fraction to get:

x = 20/3

That is the x-coordinate of the solution.

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The required simplified expression as a monomial is given as -12[z⁶].

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial and trinomial, etc. ax+b is a polynomial.

here,

Given an expression, the outcome of the multiplicative depression will be an expression of a monomial.
= [4z³][-3z³]
= 4 × 3 [-z ³⁺³]
= -12[z⁶]

Thus, the required simplified expression as a monomial is given as -12[z⁶].

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On solving the provided question, we can say that - the linear equation y = 7x - 17 at x= 0; y = -17 and m = -17

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

y = 7x - 17

at x= 0

y = -17

and m = -17

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The percent of fans that are between 18 and 27 years old is 16.80%.

From the information, the average age of a group of fans at a hockey game is 34 years with a standard deviation of 8 years and we want to calculate the percent of fans are between 18 and 27 years old.

It should be noted that this will be Illustrated through the normal curve.

The probability will be:

P(18 ≤ X ≤ 27)

= P(18 - 34/8) ≤ Z ≤ (27 - 34 / 8

= P(-2.0 ≤ Z ≤ -0.875)

= 0.1908 - 0.02275 (From the standard normal calculator)

= 16.80%

The percentage is 16.80%.

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Answer: The middle number is 15

Step-by-step explanation:

45/3= 15 so the three numbers will be around there.

14+15+16= 45

Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , 5) and a "p" distance of negative 2 units, since it's opening to the left, so

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=5\\ p=-2 \end{cases}\implies 4(-2)(~~x-0~~) = (~~y-5~~)^2\implies {\Large \begin{array}{llll} -8x=(y-5)^2 \end{array}}[/tex]

The two sets A and B triangle must have identical items, but this does not require that they be put in the same order for the sets to be equal.

A triangle is a 2D shape with three vertices, three straight edges, and three straight edges. A key feature of these shapes is that each type of triangle has three inner angles that add up to 180° in these designs. during their math lectures about these angles and how to use this quality to spot missing values.

Here,

Triangle 1 in this instance has two angles, one of 34 degrees and the other of 48 degrees.

The third angle is therefore 180-34- 48=98.

The angles in Triangle 2 are 34 and a, where an is 48, respectively.

In other words, the third angle is 180−34−a=146−a≠146−48=98.

Jennifer claims that given the information at hand, triangles 1 and 2 cannot be compared.

If 34,98,48=34,a,146a., they are equivalent.

How many degrees will Jennifer's claim be ruled untrue? To compare the triangles, use the formula a.

It is crucial to understand that while components in two sets A and B must match, the sets are not always equal if they are not listed in the same order.

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Answer: This is a horizontal translation so, the equation is f(x) = (x + 5). Whenever you translate to the right it is negative

Step-by-step explanation:

Using the fact that the triangles are similar, we will see that:

x = 5.626

On the image we can see two triangles, such that one is inscribed on the other.

Just because of that, it is obvious that the two triangles are similar.

And because the triangles are similar, the quotients between correspondent sides must be equal, that allows us to write the equation:

3/x = 8/15

The quotient is "left side over the bottom side"

We can solve that equation for x:

3/x = 8/15

3 = (8/15)*x

(15/8)*3 = x

45/8 = x

5.625 = x

That is the value of x.

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The work done on the toy car is 164.4 J.

The formula for work is:

Work = force * distance

In this case, given that:

Force = 5.2 N

Distance = 32 m

So, the work is:

Work = force * distance

Work = 5.2 * 32

Work = 166.4 J

Hence, the work done is 164.4 J.

Force is described as the rate of change of momentum with respect to time, in which momentum is mass multiplied by velocity. Work is the product of displacement and the component of force in the direction of displacement. When work is done, then the kinetic energy of an object changes.

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The graph of the linear equation 2x - 3y = -15 is a line that passes through the point (-5, 5), and has a slope of 2/3.

The linear equation

2x - 3y = -15

can be written in the form

y = mx + b,

where m is the slope and b is the y-intercept. To find the slope of this equation, we can rearrange the equation to be in the form y = mx + b, which gives us

y = (2/3)x - 5.

This means that the slope of the line is 2/3. To find the y-intercept, we can plug in 0 for x and solve for y. This gives us

y = -5.

Therefore, the graph of this equation is a line that passes through the point (-5, 5) and has a slope of 2/3.

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The probability of not getting result is found as 24.7%.

The number of times an event happened during the experiment as a percentage of all the times the experiment was run is known as the experimental probability of that event occurring.

So,

P(Result) = 0.753.

P(no result) = 1 - 0.753

P(no result) = 0.247

Thus, the probability of not getting that result is found as 24.7%.

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The correct question is-

If the probability of getting a result in an experiment is 75. 3%, what i the probability of not getting that result?