What is the value of x?


4/5 x - 1/10 = 3/10
These are the answer choices.

1/4

8/25

2/5

1/2

\(6\frac{1}{3}\rule[0.35em]{10em}{0.25pt}M\rule[0.35em]{10em}{0.25pt}6.4\)

so, let's find their difference, take half of it and give it to 6⅓.

\(\stackrel{mixed}{6\frac{1}{3}}\implies \cfrac{6\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{19}{3}} ~\hfill 6.4\implies \cfrac{64}{10}\implies \cfrac{32}{5} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{32}{5}~~ - ~~\cfrac{19}{3}\implies \cfrac{(3)32~~ - ~~5(19)}{\underset{\textit{using this LCD}}{15}}\implies \cfrac{96-95}{15}\implies \cfrac{1}{15}\)

\(\stackrel{\textit{now let's take half of that}}{\cfrac{1}{15}\div 2\implies \cfrac{1}{15}\div \cfrac{2}{1}}\implies \cfrac{1}{15}\cdot \cfrac{1}{2}\implies \cfrac{1}{30} \\\\\\ \stackrel{\textit{now let's add it to }6\frac{1}{3}}{\cfrac{19}{3}+\cfrac{1}{30}}\implies \cfrac{10(19)~~ + ~~(1)1}{\underset{\textit{using this LCD}}{30}}\implies \cfrac{191}{30}\implies {\Large \begin{array}{llll} 6\frac{11}{30} =M\end{array}}\)

(a) Find the dual of the LP.Primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\) subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n \leq\) \(b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n \leq b_m$ and $x_1, x_2,\)..., x_n\(\geq 0$\)

Let us find the dual of the above primal problem.

Dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq\)\(C_1$...$a_{1n}y_1+a_{2n}y_2+...+a_{mn}y_m \leq C_n$\)

and\($y_1, y_2, ..., y_m \geq 0$\)

(b) Find the standard form of the LP and dual.Standard form of the primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\)subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n +s_1 = b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n +s_m = b_m$\) and\($x_1, x_2, ..., x_n, s_1, s_2, ..., s_m \geq 0$\)

Standard form of the dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq 0$...$a_{1n}y\)

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Answer:

Value for x is 30.

Step-by-step explanation:

Use similarity theorem.

Answer:5.97

Step-by-step explanation.  

you have to look at the question.

you have to look around the question

The very last step is you have to answer it  

Answer:

3(a−1)

———

a+1

Step-by-step explanation:

To prove the relationship between the illumination at two different distances from a lamp, we can use the inverse square law of light propagation. According to this law, the intensity or illumination of light decreases as the distance from the source increases.

The inverse square law states that the intensity of light is inversely proportional to the square of the distance from the source. Mathematically, it can be expressed as:

I1 / I2 = (D2 / D1)^2 where I1 and I2 are the illuminations at distances D1 and D2, respectively. In this case, we are given that the illumination from the lamp at a distance of 1 m is 10 m/m^2 (meters per square meter). Let's assume that the illumination at a distance of 0.5 m is I2.

Using the inverse square law, we can write the equation as:

10 / I2 = (1 / 0.5)^2

Simplifying the equation, we have:

10 / I2 = 4

Cross-multiplying, we get:

I2 = 10 / 4 = 2.5 m/m^2

Therefore, we have proven that the illumination at a point 0.5 m away from the lamp is 2.5 m/m^2, not 40 m/m^2 as stated in the question. It seems there may be an error or inconsistency in the given values.

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To interpret scores on it, he is presently administering the test to a representative sample of all golfers. Dr. zimmer is clearly in the process of validating their test.

Validation refers to the process of evaluating the accuracy and reliability of a test or measurement instrument. When Dr. Zimmer is administering the test to a representative sample of golfers, he is collecting data that will allow him to determine the validity of the test and its ability to accurately measure golfers' knowledge of the sport's history.

This process is important for ensuring that the test results are meaningful and can be used to make accurate inferences about the population being studied.

By comparing the scores on the test to other measures of golfers' knowledge, such as interviews or other tests, Dr. Zimmer can determine the test's ability to accurately measure the construct it is intended to measure. Therefore, Dr. Zimmer is in the process of validating his test by collecting data and evaluating its accuracy and reliability.

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A sporadic issue occurs randomly and infrequently, while a chronic issue persists or repeats consistently over time.

Sporadic Issue: A sporadic issue refers to a problem or occurrence that happens irregularly or infrequently, without a predictable pattern. It occurs randomly and unpredictably, making it challenging to identify the underlying cause or find a permanent solution. For example, a sporadic issue could be an intermittent network connectivity problem that occurs only a few times a month, making it difficult to troubleshoot and resolve.

Chronic Issue: A chronic issue refers to a persistent problem or condition that persists over an extended period or occurs repeatedly. It occurs consistently or with a regular pattern, making it easier to identify and diagnose. Chronic issues often require ongoing management or long-term solutions. For example, a chronic issue could be a recurring software bug that affects the system's functionality and requires continuous updates and fixes to address the underlying problem.

Both sporadic and chronic issues can have significant impacts on systems, processes, or individuals, albeit in different ways. Sporadic issues are more challenging to troubleshoot and address due to their unpredictable nature, while chronic issues demand sustained attention and long-term strategies to mitigate their effects.

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Answer:

Two shapes are similar when they have the same shape while their sizes may be the same or different

Therefore, two similar shapes are shapes that have a relationship such that the dimensions of one of the shapes can be obtained from the dimensions of the other shape by multiplying by a scale factor

All circles have the same shape and are defined by their center and radius

Given circle with center at 'x' and radius 'r' and circle with center 'y' and radius 's', then there exist a scale factor a = s/r such that we have;

r × a = s

Where a = s/r, we get;

r × s/r = s

We can therefore, obtain a circle with with the same size as the circle with center 'y' and radius 's' by multiplying the radius of the circle with center at 'x' and radius 'r' by a

Therefore the circle with center at 'x' and radius 'r' is similar to the circle with center 'y' and radius 's'

Step-by-step explanation:

Just did it! <3

Hope this helps!

Answer:

(look at graph below)

Step-by-step explanation:

Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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Answer:

B is correct.

Step-by-step explanation:

Quadratic Expression (Standard Form) is:

\( \displaystyle \large{a {x}^{2} + bx + c}\)

To say it simply, the expression must have 2 as the highest degree.

This means that if there are any higher or lower degrees than 2 then they are not quadratic expression.

A choice is not quadratic expression because it has 1 as the highest degree.

B choice is correct because 2 is the highest degree.

C choice is wrong because 3 is the highest degree.

D choice is wrong because it is not a polynomial.

Therefore, B is correct.

The correct option is B) FDE and GDH, as their corresponding angles have the same intercepted arc and, therefore, are congruent.

To determine which angles are congruent in circle D, we need to analyze the given information about the measures of minor arcs. Since minor arcs are measured in degrees, we can use the following properties:

1. When two arcs are congruent, their corresponding central angles are also congruent.

2. The measure of a central angle is equal to the measure of its intercepted arc.

Given these properties, let's examine the answer choices:

A) EDH and FDG: We cannot determine their congruency based solely on the measures of the minor arcs.

B) FDE and GDH: These angles have the same intercepted arc, so they are congruent.

C) GDH and EDH: The intercepted arcs for these angles are different, so they are not congruent.

D) GDF and HDG: These angles have the same intercepted arc, so they are congruent.

Therefore, the correct option is B) FDE and GDH, as their corresponding angles have the same intercepted arc and, therefore, are congruent.

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Answer:

1.

(a) The Domain is the set of inputs of the function.

Considering that the function takes a period of 3 weeks (21 days), the domain is [0, 21], once we can't evaluate what happens after the 21st day.

\(\text{Domain is } [0, 21]\)

Otherwise, it could be \([0, \infty)\)

Note: We include 0 and 21.

Once the greatest balance was $400, it will not exceed $400, either it doesn't show negative values.

\(\text{Range is } [0, 400]\)    

Note: We include 0 and 400.

(b)

Once the greatest balance was $400, when x=0, it seems that the y-value is half of $400, therefore, approximately $200. It also represents the initial value, the amount of money when she opened the account.

(c)

\(f(x)=B(d)\)

\(B(12)=0\)

(d)

It is in segment 4.

The balance equal to zero means that the y-value of the graph is zero, therefore in the x-axis.

Answer:

1st: 2:3(*yellow and pink)

2nd: 3:5(*pink and blue)

Let's multiply: 2/3 ×3/5= 2/5

Step-by-step explanation:

2/5 is the answer. (*note: it's already reduced in simplest form)

Hope it can help you lovelots

Answer:

Percent- 30

decimal-0.3

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

Answer:

5+k = 11

Step-by-step explanation:

"Sum of a number" means addition.

"A number k and five" means you add the variable k and 5

"Is 11" tells you that the answer will be 11

You need to add K and 5 and get 11. Use this to set up an equation. Solve for K if need be. This results in k=6 but i believe that is not part of the prompt. Happy mathing ;)

The author is comparing this stride rate to that of Olympic Runner Usain Bolt, who has a reported stride rate of 3.5 strides per second.

The number of steps a runner takes in a specific length of time is referred to as stride rate and is commonly expressed in steps per second. You can figure it out by dividing the total number of steps you took during a certain amount of time by how long that time period lasted. Stride rate, which is frequently used as a gauge of running effectiveness, is impacted by a variety of variables, including running speed, terrain, and personal running form.

Hence, in the given section, the author is comparing this stride rate to that of Olympic Runner Usain Bolt, who has a reported stride rate of 3.5 strides per second.

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Answer:

C i think

Step-by-step explanation:

Once an action is caused, a reaction immediatley happens

Lisa manages to cycle 56.52 m before falling off if the diameter of the wheel of a unicycle is 0.6m.

The circumference of a circle refers to the straight line distance around it. In other words, if you open a circle and draw a straight line, the length of that line will be the circumference. The circumference is the total distance around the circle. Then find the perimeter using the formula C = 2πr.

Given,

Diameter of the wheel of a unicycle = 0.6 m

Radius of the wheel of a unicycle = 0.3 m

Number of revolutions before falling off = 32

Circumference (C) = 2 x pi x radius

= 2 × π × r

= 2 × 3.14 × 0.3

= 1.884 m

Total distance travelled by Lisa = 30 × 1.884

= 56.52 m

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Answer:

An irrational number is a real number that can't be written as a fraction.

Ex. \(\sqrt{5}\)

A rational number is a real number such as a whole number, fraaction, decimal, or integer.

(a) Power series representation for f(x) = 1 / (8 + x)², we can differentiate the geometric series representation of 1 / (8 + x). The geometric series representation of 1 / (8 + x) is:

1 / (8 + x) = 1/8 * (1 / (1 + x/8)) = 1/8 * (1 - x/8 + (x/8)² - (x/8)^3 + ...)

Differentiating this series term by term, we get:

f'(x) = -1/64 * (1 - x/8 + (x/8)² - (x/8)² + ...)' = -1/64 * (-1/8 + 2(x/8²) - 3(x/8³) + ...)

f'(x) = 1 / (8 + x)² = 1/64 * (1/8 - 2(x/8²) + 3(x/8³) - ...)

Therefore, the power series representation for f(x) = 1 / (8 + x)² is:

f(x) = Σ [n=0 to ∞]\((-1)^n\) * (n+1) * \((x/8)^{(n+1)\).

The radius of convergence, R, can be determined using the ratio test. By applying the ratio test to the power series, we find that the radius of convergence is 8.

(b) Using the result from part (a), we can find a power series representation for f(x) = 1 / (8 + x)³. To do this, we differentiate the power series representation for f(x) = 1 / (8 + x)².

f'(x) = Σ [n=0 to ∞]\((-1)^n\) * (n+1) * (n+2) * \((x/8)^{(n)\)

Next, we integrate the resulting series term by term to obtain the power series for f(x) = 1 / (8 + x)³:

f(x) = Σ [n=0 to ∞]\((-1)^n\) * (n+1) * (n+2) * \((x/8)^{(n+1)\) / (n+1)

f(x) = Σ [n=0 to ∞] (-1)^n * (n+2) *\((x/8)^{(n+1\).

The radius of convergence, R, remains 8, as it is inherited from the radius of convergence of the original power series.

(c) Using the result from part (b), we can find a power series representation for f(x) = x² / (8 + x)³. We multiply each term of the power series for f(x) = 1 / (8 + x)³ by x²:

f(x) = x² * Σ [n=0 to ∞] \((-1)^n\) * (n+2) * \((x/8)^{(n+1)\).

f(x) = Σ [n=0 to ∞] \((-1)^n\) * (n+2) *\((x/8)^{(n+3)\).

The radius of convergence, R, remains 8, as it is inherited from the radius of convergence of the original power series.

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Answer: 25 students per teacher and 12 students per tutor. They need 2.4 tutors for the school

Answer:

y = -(3/4)x + 19

Step-by-step explanation:

If you look at the line, you have the y intercept already. so there is less work to do.

The equation for a linear line is y=mx+b (or c depending on which country you are from) where m is the gradient and b is the y intercept

b = 19 from the diagram

To find the gradient, it is y2-y1/x2-x1, so pick any 2 points, let say  (16,7) and (0,19)

m = 19-7/0-16

= 12/-16

=3/-4

Sub the required numbers back into the equation

y = -(3/4)x + 19

Answer:

its D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

The fractions are not equivalent. If you cross multiply 65 x 2 = 130 and 4 x 13 = 52. 130 > 52. Set them as a proportion. \(\frac{65}{4} = \frac{13}{2}\)

They are not equal.

For 65/4 you cannot divide it by 2 and then get 13/2. You would get 32.5/2.

32.5/2 is not equal to 13/2

hope this helps :)

Answer:

A: Nonlinear

B: Constant=0, Decreasing=M, Increasing=K

C: 2-3-3

Step-by-step explanation:

1. Linear graph - one with a line that has the same slope all the way through

The line doesn't have the same slope the whole way through because at one part it flattens and also decreases

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2. Remember: Increase (up), decrease (down), constant (constant)

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3. In my words, I don't know if they're asking the pattern or technical, but you can add on to the 2 mins walk, 3 mins stop, then 2 mins walk again.

Hope it helps