54.06 + 33 + 29.4 = ________

The value of x is 11 and ∠LMN = 190°

What is Linear Equation in One Variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable of the form   ax + b = 0 are solved using simple algebraic techniques.

Solution:

Since, MO bisects the angle

we can say that, ∠LMO = ∠OMN

6x + 19 = 9x - 14

3x = 33

x = 11

so, ∠LMO = 66 + 19 = 85°

Therefor the ∠LMN = 190°

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The given equation 3x^2 - y^2 + z^2 = 0 represents a surface known as an elliptic paraboloid. To sketch this surface using traces, we can fix one variable (either x, y, or z) and vary the other two to observe the resulting curve.

Let's fix x at a constant value of 0. Substituting x = 0 into the equation, we get -y^2 + z^2 = 0. This equation represents a pair of intersecting lines, forming a trace. By varying x and fixing y or z, we can obtain additional traces, which are also pairs of intersecting lines.

Thus, by considering multiple traces, we can sketch the elliptic paraboloid surface, which resembles a bowl or a saddle. The traces consist of intersecting lines that form a grid-like pattern on the surface.

Now, moving on to the second question, we are given two skew lines with parametric equations. To find the distance between these lines, we can use the closest distance formula.

First, we need to find a point on each line. By setting t = 0 in the first line's equations, we find a point (2, 3, 0). Similarly, setting s = 0 in the second line's equations gives us a point (1, 6, -2).

Next, we find the direction vectors for both lines. The direction vector for the first line is <1, 6, 2>, and for the second line is <2, 14, 5>.

Using the closest distance formula, we can calculate the distance between the two lines as follows:

distance = |(2-1, 3-6, 0+2) · (1, 6, 2) x (2, 14, 5)| / |(1, 6, 2) x (2, 14, 5)|

Simplifying this expression will give us the distance between the skew lines.

Please note that the exact calculations are omitted here, but following the steps outlined above will provide the desired distance.

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Answer:

The answer is A, x=15 and y=17

Step-by-step explanation:

Step-by-step explanation:

RQT=4x-20°+3x+14°=

7x-6°=155°

7x=161°

x=23°

4x-20°=72°=RQS

The fish, the fishing pole and the water surface are all in equivalent ratio, and the fish is 21 feet from the hook

To do this, we make use of the following equivalent ratio

3 : 12.6 = 5 : x

Where x represents the distance between the fish and the hook

Express the ratio as a fraction

12.6/3 = x/5

Multiply both sides by 5

x = 5 * 12.6/3

Evaluate

x = 21

Hence, the fish is 21 feet from the hook

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\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{68\% of 32}}{\left( \cfrac{68}{100} \right)32}\implies 21.76\)

Answer: 21.76 or 0.22

Step-by-step explanation: You put in 68% and 32 then you'll get 21.76

32=100

and .68%

32=100%(1)

68%(2)

.68/100

Then 0.22 or 21.76

Answer:

please see detailed answers below

Step-by-step explanation:

to divide one fraction by another, just multiply the 2nd one upside down.

1) 2/7 ÷ 1/3  = 2/7 X 3/1 = 6/7

12) 1/2 ÷ 1/8 = 1/2 X 8/1 = 8/2 = 4

13) 3/8 ÷ 1/4 = 3/8 X 4/1 = 12/8 = 3/2

14) 2/5 ÷ 3/10 = 2/5 X 10/3 = 20/15 = 4/3

The relation n² ≡ 1 (mod 8) for any odd positive integer n.

To prove that if n is an odd positive integer, then n² ≡ 1 (mod 8), we can use direct proof.

Let's consider an odd positive integer n. We can express n as n = 2k + 1, where k is a non-negative integer.

Now let's square both sides of the equation:

n² = (2k + 1)²

n² = 4k² + 4k + 1

n² = 4k(k + 1) + 1

Now we need to consider two cases:

Case 1: k is even.

If k is even, we can write k = 2m, where m is a non-negative integer. Substituting this into the equation, we get:

n² = 4(2m)(2m + 1) + 1

n² = 8m(2m + 1) + 1

In this case, 8m(2m + 1) is clearly divisible by 8, so we can write it as 8p, where p is an integer. Therefore, we have:

n² = 8p + 1

Case 2: k is odd.

If k is odd, we can write k = 2m + 1, where m is a non-negative integer. Substituting this into the equation, we get:

\(n² = 4(2m + 1)(2m + 2) + 1 \\ n² = 4(2m + 1)(m + 1) + 1 \\ n² = 8(m + 1)(2m + 1) - 8(m + 1) + 1 \\ n² = 8(m + 1)(2m + 1) - 8m - 7

\)

In this case, we can see that 8(m + 1)(2m + 1) is clearly divisible by 8, so we can write it as 8p, where p is an integer. Therefore, we have:

n² = 8p - 8m - 7

n² = 8(p - m) - 7

Now, we need to consider two subcases:

Subcase 2.1: p - m is even.

If p - m is even, we can write p - m = 2q, where q is an integer. Substituting this into the equation, we get:

n² = 8(2q) - 7

n² = 16q - 7

Subcase 2.2: p - m is odd.

If p - m is odd, we can write p - m = 2q + 1, where q is an integer. Substituting this into the equation, we get:

n² = 8(2q + 1) - 7

n² = 16q + 1

In both subcases, we can see that n² ≡ 1 (mod 8).

Therefore, regardless of whether k is even or odd, we have shown that n² ≡ 1 (mod 8) for any odd positive integer n.

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Answer:

m<8=m<2=55° being exterior angle

To determine whether there is enough evidence to reject the null hypothesis, we need to compare the computed test statistic to the critical value.

In this case, the computed test statistic is 2.50 and the critical value is 2.33. If the computed test statistic falls in the rejection region beyond the critical value, we can reject the null hypothesis. Conversely, if the computed test statistic falls within the non-rejection region, we fail to reject the null hypothesis.In this scenario, since the computed test statistic (2.50) is greater than the critical value (2.33), it falls in the rejection region. This means that the observed data is unlikely to occur if the null hypothesis were true.

Therefore, based on the given information, there is enough evidence for the emergency room nurse to reject the null hypothesis. This suggests that there is sufficient evidence to support the claim that the average number of cases of upper respiratory infections per day at the hospital is over 21 cases.

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There is enough evidence to reject the null hypothesis in this case because the computed test statistic (2.50) is higher than the critical value (2.33). This suggests the average number of daily respiratory infections exceeds 21, providing substantial evidence against the null hypothesis.

Yes, there is enough evidence for the emergency room nurse to reject the null hypothesis. The null hypothesis is typically a claim of no difference or no effect. In this case, the null hypothesis would be an average of 21 upper respiratory infections per day. The test statistic computed (2.50) exceeds the critical value (2.33). This suggests that the average daily cases indeed exceed 21, hence providing enough evidence to reject the null hypothesis.

It's crucial to understand that when the test statistic is larger than the critical value, we reject the null hypothesis because the observed sample is inconsistent with the null hypothesis. The statistical test indicated a significant difference, upheld by the test statistic value of 2.50. The significance level (alpha) of 0.05 is a commonly used threshold for significance in scientific studies. In this context, the finding suggests that the increase in respiratory infection cases is statistically significant, and the null hypothesis can be rejected.

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The most commonly shaped base in pin curls is the arc base. In hairstyling, pin curls are a technique used to create curls in the hair. The base refers to the section of hair that is secured to the scalp before wrapping the hair around the curling tool.

The base can be positioned in different ways to create different curl patterns.

The arc base is the most commonly used base in pin curls. It involves positioning the section of hair in a semi-circular shape, with the ends pointing in the direction of the desired curl. This base shape creates a classic, versatile curl that can be used in a variety of hairstyles. Other base shapes include the rectangular base, triangle base, and square base, which create different curl patterns depending on their shape and position.

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An equation of the tangent line to the curve \(x e^y+y e^x=4\) at the point (0, 4) is \(y=-(4+e^4) x+4\).

A tangent is described as a line that intersects a circle or an ellipse only at one point. If a line touches a curve at P, the point "P" is known as the point of tangency.

Now according to the question;

To obtain the tangent at a given point, we must first obtain the slope at that point by obtaining the differentiation value at that point  \(\left.y^{\prime}\right|_{x=0, y=4}\) as-

Consider the given equation;

\(x e^y+y e^x=4\)

Differentiate both side with respect to x;

\(\begin{aligned}&\frac{d}{d x}\left(x e^y+y e^x\right)=\frac{d}{d x} 4 \\&\frac{d}{d x} x e^y+\frac{d}{d x} y e^x=0\end{aligned}\)

Now apply product rule;

\(\begin{aligned}&e^y \frac{d}{d x} x+x \frac{d}{d x} e^y+e^x \frac{d}{d x} y+y \frac{d}{d x} e^x=0 \\&e^y \frac{d}{d x} x+x \frac{d}{d y} e^y \cdot y^{\prime}+e^x y^{\prime}+y \frac{d}{d x} e^x=0\end{aligned}\)

Applying exponential and power rule;

\(\begin{aligned}&e^y \cdot 1+x e^y \cdot y^{\prime}+e^x y^{\prime}+y e^x=0 \\&\left(x e^y+e^x\right) y^{\prime}=-y e^x-e^y\end{aligned}\)

Solve the value of y'

\(y^{\prime}=\frac{-y e^x-e^y}{x e^y+e^x}\)

Now, find the value of slope m.

\(m=\left.y^{\prime}\right|_{x=0, y=4}\)

\(\frac{-4 \cdot e^0-e^4}{0 e^4+e^0}=-4-e^4\)

Now, using the point-slope formula, obtain the line equation as follows.

\(\begin{aligned}&\left(y-y_1\right)=m\left(x-x_1\right) \\&(y-4)=-(4+e^4) \cdot(x-0) \\&y=-(4+e^4) x+4\end{aligned}\)

Therefore, an equation of the tangent line to the curve is   \(y=-(4+e^4) x+4\).

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Answer:

55%

Step-by-step explanation:

Because when your doing percentages out of 20 it is 5 for each

1/20=5%

2/20=10%

3/20=15%

4/20=20%

5/20=25%

6/20=30%

7/20=35%

8/20=40%

9/20=45%

10/20=50%

And 11 out of 20=55%

Given the speeds of each runner : Liz runs 10 feet per second, Will runs 264 feet in 33 seconds, Jake runs 1 mile in 384 seconds, Zach runs 875 feet in 1 minute. We need to convert the speeds of each runner into the same unit  that is feet per second in order to compare them.

Liz runs 10 feet per second.

Will runs 264 feet in 33 seconds, which is (264/33) ≈ 8 feet per second.

Jake runs 1 mile in 384 seconds, which is (1 mile = 5280 feet) (5280/384) ≈ 13.75 feet per second.

Zach runs 875 feet in 1 minute, which is (875/60) ≈ 14.58 feet per second.

Comparing the speeds, we can see that Zach runs the fastest at approximately 14.58 feet per second.

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Answer:

Y=-0.75+6

Step-by-step explanation:

Y=mx+B

m= -0.75

when Y=0 and x=8, b=6

The case fatality rate is 400 * 100 / 1500 = 26.67 (option d).

For the first scenario, the data determine that there is a difference in average expenditure between the two countries (option c). The P-value of 0.063 suggests that there is a moderate level of statistical significance, indicating that the difference in average expenditure is likely not due to random chance.

In the second scenario, the fact that the 95% confidence interval for the average number of times participants saw their provider per year (3.3) ranges from 0.1 to 6.1 is of statistical use because it provides a range estimate within which the true population means is likely to fall. This interval helps account for the uncertainty associated with the sample estimate and provides a measure of the precision of the estimate (option a).

For the third scenario, the average operating margin is appropriate to use because it is a measure of central tendency that represents the typical financial performance of rural hospitals. The standard deviation provides information about the variability of the operating margins (option d).

In the fourth scenario, the consideration factor that will ultimately contribute to the spread of Ebola is the population density of the affected area (option b). While factors like the influence of non-indigenous people and climatic conditions may play a role, population density is a key determinant in the transmission and spread of infectious diseases.

For the fifth scenario, the case fatality rate is calculated by dividing the number of deaths from the disease (400) by the total reported cases (1500) and multiplying by 100. Therefore, the correct calculation is 400 * 100 / 1500 = 26.67 (option d). This indicates that the case fatality rate is approximately 26.67%.

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The solution of the given initial value problem is y(t) = sin(t) + H(t-2π)cos(t-2π), where H(t) is the Heaviside step function.

To solve the initial value problem, we start by finding the complementary solution, which satisfies the homogeneous differential equation y'' + y = 0. The complementary solution is given by y_c(t) = A sin(t) + B cos(t), where A and B are constants to be determined.

Next, we find the particular solution for the given non-homogeneous term δ(t-2π)cos(t). Since the forcing term is a Dirac delta function at t = 2π, we can write the particular solution as y_p(t) = K(t-2π)cos(t-2π), where K is a constant to be determined.

Applying the initial conditions y(0) = 0 and y'(0) = 1, we can solve for the constants A, B, and K. Plugging in these initial conditions into the general solution, we find A = 0, B = 1, and K = 1.

Therefore, the solution of the initial value problem is y(t) = sin(t) + H(t-2π)cos(t-2π), where H(t) is the Heaviside step function.

The initial value problem with the given conditions is solved by finding the complementary solution and the particular solution. The solution is y(t) = sin(t) + H(t-2π)cos(t-2π), where H(t) is the Heaviside step function. This solution satisfies the given initial conditions y(0) = 0 and y'(0) = 1.

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We have the following:

with a proportionality rule we can solve the question, since if 40% are 60 pieces, how many will be 100% :

The answer is 150 pieces of bubble in total

De Morgan's laws are two rules in formal logic that involve negating statements. The first law states that the negation of a conjunction (an "and" statement) is equivalent to the disjunction (an "or" statement) of the negations of the individual components.

The second law states that the negation of a disjunction is equivalent to the conjunction of the negations of the individual components.

Therefore, the negation of the original statement is "She does not make the bed, and I make the bed." This means that both she does not make the bed and I make the bed must be true in order for the negation to be true.

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Answer:

The answer is A. 10

Step-by-step explanation:

The two angles are alternate interior angles so they are congruent. Since they are congruent, you can write it in an equation.

5x - 25 = 3x - 5

subtract 3x from each side

2x - 25 = -5

add 25 to each side

2x = 20

divide 2 from each side

x = 10

Also, if you want to check your answer, you can plug 10 back into the equation to see if they're equal.

The relation between the given angles is given by the alternate interior

angles theorem.

If lines p and q are parallel then the value of x is A. 10°

Reason:

The given parameters are;

Condition; Line p, and line q, are parallel.

The angles (3·x - 5)° and (5·x - 25)° are alternate interior angles.

According to alternate interior angles theorem, we have the alternate

angles are congruent, where line p, and line q are parallel.

Therefore;

(3·x - 5)° ≅ (5·x - 25)° By alternate interior angles

(3·x - 5)° = (5·x - 25)° By definition of congruency

Solving, we get;

(3·x - 5)° + 25° = (5·x - 25)° + 25°

3·x + 20° - 3·x = 5·x - 3·x = 2·x

20° = 2·x

\(x = \dfrac{20^{\circ}}{2} = 10^{\circ}\)

The correct option is A. 10°

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Answer: y = 7x + 5 (maybe, please make sure, I'm very doubtful of myself sometimes)

Step-by-step explanation:

1. With the given numbers, m is slope, so 7 is the slope and b is y-intercept, and 5 is the y-int in this case.

2. This is hinting that the equation is in slope intercept form, which is      y = mx + b.

3. Since y = mx + b is the formula, then it means y = 7x + 5 is the likely answer

Answer:

8,12,and 5

Step-by-step explanation:

8+2=10

12-2=10

2x5=10

Answer:

Round to the nearest whole number and then add the numbers. The estimate should be close in value to the actual sum.

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

for instance when you multiply that 2x it will multiply the one inside (x-7)

Answer: 80 degrees

Step-by-step explanation:

They are corresponding angles so they have the same degree

Answer: Below

Step-by-step explanation:

First, we start with x. We see the x is opposite of 30, so x is 30.

x + y + y = 180, since they lay on a straight angle.

180 - 30 = 150

since we still have 2 y's left:

2y = 150

y = 75

Answer:

Resolver para x

⎩

⎪

⎨

⎪

⎧

​

x<

1−z

y

​

,

x∈R,

x>

1−z

y

​

,

​

z<1

y>0 and z=1

z>1

Step-by-step explanation:

The solution of the inequality x − y < z is x < z + y.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality,

x − y < z.

To solve for x:

Add y to both sides,

x < z + y

Therefore, the solution is x < z + y.

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Answer:

Lol i got u homie!

-0.02

(Sorry if that wasn't a fraction but hopefully this helps)

Step-by-step explanation:

The probability of choosing  a shade of blue and carpet is 1/6 greater than that of choosing a shade of yellow and wood flooring.

The total number of possible paint colors Daria can choose is 5 shades of blue + 2 shades of yellow + 2 shades of purple = 9 shades

The total number of flooring options Daria can choose from is carpet or wood = 2 options

The probability of choosing a shade of blue is 5/9 and the probability of choosing carpet is 1/2. So, the probability of choosing a shade of blue and carpet is (5/9) * (1/2) = 5/18.

The probability of choosing a shade of yellow is 2/9 and the probability of choosing wood flooring is 1/2. So, the probability of choosing a shade of yellow and wood flooring is (2/9) * (1/2) = 2/18

The probability of choosing a shade of blue and carpet is 5/18, and the probability of choosing a shade of yellow and wood flooring is 2/18. So, the probability of choosing a shade of blue and carpet is (5/18) - (2/18) = 3/18 or 1/6 greater than the probability of choosing a shade of yellow and wood flooring.

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