Schnider national trucking started a help wanted advertisement that an experienced driver could earn $930 per week how much is the annual salary

The linear approximation suggests that the value of f(x) at x = 1.83 is approximately 23 and the equation of the tangent line is y = 0x + 23, which simplifies to y = 23.

The equation of the tangent line to f(x) at x = 2 can be written in the form y = mx + b, where m represents the slope of the tangent line and b represents the y-intercept.

To find the slope, we calculate the derivative of f(x) with respect to x:

f'(x) = 0

Since the derivative of a constant function is zero, the slope of the tangent line is 0.

To find the y-intercept, we substitute x = 2 into the equation:

y = mx + b

23 = 0(2) + b

b = 23

Now, we can use this equation to approximate the value of f(x) at x = 1.83:

f(1.83) ≈ 23

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Complete question:

(1 point) Use linear approximation, i.e. the tangent line, to approximate 1.83 as follows: Let f(x) = 23 The equation of the tangent line to f(x) at a 2 can be written in the form y = mx + b where m is slope and b is intercept of the line.

Answer:

The area is  

\(72yd^{2}\)

(square yards)

Step-by-step explanation:

Explanation:

In the given triangle a base  24 y d  and the corresponding height  6 y d

is given, so to calculate the area we can use:

A = 1 2× b × h

If we substitute thegiven numbers we get:

A = 1 2 × 24 × 6 = 12 × 6= 72

The units of base and height are the same (yards), so the calculated area is in  y d 2  (square yards)

Answer: The area of the given triangle is  72 square yards.

Answer:

7x

Step-by-step explanation:

Suppose that, \(\displaystyle{e^{\ln ax} = ax}\), let's prove that the following equation is true for all possible x-values (identity).

First, apply the natural logarithm (ln) both sides:

\(\displaystyle{\ln \left( e^{\ln ax} \right)=\ln \left(ax\right)}\)

From the property of the logarithm - \(\displaystyle{\ln a^b = b\ln a}\). Therefore,

\(\displaystyle{\ln ax \cdot \ln e = \ln ax}\)

ln(e) = 1, so:

\(\displaystyle{\ln ax \cdot 1 = \ln ax}\\\\\displaystyle{\ln ax = \ln ax}\)

Hence, this is true. Thus, \(\displaystyle{e^{\ln ax} = ax}\), and \(\displaystyle{e^{\ln 7x} = 7x}\).

Answer:

y= -1/2x -5

Step-by-step explanation:

in slope intercept form

Answer:

y=-1/2x-5

Step-by-step explanation:

Hope it helps!

Answer: 2.5, 5.4

Step-by-step explanation:

\(-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4\)

Answer:

6 : 23

Step-by-step explanation:

\(a : b = 3 : 4 ....(given)\\ \\ let \: a = 3x \\ b = 4x \\ \\ (6a - 3b) : (5a + 2b) \\ \\ = \frac{(6a - 3b)}{(5a + 2b)} \\ \\ = \frac{6(3x) - 3(4x)}{5(3x) + 2(4x)} \\ \\ = \frac{18x- 12x}{15x+ 8x} \\ \\ = \frac{6x}{23x} \\ \\ = \frac{6}{23} \\ \\ (6a - 3b) : (5a + 2b) = 6 : 23\)

Answer:

if you mean 54% of 150, then it is 81

Answer:

36% of 150

Step-by-step explanation:

Divide 54/150 to get .36 which is just 36%

Answer:

Actually you did everything right

Step-by-step explanation:

yes

This question requires proving congruency of triangles in a given co-ordinate system we by use of ASA(angle side angle) theorem.

An isosceles right angle triangle has two equal sides and the corresponding angles will also be equal it will be of 45° - 45° - 90°.

The hypotenuse will be \(\sqrt{2}\) times of the equal sides.

A. We have chosen x-axis as a line of refection.Reflection along x-axis idicates rotation  of 180° along x axis.

B. We are sure that each point is reflected accross this line because base has same magnitude but the signs have changed and rotation along x-axis doesn't change the value of y co-ordinate.

C. Rotaion along X-axis by 180°.

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Answer:

Therefore, any value of x that is greater than or equal to -17/5 satisfies the original statement.

Step-by-step explanation:

Let's start by using algebra to translate the given statement into an equation.

Let's call the unknown number "x".

The product of 5 and the unknown number is 5x.

Subtracting 10 from the product of 5 and the unknown number gives us:

5x - 10

The statement tells us that this expression is at least -27, which we can write as:

5x - 10 >= -27

To solve for x, we need to isolate the variable on one side of the inequality.

Adding 10 to both sides of the inequality gives us:

5x >= -27 + 10

Simplifying the right side:

5x >= -17

Finally, we divide both sides by 5 to isolate x:

x >= -17/5

Therefore, any value of x that is greater than or equal to -17/5 satisfies the original statement.

Answer:

Step-by-step explanation:

Use the interest formula:

Robert:

Susan:

Difference in amounts of interest:

Susan paid $2220 more

For the first limit, we can apply L'Hospital's Rule because we have an indeterminate form of 0/0. Taking the derivative of both the numerator and denominator separately, we get:

lim x→3 (1 - √3/2) / (-3x^2)
= (1 - √3/2) / (-27)
For the second limit, we can also apply L'Hospital's Rule because we have an indeterminate form of ∞/∞. Taking the derivative of both the numerator and denominator separately, we get:
lim x→∞ (-1/x^2) / 0
= 0
Note that we can simplify the original expression before applying L'Hospital's Rule:

lim x→∞ ((x^(1/x)) - 1) / (1/x)
= lim x→∞ (e^ln(x^(1/x)) - 1) / (1/x)
= lim x→∞ ((e^ln(x^(1/x)) - e^0) / ln(x^(1/x))) * (ln(x) / x)
= lim x→∞ (e^(ln(x)/x) - 1) / (ln(x)/x)
= lim x→∞ (e^(ln(x)/x) * (ln(x)/x^2)) / (1/x)
= lim x→∞ (ln(x)/x^2) * e^(ln(x)/x)
= 0 * 1
= 0

So the final answer is 0.
Hello! I'd be happy to help you find the limits using L'Hospital's Rule. Let's start with the first limit:
lim(x→3) [(x - √3x) / (27 - x^3)]
Before applying L'Hospital's Rule, we need to check if the limit is of the indeterminate form 0/0 or ∞/∞. Plugging in x = 3, we get
(3 - √(3*3)) / (27 - 3^3) = (3 - 3√3) / (27 - 27) = 0/0
Since it is in the indeterminate form 0/0, we can apply L'Hospital's Rule. First, we'll find the derivatives of the numerator and denominator with respect to x:
d/dx(x - √3x) = 1 - (1/2)√(3/x)
d/dx(27 - x^3) = -3x^2
Now, we'll apply L'Hospital's Rule by taking the limit of the ratio of the derivatives:

lim(x→3) [(1 - (1/2)√(3/x)) / (-3x^2)]
Plugging in x = 3, we get:
(1 - (1/2)√(3/3)) / (-3(3^2)) = (1 - (1/2)) / (-27) = (1/2) / (-27) = -1/54
So, the limit for the first expression is -1/54.
Unfortunately, the second part of your question is unclear and incomplete. If you could provide the complete expression and clarify the limit you're looking for, I'd be more than happy to help you with that as well!

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The equivalent ratios to 8 to 3 following are :

16 to 6

24 to 9

To write equivalent ratios to 8 to 3, you can use multiplication.

For example, you can multiply both terms in the ratio by 2 to get 16 to 6, or by 3 to get 24 to 9.

In general, to write equivalent ratios, you can multiply or divide both terms in the ratio by the same number. For example, if the ratio is a:b, you can write equivalent ratios by multiplying or dividing both a and b by the same number.

For example, the following ratios are all equivalent to 8 to 3:

16 to 6 (obtained by multiplying both terms by 2)

24 to 9 (obtained by multiplying both terms by 3)

4 to 1.5 (obtained by dividing both terms by 2)

8 to 3 (the original ratio)

2 to 0.75 (obtained by dividing both terms by 4)

These ratios all represent the same relationship between the two quantities, but the numbers are different.

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A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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Answer:

Step-by-step explanation:

1

Answer:

Below

Step-by-step explanation:

Remember in a RIGHT triangle ,  cos = adj leg /  hypotenuse

for this one then

cos (37) = 11/x       re-arrange to

x = 11/cos 37

x = 11/ .7986 = 13.8 units

Answer:

  13.77

Step-by-step explanation:

You want the hypotenuse of a right triangle with acute angle 37° and adjacent side 11.

The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

  cos(37°) = 11/x

Solving for x, we find ...

  x = 11/cos(37°) ≈ 13.77

The measure of side x is 13.77 units.

Answer:

B - E = B + E = -240

Step-by-step explanation:

Answer:

12 for 6.97 is better

Step-by-step explanation:

for 12 pack

$6.97/12 markers = .58 per marker

for 4 pack

$2.77/4 markers = .69 per marker

thus 12 pack is better, a lower cost per marker

Answer:

12 for $6.97

Step-by-step explanation:

If u get 12 pack for $6.97 its .58 for each marker

If u get 4 pack for $2.77 its .69

And I would prefer to get a 12 pack cuz its cheaper and more markers.

I hope this helped:)

To prove that the argument is valid using propositional logic, we can apply logical rules and deductions. Let's break down the argument step by step:

(A + B) ^ (C V -B) ^ (-D --> C) ^ A ^ D

We will represent the proposition as follows:

P: (A + B)

Q: (C V -B)

R: (-D --> C)

S: A

T: D

From the given premises, we can deduce the following:

P ^ Q (Conjunction Elimination)

P (Simplification)

Now, let's apply the rules of disjunction elimination:

P (S)

A + B (Simplification)

Next, let's apply the rule of disjunction introduction:

C V -B (S ^ Q)

Using disjunction elimination again, we have:

C (S ^ Q ^ R)

Finally, let's apply the rule of modus ponens:

-D (S ^ Q ^ R)

C (S ^ Q ^ R)

Since we have derived the conclusion C using valid logical rules and deductions, we can conclude that the argument is valid.

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Answer:

The statement that is true about the relationship between ΔXYZ and ΔX'Y'Z' is option "C"

C. ΔX'Y'Z' is a translation of ΔXYZ because all points in ΔX'Y'Z' are the same distance and direction from the corresponding points in ΔXYZ

Step-by-step explanation:

The triangles Bridget drew are;

ΔXYZ and ΔX'Y'Z'

The coordinates of ΔXYZ = X(-5, 7), Y(-9, 2), Z(-3, 2)

The coordinates of ΔX'Y'Z' = X'(1, 2), Y'(-3, -3), Z'(3, -3)

From the coordinates we have;

The x-coordinates of ΔX'Y'Z' = The x-coordinates of ΔXYZ + 6

The y-coordinates of ΔX'Y'Z' = The y-coordinates of ΔXYZ - 5

Therefore, the translation that gives ΔX'Y'Z' from ΔXYZ = T₆, ₋₅

Therefore;

1) ΔX'Y'Z' is obtained from ΔXYZ by a translation as the points in ΔX'Y'Z' are obtained from ΔXYZ by adding the same value to the x-coordinates of the points on ΔXYZ and subtracting the same value to the y-coordinates of the points on ΔXYZ, such that the points in triangle ΔX'Y'Z' are equidistant from and on the same side relative to the corresponding points on ΔXYZ

2) Given that triangle ΔXYZ and ΔX'Y'Z' are not rotated or reflected, we have that the corresponding sides of ΔXYZ and ΔX'Y'Z' are parallel

The correct options are therefore option "C" and and the option "B" is only partially correct because the sides can be parallel but do not have the same size.

The terms of the series are:

\(16!, 15!(17-15), 14!(17-14), ..., 1!(17-1).\)

The series is given by \(p!(17-p)\) for p ranging from 1 to 16. To expand the series, we substitute the values of p from 1 to 16 into the expression p!(17-p). Each term of the series represents the factorial of p multiplied by the difference between 17 and p. By substituting the values, we obtain the following terms: \(16!, 15!(17-15), 14!(17-14)\), and so on, until \(1!(17-1)\). The series consists of 16 terms.

The given series is an example of a factorial series with a specific pattern. The factorial term, p!, indicates the product of all positive integers from 1 to p, while the expression (17-p) represents the decreasing difference.

By multiplying the factorial term with the difference, we generate a sequence of numbers that progressively decreases. The first term, 16!, is the highest number in the series, and each subsequent term is smaller until we reach 1!(17-1) as the last term. This series can be useful in various mathematical and combinatorial contexts where factorial calculations are involved.

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Answer:

Step-by-step explanation:

To find the inverse of a matrix, we need to put it in the reduced row echelon form (RREF) using elementary row operations. We can augment the given matrix with an identity matrix of the same size, and then apply the row operations to both matrices simultaneously until the left-hand side becomes an identity matrix. The right-hand side will then be the inverse of the original matrix.

Here are the steps:

[ 5 3 | 1 0 ]

[13 8 | 0 1 ]

R1/5 -> R1:

[ 1 3/5 | 1/5 0 ]

[13 8 | 0 1 ]

R2-13R1 -> R2:

[ 1 3/5 | 1/5 0 ]

[ 0 1/5 | -13 1 ]

R1-(3/5)R2 -> R1:

[ 1 0 | 26/5 -3/5 ]

[ 0 1 | -13 1/5 ]

So, the inverse matrix is:

[ 26/5 -3/5 ]

[-13 1/5 ]

This problem involves a Markov process where a baseball player's chance of getting a hit is dependent on whether they got a hit or not in the previous game. The chance this player will get a hit at the end of time is about 28.6%.

a) To find the transition matrix, we can use the given probabilities to determine the probability of transitioning from one state (getting a hit or not getting a hit) to another state. Let H represent the state of getting a hit and NH represent the state of not getting a hit. Then the transition matrix will be:

| 0.45 0.55 |

| 0.2 0.8 |

b) To find the probability of the player getting a hit on Wednesday given that they got a hit on Tuesday, we can use the transition matrix and the given probability to calculate:

P(HW | HT) = P(HW and HT) / P(HT)

= 0.45 * 0.35 / (0.45 * 0.35 + 0.55 * 0.65)

≈ 0.279

c) To find the chance that the player will get a hit at the end of time, we can set up the system of equations:

P(H∞) = 0.45 * P(H∞) + 0.2 * P(NH∞)

P(NH∞) = 0.55 * P(H∞) + 0.8 * P(NH∞)

Solving this system, we get:

P(H∞) = 2/7 ≈ 0.286

P(NH∞) = 5/7 ≈ 0.714

Therefore, the chance this player will get a hit at the end of time is about 28.6%.

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The simplified expression is 2cos²(x) + sinx - 1 = 0

The expression we will be simplifying is

=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.

To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:

(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)

Simplifying this expression using the distributive property, we get:

(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)

Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:

1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1

Similarly, for the second fraction, we can use the same identity to obtain:

1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1

Substituting these values back into the original expression, we get:

1 + 1 = 2sinx/(sin⁴x - cos⁴x)

Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:

sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ

Substituting this back into the expression, we get:

2 = 2sinx/(sin²ˣ - cos²ˣ)

Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):

2 = -2sinx/cos(2x)

Multiplying both sides by -cos(2x), we get:

-2cos(2x) = 2sinx

Dividing both sides by 2, we get:

-cos(2x) = sinx

Using the double-angle formula for cosine, we get:

-2cos²(x) + 1 = sinx

Simplifying this expression, we get:

2cos²(x) + sinx - 1 = 0

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The volume of the solid S in the given question is 5.48unit³.

A three-dimensional space's occupied volume is measured.

It is frequently expressed numerically in a variety of imperial or US-standard units as well as SI-derived units.

The definition of length and volume are connected.

So, the volume of the solid S:
An equilateral triangle's sides are shown as a cross-section.

An equilateral triangle's height is determined by:

\(h = sSin60 = \frac{\sqrt{3} }{2} s\)

Consequently, one triangle's area is:

\(A=\frac{1}{2} s h=\frac{1}{2} s \cdot \frac{\sqrt{3}}{2} s=\frac{\sqrt{3}}{4} s^2\)

The line equation that depicts the diagonal is:

\(\begin{aligned}& x+y=1 \\& y=-x+1 \\& x=-y+1\end{aligned}\)

This will indicate the s value integrate from 0 to 2 if we integrate along the y-axis.

\(\begin{aligned}& V=\int_0^2 \frac{\sqrt{3}}{4} s^2 d x \\& =\frac{\sqrt{3}}{4} \int_0^2(-y+1)^2 d x \\& =\frac{\sqrt{3}}{4} \int_0^2\left(y^2-2 y+1\right) d x \\& =\frac{\sqrt{3}}{4}\left[\frac{1}{3} y^3-y^2+y\right] \\& \left.=\frac{\sqrt{3}}{4}\left[\frac{1}{3}(2)^3-(2)^2+2\right)\right] \\& =5.48\end{aligned}\)

Therefore, the volume of the solid S in the given question is 5.48unit³.

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Correct question:
Find the volume V of the described solid S. The base of S is the triangular region with vertices (0, 0), (2, 0), and (0, 2). Cross-sections perpendicular to the y-axis are equilateral triangles.

Answer:

The second one : x + 90 + 61 = 180

Step-by-step explanation:

I hope this helps!

Let me know if you need the explanation.