5.
Look at the inequality below.
-6x-45-4
Which of these values of x does not make the inequality true?
A.)-4
B.)0
C.)1/7
D.)2.5

Answer:

B. 6 7/10

Step-by-step explanation:

We solve the above y by carrying out addition.

The quarts of Lemonade she made is calculated as:

1 2/5 quarts of syrup + 5 3/10 quarts of water

= 1 + 5 + (2/5 + 3/10)

Lowest common denominator = 10

= 6 ( 4 + 3/10)

= 6 7/10 quarts of Lemonade

Mrs Olive made 6 7/10 quarts of Lemonade

The 95% confidence interval for the mean is (98.58 , 121.42) with a Lower Bound of 98.58 and Upper Bound of 121.42

Given that mean x-bar = 110 , standard deviation s = 17 , n = 11

=> df = n-1 = 10

=> For 95% confidence interval , t = 2.228

=> The 95% confidence interval of the mean is

=> x-bar +/- t*s/ ✓(n)

=> 110 +/- 2.228*17/ ✓( 11)

=> (98.58 , 121.42)

=> Lower Bound = 98.58

=> Upper Bound = 121.42

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Answer:

Ummm....X, Y, Z

Step-by-step explanation:

Based on the given data and a one-sample chi-square test, the hypothesis test results reject the null hypothesis (σ < 10) in favor of the alternative hypothesis (σ > 10) at a significance level of 0.05. This indicates sufficient to suggest that the population standard deviation is greater than 10.

We test if the population standard deviation (σ) is less than 10 (H₀: σ < 10) or greater than 10 (Ha: σ > 10) using a significance level of 0.05.

To test this hypothesis, we can perform a one-sample chi-square test of variance, also known as the chi-square goodness-of-fit test. The test statistic is calculated as:

χ² = (n-1) * s² / σ₀²

where n is the sample size, s² is the sample variance, and σ₀ is the hypothesized population standard deviation under the null hypothesis.

Let's calculate the necessary values:

Sample size (n) = 40

Sample variance (s²) = Sum of (xi - X⁻)² / (n-1) = 129.7396

Hypothesized population standard deviation (σ₀) = 10

Now, we can calculate the test statistic:

χ² = (n-1) * s² / σ₀² = (40-1) * 129.7396 / 10² = 515.792

To test the hypothesis, we need to compare the test statistic to the critical value from the chi-square distribution with (n-1) degrees of freedom (39 degrees of freedom in this case) at the chosen significance level (α = 0.05).

The critical value for a right-tailed test with α = 0.05 and 39 degrees of freedom is approximately 56.891.

Since the test statistic (515.792) is greater than the critical value (56.891), we reject the null hypothesis (H₀). This means that there is proof to suggest that the population standard deviation is greater than 10.

Therefore, based on the given data and the performed hypothesis test, we reject the null hypothesis and conclude that there is sufficient to support the alternative hypothesis that the population standard deviation is greater than 10.

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3 exceptions in a sample of 100 items, the auditors are likely to conclude that the internal controls are effective since the actual deviation rate (3%) is lower than both the tolerable (8%) and expected (4%) deviation rates.

To determine the auditors' likely conclusion, we need to compare the actual deviation rate in the sample to the tolerable deviation rate and expected deviation rate specified in the sampling plan.

The tolerable deviation rate is the maximum deviation rate that the auditors find acceptable. In this case, the tolerable deviation rate is 8%.

The expected deviation rate is the deviation rate that the auditors anticipate based on their knowledge or previous experience. In this case, the expected deviation rate is 4%.

In the sample of 100 items, the auditors found 3 exceptions. The actual deviation rate in the sample can be calculated by dividing the number of exceptions by the sample size:

Actual Deviation Rate = (Number of exceptions / Sample size) * 100

= (3 / 100) * 100

= 3%

Now, let's compare the actual deviation rate to the tolerable deviation rate and expected deviation rate:

If the actual deviation rate is below the tolerable deviation rate (3% < 8%), the auditors' likely conclusion would be that the internal controls are effective. This means that the number of exceptions found in the sample is within the acceptable range.

If the actual deviation rate is above the tolerable deviation rate (3% > 8%), the auditors' likely conclusion would be that there are issues with the internal controls. This indicates that the number of exceptions found in the sample exceeds the acceptable limit.

If the actual deviation rate is closer to the expected deviation rate (3% ≈ 4%), the auditors' likely conclusion would be that the internal controls are operating as expected. The number of exceptions found in the sample aligns with the auditors' expectations.

Based on the given information, the auditors' likely conclusion would depend on the tolerable deviation rate and the expected deviation rate specified in the sampling plan. If the tolerable deviation rate is 8% and the expected deviation rate is 4%, and the actual deviation rate in the sample is 3%, it suggests that the internal controls are effective or operating as expected.

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Answer:

y=3x+6

Step-by-step explanation:

its in y=mx+b form

m is the slope

b is the y-int

Answer:

\(\sec \theta + \csc \theta = \frac{2\cdot \sqrt{3}+6}{3}\)

Step-by-step explanation:

We proceed to simplify the given trigonometric expression into a form with a single trigonometric function:

1) \(7\cdot \sin^{2}\theta + 3\cdot \cos^{2}\theta = 4\) Given.

2) \(4\cdot \sin^{2}\theta + 3\cdot (\sin^{2}\theta + \cos^{2}\theta) = 4\) Definition of addition/Associative and distributive properties.

3) \(4\cdot \sin^{2} \theta +3 = 4\)     \(\sin^{2}\theta + \cos^{2}\theta = 1\)/Modulative property

4) \(4\cdot \sin^{2}\theta = 1\) Compatibility with addition/Existence of additive inverse/Modulative property

5) \(\sin \theta = \frac{1}{2}\)  Compatibility with multiplication/Existence of multiplicative inverse/Modulative property/Definition of division

6) \(\theta = \sin^{-1} \frac{1}{2}\) Inverse trigonometric inverse.

7) \(\theta = 30^{\circ}\) Result.

By Trigonometry, we know that secant and cosecant functions have the following identities:

\(\sec \theta = \frac{1}{\cos \theta}\), \(\csc \theta = \frac{1}{\sin \theta}\) (1, 2)

In addition, we know that \(\sin 30^{\circ} = \frac{1}{2}\) and \(\cos 30^{\circ} = \frac{\sqrt{3}}{2}\), then the sum of the two trigonometric function abovementioned is:

\(\sec \theta + \csc \theta = \frac{1}{\cos \theta} + \frac{1}{\sin \theta}\)

\(\frac{2}{\sqrt{3}} + 2 = \frac{2\cdot \sqrt{3}}{3} + 2\)

\(\sec \theta + \csc \theta = \frac{2\cdot \sqrt{3}+6}{3}\)

The slope, y-intercept, and equation of each of the lines are:

a. m = 2, b = -1.

y = 2x - 1

b. m = -1; b = 2.

y = -x + 2

c. m = -2/3; b = 1

y = -2/3x + 1

d. m = 1/2; b = -2.

y = 1/2x - 2

The slope-intercept form is y = mx + b, where b equals the y-intercept and m is the slope.

a. Slope (m) = change in y/change in x = (3 -(-1))/(2 - 0) = 4/2 = 2

y-intercept (b) = -1.

The equation is: y = 2x - 1

b. Slope (m) = change in y/change in x = (2 -(-2))/(0 - 4) = 4/-4 = -1

y-intercept (b) = 2.

The equation is: y = -x + 2

c. Slope (m) = change in y/change in x = (3 -(-1))/(-3 - 3) = 4/-6 = -2/3

Substitute m = -2/3 and (x, y) = (3, -1) into y = mx + b to find the y-intercept (b):

-1 = -2/3(3) + b

-1 = -2 + b

-1 + 2 = b

1 = b

b = 1

The equation is: y = -2/3x + 1

d. Slope (m) = change in y/change in x = (0 -(-1))/(4 - 2) = 1/2 = 1/2

y-intercept (b) = -2.

The equation is: y = 1/2x - 2

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Answer:

The probability that a patient’s condition will not worsen after the procedure is 100% - 4% = 96%. Since the procedure is independent for each patient, the probability that none of the 5 patients’ conditions will worsen is 0.96^5 ≈ 81.5%. So, the best answer from the choices provided is 81.5%.

Step-by-step explanation:

The net electric charge enclosed in the gaussian surface is given asQ = ϕE.4πε0L0²/2A + A3 = 0 because the net charge enclosed by the Gaussian surface is zero.

The net electric charge enclosed in the gaussian surface is zero, as per the given values and conditions.

Given data is: Area of A1 = A2 = 0.1 m2, Distance between A1 and A3, L0 = 1 m, Dielectric constant, ε0 = 8.85×10−12 C2/Nm2. The Gaussian surface is composed of A1, A2, and A3 together.

Net charge enclosed by the Gaussian surface can be calculated using Gauss's Law, given as:ϕE = Q/ε0ϕ

E = Electric flux Q = Net electric charge enclosedε0 = Dielectric constant.

The total electric flux is given as:ϕE = EA1 + EA2 + EA3ϕE = (E.A1 + E.A2) + (E.A3)ϕE = E(A1 + A2) + E.A3. Here, the angle between E and A1 and the angle between E and A2 is 180°, so:ϕE = E(A1 + A2) + E.A3ϕE = 2EA + EA3.

The electric field E can be calculated using Gauss's Law as: E = Q/4πε0L0²

Substituting this value in ϕE,ϕE = 2Q.A + QA3/4πε0L0²Q = ϕE.4πε0L0²/2A + A3

So, the net electric charge enclosed in the gaussian surface is given asQ = ϕE.4πε0L0²/2A + A3 = 0 because the net charge enclosed by the Gaussian surface is zero.

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The probability that you pick a striped shirt AND a blue suit  is 1/4 AND a pink tie is 3/8.

According to the statement

Number of blue suit = 1

Number of black suit = 2

Number of brown suit = 1

Number of blue ties = 2

Number of red ties = 3

Number of pink ties = 3

Now we find the probability by its formula

Probability that picked suit is blue = blue suits/ total number of suits

Probability = 1/4

Now,

Probability that picked tie is pink = Pink tie / total number of ties

Probability = 3/8

So, The probability that you pick a striped shirt AND a blue suit  is 1/4 AND a pink tie is 3/8.

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The correct answer is h(t) = 14.25 + 0.25 * sin((π/26) * t)

To model the hours of daylight in a year using a sinusoidal equation, we can consider the average length of daylight, the amplitude of the variation, and the period of the function.

Given:

Summer solstice (longest day) is 14.5 hours

Winter solstice (longest night) is 14 hours

Let's analyze the information:

Average daylight: The average daylight throughout the year would be the average of the summer and winter solstices. It can be calculated as:

Average daylight = (14.5 + 14) / 2 = 14.25 hours

Amplitude: The difference between the average daylight and the longest day or night is the amplitude. In this case, the amplitude is half the difference between the summer and winter solstices. It can be calculated as:

Amplitude = (14.5 - 14) / 2 = 0.25 hours

Period: We are modeling the function over a year, which we'll consider as 52 weeks. Since we want to measure time in weeks (t), the period of the function is 52 weeks.

Putting all the information together, we can write the sinusoidal equation:

h(t) = Average daylight + Amplitude * sin((2π / Period) * t)

Substituting the values we calculated:

h(t) = 14.25 + 0.25 * sin((2π / 52) * t)

Simplifying further, the sinusoidal equation modeling the hours of daylight in a year is:

h(t) = 14.25 + 0.25 * sin(π/26 * t)

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The mean is mathematically given as given as

Mean = 43 minutes

Mean = $47

This is further explained below.

Generally, Cell phone usage Mon to Sun = 38, 62, 40, 10, 30, 55, 65

Mean = (38+62+40+10+30+ 55 + 65)/7

Mean = 43 minutes rounded

Water bills  Mean from Jan to Dec =

40+42+40+38+48+50+58+62+56+46+44+44=568

Mean = (568)/12

Mean = $47 rounded

In conclusion, the mean is

Mean = $47

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By applying the distributive property of multiplication, the students that are correct in their approach to solving the problem are: Nico, Raj and Sandra.

In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 5/2 as follows:

2/5(5 + x) = 8

Multiplying both sides by 5/2, we have:

5/2 × 2/5(5 + x) = 8 × 5/2

5 + x = 40/2

5 + x = 20

Subtracting 5 from both sides, we have:

5 + x - 5 = 20 - 5

x = 15

In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 1/2 and then 5 as follows:

2/5(5 + x) = 8

Multiplying both sides by 1/2, we have:

1/2 × 2/5(5 + x) = 8 × 1/2

1/5(5 + x) = 4

Multiplying both sides by 5, we have:

5 × 1/5(5 + x) = 4 × 5

5 + x = 20

Subtracting 5 from both sides, we have:

5 + x - 5 = 20 - 5

x = 15

In order to open the bracket and isolate the variable x, we would apply the distributive property of multiplication:

2/5(5 + x) = 8

2/5 × 5 + 2/5 × x = 8

2 + 2x/5 = 8

Subtracting 2 from both sides, we have:

2 - 2 + 2x/5 = 8 - 2

2x/5 = 6

Multiplying both sides by 5/2, we have:

5/2 × 2x/5 = 5/2 × 6

x = 30/2

x = 15.

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The simple interest rate is $46,800

Simple interest  serves as the interest that is based on the  principal amount of a loan  or in some cases the  deposit in a savings account.

interest rate  = 6.5%= 6.5/100= 0.065

time = 12 years

principal = $60,000

Simple interest formular =(Principal x Interest Rate x Time)/100

Simple interest = (12* 0.065* 60000)/100

=$46,800

Therefore, simple interest rate is $46,800

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^answer:^

~10 cubic feet~

^step by step explanation:^

first, calculate the volume of the front “panel” of the shape. (5 cubic centimeters because 5 times 3 is 15 and 15 times 1/3 is 5. 5 times 2 is 10.

Check the picture below.

Answer:

the image is missing.

Step-by-step explanation:

Answer:

r=8

Step-by-step explanation:

so first distribute -2

so you get -140=-16r-12 then add 12 to both sides to get -16r by itself

so you have -128=-16r divide both sides by -16

the - cancel each other out so you get 8=r

hope this helps

Answer:

C

Step-by-step explanation:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

C is the correct answer since it can be expressed as a fraction which equals to 7/9.

Hope it helps:)

Answer:

A

Step-by-step explanation:

Pi is an irrational number so it can't be B.

√(5) is an irrational number so it can't be D.

It could be either A or C... Hm, go with A. Let me know if it works.

Answer: 101.03 cm

Step-by-step explanation:

Given

The height of the person is \(h=175\ cm\)

Sun is \(60^{\circ}\) above the ground

Suppose x is the length of the shadow

From the figure, we can write

\(\Rightarrow \tan 60^{\circ}=\dfrac{h}{x}\\\\\Rightarrow x=\dfrac{h}{\tan 60^{\circ}}\\\\\Rightarrow x=101.03\ cm\)

So, the length of the shadow is 101.03 cm

Answer:

move to the left 3 more spaces

Step-by-step explanation:

you are at -8 already. Therefore, you (-3) more spaces, so you go to the left three more spaces. Use the saying keep change change to help with this.

Keep the first number sign, change the next sign, and the next sign.

Answer:

d

Step-by-step explanation:

Answer: -6.3

Step-by-step explanation:

\(-12+\sqrt{32\\\)

\(-12+2^2\sqrt{2\)

\(-12+4\sqrt{2\) and that is approx -6.3

For this, we need to evaluate the approximate value of root 32, that is equal to : 5.65

we simply need to put the approximate valuw in expression and find the result.

\( \longrightarrow \tt - 12 + \sqrt{32} \)

\( \longrightarrow \tt - 12 + 5.65\)

\( \longrightarrow \tt - 6.34\)

\(\longrightarrow \tt \approx - 6.3\)

Hence, the first option over there is the most suitable choice.

Answer: (((trueeee))))

Since the least squares problem always has a unique solution. Therefore, the given statement is true.

The given statement is "Least squares regression problems always have a unique solution since they are modelled by the normal equation".

The least squares problem always has a solution. The solution is unique if and only if A has linearly independent columns. S equals Span(A) := {Ax : x ∈ Rn}, the column space of A, and x = b.

Therefore, the given statement is true.

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To discover the coordinates of a polar point, you need to recognize its distance from the origin (the polar axis) and the perspective it makes with the superb x-axis.

The space is commonly denoted via the image r, and the angle is denoted by means of the image θ. To devise a polar point, you start by locating the foundation and drawing a line alongside the polar axis.

Subsequently, you measure the angle θ from the fine x-axis, shifting counterclockwise.

In the end, your degree the distance r from the starting place and plot the factor on the corresponding location.

To find the coordinates of a polar point, you can use the subsequent formulas:

x = r cos(θ)

y = r sin(θ)

Right here, x and y constitute the rectangular coordinates of the factor, while r and θ constitute the polar coordinates.

Those formulas let you convert between polar and rectangular coordinates, which can be useful for graphing and solving problems in diverse branches of mathematics and physics.

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