Given log_5 ⁡2≈0.4308 and log_5⁡27≈2.0478, evaluate the expressions. Note: you must use the given values and not values obtained from a calculator for those logarithms.
log_5 ⁡3
log_5 ⁡(27/50)

The regression equation of the formula regarding tuition will be given as y = 34000 - 2300x.

Regression method of writing an equation is used to show relation between two variables. The two variables include an independent variable and a dependent variable. The dependent variable is related to the independent variable and their relation and changes can be shown with the help of regression model. According to the question

the charge for tuition = $32000

Charge deduced from tuition per year = $2300

So we assume the tuition cost as y and the number of years as x.

The regression equation will be

y = 34000 - 2300x

where y is the tuition cost and x is the number of years in school and y is dependent variable and x is independent variable.

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After the 4th cut, we will have 1,296 pieces and after the nth cut, we will have [tex]6^{n}[/tex] pieces.

Here, we are given that a sheet of paper is cut into 6 ​same-size parts. Each of the parts is then cut into 6 ​same-size parts and so on.

Thus, after one cut we will have 6 pieces

After second cut, we will have 6*6 = 36 pieces

After the third cut, we will have 36*6 = 216 pieces

After the fourth cut, we will have 216*6 = 1,296 pieces

Now, we can clearly see a pattern here. The number of pieces follow a geometric progression with a common ratio of 6.

Thus, after the nth cut, the number of pieces will be-

a[tex]r^{n-1}[/tex]

where a = first term which is 6

and r = common ratio which is also 6

⇒ 6*[tex]6^{n-1}[/tex]

= [tex]6^{n}[/tex]

Thus, after the 4th cut, we will have 1,296 pieces and after the nth cut, we will have [tex]6^{n}[/tex] pieces.

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Given surd [tex]\frac{7}{\sqrt{7} }[/tex] after rationalization we get it as [tex]\sqrt{7}[/tex]

The process of rationalization can be thought of as the removal of a radical or an imaginary number from the denominator of an algebraic fraction. In other words, eliminate the radicals from a fraction so that the denominator is solely composed of rational numbers.

Here we use the Rationalization technique

Given surds,

[tex]\frac{7}{\sqrt{7} }[/tex]

Multiplying Numerator and Denominator [tex]\sqrt{7}[/tex]

Then,

[tex]\frac{7}{\sqrt{7} }[/tex] × [tex]\frac{\sqrt[]{7} }{\sqrt{7} }[/tex]

We get the result as [tex]\frac{7\sqrt{7} }{7}[/tex] which is equal to √7

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The table of values and the linear equations indicates

4. Andy is correct, the equation of the table of values is; y = 2·x + 4

5. The Three equations are the same

A linear equation is an equation that produces a straight line graph, when plotted on the coordinate plane and can be expressed in the form; y = m·x + c

Where;

m = The slope of the straight line graph of the equation

c = The y-intercept

4. The values in the table indicate that the difference between consecutive terms in the x-values and the first difference in the y-value is constant, therefore, the values represent a linear relationship.

The slope, m, of the linear relationship is constant and it can be found using any two pair of points as follows;

m = (4 - 2)/(0 - (-1))  = 2

The equation is therefore;

y - 2 = 2·(x - (-1)) = 2·(x + 1) = 2·x + 2

y = 2·x + 2 + 2 = 2·x + 4

The equation, y = 2·x + 4 is in the form y = m·x + c, therefore;

Andy is correct

5. The slope-intercept form of the equation of a straight line is; y = m·x + c

Therefore;

y + 1 = 2·x -3

y + 1 - 1 = 2·x - 3 - 1 (subtraction property)

y = 2·x - 4

The equation, y = 2·x - 4, is in the form, y = m·x + c

2·x - 3 = y + 1

2·x - 3 - 1 = y + 1 - 1 (subtraction property)

2·x - 4 = y

y = 2·x - 4 (symmetric property)

The equation, y = 2·x - 4 is in the form, y = m·x + c, which is the same as the first equation

2·y + 2 = 4·x - 6

2·y + 2 - 2 = 4·x - 6 - 2 (subtraction property of equality)

2·y = 4·x - 8

2·y ÷ 2 = (4·x - 8) ÷ 2 (division property)

y = 2·x - 4

The above equation is the same as the first two equations, therefore, the equations are the same

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a firm in a purely competitive industry is currently producing 1,000 units per day at a total cost of $700 then average total cost is $ 0.61

The average total cost is calculated as the total cost divided by the number of outputs. The firm's ATC at these three levels of production will be:

1. 1,000 units per day at a total cost of $700.

ATC = Total cost/output

ATC = $700/1000

ATC = $0.58

2. If the firm produced 500 units per day, its total cost would be $450.

ATC = Total cost/output

ATC = $450/500

ATC = $0.45

3. If it produced 700 units per day, its total cost would be $425.

ATC = Total cost/output

ATC = $425/700

ATC = $0.61

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The simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.

The given statement is "7-radical 7 over10+radical 3".

Write the statement in mathematical form and simplify:
[tex]\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\\\\\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\times\frac{10 - \sqrt{3}}{10 -\sqrt{3}}\\\\\frac{(7 - \sqrt{7})(10-\sqrt{3})}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex]

Hence, the simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].

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The possible amount of time that it could take Wyatt to husk 72 dozen ears of corn is 4 to 6 hours.

What are time and work?

Time is the span of any action or work that occurs or is ongoing. Work is a task or series of activities carried out to accomplish a specific goal.

Given, Wyatt can husk anywhere from  12 to  18 dozen ears of corn per hour.

Thus, to find the time taken to husk 72 dozen ears of corn,

the maximum time = 72/12 =6 hours

And, the minimum time =  72/18 =4 hours

Thus, depending on his speed, Wyatt takes anywhere from  4  to 6 hours to husk  72 dozen ears of corn.

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The measure of the given sides and angles are,

1) ZX = 1.3 inch

2) EG = 3.0 inch

3) m ∠ X = 48°

4) m ∠G = 25°

What is congruent triangles?

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.

Given: ΔXYZ ≅ ΔEGF

Because the triangles are assumed to be congruent, their corresponding angles and sides must have similar measurements and lengths.

a. ZX = _ in

ZX's length is the same as FE's length. Therefore, the length should be 1.3 inches.

b. EG = _ in

EG's length is the same as XY's length. The figure indicates that the answer should be 3.0 in.

c. m ∠X = _ °

Angle E and angle x should both have the same measure. This is stated to be 48 degrees.

d. m ∠G

Angle Z's measurement is the same as angle F's measurement.

In that case, 107° should be the value assigned to angle F.

Angle E in the triangle to the right measures 48°, while angle F measures 107°.

the sum of these angles is subtracted from 180°.

The angle G's measure, which is equal to 25°.

Hence,

1) ZX = 1.3 inch

2) EG = 3.0 inch

3) m ∠ X = 48°

4) m ∠G = 25°

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Complete question:

Complete question is attached below.

The margin of error for the population mean is 5.601

What does the term "margin of error" mean?

Your results will deviate by how many percentage points from the actual population value, according to your margin of error. It is described as a very small percentage that is allowed for error in calculations.

Given c = 0.95

The significance level is obtained as follows:

alpha = 1 - c

alpha = 1 - 0.95

alpha = 0.05

Also, it is given that n = 150 and sigma = 35 .

The critical value of Z distribution at 0.05 level of significance can be computed in MS Excel using + NORMS INV (alpha/2) function as follows:

Thus, [tex]Z_{0.005/2}=1.96[/tex]

Now, the margin of error can be computed as follows: ME = Critical Value x Standard Error

[tex]Z_{0.005/2}*\frac{sigma}{\sqrt{n} } \\= 1.96 * \frac{35}{\sqrt{150} } \\= 5.601[/tex]

Thus, the margin of error for the population mean is 5.601

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The value of the integral ∫x²dV using cylindrical coordinates is 512π / 3 .

In this case, the solid is positioned between the cylinder x² + y² = 4 and will be evaluated by using the cone z²= 16x² + 16y² .

Cylindric coordinates will be used to calculate this integral  [tex]\int\limits_e {x^2} \, dx[/tex].

The distance from the origin to the point (x, y, 0) and the angle the point (x, y, 0) makes with the x-axis, respectively, are provided by the formulas.

x = r cos θ

y= r sin θ

With these coordinates, we shall characterize the solid E.

The boundary is then x² + y² = r²

The boundary also becomes r² = 4 or ( 0 ≤ θ ≤ r² )

Again z = 16r²

The original integral must now be translated into terms of these new coordinates. It is necessary to multiply the function by the Jacobian of the change in coordinates in order to ensure that the result remains the same. The value for the cylindric coordinates is r. Then

[tex]\int_ex^2 dx = \int\limits^{2\pi}_0\int\limits^2_0\int\limits^{16r^2}_0 r(r^2cos^2\theta)dzdrd\theta[/tex]

[tex]=\int _0^{2\pi }\int _0^216r^5\cos ^2\theta drd\theta[/tex]

[tex]=\int _0^{2\pi }\frac{512}{3}\cos ^2\theta d\theta[/tex]

= 512/3 π

Hence the volume of the solid that is enclosed by the integral is given by 512/3 π .

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An important measure of location for categorical data is the mode.

While the mean and median can only be determined for numeric data, the mode can be used to describe categorical variables. The mode's principal benefit as a gauge of central tendency is this. When continuous or discrete variables are expressed as intervals, it is also helpful.

The mode represents the value that occurs most often in a dataset.

A dataset can have no mode (if no value repeats), one mode, or multiple modes.

A set of data values' mode is the value that appears the most frequently. The value x (i.e., X = x) at which the probability mass function takes its maximum value is known as the mode if X is a discrete random variable. In other words, it is the value that will be sampled most frequently.

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Answer: One solution

Step-by-step explanation:

6x+16=2x+30

4x=14

x=7/2

The triple integral f(x, y, z)dV for the following function f is 256π(256 - x - y)² as an iterated integral in cylindrical coordinates.

In two-dimensional space R2, a point with rectangular coordinates (x, y) can be identified with (r, θ) in polar coordinates and vice versa, where x=rcosθ, y=rsinθ, r2=x2+y2 and tanθ=(y.x) are the relationships between the variables.

In three-dimensional space R3, a point with rectangular coordinates (x, y, z) can be identified with cylindrical coordinates (r,θ,z) and vice versa. We can use these same conversion relationships, adding z as the vertical distance to the point from the x y-plane

According to the question:

The integrated integral in cylindrical coordinates is given by:

∫∫∫f(ρ, θ, z)dV = ∫∫∫xρcos(θ)ρsin(θ)zdρdθdz

Evaluating the integral yields:

∫∫∫f(ρ, θ, z)dV = 256π∫zdz

= 256πz²

= 256π(256 - x - y)²

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Answer:

22

Step-by-step explanation:

The p-value will be 0.9457

Sample size = 49

Meantime = 19 minutes

Standard deviation = 3.9 mins

Calculating the z-score for test statistic -

z = (x - μ) / (s / √n)

z = (19 - 18) / (3.9 / √49)

= 1 / 0.63

= 1.58

To find the p-value, we can use a standard normal table to find area under the normal curve of the z-score.

The p-value will be the area under the curve to the right of 1.58.

This value is 0.9457, which means that there is a 94.57% chance.

Now,

Since the p-value is greater than the significance level (0.9457 > 0.05),  the null hypothesis can not be rejected. Therefore, the mean time parents spend posting pictures of their children per week is not significantly different from 18 minutes at the 5% significance level.

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The null hypothesis and the alternate hypothesis for the set of elementary school children is given by H₀ :  μ₁ = 2 and H₁ : μ₂  ≠ 0 and the p-value is 0.136 .

Given x₁ = 74 , x₂ = 72

s₁ = 9 , s₂ = 11 (standard deviation)

n₁ = 50 ,n₂ = 50

Let μ₁ be the true mean for x₁

Let μ₂ be the true mean for x₂

null and alternate hypothesis:

H₀ :  μ₁ - μ₂  = 0

H₁ : μ₁ - μ₂  ≠ 0

Test statistic ,

Z = (x₁ - x₂ - D₀ ) / (√σˣ₁² /n₁ + √σˣ₂² /n₂ )

Now we will substitute the values to calculate the the test statistic.

D₀ = μ₁ - μ₂

hence Z₀ = (74 - 72) / √(81/80+121/50)

or,  Z₀ = 1.49256..

or,  Z₀ ≈ 1.49

Now we will calculate the p-value using the z-score.

p-value:

= 2P(Z > Z₀)

= 2P(Z>1.49)

= 2 {1-0.93189}

= 0.1362...

≈ 0.136

Hence the p-value is 0.136 .

A hypothesis is presented as a theory to explain a certain phenomenon. A hypothesis cannot be said to as a scientific hypothesis if it cannot be tested using the scientific process.

History-based observations that can't currently be fully explained by existing bodies of knowledge are typically where science starts. A hypothesis is a theory put out to explain an observed occurrence or a proven assertion regarding the relationship between two or more variables in a scientific field.

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Answer:

cheese is cheese

Answer:

3(n+6)

Step-by-step explanation:

3n+18= 3(n+6)

Answer:

To find the answers you just need to multiply each value by 3. This is as we are given the information that y is equal to 3x. If we know this and we know the values of x we can easily work out the output (y)!!

We can also see a pattern of +3 going upwards!!

Hope this helps, have a great day!

The equation of the ellipse in the graph, with center at (0, 0), and semi  major and minor axis of 3 and 2 can be presented as follows;

[tex]\dfrac{x^2}{2^2} +\dfrac{y^2}{3^2 } = 1[/tex]

An ellipse is the locus of a point that moves such that the sum of the distance from two points is constant.

The standard form of the equation of an ellipse can be presented as follows;

[tex]\dfrac{(x - h)^2}{b^2} + \dfrac{(y - k)^2}{a^2} = 1[/tex]

Where;

(h, k) = The coordinates of the center of the ellipse

a = The semi major axis

b = The semi minor axis

From the attached graph the coordinates of the center of the ellipse is; (0, 0)

The semi major axis, a  = 3

The semi minor axis, b = 2

Therefore;

[tex]\dfrac{(x - 0)^2}{2^2} + \dfrac{(y - 0)^2}{3^2} = 1[/tex]

The equation of the ellipse in standard form is therefore;

[tex]\dfrac{x^2}{2^2} + \dfrac{y ^2}{3^2} = 1[/tex]

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it is false that that when the direction of bias is towards love it means that the error causes the true measure of association to be overestimated

A Measurement process is biased if it systematically overstates or understates the true value of the measurement

Systematic error due to difference in accuracy or completeness of recall to memory of past or experience is the most associated with recall bias.

Positive association is biased toward the null null value it means that the error causes the true value of association to be underestimated

but in the given given question the statement states that when the direction of the bias is toward the null it means that the error causes the true measure of association to be overestimated which is false

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True, A P-value of 0.07 is less than that significance requirement of 0.1, suggesting that there is sufficient evidence to conclude that people who have a significant other are happier than single people.

The hypothesis being examined was that those who have a significant other are happier on average than those who do not. To test this hypothesis, data from a sample size of persons were collected and evaluated to compute the P-value.

The P-value of 0.07 was determined to be less than the level of significance established at 0.1, implying that there is sufficient evidence to support the hypothesis that persons with a significant other are happier on average than solitary people.

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Answer: B. Angle Bisector

Why: the line from D to be is intersecting or bisecting the 90 degree angle

Answer:

40

Step-by-step explanation:

280 divided by 7

Answer:

43.152

Step-by-step explanation:

6/5*35.96=43.152

The number of packages that can be wrapped with 12 feet of ribbon is 24.

For the stated question.

Total length of the ribbon = 12 feet.

Ribbon required to wrap a one box = 1/2 foot.

Number of boxes = Total length / required ribbon for one box

Number of boxes = 12/ (1/2)

Number of boxes = 12 x 2

Number of boxes = 24

Thus, the number of packages that can be wrapped with 12 feet of ribbon is 24.

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Why you lie you say 30 but give a 15

The statements that correctly describes the points of discontinuity of the function include the following;

A. There is an infinite discontinuity at x = -2.

C. There is a removable discontinuity at x = -1.

E. There is a jump discontinuity at x = 1.

In Mathematics, there are three (3) main types of discontinuity in a function and these include the following:

A jump discontinuity can be defined as a point on the graph of a function at which the left-hand limit [tex]\lim_{x \to x^-_0} f(x) = A_2[/tex] and right-hand limits [tex]\lim_{x \to x^+_0} f(x) = A_2[/tex] are not equal (A₁ ≠ A₂).

By critically observing the graph representing this function, we can logically deduce that there is a jump discontinuity at x is equal to 1 (x = 1).

A removable discontinuity can be defined as a point on the graph of a function at which it is not connected. This ultimately implies that, a removable discontinuity refers to a point on the graph of a function that is considered to be undefined or doesn't accurately fit the other part of a graph.

By critically observing the graph representing this function, we can logically deduce that there is a removable discontinuity at x is equal to negative 1 (x = -1) while there is an infinite discontinuity on the vertical asymptote at negative 2 (x = -2).

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Complete Question:

Which correctly describes the points of discontinuity of the function? Select all that apply.

A. There is an infinite discontinuity at x = -2.

B. There is a jump discontinuity at x = -2.

C. There is a removable discontinuity at x = -1.

D. There is an infinite discontinuity at x = 1.

E. There is a jump discontinuity at x = 1