x=y*10^z where 4 Find an expression for x^2 in standard form.

Answer:

192!!!

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(a)

calculate the lengths using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = J (- 3, - 7 ) and (x₂, y₂ ) = K (3, - 8 )

JK = \(\sqrt{(3-(-3))^2+(-8-(-7))^2}\)

    = \(\sqrt{(3+3)^2+(-8+7)^2}\)

    = \(\sqrt{6^2+(-1)^2}\)

    = \(\sqrt{36+1}\)

    = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = M (8, 3 ) and (x₂, y₂ ) = N (7, - 3 )

MN = \(\sqrt{(7-8)^2+(-3-3)^2}\)

      = \(\sqrt{(-1)^2+(-6)^2}\)

     = \(\sqrt{1+36}\)

     = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = P (- 8, 1 ) and (x₂, y₂ ) = Q (- 2, 2 )

PQ = \(\sqrt{-2-(-8))^2+(2-1)^2}\)

      = \(\sqrt{(-2+8)^2+1^2}\)

      = \(\sqrt{6^2+1}\)

      = \(\sqrt{36+1}\)

      = \(\sqrt{37}\)

(b)

JK ≅ MN ← true

JK ≅ PQ ← true

MN ≅ PQ ← true

Harry’s Fish Fry orders cooking oil every 10 days. The lead time is six days. The usage of cooking oil at Harry's Fish Fry is normally distributed with an average of 15 gallons/day and a standard deviation of 3 gallons/day.

Harry's wants a 95% service level.Assuming a normal distribution for usage of cooking oil at Harry's Fish Fry, the service level can be found using the formula; z = (x - µ)/σ where x is the demand, µ is the average demand and σ is the standard deviation of demand.

The z value can be looked up in the z-table to find the probability.The service level is the probability of the lead time demand not exceeding the order point.

Therefore, the order point can be calculated using the formula; Order point = Lead time demand + safety stock.  

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y = -3x +2

The general equation for a linear line is y = mx + b

Where:

To find the slope of a line we can use the formula \(\frac{rise}{run}\)

Rise over run can be found suing two different points on the line.

in this case: (-1,5) and (1,-1)

The rise is the difference in y values: \(y_2 -y_1\)

rise = (-1) - 5

rise  = -6

run = \(x_2 - x_1\)

run = 1 - (-1)

run = 2

rise/run = \(\frac{-6}{2}\)

rise/ run = -3

We now have y = -3x + b

To find b we just look at the graph and locate a what point x = 0

Answer:

x=45°

Step-by-step explanation:

By linear pair property

\(x+135=180\)

\(x=180-135\)

\(x=45^o\)

~

Answer:

simplified: -y^2 + 7x - 5y +9

evaluated: 7x - 5y + 9 - y^2

Step-by-step explanation:

Answer:

\(x < \dfrac{18}{5}\)

Step-by-step explanation:

      7x - 5 < 13

Add 5 to both sides

            7x < 13 + 5

            7x < 18

Divide both sides by 7,

             \(\sf x < \dfrac{18}{7}\)

Answer:

\(x < \dfrac{18}{7}\)

Step-by-step explanation:

We are being asked to solve for x as an improper fraction in simplest form given the equation: \(7x - 5 < 13\).

First, we must isolate the variables (x's) from the constants (numbers). We can achieve this by adding 5 to both sides.

\(7x - 5 + 5 < 13 + 5\)

           \(7x < 18\)

Then, we can solve for one multiple of x by dividing both sides by x's coefficient, which is 7.

\(7x < 18\\\overline{\ 7\ } \ \ \ \: \overline{\ 7\ }\)

\(x < \dfrac{18}{7}\)

Answer:

1/  24 bottle of water for $3 is a better buy

2/ $0.045

Step-by-step explanation:

12 bottles of water for $2

2 / 12 =$0.17

So, it costs $0.17 for each bottle of water.

24 bottles of water for $3

3 / 24 = $0.125

So, it costs $0.125 for each bottle of water.

0.17 - 0.125 = $0.045

So, 24 bottles of water for $3 is a better buy by $0.045

Answer:

\(\tan \theta = \dfrac{8}{15}\)

Step by step explanation:

\(\text{Given that,}\\\\~~~~~~~\sin \theta = \dfrac{8}{17}\\\\\implies \sin^2 \theta = \dfrac{64}{289}\\\\\implies 1-\cos^2 \theta = \dfrac{64}{289}\\\\\implies \cos^2 \theta = 1-\dfrac{64}{289}\\\\\implies \cos^2 \theta = \dfrac{225}{289}\\\\\implies \cos \theta =\pm\sqrt{\dfrac{225}{289}}\\\\\implies \cos \theta = \pm\dfrac{15}{17}\)

\(\text{In quadrant I, all ratios are positive, so,}~ \cos \theta = \dfrac{15}{17}\\\\\text{Now,}\\\\\tan \theta = \dfrac{\sin \theta }{\cos \theta}\\\\\\~~~~~~~~=\dfrac{\tfrac{8}{17}}{\tfrac{15}{17}}\\\\\\~~~~~~~~=\dfrac{8}{17} \times \dfrac{17}{15}\\\\\\~~~~~~~=\dfrac{8}{15}\)

The Cartesian coordinates of the point with polar coordinates (r=5.70 m, θ=250°) are approximately (x=-4.07 m, y=-3.81 m).

To convert polar coordinates to Cartesian coordinates, we can use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

Given that r = 5.70 m and θ = 250°, we can substitute these values into the formulas:

x = 5.70 m * cos(250°)

y = 5.70 m * sin(250°)

Using a calculator to evaluate the trigonometric functions, we find:

x ≈ -4.07 m

y ≈ -3.81 m

Therefore, the Cartesian coordinates of the point with polar coordinates (r=5.70 m, θ=250°) are approximately (x=-4.07 m, y=-3.81 m).

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Answer:

There are $\boxed{3}$ paths from $A$ to $B.$

Using Standard deviation, approximately, 95% of the area under the normal curve falls between 2 standard deviations.

The area under a normal curve represents the total probability of an event occurring for a normally distributed random variable.

A normal distribution is a bell-shaped curve that describes a continuous probability distribution of a variable, where most values cluster around the mean, and the curve tapers off symmetrically on both sides.

The total area under the normal curve is equal to 1 or 100%, which means that the probability of all possible outcomes adds up to 1 or 100%.

The Empirical Rule states that:

Hence,

Approximately, 95% of the area under the normal curve falls between 2 standard deviations.

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The term​ annuity is best described as​ a stream of equal installments made at equal time intervals​.

An annuity is a term used to define a series of payments of equal size at equal intervals. Equal time intervals such as months, quarters, or years, and uniform payments are the two characteristics that make a series of payments an annuity. Therefore, a series of payments can be an annuity however all series of payments are not annuities. If the series of payments is of different values or at different intervals, it is not considered to be an annuity. An annuity that provides for payments for the remainder of a person's lifetime is known as a life annuity.

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Complete question :

The line plot shows the weights of packages of meat that members of a club bought. The meat will be mixed with vegetables to make stew for a club dinner. Each serving of the stew contains 1/4 pound of meat. How many servings of the stew can the club make?

Answer:

36 servings

Step-by-step explanation:

From the plot ; we take the sum of total weight of meat packages :

(5/8 * 2) + 6/8 + 1 + (9/8 * 3) + 10/8 + 11/8

10/8 + 6/8 + 8/8 + 27/8 + 10/8 + 11/8 = 72 / 8 = 9 meat packages

Each serving of meat = 1/4

Number of servings the club can make :

Total meat package / pound of meat per serving

(9 ÷ 1/4)

9 * 4/1

= 36 servings

Answer:

36 hope this help

Step-by-step explanation:

Answer:

A = 0,

B = π/2,

C = 3π/2,

D = 2π

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

Jane and John are each hiking a trail in the city.  Jane is on her bike, and John is jogging.

At noon, Jane is at the 5 mile mark and rides at 11 miles per hour.

Also at noon, John is at the 23 mile mark and jogs at 8 miles per hour.

x is the number of hours after noon.

Will Jane catch John?  After how many hours?

15. If your car traveled 6.05 miles in 5.75 minutes and you continue driving at the same pace, it will take approximately 262.17 minutes to drive 246 miles.

16. The volume of the gold nugget with a mass of 21.75 g and a density of 19.32 g/mL is approximately 1.125 mL.

15. Using the given information, we can set up a proportion to find the time it will take to drive 246 miles. The proportion can be set up as: (6.05 miles / 5.75 minutes) = (246 miles / x minutes), where x represents the unknown time. Cross-multiplying and solving for x, we find that x ≈ 262.17 minutes. Therefore, it will take approximately 262.17 minutes to drive 246 miles at the same pace.

16. To calculate the volume of the gold nugget, we can use the formula: volume = mass / density. Plugging in the given values, we get: volume = 21.75 g / 19.32 g/mL. Performing the division, we find that the volume is approximately 1.125 mL. Therefore, the volume of the gold nugget is approximately 1.125 mL.

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Answer:

linear algebra, an n-by-n square matrix A is called invertible, if there exists an n-by-n square matrix B such that \mathbf {AB} =\mathbf {BA} =\mathbf {I} _{n}\ where Iₙ denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.

Answer:

Brainliest pls

Step-by-step explanation:

The inverse of a square matrix A, denoted by A-1, is the matrix so that the product of A and A-1 is the Identity matrix.

Answer:

umm okay 6.15

Step-by-step explanation:

The measure of <YZX is 55.2 degree.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

XY= 12.4 cm, YZ= 15.1 cm

In right ΔXYZ with hypotenuse XZ and opposite side XY to ∠YZX then

Using the sine ratio

sin <YZX= 12.4/ 15.1

sin <YZX = 0.8211

<YZX= 55.2

Hence, the measure of <YZX is 55.2 degree

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Answer: 55.2

Step-by-step explanation: just took it

Answer:

a= 1

b= 6

c= 8

Step-by-step explanation:

Answer:

Here's the correct answer for Edge 2021

Step-by-step explanation:

We will have that the common denominators are:

So, the common denominator is 32.

Answer:

a = -20

Step-by-step explanation:

In this question, you would solve for "a".

Solve:

8(a + 30)=80

Use the distributive property.

8a + 240 = 80

Subtract both sides by 240

8a = -160

Divide both sides by 8.

a = -20

Your final answer would be a = -20

Answer:

a=-20

Step-by-step explanation:

Multiply 8 by a and 30 which is 8a and 240

The equation looks like this:

8a+240=80

Subtract 240 on both sides:

8a+240-240=80-240

The equation looks like this now:

8a=-160

Divide by 8 on both sides:

8a/8=-160/8

The answer will be:

a=-20

First you will get 4dz

a) The six questions of statistical validity of a bivariate correlation are,

b) For correlations shown as bar graphs, questions regarding outliers and curved connections may be irrelevant.

Exactly two variables are needed to establish a relationship in a bivariate correlational investigation.

Scatterplot is a quantitative term (user to describe relationship)

Bar graphs are categorical (use the difference in groups to des. rel.)

For correlations shown as bar graphs, questions regarding outliers and curved connections may be irrelevant.

For correlations shown as bar graphs, questions regarding outliers and curved connections may be irrelevant.

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The diagonal matrix A' for T relative to the basis \(\(B'\)\) is:

\(\[A' = \left[ \begin{array}{ccc} 3 & -4 & 0 \\ -2 & -1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

To find the diagonal matrix A' for the linear transformation T relative to the basis B', we need to perform a change of basis using the given matrix A and basis B'.

Let's denote the standard basis as \(\(B = \{(1, 0, 0), (0, 1, 0), (0, 0, 1)\}\).\)

To perform the change of basis, we need to find the matrix P such that P[B'] = B.

We can write the vectors in B' as column vectors:

\(\[B' = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

To find \(P\), we solve the equation P[B'] = B for P:

\(\[P \cdot B' = B\]\\\\\P = B \cdot (B')^{-1}\]\)

Calculating the inverse of \(\(B'\)\):

\(\[B'^{-1} = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]^{-1} = \left[ \begin{array}{ccc} -1 & 1 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Now we can calculate \(\(P\)\):

\(\[P = B \cdot B'^{-1} = \left[ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] \cdot \left[ \begin{array}{ccc} -1 & 1 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right] = \left[ \begin{array}{ccc} -1 & 1 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Now, the diagonal matrix A' for T relative to the basis B' can be calculated as:

\(\[A' = P^{-1} \cdot A \cdot P\]\)

Calculating\(\(P^{-1}\):\)

\(\[P^{-1} = \left[ \begin{array}{ccc} -1 & 1 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right]^{-1} = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Substituting the values into the equation for \(\(A'\)\):

\(\[A' = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]^{-1} \cdot \left[ \begin{array}{ccc} -1 & -2 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{array} \right] \cdot \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Performing the matrix multiplication:

\(\[A' = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] \cdot \left[ \begin{array}{ccc} -1 & -2 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{array} \right] \cdot \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Calculating the matrix multiplication, we get:

\(\[A' = \left[ \begin{array}{ccc} 3 & -4 & 0 \\ -2 & -1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Therefore, the diagonal matrix A' for T relative to the basis B' is:

\(\[A' = \left[ \begin{array}{ccc} 3 & -4 & 0 \\ -2 & -1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

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Correlation analysis:

a. The variables used in the research study are "age" and "number of times eaten out in an average month." The level of measurement for age is an interval, and the level of measurement for the number of times eaten out is ratio.

b. Pretest Checklist for NormalityAge Histogram Interpretation:

A histogram with a bell curve, skewness equal to 0, and kurtosis equal to 3 indicates normality.

Mean = 45.17, Standard deviation = 14.89, Skewness = -.08, Kurtosis = -0.71.

The histogram for the age of respondents is approximately bell-shaped, indicating normality.

Number of times eaten out Histogram Interpretation:

A histogram with a bell curve, skewness equal to 0, and kurtosis equal to 3 indicates normality.

Mean = 8.38, Standard deviation = 8.77, Skewness = 2.33, Kurtosis = 9.27.

The histogram for the number of times the respondent eats out in an average month is positively skewed and not normally distributed. Therefore, it is not normally distributed.

Linearity:

Age vs. Number of times Eaten Out

Scatterplot Interpretation:

A scatterplot indicates linearity when there is a straight line and all data points are scattered along it. The scatterplot displays that the number of times respondents eat out increases as they get older. The relationship between the variables is linear and positive.

Homoscedasticity:

Age vs. Number of times Eaten OutScatterplot Interpretation: The scatterplot displays no fan-like pattern around the regression line, which indicates that the assumption of homoscedasticity is met.

c. Bivariate Correlation and Descriptive Statistics

Age and the number of times eaten out in an average month have a correlation coefficient of.

150, which is a small positive correlation and statistically insignificant (p = .077). The mean age of the respondents was 45.17 years, with a standard deviation of 14.89. The mean number of times the respondent eats out in an average month was 8.38, with a standard deviation of 8.77.

The scatterplot with regression line shows a positive slope that indicates a small and insignificant correlation between age and the number of times the respondent eats out in an average month.

d. The research study aimed to determine whether there is a correlation between age and the number of meals eaten outside the home. The data were analyzed using a bivariate correlation analysis, scatterplot with regression line, and descriptive statistics. The results indicated a small positive correlation (r = .150), but this correlation was statistically insignificant (p = .077).

The mean age of the respondents was 45.17 years, with a standard deviation of 14.89. The mean number of times the respondent eats out in an average month was 8.38, with a standard deviation of 8.77. The findings showed that there is no correlation between age and the number of times the respondent eats out in an average month.

Therefore, the researcher cannot conclude that age is a significant factor in the number of times a person eats out. The implications of the findings suggest that other factors may influence a person's decision to eat out, such as income, time constraints, and personal preferences. Further research could be done to determine what factors are significant in the decision to eat out.

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The length of a side of the square is 8 cm.

What do you mean by perimeter of a rectangle and square?

When a wire is bent into the shape of a rectangle, its length becomes the perimeter of the rectangle. Similarly, when the wire is reshaped into a square, its length becomes the perimeter of the square.

The perimeter of a rectangle is given by the formula \(P=2(l+w)\) , where \(l\) is the length and \(w\) is the width.

The perimeter of a square is given by the formula \(P=4s\) , where \(s\) is the length of a side.

Calculating the length of a side of the square:

The length of the rectangle is 11 cm and the width is 5 cm.

Therefore, the perimeter of the rectangle is \(P=2(11+5)=32\) cm.

Since the wire is reshaped into a square, the perimeter of the square is also 32 cm.

Using the formula \(P=4s\), we can solve for the length of a side of the square:

\(32 = 4s\)

\(s = 32/4\)

\(s = 8\)

Therefore, the length of a side of the square is 8 cm.

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Answer:x+10

Step-by-step explanation:just took the test