3x-7y=14

What is the slope of the line given by the linear equation above?

A. 3/7
B. -3/7
C. 7/3
D -7/3

Given the low sampling variability, the average annual salary for the other group of the business school graduates is most likely to be close to $96,000. Thus, extreme values, significant higher or lower than $96,000, are less likely.

In the domain of statistics, when the sampling variability is low, it means that most of the samples drawn from a population will have averages (means) that are close to the population mean. The data from the samples will be clustered around a single value.

In this context, given that the average salary of one group was $96,000, the salaries of the other groups are also likely to be around this value given the low sampling variability. Therefore, an average annual salary that is significantly higher or lower than $96,000 for another group would be least likely.

By using the concept of sampling variability, we could reasonably predict that extremes, such as $40,000 or $150,000, would be highly unlikely as average salaries for the other groups if the business school graduates' salaries are distributed normally and the sampling variability is indeed low.

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The ratios 4/6 and 8/12 are equivalent ratio of 2/3 which we obtain by multiplying or dividing both numerator and denominator by same number.

To find a ratio that is the same as 2/3, we can multiply or divide both the numerator and the denominator by the same non-zero number.

This will result in an equivalent ratio.

If we multiply both the numerator and denominator of 2/3 by 2, we get:

(2 × 2) / (3 × 2)

= 4/6

Therefore, the ratio 4/6 is the same as 2/3.

Similarly, if we multiply both the numerator and denominator of 2/3 by 2, we get:

8/12

So, the ratio 8/12 is also the same as 2/3.

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Answer:

y=1/2x-2.5

Step-by-step explanation:

4x-8y=20

Subtract 4x from both sides to get the 8y on on side.

-8y=-4x+20

divide -8 from both sides to get the y by itself.

y=1/2x-2.5

Answer:

25.5%

Step-by-step explanation:

% error = | estimate - actual | / actual × 100%

% error = | 59 - 47 | / 47 × 100%

% error ≈ 25.5%

Answer:

20.3%

Step-by-step explanation:

The formula for percent error is the experimental value minus the theoretical value divided by the theoretical value all times 100.

Experimental - Theoretical

------------------------------------------ x 100

         Theoretical

−12

------- ×100

59

=−0.20339×100

=−20.339

=20.339%

=20.3% error

Step 1: Convert [tex]\frac{5\pi }{12}[/tex], which is in radians into degrees. To convert it multiply by [tex]\frac{180}{\pi }[/tex]

[tex]\frac{5\pi }{12} =\frac{180}{\pi }[/tex]

900/12

75

Step 2: 75 degrees isn't on the unit circle but 45 degrees and 30 degrees is. Since 45 + 30 = 75 you can use the cosine of 45 and 30 to find the exact value

cos45 = [tex]\frac{\sqrt{2} }{2}[/tex]

cos30 =[tex]\frac{\sqrt{3} }{2}[/tex]

Step 3: Add the cos45 and cos30 to get cos5pi/12

[tex]\frac{\sqrt{2} }{2} +\frac{\sqrt{3} }{2} = \frac{\sqrt{2}+\sqrt{3}}{2}[/tex]

Hope this helped!

Answer:

The correct answers are:

Question 4: the first step Keisha should take is: log to the power of x equals log 9.

Question 5: step 4 could be n ln 2 equals ln 86

Question 6: the exact solution is x=ln(7)

Step-by-step explanation:

Ok,

Question 4: the equation that shows the first step Keisha should take is:

[tex]7^{x}=9[/tex]

[tex]log(7^{x} )=log(9)[/tex]

[tex]x(log(7))=log(9)[/tex] (applying the properties of logarithms)

[tex]x=\frac{log(9)}{log(7)} =1.129[/tex]

Solution: the first step Keisha should take is: log to the power of x equals log 9.

Question 5: Her first three steps are:

[tex]2^{n}-3=83[/tex]

[tex]2^{n}-3+3=83+3[/tex] (adding 3 to both sides)

[tex]2^{n}=86[/tex]

[tex]2^{n}-3+3=83+3[/tex]

[tex]nln(2)=ln(86)[/tex]

Solution: step 4 is: [tex]nln(2)=ln(86)[/tex] (applying the properties of logarithms)

Question 6: The exact solution of 2 e to the power of x equals 14 is:

[tex]2e^{x}=14[/tex]

[tex]\frac{2e^{x} }{2} =\frac{14}{2}[/tex] (dividing both sides by 2)

[tex]e^{x}=7[/tex]

[tex]xln(e)=ln7[/tex] (ln(e)=1)

[tex]x=ln(7)[/tex]

Solution: [tex]x=ln(7)[/tex]

For Keisha's equation, the first step involves taking the logarithm of both sides, and for Mary's equation, the fourth step involves taking the natural logarithm. The exact solution for the third equation is x = ln 7.

Question 4:

Keisha is solving the equation [tex]\(7^x = 9\)[/tex]. The correct first step is:

[tex]\[ \log(7^x) = \log(9) \][/tex]

So the correct option is:

[tex]\[ \text{log } 7^x = \text{log } 9 \][/tex]

Question 5:

For Mary's equation [tex]\(2^n - 3 = 83\)[/tex], Step 4 involves taking the natural logarithm:

[tex]\[ n \ln 2 = \ln 86 \][/tex]

So the correct option is:

[tex]\[ n \ln 2 = \ln 86 \][/tex]

Question 6:

The equation [tex]\(2e^x = 14\)[/tex] can be solved by taking the natural logarithm:

[tex]\[ x = \ln \left(\frac{14}{2}\right) \][/tex]

Simplifying this gives:

[tex]\[ x = \ln 7 \][/tex]

So the correct option is:

[tex]\[ \ln 7 \][/tex]

Answer:

28

Step-by-step explanation:

We can see that all the angles are inside of a triangle and the sum of the interior angle of the triangle is 180 degrees.

Knowing this, we know that the sum of all the angles present is 180 degrees.

1st angle can be seen as 90 degrees, 2nd angle is x+6 and the 3rd is 2x.

The sum can be written as ( 90 + x + 6 + 2x ) and this equals to 180 degrees.

90 + x + 6 + 2x = 180

96 + 3x = 180

( subtract 96 on both sides )

3x = 180 - 96

3x = 84

( divide by 3 on both sides )

x = 84 / 3

x = 28

Answer:

x = 28

Step-by-step explanation:

Consider the lower right triangle

The 2 given angles sum to 90° ( sum of angles in a triangle = 180° )

Hence

x + 6 + 2x = 90

3x + 6 = 90 ( subtract 6 from both sides )

3x = 84 ( divide both sides by 3 )

x = 28

Answer:

The slope of this line is 1/5

Answer:

1)center =(-2,3)

2) Vertices = (8,3) and (-12,3)

3) foci =(4,3) and (-8,3)

Step-by-step explanation:

As the general equation of ellipse with center at (h,k) is given by:

(x-h)^2/a^2 +(y-k)^2/b^2 = 1

where a=radius of the ellipse along the x-axis

b=radius of the ellipse along the y-axis

h, k= the x and y coordinates of the center of the ellipse.

Given equation of ellipse:

(x+2)^2/100 + (y-3)^2/64 = 1

1)

Finding center:

comparing with the general formula

h=-2 and k=3

Center of given ellipse is at (-2,3)

2)

Finding vertices:

comparing given equation of ellipse with the general formula:

a^2= 100 and b^2=64

then a = 10 and b=8

As a>b, it means the ellipse is parallel to x-axis

hence vertices along the x-axis are a = 10 units to either side of the center i.e (8,3) and (-12,3)

The co-vertices along the y-axis are b=8 units above and below the center i.e (-2,11) and (-2,-5)

3)

Finding Foci, c:

From equations of general ellipse we have a^2 - c^2=b^2

Putting values of a^2=100 and b^2=64 in above

100-c^2=64

c^2=100-64

     = 36

taking square root on both sides

c=6

foci of given ellipse is either side of the center (-2,3) that is (4,3) and (-8,3)!

James will have $32,270.13 after 6 years

Answer:

[tex]y=20000(1.083)^6[/tex]

Step-by-step explanation:

Let y represents the amount James have after 6 years,

Given,

Principal amount, P = $ 20,000,

Compound rate of interest per year, r = 8.3 %,

Thus, the amount after x years would be,

[tex]A=P(1+\frac{r}{100})^x[/tex]

[tex]=20,000(1+\frac{8.3}{100})^x[/tex]

[tex]=20000(1.083)^x[/tex]

Therefore, the amount after 6 years would be,

[tex]y=20000(1.083)^6[/tex]

Which is the correct equation that represents the amount, James will have after 6 years.

[tex]\cos(15^\circ) = \cos(45^{\circ}-30^{\circ}) = \cos(45^{\circ})\cos(30^{\circ})+\sin(45^{\circ})\sin(30^{\circ}) = \\ \\ =\dfrac{\sqrt 2}{2}\cdot \dfrac{\sqrt 3}{2}+\dfrac{\sqrt 2}{2}\cdot \dfrac{1}{2} = \dfrac{\sqrt 6 +\sqrt 2}{4}[/tex]

Answer:

[tex]\cos (15)=\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]

Step-by-step explanation:

We want to find the exact value of

[tex]\cos 15\degree[/tex]

We rewrite this expression using compound angles  

[tex]\cos (45\degree-30\degree)[/tex]

Recall that:

[tex]\cos (A-B)=\cos A\cos B+\sin A\sin B[/tex]

We apply this property to obtain:

[tex]\cos (45-30)=\cos 45\cos 30+\sin 45\sin 30[/tex]

[tex]\cos (15)=\frac{\sqrt{2}}{2} \times \frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2} \times \frac{1}{2}[/tex]

[tex]\cos (15)=\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]

Answer:

see explanation

Step-by-step explanation:

The rule (x + 3, y + 2) means add 3 to the original x- coordinate and add 2 to the original y- coordinate, that is

A(- 2, 2) → A'(- 2 + 3, 2 + 2) → A'(1, 4)

B(- 2, 4) → B'(- 2 + 3, 4 + 2) → B'(1, 6)

C(0, 0) → C'(0 + 3, 0 + 2) → C'(3, 2)

Answer:

b.-1/3

Step-by-step explanation:

Is means equals and of means multiply

W =5/9 * (-3/5)

W = -3/9

W = -1/3

Answer: 17x = 85

Step-by-step explanation:

X is the number in which you'd multiply 17 by to equal 85, therefore x = the number of years.

Answer: Equation would be,

17x = 85

Where, x represents the number of year.

Step-by-step explanation:

Let x represents the number of year after which the cliff erodes 85 centimeters,

Since, the cliff on the seashore is eroding at the rate of 17 centimeters per year,

So, the total eroding of cliff after x years = 17x

[tex]\implies 17x = 85[/tex]

Which is the required equation..

ANSWER

B. 10

EXPLANATION

We need to find the value of x first.

It was given that the perimeter of triangle XYZ is 24.

This means that:

XY+YZ+XZ=24

we substitute the expression in terms of x to get;

[tex](5x - 1) + (13 - x) = 24[/tex]

This implies that

[tex]5x - x = 24 - 13 + 1[/tex]

[tex]4x = 12[/tex]

Divide both sides by 4 to get;

[tex]x = 3[/tex]

|WY|=|ZX|=13-3=10

Answer:

WY = 10 units

Step-by-step explanation:

From the figure we can see a rectangle WXYZ.

Diagonals of rectangle are equal.

It is given that, Perimeter of triangle XYZ = 24

XY + YZ = 5x - 1 and XZ = 13 - x

To find the value of x

Perimeter of ΔXYZ = XY + YZ + XZ

24 = 5x - 1 + 13 - x

4x + 12 = 24

4x = 12

x = 12/4 = 3

x = 3

To find the value of WY

We have WY = XZ

XZ = 13 - x

 = 13 - 3 = 10

Therefore WY = XZ = 10 units

Answer:

It would be 7.66 and 7.19 because you can not round downward although I am a little confused on how 7.19 is able to round upwards But I am positive 7.66 rounds up to 8

Step-by-step explanation:

Answer:

A : x^2 = -12y

Step-by-step explanation:

TO ALL MY EDGE PEOPLE

Answer:

a) x^2=-12y

Step-by-step explanation:

Answer:

Final answer is c=-7.

Step-by-step explanation:

Given equation is [tex]0=-x^2+4x-7[/tex].

Now question says that Misha wrote the quadratic equation 0=-x2+4x-7 in standard form. Now we need to find about what is the value of c in her equation.

We know that standard form of quadratic equation is given by [tex]ax^2+bx+c=0[/tex].

compare given equation with the standard form, we find that -7 is written in place of +c

so that means +c=-7

or c=-7

Hence final answer is c=-7.

Answer:

A = 13 cm^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh  where b is the length of the base and h is the height

A = 1/2 (6.5) * 4

A = 13 cm^2

Let Poly = X

Andy gets twice as much as Poly so Andy = 2X

Pheobe gets three times as much as Andy, so she is 3(2x) = 6X

Now add them together to equal 270:

X + 2X + 6X = 270

Simplify:

9X = 270

Divide both sides by 9:

X =  270 /9

X = 30

Poly = X = 30

Andy = 2X = 2(30) = 60

Pheobe = 6X = 6(30) = 180

Answer:

y = 9 + 19x

Step-by-step explanation:

To find the equation matching a set of data, you simply try a few values for x and see if by solving that side of the equation you get the value of y.  If you do, you found your equation.

You have a big advantage here... since you have the value of y when x = 0.

When x = 0, y = 9, that's a very important data to have to simplify your research.

Let's try the value of 0 for x in each of the given equations:

y = 18 + 10 (0) = 18  --- NO

y = 9 + 19 (0) = 9 --- YES!  We can confirm with another value of x:

y = 9 + 19 (1) = 28 --- YES! Confirmed!

y = 9 + 19x is your answer!

Answer:

13,92838827718412‬ft

Step-by-step explanation:

a² + b² = c²

a = 13ft

b = 5ft

169 + 25 = 194

c = √194

c = 13,92838827718412‬ft

Answer:

A

Step-by-step explanation:the lines do not cross therefor the two equations do not share a solution.

Answer:

A

Step-by-step explanation:

Let's simplify step-by-step.

2(11(a−2)+12)−(2(5a−3)+a)

Distribute the Negative Sign:

=2(11(a−2)+12)+−1(2(5a−3)+a)

=2(11(a−2)+12)+−1(2(5a−3))+−1a

=2(11(a−2)+12)+−10a+6+−a

Distribute:

=(2)(11(a−2))+(2)(12)+−10a+6+−a

=22a+−44+24+−10a+6+−a

Combine Like Terms:

=22a+−44+24+−10a+6+−a

=(22a+−10a+−a)+(−44+24+6)

=11a+−14

Answer:

=11a−14

Hello! The interquartile range would be 5°

You must subtract Quartile one from quartile 3 to find iqr

Answer:

The trip will take more than one hour

Step-by-step explanation:

The complete question is

A straight road connects the towns of Winridge and Upper Lansbury. On a map on which each unit represents 10 miles, the coordinates of Winridge are (8,4) and the coordinates of Upper Lansbury are (6,10). If Ty drives from Winridge to Upper Lansbyet at an average speed of 40 miles per hour, will the trip take more than an hour? Explain your reasoning

we know that

The speed is equal to divide the distance by the time

so

s=d/t

Solve for t

t=d/s ----> the time is equal to divide the distance by the speed

step 1

Find the distance

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

(8,4), (6,10)

substitute

[tex]d=\sqrt{(10-4)^{2}+(6-8)^{2}}[/tex]

[tex]d=\sqrt{(6)^{2}+(-2)^{2}}[/tex]

[tex]d=\sqrt{40}[/tex]

[tex]d=2\sqrt{10}\ units[/tex]

Convert to miles

[tex]d=2\sqrt{10}*10=20\sqrt{10}\ miles[/tex]

[tex]d=63.2\ miles[/tex]

step 2

Find the time

we have

s=40 miles/hour

d=63.2 miles

t=d/s -----> t=63.2/40=1.58 hours

1.58 hours > 1 hour

therefore

The trip will take more than one hour

Rotations, translations and reflections are transformations that preserve areas, so they always produce congruent figures.

So, the only way you have to produce a similar but not congruent figure is to use dilation with a scale different than 1.

ANSWER

The hypotenuse is 14√2 units.

EXPLANATION

Let the hypotenuse be x, then we can use the Pythagoras Theorem to find the length of the hypotenuse.

We have from the question that, each leg of the 45-45-90 triangle measures 14 cm.

Then, the Pythagorean Theorem, gives:

[tex] {x}^{2} = {14}^{2} + {14}^{2} [/tex]

[tex] {x}^{2} = 2 \times {14}^{2} [/tex]

Take positive square root to obtain;

[tex]x = \sqrt{ {14}^{2} \times 2} [/tex]

This simplifies to

[tex]x = 14 \sqrt{2} [/tex]

The length of the hypotenuse of the 45-45-90 triangle is 19.796 cm.

In a 45-45-90 triangle, the two legs are congruent (they have the same length) and the length of the hypotenuse is equal to the length of the legs multiplied by the square root of 2.

Given that each leg of the triangle measures 14 cm, the length of the hypotenuse can be calculated as follows:

Length of hypotenuse = Length of leg × √2

Length of hypotenuse = 14 cm × √2

Using a calculator or approximating the square root of 2 to 1.414, we can find:

Length of hypotenuse ≈ 14 cm × 1.414

Length of hypotenuse ≈ 19.796 cm (rounded to three decimal places)

Therefore, the length of the hypotenuse of the 45-45-90 triangle is approximately 19.796 cm.

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Answer:

a. [tex]-3x^{5}y^{6}[/tex]

Step-by-step explanation:

We want to multiply and simplify:

[tex]-3x^2y^2\times y^4x^3[/tex]

We rearrange the product to obtain:

[tex]-3x^2\times x^3\times y^2\times y^4[/tex]

Recall that:

[tex]a^m\times a^n=a^{m+n}[/tex]

We apply this property to obtain:

[tex]-3x^{2+3}y^{2+4}[/tex]

We simplify to obtain:

[tex]-3x^{5}y^{6}[/tex]

Answer:

The correct answer option is D. 0.42.

Step-by-step explanation:

We are given the results of a survey in which people were asked if they prefer reading books or e-books.

We are to find the marginal frequency of the number of people who prefer to read books.

For that, we will divide the total number of people who prefer reading books by the total number of people surveyed.

Marginal frequency = 105/250 = 0.42