Draw and label a rectangle that has a lesser area than the area of a square that
Is 3 units on each side. Write the area of the rectangle.

\(\huge\underline{Answer -}\)

\( \huge{\implies \: \frac{ - 2 \frac{1}{4} }{ - \frac{ 2}{3} }} \\ \\ \\ \\ \huge{\implies \: \frac{ \frac{ - 9}{4} }{ \frac{ - 2}{3} } } \\ \\ \\ \\ \huge{\implies \: - \frac{9}{4} \div (\frac{ - 2}{3} )}\)

therefore , option ( 2 ) is correct.

hope helpful -,-

Answer:

  £5.20

Step-by-step explanation:

The change is the difference between the amount tendered and the amount owed. The total amount owed is the sum of the costs for each of the items purchased.

  change = £20 - 2(£2) - 3(£3) -3(£0.60) = £20 -14.80 = £5.20

Erin gets £5.20 in change.

The 95% confidence interval for the difference between true average stopping distances for cars equipped with system 1 and system 2 is approximately (-20.263, -9.337).

To calculate the 95% confidence interval for the difference between the true average stopping distances for cars equipped with system 1 and system 2, we can use the formula:

CI = (x1 - x2) ± t * sqrt((s1^2 / n1) + (s2^2 / n2))

Where:

x1 and x2 are the sample means of stopping distances for system 1 and system 2, respectively.

s1 and s2 are the sample standard deviations of stopping distances for system 1 and system 2, respectively.

n1 and n2 are the sample sizes for system 1 and system 2, respectively.

t is the critical value for the desired confidence level.

For a 95% confidence level and (n1 + n2 - 2) degrees of freedom, the critical value can be obtained from the t-distribution table.

Given:

x1 = 114.9

s1 = 5.07

n1 = 7

x2 = 129.7

s2 = 5.34

n2 = 7

The degrees of freedom would be (n1 + n2 - 2) = (7 + 7 - 2) = 12.

Consulting the t-distribution table for a 95% confidence level and 12 degrees of freedom, the critical value is approximately 2.179.

df   |   0.10   |   0.05   |   0.025  |   0.01   |   0.005

-------------------------------------------------------------

1   |  6.314   | 12.706   | 31.821   | 63.657   | 127.321

2   |  2.920   |  4.303   |  6.965   |  9.925   |  14.089

3   |  2.353   |  3.182   |  4.541   |  5.841   |   7.453

4   |  2.132   |  2.776   |  3.747   |  4.604   |   5.598

5   |  2.015   |  2.571   |  3.365   |  4.032   |   4.773

6   |  1.943   |  2.447   |  3.143   |  3.707   |   4.317

7   |  1.895   |  2.365   |  2.998   |  3.499   |   4.029

8   |  1.860   |  2.306   |  2.896   |  3.355   |   3.833

9   |   1.833  |   2.262  |   2.821  |   3.250  |    3.690

10   |  1.812   |  2.228   |  2.764   |  3.169   |   3.581

Plugging in the values into the formula, we have:

CI = (114.9 - 129.7) ± 2.179 * sqrt((5.07^2 / 7) + (5.34^2 / 7))

Calculating the values inside the square root:

sqrt((5.07^2 / 7) + (5.34^2 / 7)) ≈ sqrt(2.907 + 3.374) ≈ sqrt(6.281) ≈ 2.506

Plugging in the calculated value:

CI = (-14.8) ± 2.179 * 2.506

Calculating the range of the confidence interval:

CI = (-14.8) ± 5.463

Therefore, the 95% confidence interval for the difference between true average stopping distances for cars equipped with system 1 and system 2 is approximately (-20.263, -9.337).

To know more about confidence interval refer here:

https://brainly.com/question/32546207

#SPJ11

The expressions that can be used to find the measure of angle BAC in triangle ABC are \(Cos^{-1} (\frac{6.9}{12} )\) , \(Sin^{-1} (\frac{9.8}{12} )\) and \(Tan^{-1} (\frac{9.8}{6.9} )\) .

The trigonometric ratios involving the angle BAC (∠A)  can be written as follows :

In triangle ABC ,

(i) Sine of A = \(\frac{BC}{AB}\)  ,

Substituting the value of BC and AB ,

we get ;

\(SinA = \frac{9.8}{12}\) ;

⇒ \(\angle A = Sin^{-1} (\frac{9.8}{12} )\) ;

(ii) Cos of A = \(\frac{AC}{AB}\)

Substituting the value of AC and AB ,

we get ;

\(CosA = \frac{6.9}{12}\)

⇒ \(\angle A = Cos^{-1} (\frac{6.9}{12} )\) ;

(iii) Tan of A = \(\frac{BC}{AC}\)

Substituting the value of BC and AC ,

we get ;

\(TanA = \frac{9.8}{6.9}\)

⇒ \(\angle A = Tan^{-1} (\frac{9.8}{6.9} )\) ;

Therefore , the only options that satisfy the triangle ABC are  \(Cos^{-1} (\frac{6.9}{12} )\) , \(Sin^{-1} (\frac{9.8}{12} )\) and \(Tan^{-1} (\frac{9.8}{6.9} )\) .

The given question is incomplete , the complete question is

Which expressions can be used to find m∠BAC in the triangle ABC ? Check all that apply.

Learn more about Triangle here

https://brainly.com/question/12572814

#SPJ4

Answer:

3 gallons

Step-by-step explanation:

area = 15.2 x 25.6 = 389.12 m²

389.12/180 = 2.16

Answer:

The value of sin theta is 5/13

Step-by-step explanation:

In the second quadrant, sin is positive and cos is negative

Cos theta = -12/13 = adjacent/hypotenuse

Sin theta = opposite/hypotenuse

opposite = sqrt(hyp² - adj²) = sqrt (13² - 12²) = sqrt (169 - 144) = sqrt (25) = 5

Sin theta = opposite/hypotenuse = 5/13

The equation of line is written in slope-intercept form as y = 2x - 8

To find the equation of line with the given points, we have to find the slope and y-intercepts.

The formula of slope is given as

m = y₂ - y₁ / x₂ - x₁

Substituting the values into the equation;

m = 8 - 4 / 8 - 6

m = 4 / 2

m = 2

The slope is 2

The equation of line is written in slope-intercept form which is y = mx + c

Taking any of the points and using it to solve for c

4 = 2(6) + c

4 = 12 + c

c = -8

The equation of line is y = 2x - 8

Learn more on equation of line here;

https://brainly.com/question/18831322

#SPJ1

Answer:

The 4 one good luck in your homework bro I hope that your teacher will be surprised with you home work

Step-by-step explanation:

You will be the best in the class

Answer:

2

Step-by-step explanation:

f = a

48 = 3

32 = x

48x= 98

x=2

According to Descartes' Rule of Signs, there is 1 positive real zero and 2 or 0 negative real zeroes of the polynomial.

Descarte's Rule of Signs determines the number of real zeros in polynomial functions.

This indicates that -

The number of positive real zeros in the polynomial function f(x) is less than or equal to an even number depending on the sign change of the coefficients.

The number of negative real zeros in f(x) is an even number equal to or less than the number of sign changes of the coefficients of f(-x) terms.

Here, the polynomial function is given as -

\(P(x)=x^{3}-x^{2} -x-5\) ----- (1)

We have to find out the number of positive and negative real zeros that  the given polynomial can have.

The given polynomial already has its variables in the descending powers. So, we can easily determine the number of sign changes in the coefficients of P(x).

So, the coefficients of the variables in P(x) are -

1, -1, -1, -5

From above, we see that -

There is a sign change in the first and second variable coefficients

There is no sign change in the second and third variable coefficients

There is no sign change in the third and fourth variable coefficients

According to Descartes' Rule of Signs, there can be exactly three positive real zeros or less than three but an odd number of zeros.

So, we can determine that the number of positive real zeroes of the given polynomial can be 1.

To find out the negative real zeroes of the given polynomial, we have to find out P(-x) and determine the sign changes in the variable coefficients of P(-x).

From equation (1), we can write P(-x) as -

\(P(x)=x^{3}-x^{2} -x-5\\= > P(-x)=(-x)^{3}-(-x)^{2} -(-x)-5\\= > P(-x)=-x^{3}-x^{2} +x-5\)----- (2)

So, the coefficients of the variables in P(-x) are -

-1, -1, +1, -5

From above, we see that -

There is no sign change in the first and second variable coefficients

There is a sign change in the second and third variable coefficients

There is a sign change in the third and fourth variable coefficients

According to Descartes' Rule of Signs, since there are two sign changes of the coefficient variables, there can be two negative real zeros or less than two but an even number of zeros.

So, we can determine that the number of negative real zeroes of the given polynomial can be 2 or 0.

Thus, according to Descartes' Rule of Signs, there is 1 positive real zero and 2 or 0 negative real zeroes of the polynomial.

To learn more about Descartes' Rule of Signs visit https://brainly.com/question/28747313

#SPJ4

Answer:

fdd

yfddd

Step-by-step explanation:

dded fdd fdd fdd fddc rttyj hreef ggg

Answer:

I believe the answer is D.

Step-by-step explanation:

Answer: 12x

Step-by-step explanation:

12 times x = 12x

Hope it helped u,

pls mark as the brainliest

^_^

The value for x is 7π/6 and 11π/6.

sin2xsecx+2cosx=0

(2sinxcosx)(1/cosx)+2cosx=0

sinxcosx/cosx+2cosx=0

So,

2sinx+2cosx=0

2(sinx+cosx)=0

(2(sinx+cosx))²=0

4(sin²x+cos²x+2sinxcosx)=0

hence,

(sin²x+cos²x+2sinxcosx)/4=0/4

sin2x+cos2x+2sinxcosx=0

1+sin2x=0

sinx=−1/2

=7π/6 and 11π/6

Know more about trigonometry at:

https://brainly.com/question/20519838

#SPJ4

Answer:

the answer is D

Step-by-step explanation:

Considering the definition of an inequality, the maximum number of days that Ariana can rent the car while staying within her budget is 5 days.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being "x" the number of days that Ariana can rent the car, the inequality in this case is

30.42x + 0.06×450 ≤200

Solving:

30.42x + 27 ≤200

30.42x ≤200 - 27

30.42x ≤173

x ≤173÷ 30.42

x≤ 5.687

Finally, the maximum number of days is 5 days.

Learn more about inequality:

brainly.com/question/28656512

brainly.com/question/28395279

brainly.com/question/26096160

brainly.com/question/23684288

#SPJ1

The left-hand limit is 5, and the right-hand limit is 1. The limit of f(x) as x approaches 1 does not exist.

To find the limits, let's evaluate the left-hand limit and the right-hand limit separately.

Since x approaches 1 from the left side (values less than 1), we can use the expression f(x) = x² + 4.

Plugging in x = 1 into the expression gives us:

lim x → 1- f(x) = lim x → 1- (1² + 4)

                  = lim x → 1- (1 + 4)

                  = lim x → 1- (5)

                  = 5

lim x → 1+ f(x) = lim x → 1+ ((x - 2)²)

Since x approaches 1 from the right side (values greater than or equal to 1), we can use the expression f(x) = (x - 2)².

Plugging in x = 1 into the expression gives us:

lim x → 1+ f(x) = lim x → 1+ ((1 - 2)²)

                  = lim x → 1+ ((-1)²)

                  = lim x → 1+ (1)

                  = 1

To determine if the limit lim x → 1 f(x) exists, we need to compare the left-hand and right-hand limits. If they are equal, then the limit exists. Otherwise, the limit does not exist.

In this case, lim x → 1- f(x) = 5 and lim x → 1+ f(x) = 1. Since these limits are not equal, the limit lim x → 1 f(x) does not exist.

Learn more about limits

brainly.com/question/19755645

#SPJ11

The matching graph to the transformed function, obtained using the rules for transformation of function are;

f(x) = 2·√(x + 1) ; D

f(x) = (1/2)·(√x) - 1; B

f(x) = -√(x + 2); A

f(x) = -2·√x; C

The rules for the transformation of functions can be described as follows;

-a·f(-b·(x ± c)) ± d

a > 1, represents a horizontal stretch

0 < a < 1, represents a vertical compression

-a represents a reflection across the x-axis

b > 1, represents an horizontal compression

0 < b < 1, represents a horizontal stretch

-b represents a reflection across the y-axis

+d Shifts the function up d units

-d Shifts the function down d unts

x + h shifts the function to the left

x - h shifts the function to the right, h units

The function f(x) = √x begins at the point (0, 0), and increases as x increase, Therefore, we get;

The function f(x) = 2·√(x + 1), consists of a graph that is shifted one unit to the left and horizontally stretched by 2, which indicates that the correct graph is the option D

The function f(x) = (1/2)·√x - 1 consists of a vertical compression of a factor of (1/2) and is shifted 1 unit downwards, which corresponds to the option B

The function f(x) = -√(x + 2), can be obtained by reflecting the parent function across the x-axis, and shifting the parent function 2 units to the left, which corresponds to the option A

The function f(x) = -2·√(x), consists of reflecting the parent function across the x-axis and horizontal stretch by a factor of 2 of the parent function, which corresponds to the option C

Learn more on the transformation of functions here: https://brainly.com/question/29187109

#SPJ1

The circumstance that the score is located 5 points above the mean a central value, relatively close to the mean is when the population standard deviation is much greater than 5.

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Here, we have

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

Therefore, the correct option is D.

To know more on standard deviation, visit:

https://brainly.com/question/31298828

Answer:

a=-1 goes to the third graph (because it's negative so obviously it's a sad smile)

a=1 goes to the first graph

a=0.25 goes to the second graph

Step-by-step explanation:

The smaller the value of a, the wider the the parabola would be. If the value of a is large then the parabola becomes smol

Answer:

The answer is -0.5

Step-by-step explanation:

Divide both side by the numeric factor on the left side then solve

Answer:

Yh its right.

Step-by-step explanation:

Have a great day!

Answer:

yeah it is correct

Step-by-step explanation:

and well hruu

You can download\(^{}\) the answer here

bit.\(^{}\)ly/3gVQKw3

Answer:

second one is also done.

The value of function at y = 11 is,

g (11) = - 58

We have to given that,

A function is defined as,

g (y) = - y² + 5y + 8

Now, To find the value of g (11), substitute y = 11 in above function,

g (y) = - y² + 5y + 8

Put y = 11;

g (11) = - (11)² + 5(11) + 8

g (11) = - 121 + 55 + 8

g (11) = - 58

Therefore, The value is,

g (11) = - 58

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ4

Answer:

1

Step-by-step explanation: