Mathematics: What is the square root of 70.891

What is the square root of 70.891, №13597847, 22.04.2021 15:48

Mathematics

So, i have a bunch of math questions and if someone can answer some or all of them that would be great. question 1: a sandwich box is shown with a right triangle side. the right triangle has hypotenuse 12 cm and base 5 cm. what is the approximate minimum height of a shelf in which this box can fit in the position shown in the picture? a) 4.1 centimeters b) 7.0 centimeters c) 8.5 centimeters d) 10.9 centimeters question 2: which of the following shows the length of the third side, in inches, of the triangle? one side of the triangle is labeled as

Step-by-step answer

P Answered by PhD

6

ANSWER TO QUESTION 1.

We use the Pythagoras Theorem to determine the height of the shelf.

Let

be the height of the triangle,

the base and

the hypotenuse.

Then by the Pythagoras Theorem,

h^2+b^2=c^2

We substitute the base, b=5

and the hypotenuse c=12

$h=\sqrt{119}$

h=10.90cm

.

Therefore the approximate minimum height of the shelf should be h=10.90cm

.

the correct answer is A

ANSWER TO QUESTION 2

We apply the Pythagoras Theorem to find the length of the third side.

See diagram

Let the length of the third side be

.

Then

We can now solve for y.

y^2+576=5476

$y=\sqrt{4900}$

y=70

The correct answer is C

ANSWER TO QUESTION 3

We use the Pythagoras Theorem to find the length of PR.

Since PR is the hypotenuse .

|PR|^2=|PQ|^2+|RQ|^2

$|PR|=\sqrt{3600}$

|PR|=60cm

The correct answer is C

See diagram in attachment.

ANSWER TO QUESTION 4

The unknown length is the variable

, which is the hypotenuse of the right angle triangle.

So we use the Pythagoras theorem to find the unknown length.

x^2=24^2+7^2

$\Rightarrow x^2=576+49$

$\Rightarrow x^2=625$

$\Rightarrow x=\sqrt{625}$

$\Rightarrow x=25$

The correct answer is C

ANSWER TO QUESTION 5.

From Pythagoras Theorem, the area of the bigger square is equal to the area of the two smaller squares added together.

See diagram in attachment.

That is x^2=6^2+8^2

.

This implies that,

x^2=36+64

$x=\sqrt{100}$

x=10cm

The correct answer is D

ANSWER TO QUESTION 6

Let

be the length of the unknown leg.

Then from the Pythagoras Theorem,

a^2+144^2=145^2

This implies that;

a^2=145^2-144^2

$a=\sqrt{289}$

a=17 units

The correct answer is option A.

It is incorrect because the length of the unknown side is $\sqrt{289}$ and not 289

.

ANSWER TO QUESTION 7

The diagonal is the hypotenuse of the right angle triangle created by the diagonal, the width and the length of the rectangle.

Since the diagonal is the hypotenuse and the two shorter sides are the width and the length of the rectangle, we can apply the Pythagoras Theorem to find the value of

.

$x=\sqrt{256}$

x=16

The correct answer is B.

ANSWER TO QUESTION 8

Since the width of the cups is 2 inches, it means the radius is half the width.

That is r=1

inch

The volume of a cylinder is given by;

$V=\pi r^2 h$

The cup with the cylindrical shape (B) will hold

$=1^2\times 7 \pi$

$=7 \pi$ cubic inches of juice

The volume of a cone is:

$V=\frac{1}{3} \pi r^2 h$

The cup with the conical shape cup(A), will hold

$V=\frac{1}{3}\times 1^2 \times 3 \pi$

$V=\pi$ cubic inches of juice

Hence cup B will hold $7\pi -\pi=6\pi=18.8$ cubic inches than cup A.

The correct answer is A
So, i have a bunch of math questions and if someone can answer some or all of them that would be gre

So, i have a bunch of math questions and if someone can answer some or all of them that would be gre

Mathematics

So, i have a bunch of math questions and if someone can answer some or all of them that would be great. question 1: a sandwich box is shown with a right triangle side. the right triangle has hypotenuse 12 cm and base 5 cm. what is the approximate minimum height of a shelf in which this box can fit in the position shown in the picture? a) 4.1 centimeters b) 7.0 centimeters c) 8.5 centimeters d) 10.9 centimeters question 2: which of the following shows the length of the third side, in inches, of the triangle? one side of the triangle is labeled as

Step-by-step answer

P Answered by PhD

6

ANSWER TO QUESTION 1.

We use the Pythagoras Theorem to determine the height of the shelf.

Let

be the height of the triangle,

the base and

the hypotenuse.

Then by the Pythagoras Theorem,

h^2+b^2=c^2

We substitute the base, b=5

and the hypotenuse c=12

$h=\sqrt{119}$

h=10.90cm

.

Therefore the approximate minimum height of the shelf should be h=10.90cm

.

the correct answer is A

ANSWER TO QUESTION 2

We apply the Pythagoras Theorem to find the length of the third side.

See diagram

Let the length of the third side be

.

Then

We can now solve for y.

y^2+576=5476

$y=\sqrt{4900}$

y=70

The correct answer is C

ANSWER TO QUESTION 3

We use the Pythagoras Theorem to find the length of PR.

Since PR is the hypotenuse .

|PR|^2=|PQ|^2+|RQ|^2

$|PR|=\sqrt{3600}$

|PR|=60cm

The correct answer is C

See diagram in attachment.

ANSWER TO QUESTION 4

The unknown length is the variable

, which is the hypotenuse of the right angle triangle.

So we use the Pythagoras theorem to find the unknown length.

x^2=24^2+7^2

$\Rightarrow x^2=576+49$

$\Rightarrow x^2=625$

$\Rightarrow x=\sqrt{625}$

$\Rightarrow x=25$

The correct answer is C

ANSWER TO QUESTION 5.

From Pythagoras Theorem, the area of the bigger square is equal to the area of the two smaller squares added together.

See diagram in attachment.

That is x^2=6^2+8^2

.

This implies that,

x^2=36+64

$x=\sqrt{100}$

x=10cm

The correct answer is D

ANSWER TO QUESTION 6

Let

be the length of the unknown leg.

Then from the Pythagoras Theorem,

a^2+144^2=145^2

This implies that;

a^2=145^2-144^2

$a=\sqrt{289}$

a=17 units

The correct answer is option A.

It is incorrect because the length of the unknown side is $\sqrt{289}$ and not 289

.

ANSWER TO QUESTION 7

The diagonal is the hypotenuse of the right angle triangle created by the diagonal, the width and the length of the rectangle.

Since the diagonal is the hypotenuse and the two shorter sides are the width and the length of the rectangle, we can apply the Pythagoras Theorem to find the value of

.

$x=\sqrt{256}$

x=16

The correct answer is B.

ANSWER TO QUESTION 8

Since the width of the cups is 2 inches, it means the radius is half the width.

That is r=1

inch

The volume of a cylinder is given by;

$V=\pi r^2 h$

The cup with the cylindrical shape (B) will hold

$=1^2\times 7 \pi$

$=7 \pi$ cubic inches of juice

The volume of a cone is:

$V=\frac{1}{3} \pi r^2 h$

The cup with the conical shape cup(A), will hold

$V=\frac{1}{3}\times 1^2 \times 3 \pi$

$V=\pi$ cubic inches of juice

Hence cup B will hold $7\pi -\pi=6\pi=18.8$ cubic inches than cup A.

The correct answer is A
So, i have a bunch of math questions and if someone can answer some or all of them that would be gre

Mathematics

The principal randomly selected six students to take an aptitude test. their scores were: 87.4 86.9 89.9 78.3 75.1 70.6 determine a 90% confidence interval for the mean score for all students. assume the population is normally distributed. give the lower limit of the interval as your answer below. round to two decimal places. (hint from class: note that you will need to calculate the sample mean (xbar) and sample standard deviation (s) for this sample data in order to find the confidence interval endpoints. in class i referred to the formula for

Step-by-step answer

P Answered by Master

79.5688 < µ < 83.1646

Step-by-step explanation:

Sample mean is the sum of all scores, divided the the total number of test takers. In this case, the sample mean is:

(87.4 + 86.9 + 89.9 + 78.3 + 75.1 + 70.6)/6 = 488.2/2 = 81.3667

The sample standard deviation is the square root of the sample variance. See attached photo 1 for calculation of these values...

The sample standard deviation is 3.1856

We need to make a 90% confidence interval for this data. Since n < 30, we will use a t-value. The degrees of freedom is always one less than the sample size so on the t-distribution chart, look under the column for Area under the curve = 0.10, and the row for 5. The t-value you should see is t = 2.015

See attached photo 2 for the construction of the confidence interval

The principal randomly selected six students to take an aptitude test. their scores were: 87.4 86.9

Mathematics

The principal randomly selected six students to take an aptitude test. their scores were: 87.4 86.9 89.9 78.3 75.1 70.6 determine a 90% confidence interval for the mean score for all students. assume the population is normally distributed. give the lower limit of the interval as your answer below. round to two decimal places. (hint from class: note that you will need to calculate the sample mean (xbar) and sample standard deviation (s) for this sample data in order to find the confidence interval endpoints. in class i referred to the formula for

Step-by-step answer

P Answered by Master

79.5688 < µ < 83.1646

Step-by-step explanation:

Sample mean is the sum of all scores, divided the the total number of test takers. In this case, the sample mean is:

(87.4 + 86.9 + 89.9 + 78.3 + 75.1 + 70.6)/6 = 488.2/2 = 81.3667

The sample standard deviation is the square root of the sample variance. See attached photo 1 for calculation of these values...

The sample standard deviation is 3.1856

We need to make a 90% confidence interval for this data. Since n < 30, we will use a t-value. The degrees of freedom is always one less than the sample size so on the t-distribution chart, look under the column for Area under the curve = 0.10, and the row for 5. The t-value you should see is t = 2.015

See attached photo 2 for the construction of the confidence interval

Mathematics

12. determine the shortest distance from the point d(5, 4) to the line represented by 3x + 5y - 4 = 0. i got my distance as the square root of 26890600/12027024 but i’m fairly certain that’s incorrect.

Step-by-step answer

P Answered by PhD

3

$\large\boxed{d=\dfrac{31\sqrt{34}}{34}\approx5.32}$

Step-by-step explanation:

The formula of a distance between a point (x₀, y₀) and a line Ax + By + C = 0:

$d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}$

We have the point D(5, 4) and the line 3x + 5y - 4 = 0.

Substitute:

$x_0=5,\ y_0=4,\ A=3,\ B=5,\ C=-4$

$d=\dfrac{|(3)(5)+(5)(4)-4|}{\sqrt{3^2+5^2}}=\dfrac{|15+20-4|}{\sqrt{9+25}}=\dfrac{|31|}{\sqrt{34}}\cdot\dfrac{\sqrt{34}}{\sqrt{34}}=\dfrac{31\sqrt{34}}{34}$

Mathematics

12. determine the shortest distance from the point d(5, 4) to the line represented by 3x + 5y - 4 = 0. i got my distance as the square root of 26890600/12027024 but i’m fairly certain that’s incorrect.

Step-by-step answer

P Answered by PhD

3

$\large\boxed{d=\dfrac{31\sqrt{34}}{34}\approx5.32}$

Step-by-step explanation:

The formula of a distance between a point (x₀, y₀) and a line Ax + By + C = 0:

$d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}$

We have the point D(5, 4) and the line 3x + 5y - 4 = 0.

Substitute:

$x_0=5,\ y_0=4,\ A=3,\ B=5,\ C=-4$

$d=\dfrac{|(3)(5)+(5)(4)-4|}{\sqrt{3^2+5^2}}=\dfrac{|15+20-4|}{\sqrt{9+25}}=\dfrac{|31|}{\sqrt{34}}\cdot\dfrac{\sqrt{34}}{\sqrt{34}}=\dfrac{31\sqrt{34}}{34}$

Mathematics

Suppose you regress the natural log of total family expenditures on household size using observations of households from the 2013 Consumer Expenditure Survey: . reg Intotexppq fam_size Source SS df MS Number of obs = 6,766 Model F(1, 6764) = 634.72 Residual Prob F = 0.0000 R-squared = 0.0858 Adj R-squared = 0.0857 Total | 5540.26944 6,765 818960744 Root MSE = .86534 Intotexppp | Coef. Std. Err. t P I t I |[95% Conf. Interval] fam_size | .1767089 .007014 25.19 0.000 cons | .0203324 404.71 0.000 From the information given, you should be able to answer

Step-by-step answer

P Answered by Specialist

Step-by-step explanation:

Please check below in the attached, you will see answer to given questions, thank you, I hope it helps.