Alex is 1.3 meters tall. His brother, Raul, is 0.6 times as tall as Alex. How tall is Raul?

The concentration of Na+ ion in the low sodium vegetable juice is 0.40 mg/mL.

To find the concentration of Na+ ion, we need to convert the amount of Na+ ion per serving into mg/mL. First, we need to convert 10 oz into mL by multiplying it with 29.57 mL/oz, which gives us 295.7 mL.
Then, we can divide the amount of Na+ ion (12 mg) by the volume of the serving (295.7 mL) to get the concentration in mg/mL.
12 mg / 295.7 mL = 0.0406 mg/mL
Rounding this to two significant figures, the concentration of Na+ ion in the low sodium vegetable juice is 0.40 mg/mL.

The concentration of Na+ ion in the low sodium vegetable juice is 0.40 mg/mL. This can be determined by first converting the serving size from ounces to milliliters. Since 1 oz is equivalent to 29.57 mL, we can multiply the serving size of 10 oz by 29.57 mL/oz to obtain 295.7 mL.
Next, we need to calculate the amount of Na+ ion per mL by dividing the amount of Na+ ion (12 mg) by the volume of the serving (295.7 mL).
12 mg / 295.7 mL = 0.0406 mg/mL
Therefore, the concentration of Na+ ion in the low sodium vegetable juice is 0.40 mg/mL. This concentration can be useful for individuals who are monitoring their sodium intake or have medical conditions that require them to limit their sodium consumption.

To know more about concentration of Na+ ion visit :-

https://brainly.com/question/29621387

#SPJ11

\(\longrightarrow{\green{ \: - 3 \: (b - ac)}}\) 

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\( \: - 7b - 9ac + 4b + 12ac\)

➼\( \: - 7b + 4b - 9ac + 12ac\)

➼\( \: - 3b + 3ac\)

➼\( \: - 3 \: (b - ac)\)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}\)

Answer:

3x + 2y = 12

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x + 2y = 6 ( subtract 3x from both sides )

2y = - 3x + 6 ( divide terms by 2 )

y = - \(\frac{3}{2}\) x + 3 ← in slope- intercept form

with slope m = - \(\frac{3}{2}\)

Parallel lines have equal slopes , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

To find c substitute (6, - 3 ) into the partial equation

- 3 = - 9 + c ⇒ c = - 3 + 9 = 6

y = - \(\frac{3}{2}\) x + 6 ← in slope- intercept form

Multiply through by 2

2y = - 3x + 12 ( add 3x to both sides )

3x + 2y = 12 ← in standard form

Step-by-step explanation:Step-by-step explanation:

For Sienna to be able to take the square root of both sides while solving a quadratic equation, she must have an expression with square on at least, the side that contains the variable she is trying to determine. Equation of the form:

(x + a) ² = b

'a' and 'b' could be any number, -1, 0, 1/3, -5/6, anything really.

So, she can take square roots of both sides then, like this

√(x + a)² = √b

x + a = ±√b

x = -a ± √b

Square roots always cancel out squares, and the '±' is because a square is satisfies by both + and -, 3² = 9, and (-3)² = 9.

It is the nature of the problem being solved that determines if we take just one or both of these answers.

Answer:

3 < X < 3√11

-3√11 < X < -3

Step-by-step explanation:

The solution consists out of two intervals, so it is unclear what you want calculated with max - min...

Confidence Interval = 0.1703 ± 0.0222 Confidence Interval ≈ (0.1481, 0.1925)  We are 95% confident that the true proportion of student loan borrowers with loans totaling more than $40,000 for their undergraduate education falls between approximately 0.1481 and 0.1925.

To construct a confidence interval to estimate the population proportion, we can use the following formula:

Confidence Interval = Sample Proportion ± Margin of Error

First, let's calculate the sample proportion:

Sample Proportion = Number of borrowers with loans > $40,000 / Total number of borrowers

Sample Proportion = 218 / 1280 ≈ 0.1703

Next, we need to determine the margin of error. For a 95% confidence level, we can use the formula:

Margin of Error = Z * sqrt((Sample Proportion * (1 - Sample Proportion)) / n)

Where Z is the z-value corresponding to the desired confidence level (in this case, 95%), and n is the sample size.

For a 95% confidence level, the critical z-value is approximately 1.96.

Margin of Error = 1.96 * sqrt((0.1703 * (1 - 0.1703)) / 1280)

Margin of Error ≈ 0.0222

Now, we can construct the confidence interval:

Confidence Interval = 0.1703 ± 0.0222

Confidence Interval ≈ (0.1481, 0.1925)

We are 95% confident that the true proportion of student loan borrowers with loans totaling more than $40,000 for their undergraduate education falls between approximately 0.1481 and 0.1925.

To  learn more about interval click here:

brainly.com/question/31551694

#SPJ11

Answer:

Step-by-step explanation:

Rewrite the equation in the form y=mx+b, where m is the slope.

2x+3y = 12

3y = -2x+12

y= -(2/3)x+4

A perpendicular line witll have a slope that is the negative inverse of the reference line.  The negative inverse of -(2/3) is (3/2),

The perpendicular line will have the form y = (3/2)x + b

Find b by using the given point, (2,6)

y = (3/2)x + b

6 = (3/2)*2 + b

6 = 3 + b

b = 3

The equation of the line that is perpendicular to the line 2x+3y=12 and that's also passes through the point (2,6)​ is y = (3/2)x + 3.

Answer:

C-110-160 miles

Step-by-step explanation:

A=260

B=-120

C=370

D=170

a) To estimate the equation log(salary) = β0 + β1LSAT + β2GPA + β3log(libvol) + β4log(cost) + β4rank + u, we can use the data in LAWSCH85.

To test the null hypothesis that the rank of law schools has no ceteris paribus effect on median starting salary, we can perform a t-test on the coefficient β4rank.

b) To determine if the features of the incoming class of students, LSAT and GPA, are individually or jointly significant for explaining salary, we can perform t-tests on the coefficients β1LSAT and β2GPA. Additionally, we should account for missing data on LSAT and GPA.

c) To test whether the size of the entering class (clsize) or the size of the faculty (faculty) needs to be added to the equation, we can perform a single test. We should account for missing data on clsize and faculty.

d) Factors that might influence the rank of the law school but are not included in the salary regression could include factors like faculty qualifications, student-faculty ratio, curriculum quality, job placement rates, alumni networks, reputation among legal professionals, and research output.

Learn more about hypothesis here: brainly.com/question/32298676

#SPJ11

Pepe Rodriquez works 42.5 hours at $6.20 per hour. The first 40 hours would be paid at the standard rate of $6.20 per hour, equaling $248.

The correct answer is B. $263.50, which is calculated by taking the standard pay of 40 hours at $6.20 per hour ($248) and adding the time-and-a-half pay of 2.5 hours at $9.30 per hour ($23.25).

Pepe Rodriquez works 42.5 hours at $6.20 per hour. The first 40 hours would be paid at the standard rate of $6.20 per hour, equaling $248. The remaining 2.5 hours would be paid at time-and-a-half, which is 1.5 times the hourly rate of $6.20, equaling $9.30 per hour. The total pay for the 2.5 hours is therefore $9.30 x 2.5 hours = $23.25. Adding the standard pay of $248 to the time-and-a-half pay of $23.25 yields a total of $263.50. Therefore, the correct answer is B. $263.50.

Learn more about rate here

https://brainly.com/question/13481529

#SPJ4

The probability that none of the 4 light bulbs work is 2.56%.

As per the given information, the probability that an individual light bulb works is 0.6.

Therefore, the probability that it does not work (i.e., fails) is:

1 - 0.6 = 0.4

Since each light bulb works independently of the other light bulbs, the probability that none of the 4 light bulbs work is the product of the individual probabilities that each light bulb fails.

Calculated as,

P(none work) = P(first fails) × P(second fails) × P(third fails) × P(fourth fails)

P(none work) = 0.4 × 0.4 × 0.4 × 0.4

P(none work) = 0.0256

Therefore, the probability that none of the 4 light bulbs work is 0.0256 or approximately 2.56%.

For similar questions on limit,

brainly.com/question/282767

#SPJ4

The ordered pair that is a solution to the inequality:

y > (1/4)*x + 5

is (4, 7)

Here we have the inequality:

y > (1/4)*x + 5

To check if an ordered pair is a solution, we just need to replace the values of the ordered pair on the inequality and see if it is true.

For example, for (12, 8)

We will get:

8 > (1/4)*12 + 5

8 > 3 + 5

8 > 8

This is false, so (12, 8) is not a solution.

The pair that is a solution is:

(4, 7)

7 > (1/4)*4 + 5

7 > 1  + 5

7 > 6

This is true.

Learn more about inequalities:

https://brainly.com/question/24372553

#SPJ1

The values of p for which the series ∑(n=1)^(∞) ((-1)^n / (n^p)) converges conditionally are p > 0.

To determine the values of p for which the series ∑(n=1)^(∞) ((-1)^n / (n^p)) converges conditionally, we can apply the alternating series test.

According to the alternating series test, a series of the form ∑((-1)^n * b_n) converges conditionally if:

1. The terms b_n are positive and decreasing (|b_n+1| ≤ |b_n|), and

2. The limit of b_n as n approaches infinity is 0 (lim(n→∞) b_n = 0).

In this case, our terms are b_n = 1 / (n^p). Let's check these conditions:

1. The terms are positive and decreasing:

  To satisfy this condition, we need to show that |(1 / ((n+1)^p))| ≤ |(1 / (n^p))| for all n.

  Taking the ratio of consecutive terms:

  |(1 / ((n+1)^p)) / (1 / (n^p))| = (n^p) / ((n+1)^p) = (n / (n+1))^p.

Since (n / (n+1)) is less than 1 for all n, raising it to the power p will still be less than 1 for p > 0. Therefore, the terms are positive and decreasing.

2. The limit of the terms as n approaches infinity is 0:

  lim(n→∞) (1 / (n^p)) = 0 for p > 0.

Based on the conditions of the alternating series test, the series converges conditionally for p > 0.

Therefore, the values of p for which the series ∑(n=1)^(∞) ((-1)^n / (n^p)) converges conditionally are p > 0.

To know more about conditionally convergent refer here:

https://brainly.com/question/31064900#

#SPJ11

The amount of money that I will have at the end of 20 years would be =$4,480. That is option D

Compound interest is defined as the interest that is being earned on an account which is based on the rate and the time the investment was made.

The total amount invested (p)= $2,000

The rate of investment (r) = 5%

The time of investment(t)= 12 year

The compound interest warm from that account;

= P×T×R/100.

= 2,000×12×5/100

= 120000/100

= $1200

For the next 8 years with the rate of 8% ;

= 2,000×8×8/100

= 128000/100

= $1280

The total compound interest = $1200+$1280= $2,480

Therefore, the amount of money that I will have at the end of 10 years would be = 2000+2480 = $4,480

Learn more about simple interest here:

https://brainly.com/question/25793394

#SPJ1

The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force

To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.

A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:

∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.

Calculating the components of F = r^2k(r^):

Fx = 0, since there is no force component in the x-direction.

Fy = 0, since there is no force component in the y-direction.

Fz = r^2kr^.

Taking the partial derivatives, we have:

∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.

∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.

Substituting these values into the curl equation, we get:

∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).

Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.

Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).

For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.

Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.

Learn more about force from this link:

https://brainly.com/question/12785175

#SPJ11

Answer:

233.5

Step-by-step explanation:

1) Find the area of the rectangle

2) Find the area of the triangle

3) Find the area of the semicircle

4) Add the results together

5) Round the nearest tenth

Have a lovely day :)

Answer:

4.2

Step-by-step explanation:

84 divided by 20  4.2

Answer:

-17

Step-by-step explanation:

-21-c

Let c = -4

-21 - -4

Subtracting a negative is like adding

-21 +4

-17

Answer:

-17

Step-by-step explanation:

- 21 - c

Put c as -4.

- 21 - (-4)

The negative signs cancel.

- 21 + 4

Add both the terms.

= -17

Verify with next one

Verified

formula

\(\\ \tt\hookrightarrow a_n=ar^{n-1}\)

\(\\ \tt\hookrightarrow a_n=32(3/2)^{n-1}\)

Answer:

\(a_n=32 \cdot \left(\dfrac32 \right)^{n-1}\)

Step-by-step explanation:

The difference between each term in the sequence is not the same, therefore the sequence is a geometric sequence.

Geometric sequence formula:  \(a_n=a r^{n-1}\)

where \(a\) is the start term and \(r\) is the common ratio

Given \(a = 32\)

To calculate \(r\), divide one term by its previous term:

\(\implies r=\dfrac{a_4}{a_3}=\dfrac{108}{72}=\dfrac32\)

Therefore, \(a_n=32 \cdot \left(\dfrac32 \right)^{n-1}\)

Answer:

Lines f and g are parallel.

Angle 2 is congruent to angle 6.

Angle 2 and angle 5 are supplementary

Step-by-step explanation:

Answer:

explain pls

Step-by-step explanation:

The right triangle possible values of 'x', substitute them back into x = b² to obtain the corresponding values of 'b'. Then use the equation a = 80 / b to the values of 'a'.

Let's assume the lengths of the two legs of the right triangle are 'a' and 'b'. According to the Pythagorean theorem, the relationship between the sides of a right triangle is given by:

a² + b² = c²

where 'c' represents the length of the hypotenuse.

In this case, we're given that the hypotenuse (c) is 2√41, so we can substitute this value into the equation:

a² + b² = (2√41)²

a² + b² = 4 ×41

a² + b² = 164

Now, given that the area of the right triangle is 40 square inches, and the area of a triangle can be calculated using the formula:

Area = (1/2) × base ×height

Since right triangle is a right angle triangle,  the legs (a and b) as the base and height. Therefore:

(1/2) × a ×b = 40

a ×b = 80

a system of equations:

a² + b² = 164

a ×b = 80

solve this system to find the values of 'a' and 'b'. There are different methods to solve systems of equations, but in this case, let's use substitution.

From the equation a × b = 80, one of the variables, for example, 'a':

a = 80 / b

Substituting this into the first equation:

(80 / b)² + b² = 164

6400 / b² + b² = 164

Multiply through by b²:

6400 + b⁴ = 164b²

the equation to obtain a quadratic equation:

b⁴ - 164b² + 6400 = 0

solve this quadratic equation for 'b'. a variable substitution:

Let x = b²

The equation becomes:

x² - 164x + 6400 = 0

Solve this quadratic equation for 'x' using factoring, completing the square, or the quadratic formula. Once you find the possible values of 'x', substitute them back into x = b² to obtain the corresponding values of 'b'. Then use the equation a = 80 / b to find the values of 'a'.

To know more about right triangle here

https://brainly.com/question/30966657

#SPJ4

The zeros for this quadratic equation is [-1, 0].

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Next, we would solve the quadratic function by using the factorization method as follows;

y = x² + 2x + 1

x² + 2x + 1 = 0

x² + x + x + 1 = 0

x(x + 1) + 1(x + 1) = 0

(x + 1)(x + 1) = 0

x = -1.

Read more on quadratic functions here: brainly.com/question/29499209

#SPJ1

Answer:

108.5 liters

Step-by-step explanation:

you multiply 3.5 by the days there are in January

The pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²

A pentagonal prism is a prism that has two pentagonal bases like top and bottom and five rectangular sides.

Given that, the volume of a pentagonal prism is 360 in³, with a height of 3 inches,

We need to find the area of the base,

We know that, the volume of a pentagonal prism is =

V = 1/4 √(5(5+2√5)·a²h

Where a is the base edge and h is the height,

360 = 1/4·3 √(5(5+2√5)·a²

1/4·√(5(5+2√5)·a² = 120

Since, the base of a pentagonal prism is a pentagon, and the area of a pentagon = 1/4 √(5(5+2√5)·a²

And we have,

1/4 √(5(5+2√5)·a² = 120

Therefore, the base area is 120 in²

Hence, the pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²

Learn more about pentagonal prism, click;

https://brainly.com/question/26709266

#SPJ1

Answer:

C

Step-by-step explanation:

Since GJ bisects ∠ FGH , then ∠ FGJ = ∠ JGH = x + 14

∠ FGH = ∠ FGJ + ∠ JGH , substitute values

4x + 16 = x + 14 + x + 14 = 2x + 28 ( subtract 2x from both sides )

2x + 16 = 28 ( subtract 16 from both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Thus

∠ FGJ = x + 14 = 6 + 14 = 20° → C

The two figures shown are made of unit squares. The positive difference of the perimeters, in units, is 8.

Perimeter is the total distance around the boundary of the shape. Since each square has a side length of 1 unit, the perimeter is equal to the number of sides.

1. Figure A: Counting the number of unit squares on the boundary of the shape, the perimeter of the first shape is:   8+4+4+4+4=24 units.

2. Figure B:Counting the number of unit squares on the boundary of the shape, the perimeter of the second shape is: 10+2+10+2=24 units.

The positive difference of the perimeters in units = |24 - 24| = 0 units. Therefore, the positive difference of the perimeters, in units is 0.

Know more about perimeters here:

https://brainly.com/question/397857

#SPJ11

Answer:

7. 2:3<__4:1

8. 1:2<__3:6

9. 3:5>__2:4

10. 6:7>__4:8

Step-by-step explanation:

Answer:

z=-9

x=-35

y=1/3

z=27/2

plz mark as brainliest :)

To determine the distance between the buildings, we can use trigonometry and the given information. Let's consider the triangle formed by Sari, building A, and building B. The side opposite the 40° angle is the distance between the buildings that we want to find.

Using the tangent function, we can set up the following equation: tan(40°) = opposite/adjacent. tan(40°) = distance between the buildings/20 meters. To find the distance between the buildings, we rearrange the equation: distance between the buildings = 20 meters * tan(40°). Using a calculator, we can evaluate the expression: distance between the buildings ≈ 20 meters * 0.8391 ≈ 16.782 meters. Therefore, the buildings are approximately 16.782 meters apart. To determine the distance between the buildings, we can use trigonometry and the given information. Let's consider the triangle formed by Sari, building A, and building B. The side opposite the 40° angle is the distance between the buildings that we want to find.

learn more about trigonometry here:

https://brainly.com/question/27246360

#SPJ11

The volume of the rectangular building is 2,731,050 feet³ depending on the given height, base and width.

The volume of the building will be calculated by the formula -

Volume = length × breadth × height

Thus, keeping the value of each component of building in the formula to find the volume of the building.

Volume of building = 255 × 255 × 42

Performing multiplication on Right Hand Side of the equation to find the value of volume

Volume of building = 2,731,050 feet³

Therefore, the volume of the building is 2,731,050 feet³.

Learn more about volume -

https://brainly.com/question/463363

#SPJ4