problem 4: a wire carrying a 42.5 a current passes between the poles of a strong magnet so that it is perpendicular to the field and experiences a 2.17 n force on the 3.5 cm of wire in the field.

Using Hypothesis testing,

a) Two samples are independent.

b)H₀: an expectant mother's cigarette smoking has any not effect on the bone mineral content of her otherwise healthy child.

Hₐ : an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

c) Null hypothesis is accepted.

so, an expectant mother's cigarette smoking has no effect on the bone mineral.

We have given that,

A study which is conducted for check an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

For new-born whose mother's cigarette smoking

sample size , n₁= 77

X-bar, x₁-bar = 0.098 g/cm

standard deviations, s₁ = 0.026 g/cm

For new-born whose mother did not cigarette smoking

sample size , n₂ = 161

standard deviations, s₂ = 0.025 g/cm.

mean (X-bar) , x₂-bar = 0.095 g/cm

a) the two samples are independent since they are different types of mothers, smoking mothers and non smoking mothers

b)H₀: an expectant mother's cigarette smoking has any not effect on the bone mineral content of her otherwise healthy child.

Hₐ: an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

c) Test statistic:

t = (x₁-bar - x₂-bar )/S (√1/n₁+1/n₂)

where , S = √(s₁²(n₁ - 1) + s₂²(n₂ -1))/n₁+n₂ - 2

S = √((0.026)²(76) +(0.025 )²(160))/236

= 0.0253

then, t = (0.098 - 0.095 )/0.0253(√1/77 +1/161 )

=> t = 0.859

Using the critacal table critical t is

Critical t = ±1.970065

Degrees of freedom =236.0000

P-Value=0.3935 which is greater than α(0.05),

So , we accept H₀

Thus, an expectant mother's cigarette smoking has not effect on the bone mineral content of her otherwise healthy child.

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Answer: 52.5

Step-by-step explanation: We can divide 50 by 20 to find what the number is. In this problem, the number is 2.5. Since we know this, we can multiply 2.5 and 21 to get 52.5.

hope this helps!

please give brainliest!

Answer:

21st term = 52.5

Step-by-step explanation:

Given that,

→ 20th term of a sequence is 50.

The common difference is,

→ 50 ÷ 20

→ 50/20

→ 2.5

Now the 21st term will be,

→ n × 2.5

→ 21 × 2.5

→ 52.5

Hence, the answer is 52.5.

The average value of the function f(t) is [tex]4.433*10^{10}[/tex] .

Given,

[tex]f(t)=te^{3t^2}[/tex] over interval [1,3]

To find average value of the function use formula,

[tex]f(x)_{avg} =\frac{1}{b-a}\int\limits^a_b {f(x)} \, dx[/tex] over the interval {a,b}

[tex]f(x)_{avg} =\frac{1}{3-1}\int\limits^3_1 {te^{3t^2}} \, dt\\\\\\f(x)_{avg} =\frac{1}{2}\int\limits^3_1 {te^{3t^2}} \, dt\\[/tex]

let

[tex]u=3t^2\\\\du=6tdt \\\\tdt=\frac{du}{6}[/tex]

replacing u and du ,

[tex]f(x)_{avg} =\frac{1}{2*6}\int\limits^3_1 {e^{u}} \, du\\\\f(x)_{avg} =\frac{1}{12}\ e^u\|\limits^3_1\\ \\f(x)_{avg} =\frac{1}{12}\ e^{3x^2}\|\limits^3_1\\\\f(x)_{avg} =\frac{1}{12}\ [e^{3(3)^2}-e^{3(1)^2}]\\\\f(x)_{avg} =\frac{1}{12}\ [e^{27}-e^{3}]\\\\f(x)_{avg}=4.433*10^{10}[/tex]

Thus, the average value of the function f(t) is [tex]4.433*10^{10}[/tex] .

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The item that can be received at 45°F (7° C) is Milk , the correct option is (b) .

In the question ,

the receiving temperature of the items is given ,

we have to identify the item that can be received at  45°F (7° C) .

From the given options ,

we see that cold feed is received at 41°F (5° C) ,

Milk at 45°F (7° C) and Hot Food at 135°F (57° C) .

So , we can conclude that the option (b) Milk can be received at  45°F (7° C) .

Therefore , The item that can be received at 45°F (7° C) is Milk , the correct option is (b) .

The given question is incomplete , the complete question is

Temperature criteria for receiving items is given as follows ;

(a) Cold Food is received at 41°F (5° C) or lower ,

(b) Milk is received at  45°F (7° C) or lower ,

(c) Hot Food is received at 135°F (57° C) or lower .

Find the item that can be received at  45°F (7° C) ?

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The average time a customer spend on department store is 1.33 hours.

Average:

In math, mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set is referred as average.

Given,

If there are on average 80 customers at any particular time and 60 customers go through the checkouts every hour

Here we need to find the average time spend by a customer.

Let us consider x be the time spend by the customer on department store.

While we looking into the given question we know that,

Number of customer = 80

Check out per hour = 60.

So, the average time is 1.33 hours.

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The rule to describe the translation is (x , y) ---> ( x + 3 , y + 5 )

Translation is Changing scale , shifting or reflection of a parent figure.

Scale means Changing  size and shape of figure

Shifting means moving the figure to new location this could be upwards downwards , left and right

Reflection means making a mirror image or figure to different quadrant or along different axis.

According to the question,

A rectangle on a coordinate plane whose coordinates are (x, y) is translated 5 units up and 3 units to left

Shifting a plane upwards means changing the y coordinates so ,

y +5

shifting towards left means shifting to left side of x - axis

so , x + 3

Hence , the rule to describe this translation is

(x , y) ---> ( x + 3 , y + 5 )

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The stream velocity has no influence on the amount of dissolved load it contains. The amount of dissolved material depends on erosion and deposition carried out in the watercourse. These are affected by factors such as the slope of the land, the resistance of the material to erosion, the size of the sediments transported, etc.

Stream velocity plays an important role in the transport of sediments and dissolved loads in a watercourse. It affects the erosion and deposition processes that occur in the watercourse, which in turn affect the amount of sediment and dissolved load that is carried by the stream. For example, faster stream velocities can cause more erosion of the stream bed, leading to more material being carried in the water.

Sediment is any particulate matter that is transported by a fluid, and it can come in many different forms. The three main types of sediment are:

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The integers are  3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,

An integer is the number zero (0), a positive natural number (1, 2, 3, etc.) or a negative integer with a minus sign.

A rational number is any number that can be written as a fraction, where both the numerator or demoninator that is the top and the bottom number  are integers, and the denominator is cannot be zero

An irrational number is a type of real number which cannot be represented as a simple fraction.

A integer can always be a rational number but vice versa is not true.

Integer = 3√25 = 3x5 = 15

-185/5 = -37

rational = -1/4, 0.75, 3√25, -185/5, 4√8

irrational = √13,

Therefore, the integers are  3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,

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By using t test, it can be concluded that

The value of t at level of significance = 0.10 with 5 degree of freedom is greater than the value of t at level of significance = 0.10 with 10 degree of freedom

What is t test?

If the observations are from a normal population and the population standard deviation is not known, the distance between the sample mean and the population mean can be calculated by using t test

By using t- table

The value of t at level of significance = 0.10 with 5 degree of freedom = 2.015

The value of t at level of significance = 0.10 with 10 degree of freedom = 1.812

Since 2.015 > 1.812,

The value of t at level of significance = 0.10 with 5 degree of freedom is greater than the value of t at level of significance = 0.10 with 10 degree of freedom

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The rate of change of capital in terms of units of labor is -2.0 As more labor is used, available capital decreases As more capital is used, available labor decreases.

[tex]100x^{0.75} y^{0.25} = 135540[/tex]

x = 1500 units and y = 1000 units

A) [tex]\frac{d}{dx}(100x^{0.75}y^{0.25} = \frac{d}{dx}(135540)[/tex]

[tex]100[{\frac{d}{dx}(x^{0.75})y^{0.25} + x^{0.75}\frac{d}{dx}(y^{0.25})] = 0[/tex]

[tex]0.75 x^{-0.25} y^{0.25} + x^{0.75} (0.25y^{-0.75\frac{dy}{dx} }) = 0[/tex]   ______(1)

X & Y values in equation 1

[tex]0.75(1500^{-0.25}(1000)^{0.25}+(1500)^{0.75}(0.25)(1000)^{-0.75}\frac{dy}{dx} = 0[/tex]

(0.75) (0.16) (5.62) + (0.41) (0.25) (0.0056) [tex]\frac{dy}{dx}[/tex] = 0

0.6744 + 0.3374 [tex]\frac{dy}{dx}[/tex] = 0

0.3374 [tex]\frac{dy}{dx}[/tex] = -0.6744

[tex]\frac{dy}{dx}[/tex] = -1.9988

[tex]\frac{dy}{dx}[/tex] ≈ -2.0

B) If the labor x is increased then the capital invested in manufacturing process decreased

C) As more capital is used then the available labor is reduced

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The expression to show the total number of shows Jonah hill recorded after w weeks is 32 + 6w

Jonah hill has recorded 32 shows using his cable television service. Each week he record 6 new shows.

The expression to show the total number of shows Jonah hill recorded after w weeks is as follows:

Hence,

let

w = number of weeks

Therefore, the expression to represent the situation is as follows:

total number of shows = 32 + 6w

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This set of linear equations, y - x = 6, and y + x = - 10, has the following solution.

What are linear equation systems?

In mathematics, a system of linear equations is the collection of two or more linear equations that share the same variables. The maximum power of the variable in the linear equations in this situation is 1, making them first-order equations. A linear equation may have one, two, or three variables.

Knowing that;

Y - x = 6

Y + x = -10

Since both equations are equivalent to y, let's equalize them.

x + 6 = - x - 10

By additional computation;

x + x = - 10 - 6

2x = - 16

Subtract 2 from both sides;

x = -8

In either equation, x should be changed to the appropriate value;

y - x = 6

y - (-8) = 6

Hence, we do;

y + 8 = 6

y = 6 - 8

y = - 2

Therefore,the answer to this set of linear equations is y + x = -10 and y - x = 6. (-8, -2).

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Answer:

The double of 8 is 16. Answer is 16.

The interest that Elizabeth will get based on the information is $480.

From the information, Elizabeth deposited her 1/2 of the profit from selling her fathers house. the full profit was $12000. The profit deposited will be:

= 1/2 × $12000

= $6000

The simple Interest will be calculated thus:

= Principal × Rate × Time

= $6000 × 4% × 2

= $6000 × 0.04 × 2

= $480

The interest is $480.

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Two years ago, elizabeth deposited her 1/2 of the profit from selling her fathers house. the full profit was $12000. she was promised 4% simple interest. How much was the interest?

To simplify complex fractions with LCD multiply each term in the numerator and denominator by the LCD

Given,

LCD;- Least Common Denominator

When two or more fractions are supplied, the least common denominator is the smallest number among all the common multiples of the denominators.

We have to find the method of simplification of complex fractions with LCD;

Here,

Multiply each term in the numerator and denominator by the LCD to simplify this complicated fraction. It doesn't matter how complicated these fractions are; all you need to do is discover the LCD to convert the complicated fraction into a simpler one. The technique is done more frequently the more fractions there are in an issue

That is,

To simplify complex fractions with LCD multiply each term in the numerator and denominator by the LCD

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The three angle bisector of a triangle intersect at a single point that point of concurrency of the angle of bisectors is called the incenter.

Given:

the 3 angle bisectors of a triangle intersect.

when three angle bisector of a triangle intersect then that point of concurrency is called incenter.

Incenter:

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle. In other words, it can be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.

Incenter formula:

= (ax1+bx2+x3 / a+b+c  , ay1+by2+y3 / a+b+c).

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The alternative hypotheses that make a hypothesis test one-tailed are 1. Parameter is less than a value and 2. Parameter is greater than a value.

An explanation for a phenomena or a forecast of the results of an experiment are both examples of hypotheses. It is a speculative claim about how two or more variables are related, and it can be verified via more investigation, testing, and data gathering. Usually based on existing information and observations, hypotheses can be confirmed or refuted via scientific investigation.

A hypothesis is created by making an educated guess or prediction about how an experiment will turn out based on prior knowledge and observations. This hypothesis provides the basis for further research, and it may be improved upon and put to the test by gathering more information.

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The required value of m is given as 25/4 as of the given proportionality.

Given that,

P is inversely proportional to the square root of m. P = 10 when m = 1/4 to work out the value of m when P = 2​.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

here,

According to the question,

P ∝ 1 / √m

Now,

P₁/P₂ = √m₂/√m₁

Substitute the value in the above equation,

10/2 = √m₂/√1/4

√m₂ = 5/2

m₂ = 25/4 researchers

Thus, the required value of m is given as 25/4 as of the given proportionality.

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Answer:

I think it will be one eighth times the volume

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

66-48=18

The slope and y intercept of the line formed are 5 and 2 respectively .

Part A:

Yes. There is a correlation between the number of workers in a factory and the number of units produced daily.

Let us consider the coordinates [tex](x_{1},y_{1})\text{ and }(x_{2},y_{2})[/tex] to be (10, 52) and (20, 102)

The slope = m

[tex]m =\frac{y _{2}-y_{1}}{x_{2}- x _{1}} \\\\=\frac{102-52}{20- 10} \\\\= \frac{50}{10} \\\\= 5[/tex]

The value of slope = m = 5

The slope - intercept form of the equation is y = mx + b ----(1)

Let us find y intercept b (x = 0),

From the given table,

When x = 0 , y = 2

So ,b = 2

Substituting m = 5 and b =2 in the equation (1)

y = 5x + 2

Thus, there is a correlation between the number of workers in a factory and the number of units produced daily.

Part B :

Substituting m = 5 and b =2 in the equation (1)

y = 5x + 2

So,  y = 5x + 2 is the function that best fits the data.

Part C:

Here, the slope indicates that the rate of change of number of units produced daily over the rate of change of number of workers.

The y - intercept indicates that the number of units produced daily by the number of workers.

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Mr. Arnett will have to pay $15.75 for the trail mix if it cost $4.50 per pound.

According to the question,

We have the following information:

Amount of trail mix: 15 oz, 14 oz, 10 oz and 17 oz

Cost of 1 pound of trail mix = $4.50

Total amount of trail mix in oz:

15+14+10+17

56 oz

We know that 1 ounce = 0.0625 pounds

So, we have the following expression:

56 oz = 56*0.0625 pounds

56 oz = 3.5 pounds

Now, the cost of trail mix:

3.5*4.50

$15.75

Hence, Mr. Arnett will have to pay $15.75 for the trail mix if it cost $4.50 per pound.

The complete question is here:

At the grocery store, Mr. Arnett allowed each of his children to fill their own bag with trail mix for their hike. The table shows the amount of trail mix for each child.

Child-amount of trail mix in oz

Ava-15

Grayson-14

Mason-10

Tyler-17

The trail mix costs $4.50 per pound. How much will Mr. Arnett pay for all the trail mix?

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The teacher has offered his students a(n): algorithm

What is algorithm?

A method which solve a puzzle or carry out a calculation is known as an algorithm. Algorithms are precise lists of instructions that, in either software or hardware-based routines, carry out predetermined operations step by step. In many facets of IT, algorithms are commonly utilized. An algorithm is typically a short process that resolves a recurring issue in mathematics and computer science. Automated systems heavily rely on algorithms, which are also utilised as guidelines for carrying out data processing. Pseudocode, flowcharts, control tables, and plain languages are all ways to express algorithms. Since they are more ambiguous, natural language expressions are uncommon. Algorithms that a computer executes are typically expressed in programming languages.

A high school physics teacher reassures his class that no matter how confusing this week's word problems appear,

And they all may be solved quite handily through the use of the formula F = MA.

Hence this is the prime example of the algorithm.

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The value of the coordinate x in the point P(x, 3) s -2

From the question, we have the following coordinate points

Point P = (x, 3)

Point Q = (3, 5)

Point R = (-4, -2)

The point P is equidistant from the points Q and R

This means that

PQ = PR

These lengths can be calculated using the following distance formula

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

So, we have

PQ = √[(x - 3)² + (3 - 5)²]

PR = √[(x + 4)² + (3 + 2)²]

Recall that PQ = PR

So, we have

√[(x - 3)² + (3 - 5)²] = √[(x + 4)² + (3 + 2)²]

Square both sides

(x - 3)² + (3 - 5)² = (x + 4)² + (3 + 2)²

So, we have

(x - 3)² + 4 = (x + 4)² + 25

Open the brackets

x² - 6x + 9 + 4 = x² + 8x + 16 + 25

Evaluate the like terms

8x + 6x = 9 + 4 - 16- 25

Evaluate the like terms

14x = -28

This gives

x = -2

Hence, the value of x is -2

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Answer:

$770

$40,040

Step-by-step explanation:

Last week: 11% of $7,000

11% of $7000 = 11/100 × $7000 = $770

Full year is 52 weeks.

52 × $770 = $40,040

Rigoberto invests $8,000, at 6% interest, compounded semiannually for 1 year the compound interest for his investment is 8487.2

A = P(1 + r/n)²

In the formula

A = Accrued amount (principal + interest)

P = Principal amount = 8000

r = Annual nominal interest rate as a decimal = 0.06

R = Annual nominal interest rate as a percent

r = R/100

n = number of compounding periods per unit of time

t = time in decimal years;

A = 8000(1 + 0.06/2)²

= 8000(1 + 0.03)²

= 8000(1.0609)

= 8487.2

Therefore, the compound interest for his investment is 8487.2

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consider ventilation of a well-mixed room, the differential equation for mass concentration in the room as a function of time is given as follow:

There are three characteristic parameters in such a situation:

L, a characteristic length scale of the room (assume L = V^1/3); V the volume flow rate of fresh air into the room, and [tex]c_{limit}[/tex], the maximum mass concentration that is not harmful.

Using these three characteristic parameters, define dimensionless forms of all the variables in the equation.  c* = c/[tex]c_{limit}[/tex].)

Rewrite the equation in dimensionless form, and identify any established dimensionless groups that may appear.

V = dc/dt = S - [tex]V_c[/tex] - c[tex]A_sk_w[/tex]

Although several models are available in legal contexts, the current implementations seem to be unable to correctly simulate concentration changes that actually occur in volatile mixtures and in particular in thin films.

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Full question:

Consider ventilation of a well-mixed room as in  The differential equation for mass concentration in the room as a function of time is given in  and is repeated here for convenience,

V = dc/dt = S - [tex]V_c[/tex] - c[tex]A_sk_w[/tex].

The equation of line that passes through the point (-8, 5) and perpendicular to y = 4x - 2 is, [tex]y=-\frac{1}{4}x+3[/tex].

What is point slope form of the line?

The general form of a linear equation is y - y1 = m(x - x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.

Consider the given equation of line

y = 4x - 2

And the point is (-8, 5).

We have to find the equation of line that passes through the given point and perpendicular to the given line.

First to find the slope of the line.

Since, slope of the perpendicular line is negative reciprocal of the slope of the given line.

Here, slope of the line is 4.

So, the slope of the perpendicular line is -1/4.

Now, consider the point slope form of the line,

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex](x_1, y_1) = (-8, 5), m = -\frac{1}{4}[/tex]

[tex]y-5=-\frac{1}{4}(x-(-8)) \\y-5=-\frac{1}{4}(x+8)\\ y-5=-\frac{1}{4}x-2\\y=-\frac{1}{4}-2+5\\ y=-\frac{1}{4}+3[/tex]

Hence, the equation of line perpendicular to the given line is, [tex]y=-\frac{1}{4}x+3[/tex].

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