(Order is anti-symmetric) If a > b and b > a, then a = b. (e) a

Answer:

a) [tex](3x+y)^5=243x^5+405x^4y+270x^3y^2+90x^2y^3+15xy^4+y^5[/tex].

b) The middle term in the expansion is [tex]\frac{6}{x}[/tex].

c) The coefficient of [tex]x^{11}[/tex] is 120.

Step-by-step explanation:

Remember that the binomial theorem say that [tex](x+y)^n=\sum_{k=0}^{n} \binom{n}{k}x^{n-k}y^{k}[/tex]

a) [tex](3x+y)^5=\sum_{k=0}^5\binom{5}{k}3^{n-k}x^{n-k}y^k[/tex]

Expanding we have that

[tex]\binom{5}{0}3^5x^5+\binom{5}{1}3^4x^4y+\binom{5}{2}3^3x^3y^2+\binom{5}{3}3^2x^2y^3+\binom{5}{4}3xy^4+\binom{5}{5}y^5[/tex]

symplifying,

[tex](3x+y)^5=243x^5+405x^4y+270x^3y^2+90x^2y^3+15xy^4+y^5[/tex].

b) The middle term in the expansion of [tex](\frac{1}{x} +\sqrt{x})^4=\sum_{k=0}^{4}\binom{4}{k}\frac{1}{x^{4-k}}x^{\frac{k}{2}}[/tex] correspond to k=2. Then [tex]\binom{4}{2}\frac{1}{x^2}x^{\frac{2}{2}}=\frac{6}{x}[/tex].

c) [tex](x^2+\frac{1}{x})^{10}=\sum_{k=0}^{10}\binom{10}{k}x^{2(10-k)}\frac{1}{x^k}=\sum_{k=0}^{10}\binom{10}{k}x^{20-2k}\frac{1}{x^k}=\sum_{k=0}^{10}\binom{10}{k}x^{20-3k}[/tex]

Since we need that 11=20-3k, then k=3.

Then the coefficient of [tex]x^{11}[/tex] is [tex]\binom{10}{3}=120[/tex]

Answer:

(a) in the step-by-step explanation

(b) The optimal solution is 8 chairs and 4 tables.

(c) Graph attached

Step-by-step explanation:

(a)

C: number of small chairs

T: number of large tables

Maximize Income = 9T + 3C

Restrictions:

Wood: 4T+C<=24

Glazing: 2T+C<=16

In the graph its painted in green the "feasible region" where lies every solutions that fit the restrictions.

One of the three points marked in the graph is the optimal solution.

Point 1 (C= 16, T= 0)

Income = 9*0+3*16=$ 48

Point 2 (C=8, T=4)

Income = 9*4+3*8 = $ 60

Point 3 (C=0, T=6)

Income = 9*6+3*0 = $ 54

The optimal solution is 8 chairs and 4 tables.

Answer:

Considering the fire point at (0,h), x-direction positive to the right (→) and y-direction positive to up (↑) and the only force acting after fire is the projectile weight = -mg in the y-direction.

[tex]\\ x(t)=Vo*cos(e)*t\\ v_x(t)=Vo*cos(e)\\ a_y(t)=0\\ y(t)=h+Vo*sin(e)*t-\frac{g}{2}t^{2}\\ v_x(t)=Vo*sin(e)-gt\\ a_y(t)=-g[/tex]

Step-by-step explanation:

First, we apply the Second Newton's Law in both x and y directions:

x-direction:

[tex]\sum F_x= m\frac{dv_x}{dt} =0[/tex]

Integrating we have

[tex]\int\limits^{V_x} _{V_{0x}}{}\, dV_x =\int\limits^{t} _0{0}\, dt\\ V_{0x}=Vo*cos(e)\\ V_x(t)=Vo*cos(e)[/tex]

Taking into account that a=(dv/dt) and v=(dx/dt):

[tex]a_x(t)=\frac{dV_x(t)}{dt}=0\\V_x(t)=\frac{dx(t)}{dt}-->\int\limits^x_0 {} dx = \int\limits^t_0 {Vo*cos(t)} \, dt \\x(t)=Vo*cos(e)*t[/tex]

y-direction:

[tex]\sum F_y= m\frac{dv_x}{dt} =-mg[/tex]

Integrating we have

[tex]\int\limits^{V_y} _{V_{0y}}{}\, dV_y =\int\limits^{t} _0 {-g} \, dt\\ V_{0y}=Vo*sin(e)\\ V_y(t)=Vo*sin(e)-g*t[/tex]

Taking into account that a=(dv/dt) and v=(dy/dt):

[tex]a_y(t)=\frac{dV_y(t)}{dt}=-g\\V_y(t)=\frac{dy(t)}{dt}-->\int\limits^y_h {} dy = \int\limits^t_0 {(Vo*sin(t)-g*t)} \, dt \\y(t)=h+Vo*sin(e)*t-\frac{g}{2}t^{2}[/tex]

Answer:

a) 3 inch pulley: 11,309.7 radians/min

6) 6 inch pulley: 5654.7 radians/min

b) 900 RPM (revolutions per minute)

Step-by-step explanation:

Hi!

When a pulley wirh radius R rotantes an angle θ, the arc length travelled by a point on its rim is Rθ.  Then the tangential speed V is related to angular speed  ω as:

[tex]V=R\omega[/tex]

When you connect two pulleys with a belt, if the belt doesn't slip, each point of the belt has the same speed as each point in the rim of both pulleys: Then, both pulleys have the same tangential speed:

[tex]\omega_1 R_1 = \omega_2 R_2\\[/tex]

[tex]\omega_2 = \omega_1 \frac{R_1}{R_2} =1800RPM* \frac{3}{6}= 900RPM[/tex]

We need to convert RPM to radias per minute. One revolution is 2π radians, then:

[tex]\omega_1 = 1800*2\pi \frac{radians}{min} = 11,309.7\frac{radians}{min}[/tex]

[tex]\omega_2 = 5654.7 \frac{radians}{min}[/tex]

The saw rotates with the same angular speed as the 6 inch pulley: 900RPM

a. The angular speed of the 3 inch pulley is 3600π radians/min and the angular speed of the 6 inch pulley is 7200π radians/min. b. The revolutions per minute of the saw is 900.

a. To find the angular speed in radians per minute, we need to convert the revolutions per minute to radians per minute. Since 1 revolution is equal to 2π radians, we can calculate the angular speed of the 3 inch pulley as follows:

Angular speed = (Revolutions per minute) x (2π radians per revolution)

Angular speed = (1800 rev/min) x (2π radians/rev) = 3600π radians/min

Similarly, for the 6 inch pulley:

Angular speed = (Revolutions per minute) x (2π radians per revolution)

Angular speed = (1800 rev/min) x (2π radians/rev) = 7200π radians/min

b. To find the revolutions per minute of the saw, we need to use the ratio of the diameters of the two pulleys. Since the diameter of the 6 inch pulley is twice the diameter of the 3 inch pulley, the revolutions per minute of the saw will be half of the revolutions per minute of the motor. Therefore, the revolutions per minute of the saw is 900.

Answer:

The value of x is 16 and the value of y is 8.

Step-by-step explanation:

Consider the provided equation.

[tex]\frac{3}{4}x -\frac{1}{2}y= 8\ and\ 2x +y=40[/tex]

Isolate x for [tex]\:\frac{3}{4}x-\frac{1}{2}y=8[/tex]

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

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

Multiply both side by 4 and simplify.

[tex]3x=32+2y[/tex]

[tex]x=\frac{32+2y}{3}[/tex]

Substitute the value of x in [tex]2x +y=40[/tex]

[tex]2\cdot \frac{32+2y}{3}+y=40[/tex]

[tex]\frac{64}{3}+\frac{7y}{3}=40[/tex]

[tex]64+7y=120[/tex]

[tex]7y=56[/tex]

[tex]y=8[/tex]

Now substitute the value of y in [tex]x=\frac{32+2y}{3}[/tex]

[tex]x=\frac{32+2\cdot \:8}{3}[/tex]

[tex]x=16[/tex]

Hence, the value of x is 16 and the value of y is 8.

Answer: Our required values would be -10x+5, 2x+5 and -25.

Step-by-step explanation:

Since we have given that

g(x) = -4x+5

and

h(x) = 6x

We need to find  (g-h)(x) and (g+h)(x).

So, (g-h)(x) is given by

[tex]g(x)-h(x)\\\\=-4x+5-6x\\\\=-10x+5[/tex]

and (g+h)(x) is given by

[tex]g(x)+h(x)\\\\=-4x+5+6x\\\\=2x+5[/tex]

and (g-h)(3) is given by

[tex]-10(3)+5\\\\=-30+5\\\\=-25[/tex]

Hence, our required values would be -10x+5, 2x+5 and -25.

Answer:

The exact interest on $5,870 at 12% is $58.70.

Step-by-step explanation:

Given information:

Principal = $5870

Interest rate  = 12% = 0.12

Time = June-December = 7 months.

We know that

1 year = 12 months

1/12 year = 1 month

7/12 year = 7 month

Time = 7/12 year

Formula for simple interest:

[tex]I=P\times r\times t[/tex]

where, P is principal, r is rate of interest and t is time in years.

Substitute P=5870, r=0.12 and t=7/12 in the above formula.

[tex]I=5870\times 0.12\times \frac{1}{12}[/tex]

[tex]I=5870\times 0.01[/tex]

[tex]I=58.70[/tex]

Therefore the exact interest on $5,870 at 12% is $58.70.

Answer:

1880 Milliliters(mL) = 3.97 pints

Step-by-step explanation:

This can be solved as a rule of three problem.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Unit conversion problems, like this one, is an example of a direct relationship between measures.

Each ml has 0.002 pints. How many pints are there in 1880mL. So:

1ml - 0.002 pints

1880ml - x pints

[tex]x = 1800*0.002[/tex]

[tex]x = 3.97[/tex] pints

1880 Milliliters(mL) = 3.97 pints

Answer:

4.00512 cents

Step-by-step explanation:

Given:

Power output = 48 Watts

Time for which owner paddles = 8 hours

Selling price of the electricity = 10.43 cents/kWh

Now,

Power = Energy × Time

or

Power generated = 48 × 8 = 384 Wh = 0.384 kWh

now,

Money earned will be = Power generated × selling price per kWh

or

Money earned = 0.384 kWh ×  10.43 cents/ kWh = 4.00512 cents

Answer:

Step-by-step explanation:

given number,

247₁₀ to be converted into

a) base 7

divide the number by 7 and write the remainder on the left side

solution is (502)₇

b) base 2

divide the number by 2 and write the remainder on the left side and write in the direction from down to up as shown in the diagram attached below.

solution is (11110111)₂

c) base 8

divide the number by 8 and write the remainder on the left side

solution is (367)₈

d) base 16

divide the number by 16 and write the remainder on the left side

solution is (F 7)₈

15 - F

diagram is attached below.

Answer:

The maximum number of fruits bag Harper can buy are 3.

Step-by-step explanation:

Let there be x bags of fruits.

Let there be y boxes of chocolates

Cost of 1 bag of fruit = $4.75

So, cost of x bags = $4.75x

Cost of one box of crackers costs = $3.50

As per the given situation, the inequality forms:

[tex]4.75x+3.50y\leq 15[/tex]

So, the maximum number of bags of fruit Harper can buy, is when she buys no box of cracker.

So, putting y = 0 in above inequality , we have,

[tex]4.75x+3.50(0)\leq 15[/tex]

=> [tex]4.75x+0\leq 15[/tex]

=> [tex]4.75x \leq 15[/tex]

[tex]x\leq 3.15[/tex] rounding to 3.

Hence, the maximum number of fruits bag Harper can buy are 3.

Answer:

  {3, 4, 5, 6, 7, 8}

Step-by-step explanation:

Integers that are less than 9 and greater than 2 include the integers 3 through 8.

The correct set equal to {x | x < 9 and x > 2} is {3, 4, 5, 6, 7, 8}, as it includes all the integers that satisfy the given condition.

The given set is {x | x < 9 and x > 2}, which translates to all numbers greater than 2 and less than 9. When comparing this to the options provided, we need to ensure that the numbers within the set are all and only the integers that satisfy these conditions, regardless of their order. The set {3, 4, 5, 6, 7, 8} matches this description exactly, as it includes all the integers that are greater than 2 and less than 9. Sets in mathematics do not consider the order of elements; they only consider the presence of elements. Therefore, the correct option that is equal to the given set is {3, 4, 5, 6, 7, 8}.

Answer:

Part a) value of [tex]\lambda [/tex] such that all the solutions tend to zero equals 1.

Part b)

For a particular solution to tend to 0 will depend on the boundary conditions.

Step-by-step explanation:

The given differential equation is

[tex]y'+\lambda y=e^{-t}[/tex]

This is a linear differential equation of first order of form [tex]\frac{dy}{dt}+P(t)\cdot y=Q(t)[/tex] whose solution is given by

[tex]y\cdot e^{\int P(t)dt}=\int e^{\int P(t)dt}\cdot Q(t)dt[/tex]

Applying values we get

[tex]y\cdot e^{\int \lambda dt}=\int e^{\int \lambda dt}\cdot e^{-t}dt\\\\y\cdot e^{\lambda t}=\int (e^{(\lambda -1)t})dt\\\\y\cdot e^{\lambda t}=\frac{e^{(\lambda -1)t}}{(\lambda -1)}+c\\\\\therefore y(t)=\frac{c_{1}}{\lambda -1}(e^{-t}+c_{2}e^{-\lambda t})[/tex]

here [tex]c_{1},c_{2}[/tex] are arbitrary constants

part 1)

For all the function to approach 0 as t approaches infinity we have

[tex]y(t)=\lim_{t\to \infty }[\frac{c_{1}}{\lambda -1}(e^{-t}+c_{2}e^{-\lambda t})]\\\\y(\infty )=\frac{c_{1}}{\lambda -1}=0\\\\\therefore \lambda =1[/tex]

Part b)

For a particular solution to tend to 0 will depend on the boundary conditions as [tex]c_{1},c_{2}[/tex] are arbitrary constants

The maximum potential error is 92% as per the concept of percentage.

The pharmacist weighed 0.050 g of a substance on a balance insensitive to quantities smaller than 0.004 g.

To find the maximum potential error in terms of percentage, we need to determine the difference between the actual weight of the substance and the closest value that the balance can measure, which is 0.004 g.

The difference is 0.050 g - 0.004 g = 0.046 g.

The maximum potential error is the difference between the actual weight and the closest value that the balance can measure, divided by the actual weight, multiplied by 100%.

Therefore, the maximum potential error in terms of percentage is (0.046 g / 0.050 g) x 100% = 92%.

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The question deals with the calculation of the maximum potential error in a measurement. Given the insensitivity of the balance to 0.004 g and the actual measurement of substance of 0.050 g, the maximum potential error by calculation comes out to be 8%.

The question is asking about the potential error in a measurement made by a pharmacist. The error is the difference between the smallest measurable quantity by the balance and the actual measurement. In this case, we have a balance that is insensitive to quantities smaller than 0.004 g, and the pharmacist is measuring 0.050 g of a substance.

To find the potential error percentage, we take the maximum potential error (which is defined by the sensitivity of the balance, 0.004 g), divide it by the actual measurement (0.050 g) and multiply by 100 to make it a percentage.

Maximum potential error percentage = (0.004 g / 0.050 g) * 100% = 8%

So the maximum potential error in this measurement is 8%.

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Answer:

The energy of each photon is [tex]6.468 \times 10^{-26}[/tex] Joule.

Step-by-step explanation:

Consider the provided information.

According to the plank equation:

[tex]E=h\nu[/tex]

Where E is the energy of photon, h is the plank constant and [tex]\nu[/tex] is the frequency.

It is given that [tex]h= 6.6 \times10^{-34}[/tex] and [tex]\nu=98MHz[/tex]

98Mhz = [tex]98\times 10^6Hz[/tex]

Substitute the respective value in plank equation.

[tex]E=6.6\times 10^{-34}\times 98\times 10^6[/tex]

[tex]E=6.6\times 98\times 10^{-34+6}[/tex]

[tex]E=646.8 \times10^{-28}[/tex]

[tex]E=6.468 \times 10^{-26}[/tex]

Hence, the energy of each photon is [tex]6.468 \times 10^{-26}[/tex] Joule.

Answer:

False

Step-by-step explanation:

In the above situation where the professor took a random sample of size 10 from each, conducted a test and found out that the variances are equal.  should not use a t test with related samples. The professor should use the t test for the difference in means testing for independence. Hence, the statement is false.

According to the hypothesis tested, it is found that it is true that the professor should use a t test with related samples, hence option A is correct.

A t-test should be used when we do not have the standard deviation for the population, which is the case in this problem, as we have it for the sample.

Related samples are used when comparisons are made between two samples, which is the case here for the samples of upper and lower classmen.

Hence, option A is correct.

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Approximately 0.02 mg of the drug miglitol (Glyset) would be detected in human breast milk.

Given that, approximately 0.02% of a 100-mg dose appears in human breast milk.

To calculate the quantity of drug detected in milligrams following a single dose, we can use the given information that approximately 0.02% of a 100-mg dose appears in human breast milk.

Step-by-step calculation:

1. Convert 0.02% to a decimal by dividing it by 100: 0.02/100 = 0.0002.

2. Multiply the decimal by the dose of the drug: 0.0002 * 100 mg = 0.02 mg.

Therefore, following a single dose, approximately 0.02 mg of the drug miglitol (Glyset) would be detected in human breast milk.

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Answer:

the [tex]95\%[/tex] confidence interval for the population proportion is:

[tex]\left [0.3469, \hspace{0.1cm} 0.4387\right][/tex]

Step-by-step explanation:

To solve this problem, a confidence interval of [tex](1-\alpha) \times 100\%[/tex] for the population proportion will be calculated.

[tex]$$Sample proportion: $\bar P=0.3928$\\Sample size $n=751$\\Confidence level $(1-\alpha)\times100\%=99\%$\\$\alpha: \alpha=0.01$\\Z values (for a 99\% confidence) $Z_{\alpha/2}=Z_{0.005}=2.5758$\\\\Then, the (1-\alpha) \times 100\%$ confidence interval for the population proportion is given by:\\\\\left [\bar P - Z_{\frac{\alpha}{2}}\sqrt{\frac{\bar P(1- \bar P)}{n}}, \hspace{0.3cm}\bar P + Z_{\frac{\alpha}{2}}\sqrt\frac{\bar P(1- \bar P)}{n} \right ][/tex]

Thus, the [tex]95\%[/tex] confidence interval for the population proportion is:

[tex]\left [0.3928 - 2.5758\sqrt{\frac{0.3928(1-0.3928)}{751}}, \hspace{0.1cm}0.3928 + 2.5758\sqrt{\frac{0.3928(1-0.3928)}{751}} \right ]=\left [0.3469, \hspace{0.1cm} 0.4387\right][/tex]

Answer:

Step-by-step explanation:

[tex]\dfrac{x}{3}=\dfrac{4}{9} \qquad\text{has x-coefficient $\frac{1}{3}$}[/tex]

Multiply by the reciprocal of the x-coefficient. Then you have ...

[tex]x=\dfrac{4}{3}[/tex]

Answer:

False

Step-by-step explanation:

Correlation measures the strength of the relation between two variables.

Further, Correlation is said to be positive if increasing/decreasing the one variable, also increases/decreases the values of another variable.

Correlation is said to be negative if increasing/decreasing the one variable, also decreases/increases the values of another variable.

Since we don't know here exists a positive correlation or negative correlation.

So here are two possible conditions:

The person who has Gum disease also has heart disease.

And, the person has Gum disease can never have heart disease.

Thus, the given statement is false.

The statement is false because a correlation found in a study does not necessarily mean one factor (gum disease) is the cause of the other (heart disease). The cause and effect relationship must be established through further studies.

The statement 'A recent study found a correlation between gum disease and heart disease. This result indicates that gum disease causes people to develop heart disease.' is False. A correlation implies a relationship between two elements, but it does not indicate a cause and effect relationship.

This means although the study shows a link or association between gum disease and heart disease, it does not mean gum disease causes heart disease. It could be that people with poor gum health also tend to have poor overall health including heart health. Alternatively, there could be a third underlying factor that leads to both conditions. Therefore, the cause and effect relationship must be established through further studies.

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Answer:

3x + y = 20

Step-by-step explanation:

The equation of line passing through two points is determined by formula:

[tex]y-y_{1}=\frac{y_{2}-y_{1}}{x_{2} - x_{1}}(x - x_{1})[/tex]

Here, (x₁ , y₁) = (4, 8)

and (x₂, y₂) = (6, 2)

Putting these value in above formula. We get,

[tex]y-8=\frac{2-8}{6 - 4}(x - 4)[/tex]

⇒ [tex]y-8=\frac{-6}{2}(x - 4)[/tex]

⇒ ( y - 8) = -3 (x - 4)

⇒ y - 8 = -3x + 12

⇒ 3x + y = 20

which is required equation.

Answer:  The proof is given below.

Step-by-step explanation:  We are given to show that the following equality is true :

[tex]^{n+1}C_r=^nC_{r-1}+^nC_r.[/tex]

We know that

the number of combinations of n different things taken r at a time is given by

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}.[/tex]

Therefore, we have

[tex]R.H.S.\\\\=^nC_{r-1}+^nC_r\\\\\\=\dfrac{n!}{(r-1)!(n-(r-1))!}+\dfrac{n!}{(r)!(n-r)!}\\\\\\=\dfrac{n!}{(r-1)!(n-r+1)!}+\dfrac{n!}{(r)!(n-r)!}\\\\\\=\dfrac{n!}{(r-1)!(n-r+1)(n-r)!}+\dfrac{n!}{r(r-1)!(n-r)!}\\\\\\=\dfrac{n!}{(r-1)!(n-r)!}\left(\dfrac{1}{n-r+1}+\dfrac{1}{r}\right)\\\\\\=\dfrac{n!}{(r-1)!(n-r)!}\left(\dfrac{r+n-r+1}{(n-r+1)r}\right)\\\\\\=\dfrac{n!}{(r-1)!(n-r)!}\times\dfrac{n+1}{(n-r+1)r}\\\\\\=\dfrac{(n+1)!}{r!(n-r+1)!}\\\\\\=\dfrac{(n+1)!}{r!((n+1)-r)!}\\\\\\=^{n+1}C_r\\\\=L.H.S.[/tex]

Thus, [tex]^{n+1}C_r=^nC_{r-1}+^nC_r.[/tex]

Hence proved.

Answer and Explanation:

Given : A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample.

The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2.

To find :

1) Does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy?

2)Compute the value of the appropriate test statistic ?

Solution :

1) n=16 number of sample

The target accuracy is a variance in measurements of 1.2 or less i.e. [tex]\sigma_1^2 =1.2[/tex]

The variance of the measurements in the sample is 2.2 i.e. [tex]\sigma_2^2=2.2[/tex]

According to question,  

We state the null and alternative hypotheses,

Null hypothesis [tex]H_o : \text{var}^2 \geq 1.2[/tex]

Alternative hypothesis [tex]H_a : \text{var}^2<1.2[/tex]

We claim the alternative hypothesis.

2) Compute the value of the appropriate test statistic.

Using Chi-square,

[tex]\chi =\frac{(n-1)\sigma_2^2}{\sigma_1^2}[/tex]

[tex]\chi =\frac{(16-1)(2.2)}{(1.2)}[/tex]

[tex]\chi =\frac{(15)(2.2)}{1.2}[/tex]

[tex]\chi =\frac{33}{1.2}[/tex]

[tex]\chi =27.5[/tex]

Therefore, The value of the appropriate test statistic is 27.5.

To determine if the lab technician's accuracy is within the target accuracy, a one-sample variance test can be performed using the chi-square statistic.

To determine if the lab technician's accuracy is within the target accuracy, we can perform a hypothesis test. We will use a one-sample variance test to compare the sample variance to the target variance.

The appropriate test statistic for a one-sample variance test is the chi-square statistic. The chi-square statistic is calculated by taking the sample variance and dividing it by the target variance, then multiplying by the degrees of freedom.

In this case, we have 16 measurements and a target variance of 1.2. The sample variance is 2.2. We can calculate the test statistic using the formula chi-square = (n-1) * (sample variance / target variance). Plugging in the values, we get chi-square = (16-1) * (2.2 / 1.2) = 29.67.

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Answer:

[tex]\frac{16}{195}[/tex]

Step-by-step explanation:

To obtain the result of a fractions multiplication we need to multiply both numerators and the divide by the multiplication of the denomitators. In general, given a,b,c,d real numbers with b and d not zero, we have that

[tex]\frac{a}{b}*\frac{c}{d}=\frac{a*c}{b*d}[/tex]

Substituting a,b,c and d for 8,15,2 and 13 we obtain that

[tex]\frac{8}{15}* \frac{2}{13} =\frac{16}{195}[/tex]

To find the value of 8/15 x 2/13, multiply the numerators together and multiply the denominators together. The fraction 16/195 is the final answer.

To find the value of 8/15 x 2/13, we multiply the numerators together (8 x 2) and multiply the denominators together (15 x 13). This gives us 16 in the numerator and 195 in the denominator.

The fraction 16/195 cannot be simplified further, so that is the final answer.

Calculation:

We have 8/15 x 2/13 = (8 x 2)/(15 x 13) = 16/195.

Answer:

16.

Step-by-step explanation:

The ratio is 4:1 so 4 / (4 + 1) = 4/5 of the total is green peppers.

So it is 20 * 4/5 = 16 .

Answer:

the estimated answer is A: 9.75.

(the actual answer is 9.66, so rounding up makes it 9.75)

Answer:  15

Step-by-step explanation:

Given : Elena has 60 colored pencils, and Lucy has 26 colored pencils.

Total colored pencils = [tex]60+26=86[/tex]

Let 'x' denotes the number of pencils Lucy has when she get pencils from Elena , and Elena left with 'y' pencils.

Then, by considering the given information we have the following system :-

[tex]\text{Total pencils : }x+y=86-----(1)\\\\\text{Colored pencils left with Elena : }y=4+x-----(2)[/tex]

We can rewritten the equation (2) as

[tex]y-x=4[/tex]

Now, add equation (1) and (2), we get

[tex]2y=90\\\\\Rightarrow\ y=\dfrac{90}{2}=45[/tex]

Put the value of y in (2), we get

[tex]45=4+x\\\\\Rightarrow\ x=45-4=41[/tex]

It means, the number of pencils Lucy has now =41

The number of pencils Elena give to Lucy= [tex]41-26=15[/tex]

Hence, Elena must give 15 pencils to lucy so that elena will have 4 more colored pencils than Lucy.

Answer:

Step-by-step explanation:

Here is the recommended solution method:

  3.4 + 2(9.7 – 4.8x) = 61.2 . . . . . given

  3.4 + 19.4 - 9.6x = 61.2 . . . . . . . distribute 2 to 9.7 and -4.8x

  22.8 - 9.6x = 61.2 . . . . . . . . . . . . combine 3.4 and 19.4

  -9.6x = 38.4 . . . . . . . . . . . . . . . . . subtract 22.8 from both sides

  x = -4 . . . . . . . . . . . . . . . . . . . . . . divide both sides by -9.6

_____

Alternate solution method using different steps

You can also "undo" what is done to the variable, in reverse order. The variable has these operations performed on it:

So, another possible solution method is this:

  3.4 + 2(9.7 – 4.8x) = 61.2 . . . . . given

  2(9.7 -4.8x) = 57.8 . . . . . . . . . . . add the opposite of 3.4 (undo add 3.4)

  9.7 -4.8x = 28.9 . . . . . . . . . . . . . divide by 2 (undo multiply by 2)

  -4.8x = 19.2 . . . . . . . . . . . . . . . . . add the opposite of 9.7 (undo add 9.7)

  x = -4 . . . . . . . . . . . . . . . . . . . . . . divide by -4.8 (undo multiply by -4.8)

Linear equation solutions are indeed the points where the lines or planes describing various linear equations intersect or connect. The candidate solution of a set of linear equations is indeed the collection of all feasible solution' values again for variables, and further calculation can be defined as follows:

Given:

[tex]\to \bold{3.4 + 2(9.7 -4.8x) = 61.2}\\\\[/tex]

To find:

Solve the linear equation=?

Solution:

[tex]\to \bold{3.4 + 2(9.7 -4.8x) = 61.2}\\\\\to \bold{3.4 + 19.4 -9.6x = 61.2}\\\\\to \bold{22.8 -9.6x = 61.2}\\\\\to \bold{ -9.6x = 61.2- 22.8}\\\\\to \bold{ -9.6x = 38.4}\\\\\to \bold{ x =- \frac{38.4}{9.6}}\\\\\to \bold{ x =- 4}\\\\[/tex]

Therefore, the steps are:

Distribute 2 to [tex]\bold{9.7\ and\ -4.8x}[/tex].    

Combine [tex]\bold{3.4\ and \ 19.4}[/tex].              

Subtract [tex]22.8[/tex] from both sides.      

Divide both sides by[tex]-9.6[/tex].            

Learn more:

brainly.com/question/10374924

Answer:

a) It is a proposition .

b) It is not a proposition.

c) It is a proposition.

d) It is a proposition.

e) It is a proposition.

f) It is not a proposition.

Step-by-step explanation:

a) The integer 36 is even: It is a proposition, since this statement can be assigned a true value. If 36 is an even number, the statement is true, but if 36 is an odd number, the statement is false.

b) Is the integer 315 - 8 even ?: It is not a proposition, since this question cannot be assigned a true value.

c) The product of 3 and 4 is 11: It is a proposition, since this statement can be assigned a true value. If 3x4 = 11, the statement is true, but if 3x4 is not 11, the statement is false.

d) The sum of x and y is 12: It is a proposition, since, this statement can be assigned a true value. If x + y = 12, the statement is true, but if x + y is not 12, the statement is false.

e) If x> 2, then x 2> 3: It is a proposition, since, this statement can be assigned a truth value.

f) 52 - 5 + 3: It is not a proposition, since this statement cannot be assigned a true value.

Answer:

R2 = 43.03 ohms

Step-by-step explanation:

If R2=R4-15, then R4 = R2+15

According to the Wheastone bridge equation we have:

[tex]\frac{R1}{R2} =\frac{R3}{R4}\\\frac{10}{R2} =\frac{6470}{R2+15}\\\\10*(R2+15) = 6470*R2\\10*R2+150 = 6470*R2\\150=(6470-15)*R2\\R2=\frac{6455}{150}= 43.03333[/tex]