Amy filled bags with mixed nuts. The weights of the bags are 1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/4 lb, 1/8lb, 1/2 lb, 1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/8 lb, 1/4 lb, and 1/2 lb.




Part A: Organize the information in a line plot. (on your own paper)




Part B: What is the average weight of the bags? ________ lb

Answer:

(a) A(0)= 0 (kg)

(b) [tex]R_{in}=0.28\dfrac{kg}{min}[/tex]

(c) [tex]C(t)=\dfrac{A(t)}{2840}[/tex]

(d) [tex]R_{out}=\dfrac{A(t)}{710}[/tex]

(e) [tex]\dfrac{dA}{dt}=0.28-\dfrac{A(t)}{710}[/tex]

Step-by-step explanation:

A tank contains 2840L of pure water.

A solution that contains 0.07 kg of sugar per liter enters a tank at the rate 4 L/min. The solution is mixed and drains from the tank at the same rate.

(a) Amount of sugar initially in the tank.

Since the tank initially contains pure water, the amount of sugar in the tank

A(0)= 0 (kg)

(b) Rate at which the sugar is entering the tank. (kg/min)

[tex]R_{in}[/tex]=(concentration of sugar in inflow)(input rate of the solution)

[tex]=(0.07\dfrac{kg}{liter}) (4\dfrac{liter}{min})\\R_{in}=0.28\dfrac{kg}{min}[/tex]

(c) Concentration of sugar in the tank at time t

Volume of the tank =2840 Liter

Concentration c(t) of the sugar in the tank at time t

Concentration, C(t)= [tex]\dfrac{Amount}{Volume}[/tex]

[tex]C(t)=\dfrac{A(t)}{2840}[/tex]

(d) Rate at which the sugar is leaving the tank

[tex]R_{out}[/tex]=(concentration of sugar in outflow)(output rate of solution)

[tex]=\dfrac{A(t)}{2840})( 4\dfrac{Liter}{min})=\dfrac{A}{710}\\R_{out}=\dfrac{A(t)}{710}[/tex]

(e) Differential equation representing the rate at which the amount of sugar in the tank is changing at time t.

[tex]\dfrac{dA}{dt}=R_{in}-R_{out}\\\dfrac{dA}{dt}=0.28-\dfrac{A(t)}{710}[/tex]

Answer:

  1

Step-by-step explanation:

Eliminate parentheses using the distributive property.

  = -4i +1/4 -5i +3/4 -8i +17i

  = (1/4 +3/4) +i(-4 -5 -8 +17)

  = 1 + 0i

  = 1

Answer:

Option (E)

Step-by-step explanation:

In the figure attached,

Given a isosceles right triangle with two equal legs measuring [tex]3\sqrt{2}[/tex] units

By Pythagoras theorem,

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

Since, hypotenuse = h

Leg 1 = Leg 2 = 3√2

Now we substitute the values,

h² = (3√2)² + (3√2)²

h² = 18 + 18

h = √36

h = 6 units

Therefore, length of the hypotenuse is 6 units.

Option (E) will be the answer.

Using the Pythagorean Theorem, the length of the hypotenuse is: E. 6.

Given that the hypotenuse length of a right triangle is c, and the other legs are a and b, the Pythagorean Theorem states that: c = √(a² + b²).

Thus:

h = √((3√2)² + (3√2)²)

h = √(18 + 18)

h = √36

h = 6

Therefore, using the Pythagorean Theorem, the length of the hypotenuse is: E. 6.

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Answer:

77.98% probability that the height of a randomly chosen child is between 38.9 and 61 inches

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 54, \sigma = 8[/tex]

What is the probability that the height of a randomly chosen child is between 38.9 and 61 inches

This is the pvalue of Z when X = 61 subtracted by the pvalue of Z when X = 38.9. So

X = 61

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{61 - 54}{8}[/tex]

[tex]Z = 0.875[/tex]

[tex]Z = 0.875[/tex] has a pvalue of 0.8092

X = 38.9

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{38.9 - 54}{8}[/tex]

[tex]Z = -1.89[/tex]

[tex]Z = -1.89[/tex] has a pvalue of 0.0294

0.8092 - 0.0294 = 0.7798

77.98% probability that the height of a randomly chosen child is between 38.9 and 61 inches

Answer:

53.375 or 427/8 or 53 3/8

Step-by-step explanation:

To solve this you must find the area of both the carpet and the tiled floor. You use the equation area = length x width

Carpet: 10.5 x 7 = 73.5

Tile: 5.75 x 3.5 = 20.125

The you subtract the area of the tiled floor from the carpet

73.5 - 20.125 = 53.375

(I prefer to work in decimals but most of the time they want fraction answers so 53.375 = 427/8 = 53 3/8

Answer:

graph of exponential rising up to the right, through the point 0, negative 2

Step-by-step explanation:

I graphed the function on the graph below so you can see that it rises to the right and goes through the point (0,-2).

Answer:

graph of exponential rising up to the right, through the point 0, negative 2

Step-by-step explanation:

f(x)=3x-2

f(0)=3*0-2= -2

(0, -2) is the last given option

Answer:

Because of the presence of an outlier (30), an extremely higher value when compared to others. Outliers affects the value of mean, thereby mean should not be used for data with outliers.

Step-by-step explanation:

For the set of data above, it would be misleading to use the mean as the center of measure for the number of points that she scored in each game because of the presence of outliers, the presence of extremely lower or extremely higher value makes the use of mean as a measure of central tendency inaccurate because the mean take into consideration all the values in a data including the outliers for its calculation, and the mean would tend to shift towards the outliers thereby misinterpreting the data. The presence of outlier which is 30 in the data given would shift the mean to the right towards 30, thereby misleading to represent the measure of central tendency. 30 is an outlier because it is extremely higher than the rest of the data (10,8,9,8,30).

In the presence of outliers it's best to use median or mode as an acceptable measure of central tendency.

CLICK ON THE POIN AND SCHROOL DOWN

Answer:

By asking the question.

Answer:

700

Step-by-step explanation:

Since 3 + 4 = 7, then 300 + 400 = 700

Answer: 700

Step-by-step explanation:

300+400

700

easier way to do it in your brain is

4+3 is 7 and add the 2 zeros

so the answer is 700

Hope this helps :)

Answer:

4/5

Step-by-step explanation:

[tex]y=\dfrac{1}{3}x+\dfrac{11}{15} \\\\1=\dfrac{1}{3}x+\dfrac{11}{15}\\\\\dfrac{4}{15}=\dfrac{1}{3}x\\\\\dfrac{4}{5}=x[/tex]

Hope this helps!

Answer:

x=4/5

Step-by-step explanation:

y=1/3x+11/15

1=1/3x+11/15

4/15=1/3x

multiply both sides by 3

4/5=x

Answer:

Dear user,

Answer to your query is provided below

The value of f(10) using synthetic division is 396.

Explanation:

Cubic polynomials cannot be factorized by splitting the middle term. Quadratic polynomials can be factorized by splitting the middle term.

A cubic polynomial can have a maximum of three linear factors. To factorize a cubic polynomial, we first find a factor by hit and trial method or using factor theorem and reduce it into the product of a quadratic polynomial and a linear polynomial. The quadratic polynomial can then be factorized in linear factors.

The value of f(10) using synthetic division method is 396.

"The synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division."

The given function is:

f(x) = x³ – 7x² + 8x + 16

Therefore using synthetic division, we get:

(10)    | (1)    (- 7)       (8)      (16)

        |         (10)      (30)    (380)

        |............................................

                                        (396)

Therefore, f(10) = 396.

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Answer:

They would arrive at their destination at 2pm.

Step-by-step explanation:

We have that:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance and t is the time.

We first have to find how long the trip takes.

60 miles per hour, so [tex]v = 60[/tex]

600 miles, so [tex]d = 600[/tex]

Then

[tex]v = \frac{d}{t}[/tex]

[tex]60 = \frac{600}{t}[/tex]

[tex]60t = 600[/tex]

[tex]t = \frac{600}{60}[/tex]

[tex]t = 10[/tex]

The trip lasts 10 hours. Your family left at 4am. When they arrive.

10 hours after 4 am is 10 + 4 = 14 hours, which in the am/pm scale is 2 pm.

So they would arrive at their destination at 2pm.

Answer: C≈ 37.7cm

Step-by-step explanation: C=2πr=2·π·6≈37.69911cm

Hope this helps.

Answer:

C = 37.7 cm

Step-by-step explanation:

Circumference = 2πr

Where r = 6 cm, π = 3.14

C = 2(3.14)(6)

C = 37.69

C ≈ 37.7 cm

Answer:

A 206 degrees

Step-by-step explanation:

circles have a total of 360 degrees

360-154 = 206

If this helps please consider giving me brainliest.

Answer:

206°

Step-by-step explanation:

<JLK = 360° -154 ° = 206°

Note : angle at a point is 360°.

Answer:

4/51

Step-by-step explanation:

The probability of rolling a 2 is 1/6.

There are a total of 17 cards, so the probability of a blue card is 8/17.

The probability of both events is:

(1/6) (8/17) = 4/51

We want to find the probability of rolling a 2 and then getting a blue card. We will see that this probability is equal to 0.078

First, we must find the probability of rolling a 2 with a six-sided dice.

A six-sided dice has 6 possible outcomes, only one of these is a 2, then the probability of rolling a 2 is just:

p = 1/6

Then we find the probability of drawing a blue card.

There are:

So there is a total of 3 + 8 + 6 = 17 cards, and 8 of these are blue, then the probability of randomly drawing a blue card is:

q = 8/17

The joint probability is given by the product of the two individual probabilities, so we get:

P = p*q = (1/6)*(8/17) = 0.078

So the probability of rolling a 2 and then getting a blue card is P = 0.078

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Answer:

Step-by-step explanation:

Using either the critical value rule or the p-value rule, a conclusion can be drawn at a level of significance (alpha)

The null hypothesis: u = hypothesized mean

Alternative hypothesis: u > u0 or u < u0 for a one tailed test

Alternative hypothesis for a two tailed test: u =/ u0

To draw a conclusion by failing to reject the null hypothesis as stated then: using critical value

Observed z score > critical z score for both the one and two tailed test.

Or using p value:

P-value > alpha for a one tailed test

P-value > alpha/2 for a two tailed test

Thus, if a one-sided null hypothesis for a single mean cannot be rejected at a given significance level, then the corresponding two-sided null hypothesis will also not be rejected at the same significance level.

Answer:

Total no. of buttons = 300 + 700 + 1000

+ 500 = 2500

Possibility for a person to pick a pink button = 300/2500 = (3/25)%

Amount of pink buttons she can expect her friends to pick = 50(3/25) = 6

She can expect to make 6 pink barrettes

Step-by-step explanation:

Answer:0.9966

Step-by-step explanation:

Given

Probability that flash light does not  work is [tex]P_o=0.15[/tex]

If owner has 3 three flashlights then

Probability that atleast one of them works [tex]=1-P(\text{none of them works})[/tex]

Probability that flashlight will work [tex]=1-P_o=1-0.15[/tex]

[tex]=0.85[/tex]

Required Probability[tex]=1-0.15\times 0.15\times 0.15[/tex]

[tex]=1-0.003375[/tex]

[tex]=0.9966[/tex]

Now, Probability that second works given that first works is given by

[tex]P=P(\text{First works})\times P(\text{Second works})[/tex]

[tex]P=0.85\times 0.85[/tex]

[tex]P=0.7225[/tex]

Answer:

the like terms are - q and (3/7)q

Step-by-step explanation:

3.6 p minus q minus 4 + StartFraction r over 3 EndFraction + StartFraction 3 over 7 EndFraction q = 3.6p - q- 4 + r/3 + (3/7)q

The like terms are the terms with same letters, alphabet .

For the above expression, the like terms are -q and (3/7)q

All others do not have a like term.

Answer:

-q and 3/7q btw sorry im late

Step-by-step explanation:

Answer:

-37

Step-by-step explanation:

Answer:

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the CAI technique performs differently than the traditional method (P-value = 0.1844).

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the CAI technique performs differently than the traditional method.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=11.7\\\\H_a:\mu\neq 11.7[/tex]

The significance level is 0.1.

The sample has a size n=23.

The sample mean is M=11.3.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=1.4.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{1.4}{\sqrt{23}}=0.29[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{11.3-11.7}{0.29}=\dfrac{-0.4}{0.29}=-1.37[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=23-1=22[/tex]

This test is a two-tailed test, with 22 degrees of freedom and t=-1.37, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t<-1.37)=0.1844[/tex]

As the P-value (0.1844) is bigger than the significance level (0.1), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the CAI technique performs differently than the traditional method.

Answer:

C.

Step-by-step explanation:

the standard form of a QE is ax2+bx+c. This includes x squared, and when graphed, it forms the graph of a QE, a parabola.

Hope this helps!

The parent function of f(x) = x^2 is the quadratic parent function.

We have given that,

f(x) = x^2

We have to determine the parent function of the given function.

Here the highest power of the x is 2.

We remember that the quadratic equation has the highest power is 2.

The standard form of a quadratic equation is ax^2+bx+c.

This includes x squared and when graphed it forms the graph of a quadratic equation is a  parabola.

We have given function is  f(x) = x^2

Therefore the value of the a,b and  c  are,

a=1

b=0 and c=0

Therefore, option C is correct.

The parent function of f(x) = x^2 is the quadratic parent function.

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Answer:

The value of the test statistic = 2.58

Test statistic Z = - 4.805

|Z| = 4.805 > 2.58

Null hypothesis is rejected The value of the test statistic = 2.58

There is  significant difference between in the mean number of times men and women send a Twitter message in a day

Step-by-step explanation:

Step(i):-

Sample size of men  n₁ = 25

mean of the first sample x₁⁻ = 20

Standard deviation of the first sample σ₁ = 5

Sample size of women n₂ = 30

mean of the second sample x₂⁻ = 30

Standard deviation of the first sample σ₂ = 10

Level of significance ∝= 0.01

Step(ii):-

Null Hypothesis : H₀: There is no significant difference between in the mean number of times men and women send a Twitter message in a day

Alternative Hypothesis :H₁:There is  significant difference between in the mean number of times men and women send a Twitter message in a day

Test statistic

[tex]Z = \frac{x^{-} _{1} - x^{-} _{2} }{\sqrt{\frac{S.D_{1} ^{2} }{n_{1} }+\frac{ S.D_{2} ^{2}}{n_{2} } } }[/tex]

[tex]Z = \frac{20 - 30 }{\sqrt{\frac{(5)^{2} }{25 }+\frac{ (10)^{2} }{ 30} } }[/tex]

Z =  [tex]\frac{-10}{2.081} = - 4.805[/tex]

The value of the test statistic = 2.58 C

|Z| = 4.805 > 2.58

Null hypothesis is rejected The value of the test statistic = 2.58

Conclusion:-

There is  significant difference between in the mean number of times men and women send a Twitter message in a day

Answer:

H = 49.56 m

Step-by-step explanation:

We have,

A kite is flying in the air has a 91 ft string attached to it.

The angle of elevation of the kite is 57 degrees.

It is required to find the height of the kite. If we consider a right angled triangle, 91 ft is the hypotenuse. Let H is the height of the kite.

[tex]\cos\theta=\dfrac{H}{91}\\\\H=91\times \cos(57)\\\\H=49.56\ m[/tex]

Hence, the height of the kite is 49.56 m.

An equation that represents a line that is perpendicular to the given line is [tex]2y=3x+1[/tex].

Given the following data:

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

To determine an equation that represents a line that is perpendicular to the given line:

In Mathematics, the slopes of two lines are said to be perpendicular when the product of these slopes is equal to negative one (-1).

Mathematically, this is given by the formula:

[tex]m_1 \times m_2 = -1[/tex]

Note: Slope, [tex]m_1[/tex] = [tex]\frac{2}{3}[/tex]

Substituting the given parameters into the formula, we have;

[tex]\frac{2}{3} \times m_2=-1\\\\2m_2=-3\\\\m_2=\frac{3}{2}[/tex]

For the perpendicular line:

[tex]y=mx+b\\\\y=\frac{3}{2}x +1\\\\2y=3x+1[/tex]

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Answer:

a. The 95% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).

b. It means that we are 95% sure that the true proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 451, \pi = 0.015[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.015 - 1.96\sqrt{\frac{0.015*0.985}{451}} = 0.0038[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.015 + 1.96\sqrt{\frac{0.015*0.985}{451}} = 0.0262[/tex]

The 95% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).

b. Explain in a complete sentence what the confidence interval means

It means that we are 95% sure that the true proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).

−2(x+3)+6x

Distribute:

=(−2)(x)+(−2)(3)+6x

=−2x+−6+6x

Combine Like Terms:

=−2x+−6+6x

=(−2x+6x)+(−6)

=4x+−6

Answer:

Step-by-step explanation:

F/4 = 18

Multiply both sides by 4

F = 72 N

answer is A

Answer:

72N

Step-by-step explanation:

pressure=force/Area

MAKE FORCE SUBJECT OF THE FORMULA

:. FORCE=PRESSURE ×AREA

Force=18Nm² × 4m²

Force= 18N ×4

:. Force=72N

PLEASE MARK AS BRILLIANT ANSWER

Answer: C

Step-by-step explanation:

When looking at compound inequalities, the inequalities are very important. You can see that on the graphs, there are some points that have a white open circle and others have blue, closed circle. The 2 different circles tells you the inequality itself. If you see ≤ or ≥, it is a closed circle. This is a closed circle because it is less than/greater than or equal to. That means it is also equal to the point, therefore it is a closed circle. If you see < or >, it is an open circle. That means it is not closed because it is greater than. It is not equal to on that specific point.

Now that we have covered the basics, we can start to eliminate. our first condition is n<-2. Above, we have established that < is an open circle. We can eliminate A and B because the points on -2 are both closed circles.

That leaves us with C and D. Since C and D both follow the points, let's look carefully at what the inequality tells us. n<-2 means n is less than -2. This means the arros should be pointing in the left side. As you go more towards the negative, the smaller the number becomes.

We can eliminate D because at -2, the numbers are going towards the right, not the left.

Therefore, our answer is C.

Answer:

(2x + 3)3

Step-by-step explanation:

Simplify:  (2x+3)(3)

Answer: (2x + 3)3

Hope this helps.