Students of a large university spend an average of $5 a day on lunch. The standard deviation of the expenditure is $3. A simple random sample of 36 students is taken. a) What is the expected value, standard deviation, and shape of the sampling distribution of the sample mean

Answer:Sqrt(8^2 + 3^2)

Step-by-step explanation:

Answer:

x=5  x=-3

Step-by-step explanation:

x^2 − 2x − 15 =0

Factor

What two numbers multiply to -15 and add to -2

-5*3 = -15

-5+3 =-2

(x-5) (x+3)=0

Using the zero product property

x-5 =0   x+3 =0

x=5  x=-3

Answer:

x^2 - 2x - 15 = 0

(x - 5) (x + 3) = 0

x - 5 = 0

x = 5

x + 3 = 0

x = -3

Answer:

X = 2

Step-by-step explanation:

[tex]if \: {x}^{3} + {3}^{x} = 17 \: we \: can \: conclude \: that \: x \: is \: equal \: to \: two \\ {2}^{3} + {3}^{2} = 8 + 9 = 17[/tex]

Answer:

5! = 120

Step-by-step explanation:

5! is basically 5(4)(3)(2)(1).

Answer:

The probability of spending between 4 and 7 days in recovery

P(4≤x≤7) = 0.5445

Step-by-step explanation:

Step(i):-

Given mean of the Population μ = 5.3 days

Given standard deviation of the population 'σ' = 2 days

Let 'X' be the random variable in normal distribution

Let    x₁ = 4

[tex]Z_{1} = \frac{x_{1}-mean }{S.D} = \frac{4-5.3}{2} = -0.65[/tex]

Let    x₂ = 7

[tex]Z_{2} = \frac{x_{2}-mean }{S.D} = \frac{7-5.3}{2} = 0.85[/tex]

Step(ii):-

The probability of spending between 4 and 7 days in recovery

P(4≤x≤7) = P(-0.65≤Z≤0.85)

             =  P(Z≤0.85) - P(Z≤-0.65)

            = 0.5 + A( 0.85) - ( 0.5 - A(-0.65)

            = 0.5 + A( 0.85) -  0.5 +A(0.65)   ( ∵A(-0.65) = A(0.65)

           =   A(0.85) + A(0.65)

          = 0.3023 + 0.2422

         = 0.5445

Final answer:-

The probability of spending between 4 and 7 days in recovery

P(4≤x≤7) = 0.5445

Answer:

Each table is $6 and each chair is $2.50

Step-by-step explanation:

Answer:

12, 1

Step-by-step explanation:

12- 6(1)=

12-6= 6

Answer:

Ans) 42.7%

Step-by-step explanation:

For a continuous probability distribution, a curve known as probability density function contains information about these probabilities.

in the given range -

The probability that a continuous random variable = equal to the area under the probability density function curve

The probability that the value of a random variable is equal to 'something' is 1.

As per the diagram,

Weight of chocolate bar between 4 ounces and 7 ounces is highlighted in the blue part. That area is said to be 0.42739 and the total area under the curve is 1.

Hence required probability

=0.42739/1=0.42739

Ans) 42.7%

Round to nearest tenth of a percent

Answer:

-6, -3

3, 8

Step-by-step explanation:

In order to find the number that are solutions to the compound inequalities, you first solve fr x on each inequality.

First inequality:

[tex]4(x+3)\leq 0\\\\4x+12\leq0\\\\4x\leq-12\\\\x\leq-3[/tex]  interval = (-∞ , -3]

Second inequality:

[tex]x+1>3\\\\x>2[/tex]   interval = (2 , ∞)

The interval solution is (-∞ , -3] U (2 , ∞)

The number that are included in the previous interval are:

-6, -3

or

3, 8

Answer: any except 0

Step-by-step explanation:

Answer:2/3

Step-by-step explanation:

Given that the length of the rectangle is described by the function y = 3x + 6, where x is the width of the rectangle. The domain of the function is (0, ∞).

The domain of a function is the set of all possible inputs for the function. In other words, domain is the set of all possible values of x. In this question, x is the width of the rectangle. Width of a rectangle existing in two dimensional space, cannot be negative or zero. Thus it is the set of all positive real numbers, or we say, (0, ∞).

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Answer:

The answer is

Step-by-step explanation:

For an nth term in an arithmetic sequence

[tex]U(n) = a + (n - 1)d[/tex]

where n is the number of terms

a is the first term

d is the common difference

From the question

a = 15

d = 24 - 15 = 9

n = 61

So the 61st term of the arithmetic sequence is

U(61) = 15 + (61-1)9

= 15 + 9(60)

= 15 + 540

= 555

Hope this helps you.

Answer:

(a)$29.95

(b)A

Step-by-step explanation:

The​ cost, in​ dollars, of producing x cellphone cases is given by:

[tex]C(x)=-0.05 x^2+55 x.[/tex]

We are required to evaluate: [tex]\dfrac{C(251)-C(250)}{251-250}[/tex]

[tex]C(251)=-0.05(251)^2+55(251)=10654.95\\C(250)=-0.05(250)^2+55(250)=10625\\\text{Therefore:}\\\\\dfrac{10654.95-10625}{251-250}=29.95[/tex]

[tex]\dfrac{C(251)-C(250)}{251-250}=\$29.95[/tex]

The value calculated above represents the additional cost to produce one more item after making 250 items.

Answer:

21900

Step-by-step explanation:

There are 12 months in a year, so multiply the yearly amount by 12

1825 * 12

21900

Answer:

Bob makes $21,000 in a year.

Step-by-step explanation:

There are 12 months in a year, so if he earns $1,825 every month to get his yearly pay you need to add 1,825 twelve times. Thus, 1,825×12=21,000. Hope this helps!

Answer:

D

Step-by-step explanation:

The numbers that are less than 0 are negative. Negative numbers have the "-" sign in front of them so the answer is D.

Answer:

d

Step-by-step explanation:

The other ones will always be positive four

Answer:

Sides:

Angles:

Step-by-step explanation:

Apply the law of sines to find the sine of [tex]\angle A[/tex]:

[tex]\displaystyle \frac{\sin{A}}{\sin{C}} = \frac{a}{c}[/tex].

[tex]\displaystyle\sin A = \frac{a}{c} \cdot \sin{C} = \frac{103}{159} \times \left(\sin{104^{\circ}}\right) \approx 0.628556[/tex].

Therefore:

[tex]\angle A = \displaystyle\arcsin (\sin A) \approx \arcsin(0.628556) \approx 38.9^\circ[/tex].

The three internal angles of a triangle should add up to [tex]180^\circ[/tex]. In other words:

[tex]\angle A + \angle B + \angle C = 180^\circ[/tex].

The measures of both [tex]\angle A[/tex] and [tex]\angle C[/tex] are now available. Therefore:

[tex]\angle B = 180^\circ - \angle A - \angle C \approx 37.1^\circ[/tex].

Apply the law of sines (again) to find the length of side [tex]b[/tex]:

[tex]\displaystyle\frac{b}{c} = \frac{\sin \angle B}{\sin \angle C}[/tex].

[tex]\displaystyle b = c \cdot \left(\frac{\sin \angle B}{\sin \angle C}\right) \approx 159\times \frac{\sin \left(37.1^\circ\right)}{\sin\left(104^\circ\right)} \approx 98.8[/tex].

Answer: No there isn't

Explanation:

A score of 53.7% is quite close to 50% and this is a true or false exam. Charlie could have easily gotten this result by indeed guessing and not studying. This test mark is therefore not high enough to disregard the teachers's claim. Were the results to be significantly high enough above 50% then it could be said that indeed Charlie does study for his exams.

Answer:

[tex]153.86 \: {units}^{2} [/tex]

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ = 3.14 \times 7 \times 7 \\ = 3.14 \times 49 \\ = 153.86 \: {units}^{2} [/tex]

Answer:

153.86 [tex]units^{2}[/tex]

Step-by-step explanation:

Areaof a circle = πr^2

[tex]\pi = 3.14[/tex](in this case)

[tex]r^{2} =7[/tex]

A = πr^2

= 49(3.14)

= 153.86

Answer:

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

(11,688.68 , 12,511.32)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 17

mean of the sample x⁻ = 12,100

Standard deviation of the sample (S) = 800

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

Degrees of freedom ν =n-1 = 17-1 =16

[tex]t_{(16 , 0.05)} = 2.1199[/tex]

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )[/tex]

[tex](12,100 - 2.1199\frac{800}{\sqrt{17} } , 12,100 + 2.1199 \frac{800}{\sqrt{17} } )[/tex]

(12,100 - 411.32 , 12,100 + 411.32)

(11,688.68 , 12,511.32)

Answer:

[tex]\displaystyle AB \approx 8.39 \text{ inches} \text{ and } AC \approx 13.05 \text{ inches}[/tex]

Step-by-step explanation:

Note that we are given the measure of ∠C and the length of side BC.

To find AB, we can use the tangent ratio. Recall that:

[tex]\displaystyle \tan\theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]

Substitute in appropriate values:

[tex]\displaystyle \tan 40^\circ = \frac{AB}{BC} = \frac{AB}{10}[/tex]

Solve for AB:

[tex]\displaystyle AB = 10\tan 40^\circ \approx 8.39\text{ inches}[/tex]

For AC, we can use cosine ratio since we have an adjacent and need to find the hypotenuse. Recall that:

[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]

Substitute in appropriate values:

[tex]\displaystyle \cos 40^\circ = \frac{BC}{AC} = \frac{10}{AC}[/tex]

Solve for AC:

[tex]\displaystyle \begin{aligned} \frac{1}{\cos 40^\circ} & = \frac{AC}{10} \\ \\ AC & = 10\cos 40^\circ \approx 13.05\text{ inches} \end{aligned}[/tex]

In conclusion, AB is about 8.39 inches and AC is about 13.03 inches.

Let's solve the first equation and see if both -6−6minus, 6 and 666 are possible values of ccc.

Hint #22 / 4

\begin{aligned} c^2&=36\\\\ \sqrt{c^2}&=\sqrt{36}&\\\\ c &=\pm 6 \end{aligned}

c

2

c

2

​

c

​

=36

=

36

​

=±6

​

​

Yes, both -6−6minus, 6 and 666 are possible values of ccc for the first equation!

Hint #33 / 4

Let's do the same for the second equation.

\begin{aligned} c^3&=216\\\\ \sqrt[\scriptstyle 3]{c^3}&=\sqrt[\scriptstyle 3]{216}&\\\\ c &=6 \end{aligned}

c

3

3

c

3

​

c

​

=216

=

3

216

​

=6

​

​

No, both -6−6minus, 6 and 666 are not possible values of ccc for the second equation.

Hint #44 / 4

The following equation has both -6−6minus, 6 and 666 as possible values of ccc:

c^2 = 36c

2

=36

The equation that has both -6 and 6 as possible values is c² = 36.

Option A is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

If c is a possible value of 6, then c - 6 = 0.

Similarly, if c is a possible value of -6, then c + 6 = 0.

A)

c² = 36

We can factor this equation as c² - 36 = 0, which gives us (c - 6) (c + 6) = 0. Therefore, both c = 6 and c = -6 are solutions to this equation.

B)

c³ = 216

We can factor 216 as 6³, so c³ - 6³ = (c - 6) (c² + 6c + 36) = 0.

The quadratic factor c² + 6c + 36 does not have any real roots, so the only solution to this equation is c = 6.

Therefore, -6 is not a possible solution to this equation.

Thus,

The equation that has both -6 and 6 as possible values is c² = 36.

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Answer:

Step-by-step explanation:

The average weight of a package of rolled oats is supposed to be at least 18 ounces

Null hypothesis: u >= 18

Alternative: u < 18

Using the t-test formula, we have

t = x-u/ (sd/√n)

Where x is 17.78, u = 18, sd = 0.41 and n = 18

t = 17.78-18 / (0.41/√18)

t = -0.22 / (0.41/4.2426)

t = -0.22/ 0.0966

t = -2.277

Since, this is a left tailed test, at a significance level of 0.05, the p value is 0.01139. Since the p value is less than 0.05, we will reject the null hypothesis and conclusion that the true mean smaller than the actual specification.

Consider the standard form of each of the following options given, and note the hyperbola properties through that derivation -

[tex]Standard Form - \frac{\left(x-5\right)^2}{\left(\sqrt{7}\right)^2}-\frac{\left(y-\left(-5\right)\right)^2}{3^2}=1,\\Properties - \left(h,\:k\right)=\left(5,\:-5\right),\:a=\sqrt{7},\:b=3\\[/tex]

Similarly we can note the properties of each of the other hyperbolas. They are all similar to one another, but only option C is correct. Almost all options are present with a conjugate axis of length 6, but only option c is broad enough to include the point ( 1, - 5 ) and ( 9, - 5 ) in a given radius.

Solution = Option C!

Answer:

-2x + y = -1.

Step-by-step explanation:

The slope of the line = rise / run

= (11-9) / (6-5) = 2.

The point-slope form of the line is

y - y1 = 2(x - x1) where (x1, y1) is a point on the line so we have:

y - 11 = 2(x - 6)     ( using the point  (6, 11)

y = 2x - 12 + 11

y = 2x - 1

Convert to standard form:

-2x + y = -1.

Answer:

The rising tide gobbled up the sandcastle that the children had so carefully crafted.

Step-by-step explanation:

personification is when you use human characteristics to describe something non-human.

Answer:

The standard error for the difference in proportions of males and females who use public transportation every working day is 0.015.

The conditions are met.

Step-by-step explanation:

The sample 1 (males), of size n1=2570 has a proportion of p1=0.389.

[tex]p_1=X_1/n_1=1000/2570=0.389[/tex]

The sample 2 (females), of size n2=2055 has a proportion of p2=0.745.

[tex]p_2=X_2/n_2=1532/2055=0.745[/tex]

The difference between proportions is (p1-p2)=-0.356.

[tex]p_d=p_1-p_2=0.389-0.745=-0.356[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{1000+1532}{2570+2055}=\dfrac{2532}{4625}=0.547[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.547*0.453}{2570}+\dfrac{0.547*0.453}{2055}}\\\\\\s_{p1-p2}=\sqrt{0.000096+0.000121}=\sqrt{0.000217}=0.015[/tex]

Conditions for a normal distribution approximation:

The expected number of "failures" or "successes", whichever is smaller, has to be larger than 10.

For the males sample, we have p=0.389 and (1-p)=0.611. The sample size is n=2570, so we take the smallest proportion and chek the condition:

[tex]n\cdot p=2570\cdot 0.389=999>10[/tex]

For the females sample, we have p=0.745 and (1-p)=0.255. The sample size is n=2055, so we take the smallest proportion and chek the condition:

[tex]n\cdot (1-p)=2055\cdot 0.255=524>10[/tex]

The conditions are met.

Answer:

a) Null and alternative hypothesis:

[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]

b) A Type I error is made when a true null hypothesis is rejected. In this case, it would mean a conclusion that the proportion is significantly bigger than 10%, when in fact it is not.

c) The consequences would be that they would be more optimistic than they should about the result of the investment, expecting a proportion of students that is bigger than the true population proportion.

d) A Type II error is made when a false null hypothesis is failed to be rejected. This would mean that, although the proportion is significantly bigger than 10%, there is no enough evidence and it is concluded erroneously that the proportion is not significantly bigger than 10%

e) The consequences would be that the investment may not be made, even when the results would have been more positive than expected from the conclusion of the hypothesis test.

Step-by-step explanation:

a) The hypothesis should be carried to test if the proportion of students that would eat there at least once a week is significantly higher than 10%.

Then, the alternative or spectulative hypothesis will state this claim: that the population proportion is significantly bigger than 10%.

On the contrary, the null hypothesis will state that this proportion is not significantly higher than 10%.

This can be written as:

[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]

Answer:

Option 4

Step-by-step explanation:

The central angles are "Angles in the center"

So,

Central Angles are <AOB, <BOC and <AOC

Answer:

<AOB, <BOC and < AOC

Step-by-step explanation:

There are 3 angles at center O . The largest is <AOC ( = 180 degrees). Thn you have 2 more each equal to 90 degrees.

Answer:

8

Step-by-step explanation:

Because it is equal to the 4 side