To test H0​: μ=100 versus H1​:≠​100, a simple random sample size of nequals=24 is obtained from a population that is known to be normally distributed. Answer parts​ (a)-(d).(a) If x =104.2 and s=9.6, compute the test statistic.t= _ ​(Round to three decimal places as​ needed.)(b) If the researcher decides to test this hypothesis at the α=0.01 level of​ significance, determine the critical values.The critical values are __ .(c) Draw a​ t-distribution that depicts the critical​ region(s). Which of the following graphs shows the critical​ region(s) in the​t-distribution?(d) Will the researcher reject the null​ hypothesis?

Answer:

[tex] \frac{1}{6} [/tex]

Step-by-step explanation:

the ways of choosing 2 cards out of 4, is calculator by

[tex] \binom{4}{2} = 6[/tex]

so, 6 ways to select 2 cards.

but in only one way we can have 2 even cards. thus, the answer is

[tex] \frac{1}{6} [/tex]

Answer:

Answer is A

Step-by-step explanation:

The equation (x - 3)² + (y - 1)² = 9, is represented by the second graph as its center is at point (3, 1) and its radius is 3 units, both similar to the equation. Thus, option B is the right choice.

The general equation of a circle is of the form (x - h)² + (y - k)² = r², where (h, k) is the point where the center of the given circle lies, and r is the radius of this given circle.

In the question, we are asked to find the graph from the given options which represents the equation (x - 3)² + (y - 1)² = 9.

Comparing the given equation, (x - 3)² + (y - 1)² = 9, to the general equation, (x - h)² + (y - k)² = r², we can say that h = 3, k = 1, and r = 3.

Thus the center of the given circle lies at the point (3, 1) and its radius is 3 units.

Now we check the options to find the matching circle:

Therefore, the equation (x - 3)² + (y - 1)² = 9, is represented by the second graph as its center is at point (3, 1) and its radius is 3 units, both similar to the equation. Thus, option B is the right choice.

Learn more about circles at

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▹ Answer

2,013 cartons

▹ Step-by-Step Explanation

72,468 ÷ 36 = 2,013 cartons

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

72,468 eggs divided by 36 eggs per carton=2,013 cartons

Step-by-step explanation:

Answer:

A. f(x) = x^2 + 4x + 3

D. f(x) = -2x^2 - 8x + 1

Step-by-step explanation:

The axis of symmetry is found by h = -b/2a  where ax^2 +bx +c

A. f(x) = x^2 + 4x + 3

  h = -4/2*1 = -2    x=-2

B. f(x) = x^2 - 4x - 5

h = - -4/2*1 = 4/2 =2  x=2  not -2

C. f(x) = x^2 + 6x + 2

h =  -6/2*1 = -3/2 =  x=-3/2  not -2

D. f(x) = -2x^2 - 8x + 1

h = - -8/2*-2 = 8/-4 =-2  x=-2  

E. f(x) = -2x^2 + 8x - 2

h = - 8/2*-2 = -8/-4 =2  x=2  not -2

Answer:

Hey there! The answer to this question is

A. f(x) = x^2 + 4x + 3

D. f(x) = -2x^2 - 8x + 1

Answer: a) additive inverse (addition)

              b) multiplicative inverse (division)

Step-by-step explanation:

Step 2: 6 is being added to both sides

Step 4: (3/4) is being divided from both sides

It is difficult to know what options are provided in the drop-down menu without seeing them. If I was to complete a proof and justify each step, then the following justifications would be used:

Step 2: Addition Property of Equality

Step 4: Division Property of Equality

Answer:

c=21

Step-by-step explanation:

[tex]3(c-5)=48\\3c-15=48\\3c=48+15\\3c=63\\c=63/3\\c=21[/tex]

Hope this helps,

plx give brainliest

Answer:

c=21

Step-by-step explanation:

3(c−5)=48

Divide both sides by 3.

c-5=48/3

Divide 48 by 3 to get 16.

c−5=16

Add 5 to both sides.

c=16+5

Add 16 and 5 to get 21.

c=21

Answer:

85

Step-by-step explanation:

im new↑∵∴∵∴∞

Answer:

Jill bought 16 books and Sam bought 9 books

Step-by-step explanation:

Let the number of books that Jill bought be j.

Let the number of books that Sam bought be s.

Jill bought 7 more books than Sam:

j = 7 + s

They bought 25 books altogether:

j + s = 25

Put j = 7 + s into the second equation:

7 + s + s = 25

7 + 2s = 25

2s = 25 - 7 = 18

s = 18/2 = 9 books

Therefore:

j = 7 + s = 7 + 9

s = 16 books

Jill bought 16 books and Sam bought 9 books.

Answer:

8.5 inches

Step-by-step explanation:

First let's find the time t when the depth of the snow is 7 inches.

To do this, we just need to use the value of D = 7 then find the value of t:

[tex]7 = 1.5t + 4[/tex]

[tex]1.5t = 3[/tex]

[tex]t = 2\ hours[/tex]

We want to find the depth of snow one hour from now, so we just need to use the value of t = 3 to calculate D:

[tex]D = 1.5*3 + 4[/tex]

[tex]D = 4.5 + 4 = 8.5\ inches[/tex]

The depth of snow one hour from now will be 8.5 inches.

The depth of the snow one hour from now is 8.5 inches.

Let D represent the depth of snow in inches at time t. It is given by the relationship:

D=1.5t + 4

Since  the depth of the snow is 7 inches now, hence, the time now is:

7 = 1.5t + 4

1.5t = 3

t = 2 hours

One hour from now, the time would be t = 2 + 1 = 3 hours. Hence the depth at this time is:

D = 1.5(3) + 4 = 8.5 inches

Therefore the depth of the snow one hour from now is 8.5 inches.

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Hey there! I'm happy to help!

We see that if the river isn't moving at all the boat can move at 18 mph (most likely because it has an engine propelling it.)

We want to set up a proportion where our 21 miles downstream time is equal to our 15 miles upstream time so we can find the speed. A proportion is basically showing that two ratios are equal. Since our downstream distance and upstream distance can be done in the same amount of time, we will write it as a proportion.

We want to find the speed of the river. We will use r to represent the speed of the river. When going downstream, the boat will go faster, so it will have a higher mph. So, our speed going down is 18+r. When you are going upstream, it's the opposite, so it will be 18-r.

[tex]\frac{distance}{speed} =\frac{21}{18+r} = \frac{15}{18-r}[/tex]

So, how do we figure out what r is now? Well, one nice thing to know about proportions is that the product of the items diagonal from each other equals the product of the other items. Basically, that means that 15(18+r) is equal to 21(18-r). This is a very nice trick to solve proportions quickly. We see that we have made an equation and now we can solve it!

15(18+r)=21(18-r)

We use the distributive property to undo the parentheses.

270+15r=378-21r

We subtract 270 from both sides.

15r=108-21

We add 21 to both sides.

36r=108

We divide both sides by 36.

r=3

Therefore, the speed of the river is 3 mph.

You also could have noticed that 18mph to 21 mph is +3, and 18mph to 15 mph -3 in -3 mph, so the speed of the river is 3 mph. That would have been a quicker way to solve it XD!

Have a wonderful day!

Assuming the coin is not weighted and is a fair and standard coin - the chance of flipping head is 1/2. You can either flip head or tails, there are no other possible outcomes.

Answer:

[tex]\Large \boxed{\sf \ \ 28 \ \text{ and } \ 62 \ \ }[/tex]

Step-by-step explanation:

Hello, let's note a and b the two numbers.

We can write that

a = 6 + 2b

ab = 1736

So

[tex](6+2b)b=1736\\\\ \text{***Subtract 1736*** } <=> 2b^2+6b-1736=0\\\\ \text{***Divide by 2 } <=> b^2+3b-868=0 \\ \\ \text{***factorize*** } <=> b^2 +31b-28b-868=0 \\ \\ <=> b(b+31) -28(b+31)=0 \\ \\ <=> (b+31)(b-28) =0 \\ \\ <=> b = 28 \ \ or \ \ b = -31[/tex]

We are looking for positive numbers so the solution is b = 28

and then a = 6 +2*28 = 62

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

  A.  (2, 4)

Step-by-step explanation:

The ordered pairs represent (x, y). Since you have y =2x, this is the same as ...

  (x, 2x)

That is, the second number in the pair needs to be twice the first number in the pair. Since you know your times tables, you know that this is not the case for (1, 0), (10, 5) or (4, 12). Those values of x would give (1, 2), (10, 20), (4, 8).

It is the case that you have (x, 2x) for (2, 4).

The point (2, 4) lies on the graph of y = 2x.

Answer:

we dont see aa figure

Step-by-step explanation:

Answer:

y(x) = (7/25)x^2 + 4

Step-by-step explanation:

Given:

x = 5*sqrt(t) .............(1)

y = 7*t+4 ..................(2)

solution:

square (1) on both sides

x^2 = 25t

solve for t

t = x^2 / 25  .........(3)

substitute (3) in (2)

y = 7*(x^2/25) +4

y= (7/25)x^2 + 4

Answer:

[tex]t=\frac{50.857-51}{\frac{5.014}{\sqrt{7}}}=-0.075[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=7-1=6[/tex]  

The p value for this case would be given:

[tex]p_v = 2*P(t_6 <-0.075)=0.943[/tex]

The p value for this case is lower than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 51

Step-by-step explanation:

Info given

50, 53, 55, 43, 50, 47, 58.

We can calculate the sample mean and deviation with this formula:

[tex]\bar X=\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2)}{n-1}}[/tex]

represent the mean height for the sample  

[tex]s=5.014[/tex] represent the sample standard deviation for the sample  

[tex]n=7[/tex] sample size  

represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to test if the true mean is equal to 51, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 51[/tex]  

Alternative hypothesis:[tex]\mu \neq 51[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing we got:

[tex]t=\frac{50.857-51}{\frac{5.014}{\sqrt{7}}}=-0.075[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=7-1=6[/tex]  

The p value for this case would be given:

[tex]p_v = 2*P(t_6 <-0.075)=0.943[/tex]

The p value for this case is lower than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 51

Answer:

(c) [tex]f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.[/tex]

(b) The probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.

(c) The probability that cooking or preparation time is within 2 mins of the mean time is 0.40.

Step-by-step explanation:

The random variable X follows a Uniform (25, 35).

(a)

The probability density function of an Uniform distribution is:

[tex]f_{X}(x)=\left \{ {{\frac{1}{B-A};\ A<X<B} \atop {0;\ Otherwise}} \right.[/tex]

Then the probability density function of the random variable X is:

[tex]f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.[/tex]

(b)

Compute the value of P (X > 33) as follows:

[tex]P(X>33)=\int\limits^{35}_{33} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{35}_{33} {1} \, dx \\\\=\frac{1}{10}\times [x]^{35}_{33}\\\\=\frac{35-33}{10}\\\\=\frac{2}{10}\\\\=0.20[/tex]

Thus, the probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.

(c)

Compute the mean of X as follows:

[tex]\mu=\frac{A+B}{2}=\frac{25+35}{2}=30[/tex]

Compute the probability that cooking or preparation time is within 2 mins of the mean time as follows:

[tex]P(30-2<X<30+2)=P(28<X<32)[/tex]

                                      [tex]=\int\limits^{32}_{28} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{32}_{28}{1} \, dx \\\\=\frac{1}{10}\times [x]^{32}_{28}\\\\=\frac{32-28}{10}\\\\=\frac{4}{10}\\\\=0.40[/tex]

Thus, the probability that cooking or preparation time is within 2 mins of the mean time is 0.40.

Answer:

Here you go!! :)

Step-by-step explanation:

Given that the sides of the quadrilateral are 3.3

The measure of one angle is 116°

We need to determine the value of x.

Value of x:

Since, the given quadrilateral is a rhombus because it has all four sides equal.

We know the property that the opposite sides of the rhombus are equal.

The measure of the opposite angle is 116°

x = measure of opposite angle

x = 116°

Then, the value of x is 116°

Therefore, the value of x is 116°

Answer:

In the diagram, the measurement of x is 87°

Step-by-step explanation:

In this diagram, this shape is a quadrilateral. This quadrilateral in this picture is known as rhombus. In a rhombus, the consecutive angles are supplementary meaning they have a sum of 180°. Consecutive means the angles are beside each other. So, we will subtract 93 from 180 to find the value of x.

180 - 93 = 87

The measurement of x is 87°

Answer:

a. t>w

Step-by-step explanation:

Sin t= 0.29

t = sin^-1(0.29)

t= 16.86°

Sin w= 0.43

W = sin^-1(0.43)

W= 25.47°

Angles in the second quadrant are positive in sine and they are generally determined by subtracting the initial value from 180°

For t= 180°-16.86°

t = 163.14°

For w = 180°-25.47°

W= 154.53°

163.14°>154.53°

t>w

Answer:

A digit that makes this sentence true is 4.

Step-by-step explanation:

Since the first digit in the number to the left is 3, you simply have to find a digit greater than 3. Here are the possibilities:

4

5

6

7

8

and

9

Out of any of these you can choose, I chose 4.

9514 1404 393

Answer:

   3, or any greater digit

Step-by-step explanation:

Suppose the digit is 'd'. Then the value on the right is ...

  69.436 +100d

Subtracting the value on the left, we want the difference greater than 0.

  69.436 +100d - 352.934 > 0

  100d -293.498 > 0 . . . . simplify

  100d > 293.498 . . . . . . . add 293.498

  d > 2.93498 . . . . . . . . . . divide by 100

That is d is any single digit greater than 2.9. Those digits are ...

  d ∈ {3, 4, 5, 6, 7, 8, 9}

Any digit 3 or greater makes the sentence true.

Answer:

y = (x + 3)^2 - 6.

Step-by-step explanation:

The vertex formula is Y = a(x - h)^2 + k.

To find the vertex formula, we need to find h and k, by finding the vertex of x^2 + 6x + 3.

h = -b/2a

a = 1, b = 6.

h = -6 / 2 * 1 = -6 / 2 = -3

k = (-3)^2 + 6(-3) + 3 = 9 - 18 + 3 = -9 + 3 = -6

So far, we have Y = a(x - (-3))^2 + -6, so y = a(x + 3)^2 - 6.

In this case, the coefficient of x^2 of the given formula is 1, which means that a will be 1.

The vertex form of x^2 + 6x + 3 is y = (x + 3)^2 - 6.

To check our work...

y = (x + 3)^2 - 6

= x^2 + 3x + 3x + 9 - 6

= x^2 + 6x + 3

Hope this helps!

Answer:

(a) -3125, 15625

(b)

[tex]a_n=-5a_{n-1}, \\n\geq 2 \\a_1=1[/tex]

(c)[tex]a_n=(-5)^{n-1}[/tex]

Step-by-step explanation:

The sequence [tex]a_n$ _{n=1}^\infty[/tex] is given as:

[tex]\{1,-5,25,-125,625,\cdots\}[/tex]

(a)The next two terms of the sequence are:

625 X -5 = - 3125

-3125 X -5 =15625

(b)Recurrence Relation

The recurrence relation that generates the sequence is:

[tex]a_n=-5a_{n-1}, \\n\geq 2 \\a_1=1[/tex]

(c)Explicit Formula

The sequence is an alternating geometric sequence where:

Therefore, an explicit formula for the sequence is:

[tex]a_n=1\times (-5)^{n-1}\\a_n=(-5)^{n-1}[/tex]

Answer:

873

Step-by-step explanation:

so the equation is: 5x+1

sum is:

[tex] \frac{first \: one \: + \: last \: one}{2} \times quantity \: of \: terms \\ [/tex]

we have 6( 5×1+1) to 91 (5×18+1)

so we have 18 terms

then:

[tex] \frac{91 + 6}{2} \times 18 = 873[/tex]

Answer:

1/8

Step-by-step explanation:

Total cards = 8

Card with 4 = 1

P(4) = 1/8

Answer:

The  probability of a bulb lasting for at most 552 hours.

P(x>552)  = 0.0515

Step-by-step explanation:

Step(i):-

Given mean of the life time of a bulb = 510 hours

Standard deviation of the lifetime of a bulb = 25 hours

Let 'X' be the random variable in normal distribution

Let 'x' = 552

[tex]Z = \frac{x-mean}{S.D} = \frac{552-510}{25} =1.628[/tex]

Step(ii):-

The  probability of a bulb lasting for at most 552 hours.

P(x>552) = P(Z>1.63)

               = 1- P( Z< 1.63)

               =  1 - ( 0.5 + A(1.63)

              =   1- 0.5 - A(1.63)

              =   0.5 -A(1.63)

              =   0.5 -0.4485

             =  0.0515

Conclusion:-

The  probability of a bulb lasting for at most 552 hours.

P(x>552)  = 0.0515

Answer:

x  =  8   ( 20$ bills)

y  = 5    ( 10 $ bills)

z = 2     ( 5  $  bills)

Step-by-step explanation:

Let call x, y, and z the number of bill of 20, 10, and 5 $ respectively

then according to problem statement, we can write

20*x + 10*y + 5*z = 220         (1)

We also know the total number of bills (15), then

x + y + z = 15     (2)

And that quantity of 20 $ bill is equal to

x = 3 + y     (3)

Now we got a three equation system we have to solve for x, y, and z for which we can use any valid procedure.

As    x = 3 + y    by substitution in equation (2)   and (1)

( 3 + y ) + y + z  = 15       ⇒   3 + 2*y + z = 15  ⇒  2*y + z = 12

20* ( 3 + y ) + 10*y + 5*z  = 220  ⇒ 60 + 20*y + 10*y + 5*z = 220

30*y + 5*z  = 160      (a)

Now we have only 2 equations

2*y + z = 12   ⇒    z = 12 - 2*y

30*y + 5*z  = 160     30*y  + 5* ( 12 - 2*y) = 160

30*y  + 60 - 10*y = 160

20*y = 100

y = 100/20       y = 5      Then by substitution in (a)

30*y + 5*z = 160

30*5  + 5*z = 160

150 + 5*z  = 160    ⇒     5*z = 10     z = 10/5      z = 2

And x

x + y + z = 15

x + 5 + 2 = 15

x = 8

Answer:

x=8 y=5 x=2

Step-by-step explanation:

Answer:

I noticed a pattern:

3 * 2 + 6 = 12 and 2 * 2 + 5 = 9

This means that a*b = 2a + b.

Answer:

option 1

Step-by-step explanation:

[tex]r=\sqrt{(5\sqrt{2})^{2}+(-5\sqrt{2})^{2} } \\\\=\sqrt{25*2+25*2}\\\\ =\sqrt{50+50}\\\\=\sqrt{100}\\\\=10[/tex]

[tex]x=tan^{-1}(\frac{-5\sqrt{2}}{5\sqrt{2}})\\\\x=tan^{-1} (-1)\\x=\frac{7\pi}{4}[/tex]

[tex]re^{ix}=10e^{i\frac{7\pi}{4}}[/tex]

Answer:

it indicates that it is infinitely many solutions