Staples sells boxes of pens ($10) and rubber bands ($5). Leona ordered a total of 24 cartons for $200. How many boxes of each did Leona order? Hint: Let P = Pens.

Answer:

Step-by-step explanation:

We would assume that triangle ABC is a right angled triangle. This means that we can apply Pythagoras theorem in determining the unknown side length.

For the case of the minimum side length, we would assume that the unknown length, L is one of the shorter legs of the triangle. By applying Pythagoras theorem, it becomes

11² = 9² + L²

L² = 121 - 81 = 40

L = √40 = 6.32

For the case of the maximum side length, we would assume that the unknown length, L is one of the hypotenuse of the triangle. By applying Pythagoras theorem, it becomes

L² = 9² + 11²

L² = 81 + 121 = 202

L = √202 = 14.21

The minimum side length is 6.32 and the maximum side length is 14.21

Answer:

D

Step-by-step explanation:

Two lines are parallel if they have the same slope

those with same m,

It only appears in the last option where m= -5 for both lines, so option d

A function assigns values. The graph of the equation y-1=2/3(x-3) is the second graph.

A function assigns the value of each element of one set to the other specific element of another set.

As the function is given to us that y-1=2/3(x-3), now substitute the value of x as 0 and y as 0 to get the intercept of the function. Therefore,

x-intercept

[tex]y-1=\dfrac23(x-3)\\0-1= \dfrac23x-\dfrac23(3)\\\\-1 = \dfrac23x - 2\\\\-1+2 = \dfrac23x\\\\x = \dfrac32[/tex]

y-intercept

[tex]y-1=\dfrac23(x-3)\\\\y-1=\dfrac23(0-3)\\\\y-1=\dfrac23(-3)\\\\y= -2+1\\\\y=-1[/tex]

Thus, we need to look for the graph which intersects the x-axis at 3/2 while the y-axis at -1. Therefore, as shown the below graph.

Hence, the graph of the equation y-1=2/3(x-3) is the second graph.

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Answer:The answer for the first one is log2(.25)=-2

The answer for the second one is 8^3=512

Step-by-step explanation:

Answer:

1. 9x-8y=9

2. -18x+16y= -18 ⇒ -9x+8y= -9 ⇒ 9x-8y=9

as we see both equations are same, it means the lines overlap and there is infinite number of solutions

Answer:

The answer is drawing the 6 of clubs or the 6 of spades because those are the only black 6's.

Answer:

-The arrows should be a length of 6

-The arrows should point in the negative direction

-The arrows should start at zero

Step-by-step explanation:

Hope this helps!

Answer:

B

D

E

Step-by-step explanation:

Answer:

6

Explanation:

According to secant-secant theorem,

(PB)(PA)=(PD)(PC)

(7)(12)=(PD)(14)

NOW

84/14 = PD

PD = 6

Answer:

[tex]P(-1.94<X<-1.5)=P(\frac{-1.94-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{-1.5-\mu}{\sigma})=P(\frac{-1.94-0}{1}<Z<\frac{-1.5-0}{1})=P(-1.94<z<-1.5)[/tex]

And we can find this probability with this difference:

[tex]P(-1.94<z<-1.5)=P(z<-1.5)-P(z<-1.94)=0.0668-0.026= 0.0408[/tex]

Step-by-step explanation:

Let X the random variable that represent the temperatures of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(0,1)[/tex]  

Where [tex]\mu=0[/tex] and [tex]\sigma=1[/tex]

We are interested on this probability

[tex]P(-1.94<X<-1.5)[/tex]

And using the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

And using this formula we got:

[tex]P(-1.94<X<-1.5)=P(\frac{-1.94-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{-1.5-\mu}{\sigma})=P(\frac{-1.94-0}{1}<Z<\frac{-1.5-0}{1})=P(-1.94<z<-1.5)[/tex]

And we can find this probability with this difference:

[tex]P(-1.94<z<-1.5)=P(z<-1.5)-P(z<-1.94)=0.0668-0.026= 0.0408[/tex]

Answer:

3

Step-by-step explanation:

x^2 + y^2 = 9

The equation of a circle is

(x-h)^2 + (y-k)^2 = r^2

( h,k) is the center and r is the radius

x^2 + y^2 = 3^2

The radius is 3

Answer:

Step-by-step explanation:

a) Find the gradient

[tex]\nabla f(x,y) =f_x(x,y)\bold{i} +f_y (x,y)\bold{j}[/tex]

[tex]Also, sin(4x+3y)= sin(4x)cos(3y)+sin(3y)cos (4x)[/tex]

[tex]f_x(x,y) = 4cos(4x)cos(3y)-4sin(3y)sin(4x) = 4 cos(4x-3y)[/tex]

[tex]f_y(x,y) = -3sin(4x)sin(3y)+3cos(3y)cos(4x)=3cos(4x-3y)[/tex]

Hence

[tex]\nabla f(x,y) = 4cos(4x-3y)\bold{i}+3cos(4x-3y)\bold{j}[/tex]

b) At point (-6, 8) just replace the values in gradient to find it out. You can do it.

c) directional derivative in the direction u.

[tex]D_uf(x,y)=\nabla f(x,y). u[/tex]

I stuck with your 1 2 3 i -j . What does 1 2 3 mean? is it not 123 or 1 2/3 or else?

Answer:

  y = -2

Step-by-step explanation:

A horizontal line has an equation of the form ...

  y = constant

In order for the line to go through a point with a y-coordinate of -2, the constant must be -2.

  y = -2 . . . . horizontal line through (-5, -2)

Answer:

15/4

Step-by-step explanation:

3/4:1/5= 3/4*5= 15/4

Complete Question

1 Explain what is meant by the equation lim x → 8 f(x) = 9.

A If |x1 − 8| < |x2 − 8|, then |f(x1) − 9| < |f(x2) − 9|.

B The values of f(x) can be made as close to 8 as we like by taking x  sufficiently close to 9.

C  f(x) = 9 for all values of x.

D If |x1 − 8| < |x2 − 8|, then |f(x1) − 9|≤ |f(x2) − 9|.

E The values of f(x) can be made as close to 9 as we like by taking x sufficiently close to 8.

2  Is it possible for this statement to be true and yet f(8) = 6? Explain.

A Yes, the graph could have a hole at (8, 9) and be defined such that f(8) =6.

B Yes, the graph could have a vertical asymptote at x = 8 and be defined such that f(8) = 6.

C No, if f(8) = 6, then lim x→8 f(x) = 6.

D No, if lim x→8 f(x) = 9, then f(8) = 9.

Answer:

1

   The correct option is  D

2

    The correct option is   A

Step-by-step explanation:

Generally a a limit function  [tex]\lim_{n \to x } f(x) = L[/tex]

Tell us that as n tends toward x the values of  f(x) tends towards L hence for the first question E is the correct option

Now looking at the second question

  Yes it is possible for  lim x → 8 f(x) = 9.  to be true and  f(8) = 6 this is because the graph defined by this limit equation can have a hole the point

(8, 9) and created in such a way that f(8) = 6

Calculus's basic idea of limits in mathematics describes how a function behaves when its input approaches a specific value. No, if f(8) = 6, then lim x → 8 f(x) = 6. The correct option is C.

The statement "lim x → 8 f(x) = 9" means that as x approaches 8, the limit of f(x) is equal to 9. This implies that the function f(x) gets arbitrarily close to 9 as x gets arbitrarily close to 8.

If f(8) = 6, it means that the function f(x) has a specific value of 6 at x = 8. This contradicts the idea that f(x) gets arbitrarily close to 9 as x approaches 8.

Therefore, if f(8) = 6, it is not possible for the statement "lim x → 8 f(x) = 9" to be true.

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Answer:

  36 bottles

Step-by-step explanation:

Each spherical bottle will have a volume of ...

  V = (4/3)πr³ = (4/3)π(4.57³) = 399.8 . . . . cubic inches

Each box (12-pack?) will have a volume of ...

  V = LWH = (15 in)(5 in)(4.4 in) = 330 in³

This is a smaller volume than even one spherical bottle, so 36 bottles will have the larger volume.

Answer:

Step-by-step explanation:

Volume has three parameters and is three dimensional, thus needing a unit in the third power

In difference,

Area is two-dimensional and has only 2 parameters, thus needing a unit only in the second power

Answer:

see below

Step-by-step explanation:

Area is found by multiplying two dimensions  together ( l*w)

Volume is found by multiplying three dimensions together ( l*w*n)

Answer: Needs to be flat with opposite sides that are parallel and are the same in length

Answer:

Step-by-step explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation = 21.8

n = number of samples = 17

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 17 - 1 = 16

Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01

α/2 = 0.01/2 = 0.005

the area to the right of z0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995

Looking at the t distribution table,

z = 2.921

Margin of error = 2.921 × 21.8/√17

= 15.44

The confidence interval for the mean wake time for a population with drug treatments is

90.3 ± 15.44

The upper limit is 90.3 + 15.44 = 105.74 mins

The lower limit is 90.3 - 15.44 = 74.86 mins

The result suggests that the mean wake time might have really reduced since the values barely fall above 100 minutes as in before treatment with a high degree of confidence. Therefore, the drug is effective.

Answer:

P(X≥112) = 0.9495

The  percentage of the games that Easton bowls does  he score higher than 112 = 94.95%

Step-by-step explanation:

Given mean of the Population = 130

Given standard deviation of the Population = 11

Let X= 112

[tex]Z =\frac{x-mean}{S.D} =\frac{112-130}{11}=-1.636[/tex]

P(X≥112) = P(Z≥ z)

               = 1-P(Z≤z)

               = 1- ( P(Z≤-1.636)

             =  1- (0.5-A(-1.636)

            = 0.5 +A(1.636)

            = 0.5 + 0.4495

P(X≥112) = 0.9495

The  percentage of the games that Easton bowls does

he score higher than 112 = 94.95%

Answer:

a) [tex] t_{\alpha/2}=\pm 2.447[/tex]

b) [tex] t_{\alpha/2}=\pm 2.718[/tex]

c) [tex] t_{\alpha/2}=\pm 2.779[/tex]

d) [tex] t_{\alpha/2}=\pm 2.650[/tex]

Step-by-step explanation:

Part a

The degrees of freedom are given by:

[tex] df=n-1= 7-1=6[/tex]

The confidence is 95% or 0.95 the significance would be [tex]\alpha=0.05[/tex] and the critical values would be:

[tex] t_{\alpha/2}=\pm 2.447[/tex]

Part b

The degrees of freedom are given by:

[tex] df=n-1=12-1=11[/tex]

The confidence is 98% or 0.98 the significance would be [tex]\alpha=0.02[/tex] and the critical values would be:

[tex] t_{\alpha/2}=\pm 2.718[/tex]

Part c

The degrees of freedom are given by:

[tex] df=n-1=27-1=26[/tex]

The confidence is 99% or 0.99 the significance would be [tex]\alpha=0.01[/tex] and the critical values would be:

[tex] t_{\alpha/2}=\pm 2.779[/tex]

Part d

The degrees of freedom are given by:

[tex] df=n-1=14-1=13[/tex]

The confidence is 98% or 0.98 the significance would be [tex]\alpha=0.02[/tex] and the critical values would be:

[tex] t_{\alpha/2}=\pm 2.650[/tex]

A value of a test statistic defines the upper bounds of a confidence interval, statistical significance in a test statistic is known as the crucial value.

For part a )

n = 7

Calculating the degrees of freedom [tex]= df = n - 1 = 7 - 1 = 6[/tex]

At [tex]95\%[/tex] the confidence level, the t:

[tex]\alpha = 1 - 95\% = 1 - 0.95 = 0.05\\\\\frac{\alpha}{ 2} = \frac{0.05}{ 2} = 0.025\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.025,6} = 2.447\\\\[/tex]

The critical value = 2.447

For part b )

n =12

Calculating the degrees of freedom[tex]= df = n - 1 = 12 - 1 = 11[/tex]

At [tex]98\%[/tex] the confidence level , the t:

[tex]\alpha = 1 - 98\% = 1 - 0.98 = 0.02\\\\\frac{\alpha}{ 2}= \frac{0.02}{ 2} = 0.01\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.01,11} =2.718\\\\[/tex]

The critical value =2.718

For part c )

n = 27

Calculating the degrees of freedom [tex]= df = n - 1 = 27 - 1 = 26[/tex]

At [tex]99\%[/tex] the confidence level, the t:

[tex]\alpha = 1 - 99\% = 1 - 0.99 = 0.01\\\\\frac{\alpha}{ 2} = \frac{0.01}{ 2} = 0.005\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.005,26}=2.779\\\\[/tex]

The critical value =2.779

For part d )

n = 14

Calculating the degrees of freedom [tex]= df = n - 1 = 14 - 1 = 13[/tex]

At [tex]98\%[/tex] the confidence level, the t:

[tex]\alpha = 1 - 98\% = 1 - 0.98 = 0.02\\\\\frac{\alpha}{ 2} = \frac{0.02}{ 2} = 0.01\\\\t_{\frac{\alpha}{ 2}} \\\\df = t_{0.01,13} =2.650[/tex]

The critical value =2.650

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Answer:

25pi

Step-by-step explanation:

If the circle has a diameter of 10, it has an radius of 5. The area of a circle is pi*r^2. If r=5, then it is 25pi.

Answer:

25π feet^2

Step-by-step explanation:

The area of a circle can be found using the following formula.

a=πr^2

We are given the diameter, but we need to find the radius. The radius is half of the diameter, or

r=d/2

We know the diameter is 10 feet. Therefore, we can substitute 10 in for d.

r=10/2

Divide 10 by 2

r=5

The radius is 5 feet.

Now we know the radius, and can substitute it into the area formula.

a=πr^2

r=5

a=π*5^2

Evaluate the exponent.

5^2 is equal to 5*5, which is 25.

a=π*25

a=25π

Add appropriate units. Area always uses units^2, and the units in this problem are feet.

a=25π feet^2

The area of the circle is 25π square feet

Answer:

D

Step-by-step explanation:

Answer:

C.)

Step-by-step explanation:

C.) Because it states the exact decimals rather than just stating about $2.36. Also, the other options were not specific. Hope this helps!  

Answer:

1 / 2,787,760,560

Step-by-step explanation:

The number of permutations is:

41 × 40 × 39 × 38 × 37 × 31 = 2,787,760,560

So the probability of winning the jackpot is 1 / 2,787,760,560.

Answer:

a

Step-by-step explanation:

increase the significance level to increase the probability of type 1 error

You can use the definition of type I and type II error to find the correct option.

To avoid the more consequential error, the researchers should do:
Option D: Decrease the significance level to decrease the probability of Type I error.

Firstly the whole story starts from hypotheses. The null hypothesis is tried to reject and we try to accept the alternate hypothesis.

The negative is just like the doctor's test getting negative means no disease. Similarly, if we conclude null hypothesis negative means it is accepted. If it is accepted wrongly means the negative test result was false, thus called false negative. This error is called type II error.

The probability of committing the type I error is called the significance level of the hypothesis test.

Since in the given context, by using the definitions of the type I error and the type II error, we have

More consequential error for educators : For the educators, the more consequential error would be that the program does not help children improve their reading skills but the test indicated that it does help.

Thus, the more consequential error for the educators is committing the type I error.

To prevent committing this error, they need to decrease type I error's probability which is denoted by level of significance, need to decrease the level of significance of the hypothesis test.

Thus,

Option D: Decrease the significance level to decrease the probability of Type I error.

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Answer:

1,300,000,000

Step-by-step explanation:

 78    300   000

 550  400   000

 648  700   000

1  277  400   000

To the nearest million

1,2 | 77 400 000            more than 4, so +1

1,300,000,000

Answer:

20 ton

Step-by-step explanation:

We created a system of two separate equations to answer these questions.

"y" will be the total cost to transport the sugar

"x" will be the amount of sugar transported

Therefore, we have to:

y = 3995 + 225.50 * x

y = 6500 + 100.25 * x

We must establish these equations equal to each other because it asks how much of x is necessary to make the same amount of y, therefore:

3995 + 225.50 * x = 6500 + 100.25 * x

solved we have:

225.50 * x - 100.25 * x  = 6500 - 3995

125.25 * x = 2505

x = 2505 / 125.25

x = 20

which means that when the amount of sugar transported is 20 tons, the price is the same

Answer:

11 5/8

Step-by-step explanation:

Simply the 5/8 to 16th

5/8 equals to 10/16

Then add the 16ths together

The divide it by 16

Then add the whole numbers

Then add of them together to get your answer

Answer:

Exact Form:

93 /8

Decimal Form:

11.625

Mixed Number Form:

11  5 /8

Step-by-step explanation:

If you add every side together:

3 3/16 + 2 5/8 + 3 3/16 + 2 5/8 = 93/8

It's quite easy, just add everything together ;)

Answer:

What we know about the p-value for the test is that it will be less than 0.05

Step-by-step explanation:

The complete question is as follows;

Suppose that you had consumer group wanted to test to see if weight of participants in a weight loss program changed (up or down). They computed a 95% confidence interval of the result (-4.977, -2.177). Suppose that we had a significance test with the following hypothesis:

H0: population mean weight loss = 0

Ha: population mean weight loss does not equal 0

What do we know about the p-value for the test?

solution;

Given the information in the question, we are concerned with saying what we know about the p-value for the test

To answer this question, we shall be looking at it from the angle of the confidence interval

The confidence interval given is 95%.

Now what does this indicate?

It indicates that 95% confidence interval contains only values which are less than 0.

What does this mean for the p-value?

This means that the p-value will be less than 0.05