A manager recorded how many hours each of 11 cashiers worked in a week. Which interval contains the median number of hours worked?

Answer:

The answer is Steps 1 and 2.                                Step 1: -3(x+2) = 5(x-7)

                                                                               Step 2: -3x-6 = 5x-35

Step-by-step explanation:

Answer:

Steve should use:

Step-by-step explanation:

Let Steve cut the wire so that the first piece has length x.

Therefore, the second piece will have a length of (52 - x).

The wire of length x is used to make a circle

Circumference of a Circle,

[tex]c = 2\pi r\\Therefore\\2\pi r=x\\r=\dfrac{x}{2\pi}[/tex]

[tex]\text{Area of a circle, A}=\pi r^2= \pi (\dfrac{x}{2\pi})^2=\pi (\dfrac{x^2}{4\pi^2})\\A=\dfrac{x^2}{4\pi}[/tex]

The wire of length (52-x) is used to make a square.

[tex]\text{Side length of the Square,}[/tex] [tex]s= \dfrac{52-x}{4}[/tex]

[tex]\text{Area of the Square},s^2= \left(\dfrac{52-x}{4}\right)^2=\dfrac{(52-x)^2}{16}=\dfrac{x^2-104x+2704}{16}[/tex]

Total Area = Area of Circle + Area of Square

[tex]Area=\dfrac{x^2}{4\pi}+\dfrac{x^2-104x+2704}{16}[/tex]

Let us simplify the expression

[tex]Area=\dfrac{16x^2+\pi(x^2-104x+2704)}{16\pi}\\=\dfrac{16x^2+\pi x^2-104\pix+2704\pi}{16\pi}\\=\dfrac{x^2(16+\pi)-104\pi x+2704\pi}{16\pi}\\=\dfrac{x^2(16+\pi)}{16\pi}-\dfrac{104\pi x}{16\pi}+\dfrac{2704\pi}{16\pi}\\A=\dfrac{x^2(16+\pi)}{16\pi}-6.5x+169[/tex]

This is the function of a parabola which opens up.

To find where A is minimum, find the axis of symmetry.

[tex]$Using \: x=-\frac{b}{2a}[/tex]

[tex]a=\dfrac{16+\pi}{16\pi}, b=-6.5\\ x=-\dfrac{-6.5}{2(\dfrac{16+\pi}{16\pi})}=8.53\:Inches[/tex]

Steve should cut the wire so that the length of wire used to make a circle is 8.53 Inches.

Length of wire used to make the square =52-8.53=43.47 Inches

Answer:

[tex]\hat p = \frac{Lower+Upper}{2}[/tex]

And replacing the info from the problem we have:

[tex]\hat p = \frac{0.018+0.046}{2}= 0.032[/tex]

So then the best estimator for the true proportion p is given by [tex]\hat p = 0.032 [/tex] or equivalent to 3.2 %

Step-by-step explanation:

We want to find a confidence interval for a proportion p who represent the parameter of interest.

The confidence interval would be given by this formula:

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

For this case the 90% confidence interval is given by (1.8%=0.018, 4.6%=0.046) after apply the last formula

Since the confidence interval is symmetrical we can estimate the point estimator of the true percentage with this formula:

[tex]\hat p = \frac{Lower+Upper}{2}[/tex]

And replacing the info from the problem we have:

[tex]\hat p = \frac{0.018+0.046}{2}= 0.032[/tex]

So then the best estimator for the true proportion p is given by [tex]\hat p = 0.032 [/tex] or equivalent to 3.2 %

Answer:

[tex]z=\frac{7.4-7.6}{\frac{0.9}{\sqrt{130}}}=-2.534[/tex]    

[tex]z_{\alpha}=-2.054[/tex]

If the calculated value is less than the critical value we reject the null hypothesis.

P value

The p value for this test would be:  

[tex]p_v =P(Z<-2.534)=0.0056[/tex]  

Since the p value is lower than the significance level given we have enough evidence to reject the null hypothesis at the 25 of significance level given.

Step-by-step explanation:

Information given

[tex]\bar X=7.6[/tex] represent the sample mean

[tex]\sigma=0.9[/tex] represent the population deviation

[tex]n=130[/tex] sample size  

[tex]\mu_o =7.4[/tex] represent the value that we want to check

[tex]\alpha=0.02[/tex] represent the significance level for the hypothesis test.  

z would represent the statistic

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

System of hypothesis  

We want to check if the mean pressure is less then 7.6 pounds/square inch, the system of hypothesis are:  

Null hypothesis:[tex]\mu \geq 7.6[/tex]  

Alternative hypothesis:[tex]\mu < 7.6[/tex]  

The statistic would be:

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

Replacing the values we got:

[tex]z=\frac{7.4-7.6}{\frac{0.9}{\sqrt{130}}}=-2.534[/tex]    

Critical value

we need to find a critical value who accumulates 0.02 of the area in the left of the normal standard distribution and we got:

[tex]z_{\alpha}=-2.054[/tex]

If the calculated value is less than the critical value we reject the null hypothesis.

P value

The p value for this test would be:  

[tex]p_v =P(Z<-2.534)=0.0056[/tex]  

Since the p value is lower than the significance level given we have enough evidence to reject the null hypothesis at the 25 of significance level given.

Answer:

It will take 10 years for her money to double.

Step-by-step explanation:

The compound interest formula is given by:

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the number of years the money is invested or borrowed for.

In this exercise:

We want to find t for which the money doubles, that is, t when A = 2P.

Compounded monthly, an year has 12 months, so n = 12

Interest rate of 7%, so r = 0.07.

The following logarithm property is used:

[tex]\log{a^{t}} = t\log{a}[/tex]

So

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]2P = P(1 + \frac{0.07}{12})^{12t}[/tex]

[tex](1.0058)^{12t} = 2[/tex]

[tex]\log{(1.0058)^{12t}} = \log{2}[/tex]

[tex]12t\log{1.0058} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{12\log{1.0058}}[/tex]

[tex]t = 10[/tex]

It will take 10 years for her money to double.

Answer:

Communitive property of addition

Step-by-step explanation:

Answer:

a A=$47,887.81

b.A=$46,430.80

Step-by-step explanation:

a. Given the initial amount is $40,000 with a 3-year term and a 6% rate compounded daily.

-Take 1 year=365 days

#First we calculate the effective interest rate corresponding to the daily compounding;

[tex]i_m=(1+i/m)^m-1\\\\=(1+0.06/365)^{365}-1\\\\=0.06183[/tex]

#We use the calculated effective rate, 0.06183, to solve for the future value as:

[tex]A=P(1+i_m)^n\\\\=40000(1.06183)^3\\\\=47887.81[/tex]

Hence, the total future value for a daily compounding is $47,887.81

b. For a sinking fund with a 5% compounded quarterly:

#We calculate the annual effective rate:

[tex]i_m=(1+i/m)^m-1\\\\=(1+0.05/4)^4-1\\\\=0.05095[/tex]

#We use the calculated effective rate, 0.05095, to solve for the future value as:

[tex]A=P(1+i_m)^n\\\\=40000(1.05095)^3\\\\=46430.80[/tex]

Hence, the future value of the sinking fund is $46,430.80

Answer:

Adb , cbd, 1

Step-by-step explanation:

Answer:

ADB CBD 1

Step-by-step explanation:

Answer:

42,690

Step-by-step explanation:

it is the rule of LONG numbers

The value of the car in 2020 is $5532.53

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.

Given that, You purchase a car in 2010 for $25,000. The value of the car decreases by 14% annually.

The exponential decay is given by =

[tex]A = P(1-r)^t[/tex]

A = final amount

P = principal amount

r = rate of decrease.

t = 10

Therefore,

A = 25000(1-0.14)¹⁰

A = 25000×0.86¹⁰

A = 5532.53

Hence, the value of the car in 2020 is $5532.53

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Answer:

These questions focus on how the proportion of females will vary in random samples if we assume that 0.60 of the population of part-time college students is female.

1. Before we use a simulation to simulate the selection of random samples from this population, let’s make sure we are clear about who is in the population. For this situation which statement best describes the population?  part-time college students

2. What are we assuming to be true about the population? The proportion of the population that is female is 0.60

3. Which of the following sequences of sample proportions is the most likely to occur in random samples of 25 students from this population? 0.56, 0.60, 0.44, 0.68, 0.76

Answer:

133/1152

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

19+15+14 = 48 marbles

Of which 19 are red, 15 are yellow and 14 are blue.

What is the probability of pulling out a blue marble, followed by a red marble, if you replace the blue marble first

Blue marble

48 marbles, of which 14 are blue.

So [tex]P_{A} = \frac{14}{48} = \frac{7}{24}[/tex]

Red marble

48 marbles, of which 19 are red.

So [tex]P_{B} = \frac{19}{48}[/tex]

Both:

[tex]P = P_{A} \times P_{B} = \frac{7}{24} \times \frac{19}{48} = \frac{133}{1152}[/tex]

So the correct answer is:

133/1152

(d) The particle moves in the positive direction when its velocity has a positive sign. You know the particle is at rest when [tex]t=0[/tex] and [tex]t=3[/tex], and because the velocity function is continuous, you need only check the sign of [tex]v(t)[/tex] for values on the intervals (0, 3) and (3, 6).

We have, for instance [tex]v(1)\approx-0.91<0[/tex] and [tex]v(4)\approx0.91>0[/tex], which means the particle is moving the positive direction for [tex]3<t<6[/tex], or the interval (3, 6).

(e) The total distance traveled is obtained by integrating the absolute value of the velocity function over the given interval:

[tex]\displaystyle\int_0^6|v(t)|\,\mathrm dt=\int_0^3-v(t)\,\mathrm dt+\int_3^6v(t)\,\mathrm dt[/tex]

which follows from the definition of absolute value. In particular, if [tex]x[/tex] is negative, then [tex]|x|=-x[/tex].

The total distance traveled is then 4 ft.

(g) Acceleration is the rate of change of velocity, so [tex]a(t)[/tex] is the derivative of [tex]v(t)[/tex]:

[tex]a(t)=v'(t)=-\dfrac{\pi^2}9\cos\left(\dfrac{\pi t}3\right)[/tex]

Compute the acceleration at [tex]t=4[/tex] seconds:

[tex]a(t)=\dfrac{\pi^2}{18}\dfrac{\rm ft}{\mathrm s^2}[/tex]

(In case you need to know, for part (i), the particle is speeding up when the acceleration is positive. So this is done the same way as part (d).)

Answer:

[a]. sample is 25 randomly selected students

    also population is all students

[b]. (20.0, 23.0)

[c]. (8.8, 24.2)

Step-by-step explanation:

here is a step by step process to solving this, i hope you find this helpful.

1). The population is all students who graduated from his school  while the

sample is 25 randomly selected students from the email list

2). given alpha = 1-0.86=0.14

critical z value(two tailed) for 86% confidence level is:

z=normsinv(0.07) or normsinv(0.93)=1.476

Margin of error=1.476*(4.6/SQRT(20))=1.5

86% confidence interval for population mean

=21.5+/-1.5

=(20.0, 23.0)

3). if population standard deviation is not known,we will use t distribution.

df=20-1=19

t*=tinv(0.05,19)=2.093

Margin of error=2.093*(5.7/sqrt(20))=2.7

95% confidence interval for population mean

=21.5+/-2.7

=(18.8, 24.2)

cheers i hope this helps!!!!

Initial bacteria count is 3, as it doubles every 12 hours; after 2 days, totaling 48 bacteria.

To solve this problem, we can use the formula for exponential growth, which is  

[tex]- \( N \)[/tex]is the final number of bacteria,

[tex]- \( N_0 \)[/tex] is the initial number of bacteria,

[tex]- \( t \)[/tex] is the elapsed time in hours, and

[tex]- \( d \)[/tex] is the doubling time in hours.

Given that the doubling time is 12 hours and after 2 days (which is 48 hours) there are 48 bacteria, we can plug these values into the formula and solve for [tex]\( N_0 \):[/tex]

[tex]\[ 48 = N_0 \times 2^{(48/12)} \][/tex]

Solving this equation:

[tex]\[ 48 = N_0 \times 2^4 \][/tex]

[tex]\[ 48 = N_0 \times 16 \][/tex]

Now, to find [tex]\( N_0 \)[/tex]:

[tex]\[ N_0 = \frac{48}{16} \][/tex]

[tex]\[ N_0 = 3 \][/tex]

So, there were 3 bacteria at the beginning of the first day.

Answer:

$34.20

Step-by-step explanation:

First, find the cost with tax

You are paying 7.2% tax, but you are also paying for 100% of the bill

100%+7.2%=107.2%

So, you are really paying for 107.2% of the bill

Convert 107.2% to a decimal by dividing by 100 or moving the decimal 2 spaces to the right

107.2/100=1.072

Multiply the decimal by the cost of the bill

1.072*45.90=49.2048

But, we also have a coupon for $15 off

Subtract 15 from the cost with tax

49.2048-15=34.2048

Round to the nearest cent/hundreth

$34.20

Hope this helps! :)

Given:

Given that Steven purchased a box of chocolate shaped like a square pyramid.

The box is 12 inches tall and the area of the bottom of the box is 35 square inches.

We need to determine the expression that is used to find the number of chocolates that the box holds.

Expression:

The expression that is used to find the number of chocolates that the box holds can be determined using the formula,

[tex]V=\frac{1}{3} Bh[/tex]

where B is the area of the base and h is the height of the pyramid.

Substituting B = 35 and h = 12 in the above formula, we get;

[tex]V=\frac{1}{3}(35 \cdot 12)[/tex]

Thus, the expression that is used to find the number of chocolates that the box holds is [tex]\frac{1}{3}(35 \cdot 12)[/tex]

Hence, Option b is the correct answer.

Answer:

Option 2

Step-by-step explanation:

Volume of a pyramid

⅓ × base area × height

⅓ × 35 × 12

12 × 35 × ⅓

Answer: 1 = 57.2

2 = angle S

3 = the triangles are similar (the second choice)

Step-by-step explanation: i got the question right on my work on e d g e n u i t y

Consider the triangles.

Triangle C D E. Angle C is blank, angle D is 87.3 degrees, angle E is 35.5 degrees. Triangle R S T. Angle R is blank, angle S is 57.2 degrees, angle T is 87.3 degrees.

Answer the questions about these triangles.

What is the measure of angle C?

✔ 57.2

Which angle corresponds to angle C?

✔ angle S

What can be concluded about the triangles?

✔ The triangles are similar.

The measure of angle C in triangle CDE is 57.2 degrees, Angle C corresponds to angle R in triangle RST,  and the two triangles are  similar or congruent.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Since the sum of angles in a triangle is always 180 degrees, we can find the measure of angle C in triangle CDE by subtracting the measures of angles D and E from 180 degrees:

Angle C = 180 degrees - Angle D - Angle E

Angle C = 180 degrees - 87.3 degrees - 35.5 degrees

Angle C = 57.2 degrees

Therefore, the measure of angle C in triangle CDE is 57.2 degrees.

Angle C corresponds to angle R in triangle RST, since they are both unknown angles in their respective triangles.

We can conclude that the two triangles are  similar or congruent.

Hence, the measure of angle C in triangle CDE is 57.2 degrees, Angle C corresponds to angle R in triangle RST,  and the two triangles are  similar or congruent.

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Answer: f(2x)

Step-by-step explanation:

ed 2020

Answer:

It takes 3 seconds for the diver to reach the water.

Step-by-step explanation:

The height, in feet, is given by the following equation:

[tex]h(t) = -16t^{2} + 144[/tex]

How many seconds will it take for the diver to reach the water?

He reaches the water when his height is 0, that is, when h(t) = 0. So

[tex]h(t) = -16t^{2} + 144[/tex]

[tex]0 = -16t^{2} + 144[/tex]

[tex]16t^{2} = 144[/tex]

[tex]t^{2} = \frac{144}{16}[/tex]

[tex]t^{2} = 9[/tex]

[tex]t = \pm \sqrt{9}[/tex]

[tex]t = \pm 3[/tex]

There are no negative instant of time, so just t = 3.

It takes 3 seconds for the diver to reach the water.

The situation can illustrate the distributive property in math (6*(2+3)=6*2 + 6*3), representing 'a' as six cars, and 'b' and 'c' as the people in each car.

The situation described can be used to illustrate the distributive property in mathematics. The distributive property states a(b + c) = ab + ac. In this scenario, the six cars can be represented as 'a', while the 'b' and 'c' can represent the two people in front and the three in the back. Therefore, the total number of people in all cars is 6*(2+3) which according to the distributive property equals 6*2 + 6*3. That is, 12 people in the front seats and 18 in the back seats, summed up to be 30 people in total.

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Final answer:

The distributive property states that the product of a number and a sum is equal to the sum of the individual products. In this situation with the cars, we can use the distributive property to calculate the total number of people in all the cars.

Explanation:

The distributive property in mathematics states that the product of a number and a sum is equal to the sum of the individual products. In this situation with the cars, we can use the distributive property to calculate the total number of people in all the cars. Each car has 2 people in front and 3 people in back, so we can write the expression as (2 + 3) * 6. Using the distributive property, we can simplify this expression to 2 * 6 + 3 * 6, which equals 12 + 18, or 30 people in all the cars.

Answer:

The volume is 2144.66

Step-by-step explanation:

The equation i used when solving this question.

V=4/3πr3

The volume of sphere when rounded to nearest 100th will be 2143.574 cubic units

Given: a sphere of radius 8 units

To find: Volume of sphere

The volume of a sphere can be calculated using the formula [tex]V = \frac{4}{3}\pi r^3[/tex], where r is the radius of the sphere. To find the volume, plug in the value of the radius into the formula and calculate the result.

[tex]V = \frac{4}{3}\pi r^3\\[/tex]

[tex]V = \frac{4}{3}\pi (8)^3\\[/tex]

[tex]V = \frac{4}{3}\pi (8)^3 = 682.667 \pi[/tex]

If we insert the value of [tex]\pi = 3.14[/tex] we get:

[tex]V = 682.667 \times 3.14 = 2143.57438[/tex]

When rounded to nearest 100th we will get volume equal to 2143.574 cubic units.

An infinite geometric series would only converge if the common ratio is a proper fraction.

An infinite geometric series can be defined as the sum of a geometric sequence that typically has a constant common ratio between successive terms but no last term.

In Mathematics, it is a fact that if the common ratio of an infinite geometric series is a proper fraction, this would make it to converge because each successive term gets smaller and smaller.

In conclusion, an infinite geometric series would only converge if the common ratio is a proper fraction such as 3/6.

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Answer:

c. a proper fraction

b and d. -2/3 and 3/4

c. 80/3

Step-by-step explanation:

...

Answer:

2,5, and 6

Step-by-step explanation:

hope this helps

The solid will be a triangular prism .The solid will have some faces that are rectangles and some faces that are triangles.

The solid will have five faces.

Answer:

I'm just going to take a guess and say 36?

Step-by-step explanation:

Answer:

5x+20

Step-by-step explanation:

5(x+4)

Distribute

Multiply 5 by each term inside the parentheses

5*x + 5*4

5x+20

Answer:

6

Step-by-step explanation:

A triangular prism, a shape with two identical triangular faces and three identical rectangular faces, has 6 vertices where the edges of these faces meet.

In geometry, a shape's vertices are the points where two or more lines or edges meet. When we consider a triangular prism, we see that it is a figure with two triangular faces and three rectangular faces. Each triangular face has 3 vertices, and since these faces are identical, they share vertices. If you count up all these points, we find that a triangular prism has 6 vertices in total.

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Answer:

55%

Step-by-step explanation:

Answer:

4 hours

Step-by-step explanation:

We know that there are 24 hours in a day. Therefore, we will subtract from 24.

If mark spends one-third of his day sleeping, then he will be asleep for 8 hours.

[tex]\frac{1}{3}\times24 \\=\frac{24}{3} \\=8[/tex]

We also know that if Mark spends one-sixth of his day at soccer practice, he will have been practicing for 4 hours.

[tex]\frac{1}{6}\times24 \\=\frac{24}{6} \\=4[/tex]

We now simply subtract from 24:

[tex]\text{hours in a day - hours asleep - hours at school - hours practicing} \\24 - 8 - 8 - 4 \\= 4[/tex]

Therefore, Mark will have 4 hours of free time.

Answer:

the answer is A.Use the numbers in the table to create ordered pairs. and D.Draw a straight line that starts at the origin and connects all the points.

Step-by-step explanation:

I just did it on edgnuity and got it right.

Answer:

The correct answer is A C and D

Step-by-step explanation: