Benjamin has 3 gallon of punch he adds another 1/2 gallon of juice to the punch . How many gallons of punch does he have now ? How many cups? Explain

Answer:

y=7000+14^t

Step-by-step explanation:

This equation shows that the original population of bats was 7000 and grows exponentially at a rate of 14% per year.

I put the graph below so you can see it.

In this exercise we have to identify how to write an exponential function from the data informed in the text, in this way we find that:

[tex]y=7000+14^t[/tex]

From the information given in the statement we find that:

Then writing this function as:

[tex]y=7000+14^t[/tex]

See more about function at brainly.com/question/5245372

Answer:

0.3537 feet per minute.

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

[tex]\dfrac{dV}{dt}=10$ ft^3/min[/tex]

[tex]\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h[/tex]

If the Base Diameter = Height of the Cone

The radius of the Cone = h/2

Therefore,

[tex]\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}[/tex]

[tex]\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}[/tex]

Therefore: [tex]\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10[/tex]

We want to determine how fast is the height of the pile is increasing when the pile is 6 feet high.

[tex]When h=6$ feet$\\\dfrac{3\pi *6^2}{12}\dfrac{dh}{dt}=10\\9\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{9\pi}\\ \dfrac{dh}{dt}=0.3537$ feet per minute[/tex]

When the pile is 6 feet high, the height of the pile is increasing at a rate of 0.3537 feet per minute.

Answer:

Cost of tiling the floor of the restaurant = $346.5

Step-by-step explanation:

Since Mario's restaurant is in the shape of a composite figure.

Area of the composite figure = Area of the rectangle + Area of trapezoid

Area of the rectangle = 3 × 9

                                    = 27 square feet

Area of the trapezoid = [tex]\frac{1}{2}(b_{1}+b_{2}).h[/tex]

Here [tex]b_{1}[/tex] and [tex]b_{2}[/tex] are the parallel sides of the trapezoid and 'h' is the distance between these sides.

Area of the trapezoid = [tex]\frac{1}{2}[12+(31-9)]\times 12[/tex]

                                    = 17 × 12

                                    = 204 square feet

Total area of the floor = 27 + 204

                                     = 231 square feet

Cost of the tiles = $1.5 per square feet

Total Cost of tiling the floor of Mario's restaurant will be,

= per square feet cost × Area of the floor

= 1.50 × 231

= $346.5

Answer:

THE ANSWER IS .B  346.50

Step-by-step explanation:

Answer:

13 mins

Step-by-step explanation:

8.03- 1.85= 6.18

-.72=5.46

/.42=13

Answer:

D.

Step-by-step explanation:

It's a right triangle so

[tex]x^2=40^2+9^2[/tex]

x = 41

Answer: the answer is linear pair

Step-by-step explanation:

Answer:

Linear pair postulate

Step-by-step explanation:

Answer:

B. 8

Step-by-step explanation:

The question lacks the required diagram. Find the diagram in the attachment.

Before we can find d21, d22 and d23, we need to get the matrix D first as shown in the attached solution.

On comparison as shown in the attachment, d21 = 11, d22 = -10 and d23 = 7

Note that d21 refers to element in the second row and first column of the matrix

d22 is the element in the second row and second column of the matrix

d23 is the element in the second row and third column of the matrix

d21+d22+d23 = 11-10+7

d21+d22+d23 = 8

The second option is correct.

Answer:

1096750 impressions

Step-by-step explanation:

Given that :

Mean = 850,000

Standard deviation = 150,000

If we assume that X should be the numbers of impressions created;

Then ;

[tex]X \approx N (\mu , \sigma^2)[/tex]

Now ; representing x as the value for the number of impression needed ; Then ;

[tex]P(X>x) = 0.95[/tex]

[tex]P(\dfrac{X- \mu}{\sigma} > \dfrac{x -850000}{150000}) = 0.95[/tex]

[tex]P(Z> \dfrac{ x -850000}{150000}) = 0.95[/tex]

From normal tables:

[tex]P(Z >1.645) = 0.95[/tex]

[tex]\dfrac{x - 850000}{150000} =1.645[/tex]

(x- 850000) = 1.645(150000)

x - 850000 = 246750

x = 246750 + 850000

x = 1096750 impressions

Answer:

$61.12

Step-by-step explanation:

Price of the Video game = $69.99

Discount = 18%

Discount price = 18% of $69.99

                         = $69.99*18/100

                         = $12.6

Price after Discount = Price - Discount price

                                  = $69.99 - $12.6

                                  = $57.39

Sales tax = 6.5% applied to the discounted price

                = 6.5% of $57.39

sales tax in dollars = $57.39 * 6.5/100

                               = $3.73

The amount he pays for the game = $57.39 + $3.73

                                                          = $61.12

Answer:

The rate of trip 2 is 5 km/h

The time of trip 1 is 0.9-x

Step-by-step explanation:

The rate of trip 2 is 5 km/h because it tells you she walked at an avg speed of 5 km/h.

The time of trip 1 is 0.9-x. It's because the time in trip 2 is x, and it says the total is 0.9. So just subtract 0.9-x.

Also I took the test on edge and attached a pic.

Answer:

The expected completion time of this project from now is 2.5 months.

Step-by-step explanation:

To find the expected completion time for the project, we multiply each projection by it's probability.

We have that:

0.4 = 40% probability it takes 2 months to complete the project.

0.3 = 30% probability that it takes 2.5 months to complete the project.

0.2 = 20% probability it takes 3 months to complete the project.

0.1 = 10% probability it takes 3.5 months to complete the project.

What is the expected completion time (in months) of this project from now?

E = 0.4*2 + 0.3*2.5 + 0.2*3 + 0.1*3.5 = 2.5

The expected completion time of this project from now is 2.5 months.

Answer: The answer is (x-5)^2

The volume of any cylinder is

V = pi*r^2*h

where r is the radius and h is the height. We are keeping r = 2 the same the entire time, as the first part of the instructions indicate. In contrast, h is allowed to vary or change based on the values shown in the table.

If h = 1, then,

V = pi*r^2*h

V = pi*2^2*1

V = pi*4

V = 4pi

So you'll write "4pi", without quotes of course, in the V column next to h = 1. This first row shows a height of 1 leads to a volume of 4pi.

-------------

Then if h = 2, we have,

V = pi*r^2*h

V = pi*2^2*2

V = pi*8

V = 8pi  ... this is written in the second box

and finally if h = 3, we would say,

V = pi*r^2*h

V = pi*2^2*3

V = pi*12

V = 12pi .... and this is placed in the third box

---------------

The values of V we got were: 4pi, 8pi, 12pi

This is for h = 1,2 and 3 respectively in that order.

The sequence 4,8,12 is linear because we are adding 4 each time. More specifically, it fits the equation y = 4x where x = 1,2,3. Think of y = 4x as y = 4x+0 and that fits the slope intercept form y = mx+b.

Answer:

2nd option is the correct answer

Step-by-step explanation:

3 times a number decreased by 6 is - 2

Answer:

1. 100[tex]\pi[/tex]

2. 27 [tex]cm^{3}[/tex]

3. 30

Step-by-step explanation:

Area = [tex]\pi[/tex][tex]r^{2}[/tex]

       = [tex]\pi[/tex] x [tex]10x^{2}[/tex]

       = 100[tex]\pi[/tex]

Volume = l x w x h

             = 3 x 3 x 3

             = 27

Simplifying

23 + 11a + -2c = 12 + -2c

Add '2c' to each side of the equation.

23 + 11a + -2c + 2c = 12 + -2c + 2c

Combine like terms: -2c + 2c = 0

23 + 11a + 0 = 12 + -2c + 2c

23 + 11a = 12 + -2c + 2c

Combine like terms: -2c + 2c = 0

23 + 11a = 12 + 0

23 + 11a = 12

Solving

23 + 11a = 12

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-23' to each side of the equation.

23 + -23 + 11a = 12 + -23

Combine like terms: 23 + -23 = 0

0 + 11a = 12 + -23

11a = 12 + -23

Combine like terms: 12 + -23 = -11

11a = -11

Divide each side by '11'.

a = -1

Simplifying

a = -1

Answer:

7, 7, 11 are the three numbers.

Step-by-step explanation:

Given:

Mode of the three numbers = 7

Range of numbers i.e. difference between the smallest and the largest number is = 4

Value of highest number card [tex]\neq[/tex] 7

As per the definition of Mode:

Mode is the number that occurs the most number of times in the given set of numbers. In other words, mode is the number whose frequency is the highest in the given set of numbers.

Here, we have three numbers and mode is 7 that means 7 occurs at least  two times in the three numbers.

Also, we are given that 7 is not highest number, plus 4 is the range that means 7 occurs exactly two times out of three numbers.

So, two numbers are 7 and 7.

7 is not highest and 4 is the range, so third number = 7+4 = 11

So, the numbers on the cards are 7, 7 and 11.

Answer:

Step-by-step explanation:

Hello!

The objective is to  compare the VMT of mid western households and southwestern households. For this two independent random samples of households from both areas and their VMT were recorded:

Be

X₁: VMT of a mid western household

Midwest

16.2 , 14.6 , 11.2 , 24.4 , 9.4 12.9 , 18.6 , 16.6 , 20.3 ,15.1 , 17.3 , 10.8 , 16.6 , 20.9 , 18.3

n₁= 15

∑X₁= 243.20

∑X₁²= 4175.98

X[bar]₁= 16.21

S₁²= 16.64

S₁= 4.08

X₂: VMT of a southwestern household

22.2, 19.2 , 9.3 , 24.6 ,20.2 , 15.8, 18.0 , 12.2 , 20.1 , 16.0 , 17.5 , 18.2 , 22.8 , 11.5

n₂= 14

∑X₂= 247.60

∑X₂²= 4633.24

X[bar]₂= 17.69

S₂²= 19.56

S₂= 4.42

The parameters of study are the population means, if the claim is that the VMT of households is different in both areas, then you'd expect the population means to be different too.

The hypotheses are:

H₀: μ₁ = μ₂

H₁: μ₁ ≠ μ₂

α: 0.05

Assuming both populations are normal and since both population variances are equal the test to apply is an independent samples t test pooled variance:

[tex]t= \frac{(X[bar]_1-X[bar]2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]

[tex]Sa^2= \frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} = \frac{14*16.67+13*19.56}{15+14-2}= \frac{487.66}{27} = 18.06[/tex]

Sa= 4.249= 4.25

[tex]t_{H_0}= \frac{(16.21-17.69)-0}{4.25*\sqrt{\frac{1}{15} +\frac{1}{14} } }= -0.937= -0.94[/tex]

Critical value approach:

This test is two-tailed, this means that the rejection region is divided in two tails:

[tex]t_{n_1+n_2-2; \alpha /2}= t_{27; 0.025}= -2.052[/tex]

[tex]t_{n_1+n_2-2; 1-\alpha /2}= t_{27; 0.975}= 2.052[/tex]

The decision rule is:

If [tex]t_{H_0}[/tex] ≤ -2.052 or if [tex]t_{H_0}[/tex] ≥ 2.052, reject the null hypothesis.

If -2.052 < [tex]t_{H_0}[/tex] < 2.052, do not reject the null hypothesis.

The calculated value is within the "no rejection region" so the decision is to not reject the null hypothesis.

Using the p-value approach:

The p-value is the probability of obtaining a value as extreme as the calculated value of the statistic under the null hypothesis ([tex]t_{H_0}[/tex]). Just as the significance level, the p-value is two tailed, you can calculate it as:

P(t₂₇ ≤ -0.93) + P(t₂₇ ≥ 0.93)= P(t₂₇ ≤ -0.93) + (1 - P(t₂₇ < 0.93)= 0.1796 + ( 1 - 0.8204)= 0.1796*2= 0.3592

p-value= 0.3592

The p-value is always compared to the significance level, the decision rule for this approach is:

If the p-value ≤ α, reject the null hypothesis.

If the p-value > α, do not reject the null hypothesis.

The p-value is greater than α, so the decision is to not reject the null hypothesis.

At a 5% significance level, there is no significant evidence to reject the null hypothesis. You can conclude that the population means of the VMT for households of the Midwest  South ers households.

I hope this mhelps!

Answer:

For ease of writing, θ [tex]=x[/tex]

[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]

[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]

Step-by-step explanation:

Our angle is [tex]x=\frac{3\pi }{4}[/tex]

To find our answers for [tex]sin(\frac{3\pi}{4} )[/tex] and [tex]cos(\frac{3\pi}{4} )[/tex], we will need to use a unit circle. (I have attached the image of one).

Recall that the [tex]sin[/tex] of an angle is equal to the y-value of the corresponding ordered pair.

And the [tex]cos[/tex] of an angle is equal to the x-value of the corresponding ordered pair.

For the angle [tex]x=\frac{3\pi }{4}[/tex], the ordered pair is [tex](-\frac{1}{\sqrt{2}} }, \frac{1}{\sqrt{2} } )[/tex]

This means that

[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]

[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]

Answer:

The probability is 0.31

Step-by-step explanation:

To find the probability, we will consider the following approach. Given a particular outcome, and considering that each outcome is equally likely, we can calculate the probability by simply counting the number of ways we get the desired outcome and divide it by the total number of outcomes.

In this case, the event of interest is  choosing 3 laser printers and 3 inkjets. At first, we have a total of 25 printers and we will be choosing 6 printers at random. The total number of ways in which we can choose 6 elements out of 25 is [tex]\binom{25}{6}[/tex], where [tex]\binom{n}{k} = \frac{n!}{(n-k)!k!}[/tex]. We have that [tex]\binom{25}{6} = 177100[/tex]

Now, we will calculate the number of ways to which we obtain the desired event. We will be choosing 3 laser printers and 3 inkjets. So the total number of ways this can happen is the multiplication of the number of ways we can choose 3 printers out of 10 (for the laser printers) times the number of ways of choosing 3 printers out of 15 (for the inkjets). So, in this case, the event can be obtained in [tex]\binom{10}{3}\cdot \binom{15}{3} = 54600[/tex]

So the probability of having 3 laser printers and 3 inkjets is given by

[tex] \frac{54600}{177100} = \frac{78}{253} = 0.31[/tex]

Answer:

Step-by-step explanation:

From the given data:

The row percentage can be determined by: taking each box in each row and by dividing it with its total on that line, after that we will multiply it by 100 to get the result of it's equivalent percentage.

Table reconstruct the table from the question ; we have:

                y                

x              Yes          No              Total

Low           20         10                  30

Medium     15          35                 50

High           20           5                  25

Total          55           50                105

For Low; the total on the row is 30 ;

so for Yes: we have 20/30 × 100 = 66.7

for No ; we have 10/30 × 100 = 33.3

For Medium ; the total on the row is 50 ;

so for Yes: we have 15/50 × 100 = 30

for No ; we have 35/50 × 100 = 70

For High  ; the total on the row is 25;

so for Yes: we have 20/25 × 100 = 80

for No ; we have 5/25 × 100 = 20

                y                

x              Yes          No              Total

Low           66.7     33.3                100

Medium     30        70                  100

High           80       20                   100

b. The construction of a sketch percentage of the frequency bar chat with x on horizontal axis is shown in the attached file below.

Answer:

Step-by-step explanation:

A= New amount

P= Principal or Original amount which is £1500

I= Interest

t= time period

3.5% as a decimal is 3.5÷100=0.035

time period= 4 years

so 1500(1+0.035)^4 = B

Step-by-step explanation:

20fruits=100%

5fruits=?

5x100/20 5fruitsx5%

=24%

The value of a should be less than -1.

The equation of a parabola is given by the following function,

[tex]y=f(x)=\pm a(x-h)^2+k[/tex]

where,

(h, k) denotes the coordinates of its vertex,

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

[tex]f(x) = x^2[/tex]

[tex]g(x)=ax^2[/tex]

For the parabola,g(x) to be narrower than the parabola f(x) the value of a should be less than 1. also for the parabola to open downward the value of a is needed to be negative.

Hence, the value of a should be less than -1.

Learn more about Equation of parabola:

https://brainly.com/question/4443998

Answer:

c. 7.25

Step-by-step explanation:

Given the following information from an experiment:

[tex]\left\begin{array}{ccc}&$Sample Size&$Sample Mean \\$Treatment 1&5&4\\$Treatment 2&10&8\\$Treatment 3&5&9\end{array}\right[/tex]

Total Sample Size =5+10+5=20

Therefore, the overall mean

[tex]=\dfrac{(5 \times 4)+ (10 \times 8) + (5 \times 9)}{20} \\=\dfrac{145}{20}\\\\=7.25[/tex]

Answer:

By plotting the graph of f(x)=lnx, you can conclude that when x is small, dy/dx has a larger value. For instance, the gradient of the curve when x=0.5 is 2. However, as you move along the x axis, you will see that the graph levels off, indicating a decrease in the slope, or dy/dx. For example, if x=10, dy/dx = 0.1 and when x=20, dy/dx= 0.05 and so on. Eventually, when x is large enough the value of dy/dx will be negligible.

Thus, as x increases, the slope decreases.

Answer:

Explanation shown below

Step-by-step explanation:

f(x)=lnx;

The rate of change is defined as dy/dx;

dy/dx[Inx] = 1/x

and dy/dx is defined as the slope

The nature of the slope is as x increases ; the slope decreases and conversely meaning as x decreases, the slope increases.

Answer:

1.56 hours

Step-by-step explanation:

300 gal × 1 min 3.2 gal × 1 hr 60 min = 1.56 hr.

Answer:

i thought the question said a 'HORSE' fills a hot tub...

Step-by-step explanation:

lol dont mind me i just want points :D

Answer:

A sample size of at least 531 is required.

Step-by-step explanation:

We are lacking the confidence level to solve this question, so i am going to use a 90% confidence level.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Find the required sample size for the new study.

A sample size of at least n is required.

n is found when [tex]M = 0.05[/tex]

We have that [tex]\sigma = 0.7[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.05 = 1.645*\frac{0.7}{\sqrt{n}}[/tex]

[tex]0.05\sqrt{n} = 1.645*0.7[/tex]

[tex]\sqrt{n} = \frac{1.645*0.7}{0.05}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.645*0.7}{0.05})^{2}[/tex]

[tex]n = 530.4[/tex]

Rounding up

A sample size of at least 531 is required.

Answer:

Answer is m∠4=40

Step-by-step explanation:

take note that m∠6 & m∠7 are vertical angles. Vertical angles are equal to each other, therefore m∠6 is equal to m∠7.

m∠6 = m∠7 (vertical angles)

11x + 8 = 12x – 4

12x - 11x = 8 + 4

x = 12

so

m∠6 = 11x + 8  

m∠6 = 11(12) + 8

m∠6 = 132 + 8

m∠6 = 140

m∠4 = 180 - m<6

m∠4 = 180 - 140

m∠4 = 40

Answer:

A

Step-by-step explanation: Took test

Not necessarily, the more correct definition is opposite reciprocal slopes.

The example used is how horizontal and vertical lines are parallel. Horizontal lines have a slope of 0, also written as 0/1. However, vertical lines have an undefined slope, which isn't necessarily negative. It has a slope of 1/0, which is undefined. In this case, the reciprocal isn't negative.

In all other cases (1 and -1, 2 and -1/2, etc.) yes, the perpendicular pairs are negative and reciprocal.