An animal shelter has 21 puppies if the puppies are 28% of the total dog and cat population how many dogs and cats are there in the animal shelter A.59
B.70
C.49
D.75

Given the question:

7t+10(5t+5)-10

First, distribute:

7t+50t+50-10

Next, combine like terms (7t+50t and 50-10)

57t+40

This cannot be simplified further.

If a coin lands on Tails 600 times and the relative frequency of Tails is 0. 3, the coin was thrown 2000 times.

To find the number of times the coin was thrown, we need to use the relative frequency of Tails and the number of times Tails was observed. The relative frequency of Tails is defined as the ratio of the number of times Tails was observed to the total number of trials, expressed as a decimal or percentage.

In this case, the relative frequency of Tails is given as 0.3, which means that Tails was observed in 30% of the trials. We also know that Tails was observed 600 times, so we can set up a proportion:

Tails / Total trials = Relative frequency of Tails

600 / Total trials = 0.3

To solve for the total number of trials, we need to cross-multiply and simplify:

600 = 0.3 * Total trials

Total trials = 600 / 0.3

Total trials = 2000

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Answer:

4

Step-by-step explanation:

Distribute the 2 to the X and 7

4+2x+14=26

2x+18 =26

minus the 18 from 26

2x = 8

divide 2x and 8 by 2

X= 4

The indefinite integral as a power series is f(x) = C + \(\Sigma_{n=1}^{\infty}(-1)^{n+1}\left(\frac{x^{n+8}}{n(n+8)}\right)\). The radius of convergence R = 1.

The indefinite integral as a power series is f(x) = ∫x⁷ ln(1 + x)dx.

The series for In(1 + x) is

In(1 + x) = x - x²/2 + x³/3 - x⁴/4 + x⁵/5 - .....

In(1 + x) = \(\Sigma_{n=1}^{\infty}(-1)^{n+1}\left{\frac{x^n}{n}\right}\)

Now multiply by x⁷ on both sides

x⁷ In(1 + x) = \(\Sigma_{n=1}^{\infty}(-1)^{n+1}\left{\frac{x^n}{n}\right}\)x⁷

x⁷ In(1 + x) = \(\Sigma_{n=1}^{\infty}(-1)^{n+1}\left{\frac{x^{n+7}}{n}\right}\)

Take integration on both side, we get

∫x⁷ In(1 + x) = ∫\(\Sigma_{n=1}^{\infty}(-1)^{n+1}\left{\frac{x^{n+7}}{n}\right}\)dx

∫x⁷ In(1 + x) = \(\Sigma_{n=1}^{\infty}(-1)^{n+1}\int\left{\frac{x^{n+7}}{n}\right}dx\)

∫x⁷ In(1 + x) = \(\Sigma_{n=1}^{\infty}(-1)^{n+1}\frac{1}{n}\int{x^{n+7}}dx\)

∫x⁷ In(1 + x) = \(\Sigma_{n=1}^{\infty}(-1)^{n+1}\frac{1}{n}\left(\frac{x^{n+8}}{n+8}\right)\) + C

∫x⁷ In(1 + x) = C + \(\Sigma_{n=1}^{\infty}(-1)^{n+1}\left(\frac{x^{n+8}}{n(n+8)}\right)\)

Hence, f(x) = C + \(\Sigma_{n=1}^{\infty}(-1)^{n+1}\left(\frac{x^{n+8}}{n(n+8)}\right)\)

The radius of convergence for a power series is found by using the root test or the ratio test.

The root test involves taking the absolute value of the series and then taking the nth root of each of the terms in the series; the radius of convergence is the limit of this value as n approaches infinity.

Hence the radius of convergence R = 1.

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The complete question is:

Evaluate the indefinite integral as a power series.

∫x⁷ ln(1 + x)dx

f(x) = C + \(\Sigma_{n=1}^{\infty}\)_____

What is the radius of convergence R?

The solution of the system of linear equations on the graph is one solution at (1, −2).

Analyzing the intersection of the graphs of a system of linear equations on the coordinate plane will reveal how many solutions there are. The system has a single solution if the graphs meet at a single location. The system cannot be solved if the graphs are parallel and do not intersect. The system has an unlimited number of solutions if the graphs coincide, or overlap.

From the graph we observe that the two lines intersect at the point (1, -2).

The point where the lines intersect is thus the solution of the system of linear equations on the graph.

Hence, the solution of the system of linear equations on the graph is one solution at (1, −2).

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Expressing f(x) in (x-k)q(x) + r : f(x) = (x-4)(5x³ + 18x² + 57x) + 227x

f(x) = (x-k)q(x) + r

Given,

f(x) = 5\(x^{4}\) - 2x³ -15x² -x

Here,

f(x) = 5\(x^{4}\) - 2x³ -15x² -x

k = 4

f(x) = 5\(x^{4}\) -20x³ +18x³ -72x² + 57x² -228x + 227x

f(x) = 5x³(x - 4) + 18x²(x-4) + 57x (x - 4) + 227x

f(x) = (x-4)(5x³ + 18x² + 57x) + 227x

The above equation is in the form of standard equation,

f(x) = (x-k)q(x) + r

On comparing,

x - k= x - 4

q(x) = (5x³ + 18x² + 57x)

r = 227x

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Answer:

43

Step-by-step explanation:

DO the math

9514 1404 393

Answer:

Step-by-step explanation:

First differences are ...

  -38 -(-45) = 7

  -31 -(-38) = 7

  -24 -(-31) = 7

The first differences are constant, so this is an arithmetic sequence with a common difference of 7.

Answer:

A good prediction is that the number 5 will be rolled 8 times

Step-by-step explanation:

Here, we want to get the number of times 5 would occur in a roll of 50

firstly, we need the probability of having a 5 come up

To do this, we have to divide the number of 5’s by the count of possible numbers

We have this simply as 1/6

Now, we have to multiply this by 50

we have this as;

1/6 * 50 = 8.333

This is approximately 8

so we have it that in 50 rolls, we can have the number 5 coming up 8 times

Option A, which states that the ordered pair of point P' will be, is the appropriate response (-8.75, 5.25).

Given,

A scaling factor of 7/4 is used to enlarge the pentagon in the OPQRS.

In order to generate O'P'Q'R'S, we must identify the ordered pair of point P'.

Here,

To obtain the coordinates of P', multiply the coordinates of point P by the scale factor 7/4.

P(-5,3)

P' (x, y) = P (-5 x 7/4, 3 x 7/4).

= P(-8.75, 5.25) 

As a result, option A, which states that the ordered pair of point P' will be, is the appropriate response (-8.75, 5.25).

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The question is improper. Proper question is given below;

If pentagon OPQRS is dilated by a scale factor of 7/4 from the origin, to create O’P’Q’R’S’, what is the ordered pair of point P’?

A. (-8.75, 5.25)

B. (-1.25, 0.75)

C. (-3.5, 8.75)

D. (-1.75, 3.5)

Answer:

AE/AB = EF/BC

4cm/ 8cm = EF/ 5cm.....(Criss cross)

EF = 5 x 4/8

EF = 2.5 cm

Step-by-step explanation:

1/4 cant be converted as mixed no. as it is a proper fraction.

1/4=0.25

Answer:

8, 8.001, 8.01, 8.1, 9, 11, 13, 16

Step-by-step explanation:

From the instructions given, we know that variable u \(\geq\) 8. the  \(\geq\)  sign means that the number is greater than or is equal to the number, which is in this case, 8. In the numbers given, (0, 7, 7.999, 8.01, 11, 3, 7.9, 8, 8.1, 13, 5, 7.99, 8.001, 9, 16) we name the numbers greater than or equal to 8 that are stated in the list.

Answer:

it would only work with 6,0

This man will need to pay a net amount of $1,244.78.

The discount terms of a sales invoice indicate the discounts that will be applied to the invoice amount if payment is received within the specified time frame. A man who is an accounts payable officer for his company must calculate cash discounts before paying invoices.

He is paying bills on June 17 and has an invoice dated June 11 with terms 4​/10, ​n/30.

If the net price of the invoice is ​$​1,296. 64,

Given that,

Net price of the invoice = $1,296.64

Discount percent = 4%

Discount period = 10 days

Payment period = 30 days

To calculate the net amount that the man will have to pay, first calculate the amount of discount he will get, then subtract that amount from the total amount on the invoice.

The amount of discount he will get is:

Discount = Discount percent × Net price of the invoice

               = 4% × $1,296.64

               = 0.04 × $1,296.64

               = $51.86

To calculate the net amount to be paid, subtract the discount from the net price of the invoice:

Net amount = Net price of the invoice − Discount

                    = $1,296.64 − $51.86

                    = $1,244.78

Therefore, the net amount the man will need to pay is $1,244.78.  

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Answer:

6x -1

Step-by-step explanation:

Answer:

The length of the base will be: 17 m

Step-by-step explanation:

Given the area of the triangle

\(A=102\:m^2\)

Using the formula of Area of a triangle:

\(A=\frac{1}{2}\left(b\times h\right)\)

Here,

As the base of a triangle is 7 less than twice its height.

so

\(b=2h-7\)

so the formula of Area of a triangle becomes

\(102=\frac{1}{2}\left(\left(2h-7\right)\times \:h\right)\)

\(204=h\left(2h-7\right)\)

\(2h^2-7h=204\)

\(2h^2-7h-204=0\)

\(\left(2h+17\right)\left(h-12\right)=0\)

\(2h+17=0\quad \mathrm{or}\quad \:h-12=0\)

\(h=-\frac{17}{2},\:h=12\)

As height can not be negative, so:

\(h=12\) m

Hence, the length of the base:

\(b=2h-7\)

   \(= 2(12)-7\)

    \(=24-7\)

     \(= 17\) m

Therefore, the length of the base will be: 17 m

Answer:

-½ + (root2 / 2) i + root½ i

Step-by-step explanation:

\( \frac{a}{b} - \frac{c}{d} = \frac{ad - cb}{bd} \)

I used this formula to do it but let me know if it's enough or you have to simplify it further

Answer:

45

Step-by-step explanation:

Answer:

19.6375 mm^2

Step-by-step explanation:

Given data

Diameter = 5mm

Radius= 5/2= 2.5mm

The expression for the area

A=πr^2

Substitute

A=3.142*2.5^2

A=3.142*6.25

A=19.6375 mm^2

To evaluate the integral of e^(3x) / (1 + e^(3x)) dx, the best substitution to make is u = 1 + e^(3x).

Using this substitution, we can find du/dx = 3e^(3x), which implies dx = du / (3e^(3x)). Thus, the integral becomes:

integral of [e^(3x) / (1 + e^(3x))] dx = integral of [1 / (u-1)] (du / (3e^(3x)))

Now, we can replace the expression e^(3x) with (u-1) / u, and dx with du / (3e^(3x)), giving:

integral of [e^(3x) / (1 + e^(3x))] dx = integral of [1 / (u-1)] (du / (3(u-1))) = (1/3) ln|u-1| + C

Finally, we can substitute back u = 1 + e^(3x) to obtain:

integral of [e^(3x) / (1 + e^(3x))] dx = (1/3) ln|1+e^(3x)-1| + C = (1/3) ln|e^(3x)| + C = (1/3) (3x) + C = x + C, where C is the constant of integration.

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Answer:

40, leg

Step-by-step explanation:

The triangle has side lengths of 9, 40, and 41.

41 is the hypotenuse, so 40 is a leg.

Answer:

C

Step-by-step explanation:

The y intercept is when the graph passes the y axis. This occurs at (0,-2)

To find 3 rational numbers between 9.9 and 10, we need to follow the following procedure:

Step 1: Convert the given decimal numbers into fraction form.To convert decimal numbers into fraction form, we have to count the number of digits after the decimal point and place the decimal number in the numerator of the fraction and in the denominator we have to place 1 followed by the number of zeros equal to the number of digits after the decimal point.For example, 0.5 can be written as 5/10 or 1/2, 0.75 can be written as 75/100 or 3/4, and so on. So, 9.9 and 10 can be written as 99/10 and 100/10 respectively.

Step 2: Find the average of 99/10 and 100/10.The average of two rational numbers is obtained by adding the two numbers and then dividing the result by 2. Therefore, the average of 99/10 and 100/10 is ((99/10)+(100/10))/2 which equals to 199/20. So, we have found the first rational number between 9.9 and 10

.Step 3: Find the average of 99/10 and 199/20.Now, we need to find the average of the first rational number and the smallest rational number. Therefore, the average of 99/10 and 199/20 is

((99/10)+(199/20))/2 = 397/40.

So, we have found the second rational number between 9.9 and 10.

Step 4: Find the average of 199/20 and 100/10.Finally, we need to find the average of the second rational number and the largest rational number. Therefore, the average of 199/20 and 100/10 is

((199/20)+(100/10))/2 = 299/20.

So, we have found the third rational number between 9.9 and 10.In conclusion, the three rational numbers between 9.9 and 10 are 199/20, 397/40, and 299/20.

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Answer:

  1/2

Step-by-step explanation:

You want to know the average rate of change of f(x) = 1/2x -7 on the interval [2, 10].

A linear function has the same rate of change everywhere. Its instantaneous rate of change, average rate of change, and slope are all the same constant.

The given function is written in slope-intercept form, so we can identify the slope as the coefficient of x: 1/2.

The average rate of change is 1/2.

__

Additional comment

If you feel the need to "show work", you can evaluate ...

  AROC = (f(10) -f(2))/(10 -2) = (-2 -(-6))/8 = 4/8 = 1/2

Answer:

9/8 is greater

Step-by-step explanation:

9/8 is 1.125

11/12 is 0.916

The chances of Type I error, i.e., the probability of rejecting a null hypothesis when it is true.

The procedure in which your friend conducted the research has an inflated error rate because of the following reasons:

Firstly, it is not reliable to make conclusions about the entire population of cat owners based on only 30 people.

Secondly, there is a selection bias in the sample as the friend selected 30 cat owners, 30 dog owners, and 100 people without pets. This kind of bias in the sample population leads to an inflated error rate as the selection of the sample is not representative of the entire population and therefore it might be affected by external factors or not have adequate sample size.

Thirdly, the friend should have conducted a formal test instead of just comparing the results. This would have given more precise and accurate results about the data.

Finally, recruiting more cat owners after the initial test was conducted would cause inflation in the error rate as it would increase the chances of Type I error, i.e., the probability of rejecting a null hypothesis when it is true.

Hence, it is essential to conduct a formal test, use a representative sample, and analyze the data objectively and precisely to prevent an inflated error rate.

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The following statements are true: Shipping cost is 12.99 if the customer's order is less than or equal to $40.

Free shipping if the customer's order is $1000.By spending more than $500, customers save on shipping costs by paying the least.

The table rate module calculates the shipping rate depending on the order's destination and cart weight.

The shipping rate is calculated using the shipping table and the calculation type used in the module.

Therefore, the following statements are true:

Shipping cost is 12.99 if the customer's order is less than or equal to $40.

If the customer's order is less than or equal to $40, the shipping cost will be 12.99, as per the given shipping table.

Shipping cost is 9.99 if the customer's order is $50.

If the customer's order is $50, the shipping cost will be 9.99, as per the given shipping table.

Shipping cost is free if the customer's order is $1000.

If the customer's order is $1000, the shipping cost will be free, as per the given shipping table.

By spending more than $500, customers save on shipping costs by paying the least.

If the customer spends more than $500, they save on shipping costs by paying the least, as per the given shipping table.

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