Calculate the number of integers divisible by 4 between 50 and 500, inclusive.

Answer:

C.) 4

Step-by-step explanation:

we are given ABCD is an isosceles trapezoid

AB || CD

AB = m + 6

CD = 3m + 2

BC = 3m

AD = 7m - 16

Since, ABCD is an isosceles trapezoid

so, two sides must be equal

[tex]BC=AD[/tex]

now, we can plug values

[tex]3m=7m-16[/tex]

now, we can solve for m

[tex]3m-7m=7m-16-7m[/tex]

[tex]-4m=-16[/tex]

Divide both sides by -4

and we get

[tex]m=4[/tex]

Answer:

M= 4

Step-by-step explanation:

Answer:

13.

Step-by-step explanation:

Answer: [tex]a_n=5+n[/tex]

Step-by-step explanation:

The explicit formula for an arithmetic sequence is given by:-

[tex]a_n=a+d(n-1)[/tex], where a is the first term , di sthe common difference and n is the number of terms.

The given sequence : 6, 5, 4, 3, 2, . .

Common difference  d = 1

First term = 1

Now, the explicit formula for given arithmetic sequence will be:

[tex]a_n=6+1(n-1)\\\\\Rightarrow\ a_n=6+n-1\\\\\Rightarrow\ a_n=5+n[/tex]

Hence, the explicit formula for given arithmetic sequence :  [tex]a_n=5+n[/tex]

Answer:

So for everybody in the future, a clarification is d)y^2/60^2 -x^2/25^2=1

Ans: [tex]\( \frac{y^2}{60^2} - \frac{x^2}{25^2} = 1 \)[/tex]

The standard form equation of a hyperbola with the center at the origin (0,0), a vertical axis, a vertex at (0, a), and a focus at (0, c) is given by:

[tex]\[\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\][/tex]

where [tex]\(c\)[/tex] is the distance from the center to the focus, and [tex]\(b\)[/tex] is related to [tex]\(a\) and \(c\)[/tex] by the equation [tex]\(c^2 = a^2 + b^2\)[/tex].

In your case, the center is at (0,0), the vertex is at (0,60), and the focus is at (0,-65). The distance from the center to the focus is [tex]\(c = 65\)[/tex], and the distance from the center to the vertex is [tex]\(a = 60\)[/tex]. Using the relationship [tex]\(c^2 = a^2 + b^2\)[/tex], we can find b:

[tex]\[65^2 = 60^2 + b^2\][/tex]

Solving for b:

[tex]\[4225 = 3600 + b^2\][/tex]

[tex]\[b^2 = 625\][/tex]

[tex]\[b = 25\][/tex]

Now, substitute [tex]\(a\), \(b\), and \((h, k) = (0, 0)\)[/tex] into the standard form equation:

[tex]\[\frac{y^2}{60^2} - \frac{x^2}{25^2} = 1\][/tex]

So, the equation of the hyperbola is:

[tex]\[\frac{y^2}{3600} - \frac{x^2}{625} = 1\][/tex]

[tex]\( \frac{y^2}{60^2} - \frac{x^2}{25^2} = 1 \)[/tex]

Given point is (0, -2).

Given options are A(6, -2); B(-8, -2); C(0, -8); D(0, 4).

It says to select the options that are more than five units vertically away from the given point.

"Vertically away" means the x-coordinate would be same and y-coordinate would be shifted up or down.

Since it says to shift more than five units vertically away, so we must have :-

y > -2 + 5 or y < -2 - 5.  

Therefore, y > 3 or y < -7.

Hence, option C and D are correct i.e. (0, -8) and (0, 4).

[tex] |\Omega|=8\cdot7\cdot6=336\\
|A|=\underbrace{1\cdot6\cdot3}_{\text{8,any,even}}=18\\\\
P(A)=\dfrac{18}{336}=\dfrac{3}{56}=5\% [/tex]

Answer:

Interest rate - 9

Revenue - 3

Recovery - 7

Markdown - 6

Buyer's willingness to pay - 1

Markup - 10

Worker's wages - 5

2/10 net 30 - 4

Credit - 8

Rent - 2

Step-by-step explanation:

Just did this on odyssey

The conjecture about the sum of the first 15 positive even numbers is 15 * 16

Making a conjecture about the sum of the first 15 positive even numbers.

From the question, we have the following parameters that can be used in our computation:

The table of values

Where, we have

2 = 1 * 2

2 + 4 = 2 * 3

2 + 4 + 6 = 3 * 4

And so on

This means that

Sum of first n positive even numbers = n * (n + 1)

So, for the first positive even numbers, we have

n = 15

This gives

Sum of first 15 positive even numbers = 15 * (15 + 1)

Evaluate

Sum = 15 * 16

Sum = 240

Hence, the sum is 15 * 16

Answer:

The mean is 10.7 and the standard deviation is 5.6.

Step-by-step explanation:

To find the mean, add together all of the data and divide by the number of data points:

(6+7+19+7+18+7)/6 = 64/6 = 10.7

To find the standard deviation, subtract each data point from the mean, square them and find the sum:

(6-10.7)²+(7-10.7)²+(19-10.7)²+(7-10.7)²+(18-10.7)²+(7-10.7)²

=(-4.7)²+(-3.7)²+(8.3)²+(-3.7)²+(7.3)²+(-3.7)²

=22.09+13.69+68.89+13.69+53.29+13.69 = 185.34

Next divide this by 6, the number of data points:

185.34/6 = 30.89

Lastly, take the square root:

√30.89 = 5.6

Answer:

A circle with center at (-3, 6) and a radius of 10 has the following standard form equation

[tex](x+3)^2+(y-6)^2=100[/tex]

Step-by-step explanation:

This is the general standard equation for the circle centered at (h, k) with radius r

[tex](x-h)^2+(y-k)^2=r^2[/tex]

It shows all the important information at a glance: the center (h, k) and the radius r.

A circle with center at (-3, 6) and a radius of 10 has the following standard form equation

Start with:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Put in (h, k) and r

[tex](x-(-3))^2+(y-6)^2=10^2\\(x+3)^2+(y-6)^2=100[/tex]

Answer:

Assessment value of Henry's home is $50750

Step-by-step explanation:

Henry's home has a market value of $145000 and the assessment rate is 35%.

This means value of home is 35% of the total cost $145000

Now we will solve it by calculating percentage

Assessment = 35% of 145000 = [tex](145000)(\frac{35}{100})=(1450).(35)=50750[/tex]

So the answer is assessment of Henry's home = $50750.

Answer:

[tex]78\ million=7.80\times 10^7[/tex]

Step-by-step explanation:

A number N can be written in scientific notation as :

[tex]N=p{\circ}0\times 10^q[/tex]

Where

p is the any real number

q is any integer

Here, the given number is 78 million. Firstly, we must know meaning of 1 million.

Since, [tex]1\ million=10^6[/tex]

[tex]78\ million=78.0\times 10^6[/tex]

To convert the above number in scientific notation, we can shift the decimal before 8 such that,

[tex]78\ million=7.80\times 10^7[/tex]

Hence, this is the required solution.

the anser would be c fo it to be in scientific notation you have to have an exponet

Answer:

Option(C)

Step-by-step explanation:

As per histogram, given below

3 students took holidays between 5-10 days.

5 students took holidays between 10-15 days.

5 students took holidays between 15-20 days.

4 students took holidays between 20-25 days.

3 students took holidays between 25-30 days.

therefore, option (C) is correct.