What is the perimeter of the rectangle? Write your answer in scientific notation. The area is 2.76 x 10 pw12
the width is 4.6 x 10 pw5
pw is the power

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ &&(~ -1 &,& 2~) &&(~ 6 &,& 3~) \end{array} \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-2}{6-(-1)}\implies \cfrac{3-2}{6+1}\implies \cfrac{1}{7} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-2=\cfrac{1}{7}[x-(-1)]\implies y-2=\cfrac{1}{7}(x+1) \\\\\\ y-2=\cfrac{1}{7}x+\cfrac{1}{7}\implies y=\cfrac{1}{7}x+\cfrac{1}{7}+2\implies y=\cfrac{1}{7}x+\cfrac{15}{7}[/tex]

Answer:

Step 1: Choose (x1, y1). (6,3)

Step 2: x2= -1 y2=2

Step 3: 1/7

Step 4: b= 15/7

What is the equation of the line in slope-intercept form?

B) y=1/7x+15/7

Step-by-step explanation:

The bold numbers are the answers.

( I need mo pts)

After subtracting the principal and two counselors from the 83-person room capacity, dividing the remaining space by two shows that a maximum of 40 student-athletes can attend the meeting with their parents.

The maximum number of student-athletes that can attend a meeting in a conference room that has a capacity of 83 people while also accounting for their accompanying parents. Given that the principal and two counselors will also be in attendance, we need to subtract three from the total capacity to accommodate them, leaving us with 80 seats available. Since each student will bring a parent, we divide the remaining seats by two. Therefore, the maximum number of student-athletes that can attend each meeting is 40 students, with each accompanied by a parent.

The shape that best describes the cross-section cut perpendicular to the base of a right rectangular prism is a rectangle.

A cross-section cut perpendicular to the base of a right rectangular prism will always result in a rectangular shape.

This is because a rectangular prism has six faces, and the base of the prism is one of those faces.

When you make a cross-section cut perpendicular to the base, you are essentially slicing through the prism parallel to one of its other faces.

Since the base is a rectangle, the cross-section will also be a rectangle.

In summary, the cross-section cut of a right rectangular prism perpendicular to its base will consistently yield a rectangular shape due to the inherent geometry of the prism.

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The correct answer is option A: [tex]\( 88 \)[/tex] ounces per [tex]\( 1 \)[/tex] pound. This ratio allows us to convert pounds to ounces effectively and accurately, ensuring that we obtain the correct conversion result.

To convert 5.5 pounds to ounces, we need to use the conversion factor that relates pounds to ounces. We know that there are 16 ounces in 1 pound. Therefore, to convert pounds to ounces, we need to multiply the number of pounds by 16.

The appropriate ratio to use for this conversion would be option A : 16 ounces per 1  pound, or [tex]\( \frac{16 \text{ ounces}}{1 \text{ pound}} \).[/tex]

This ratio tells us that for every 1 pound, there are 16 ounces. Using this ratio, we can convert pounds to ounces by multiplying the number of pounds by 16.

Therefore, to convert  5.5  pounds to ounces, we would use the following calculation:

[tex]\[ 5.5 \text{ pounds} \times \frac{16 \text{ ounces}}{1 \text{ pound}} = 88 \text{ ounces} \][/tex]

So, the correct answer is option A: [tex]\( 88 \)[/tex] ounces per [tex]\( 1 \)[/tex] pound. This ratio allows us to convert pounds to ounces effectively and accurately, ensuring that we obtain the correct conversion result.

The complete question is:

Choose the ratio that vou would use to convert 5.5 pounds to ounces Remember that there are 16 ounces in 1 pound.

A. 88 ounces/1 pound

B. 16 ounces/1 pound

C. 1 pound/16 ounces

D. 1 ounce/88 pounds

A circle with an area of 254.47 square inches is given.

We have to determine the circumference of the circle.

Since, Area of circle = [tex] \Pi r^{2} [/tex] where r is the radius of the circle.

[tex] \Pi r^{2}=254.47 [/tex]

[tex] \frac{22}{7} \times r^{2}=254.47 [/tex]

[tex] r^{2}=\frac{254.47 \times 7}{22} [/tex]

[tex] r^{2}=80.97 [/tex]

[tex] r=\sqrt{80.97} [/tex]

r = 8.99

Therefore, r = 9 inches (approximately)

Circumference of a circle = [tex] 2\Pi r [/tex]

= [tex] 2 \times \frac{22}{7} \times 9 [/tex]

= 56.57 inches

= 56.6 inches (approximately).

Therefore, the circumference of the circle is 56.6 inches.

[tex] |\Omega|=25\cdot24\cdot23=13800\\
|A|=5\cdot4\cdot3=60\\\\
P(A)=\dfrac{60}{13800}=\dfrac{1}{230}\approx0.4\% [/tex]

The probability of an event is calculated as = [tex] \frac{Favorable outcomes}{Total number of outcomes} [/tex]

Here, the total number of outcomes = 12 red marbles + 8 blue marbles + 5 green marbles

So, total marbles = 25 marbles

Number of favorable or green marbles = 5 marbles

Probability of three green marbles if drawn with replacement = [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] ×[tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] × [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex]

Probability of three green marbles if drawn with replacement = [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex]

Probability of three green marbles if drawn with replacement = [tex] \frac{1}{125} [/tex]

Answer:

Step-by-step explanation:

To get the amount of paper required to cover the box, we find the area of the box. The dimensions of the box are as follows:length=21/2 ftwidth=11/2 ftheight=4 ftArea of the box is given by the formula:SA=2lw+2lh+2hwSA=2(21/2×11/2)+2(21/2×4)+2(11/2×4)SA=2(231/4)+2(42)+2(11/2×4)SA=115.5+84+44SA=243.5 ft²Stella will need 243.5 ft²

Answer:

[tex](x+60)=y[/tex] and [tex]1.05x+0.90(60)=1.00y[/tex]

Step-by-step explanation:

Let

x-----> pounds of hamburger worth [tex]\$1.05[/tex] per pound

we know that

The equation that represent the situation is

[tex]1.05x+0.90(60)=1.00(x+60)[/tex] ------> equation A

Let

[tex]y=(x+60)[/tex] -----> equation B

substitute equation B in equation A

[tex]1.05x+0.90(60)=1.00y[/tex]

Answer:
The two positive numbers are 12 and 8. 

Explanation:
The first phrase in the sentence tells us the difference between numbers equals 4, which can be represented a - b = 4

The second phrase tells us when multiplied together, it equals 96, which can be represented by the ab = 96, or a(b) = 96

So, first step is to list the factors of 96. I prefer to list them as pairs:
1, 96; 2, 48; 3, 32; 4, 24; 6, 16; and 8, 12

Now we plug each these pairs into the first equation to see if they satisfy the equation.

96 - 1 = 95               24 - 4 = 20
95 > 4                      20 > 4

48 - 2 = 46               16 - 6 = 10
46 > 4                       10 > 4

32 - 3 = 29               12 - 8 = 4
29 > 4                       4 = 4

Because a = 12 and b = 8 satisfies both equations that represent the given sentence, the two positive numbers are 12 and 8.

Answer:

C

Step-by-step explanation:

If youre doing the test ;)

Answer:

30°C

Step-by-step explanation:

The following expression can be used to convert Farenheit degrees (°F) to Celsius degrees (°C).

°C = 5 . (°F - 32) / 9

If the temperature in Centerville is 86°F, we can replace this value in the previous expression to find its value in the Celsius scale.

°C = 5 . (°F - 32) / 9

°C = 5 . (86 - 32) / 9

°C = 5 . (54) / 9

°C = 270 / 9

°C = 30°C

Final answer:

Jenya has 2 $1 bills, 4 $5 bills, and 6 $10 bills, which all adds up to her total of $82.

Explanation:

Jenya has a combination of $1, $5, and $10 bills in her wallet adding up to $82. To find out how many of each she has, we need to set up a system of equations based on the information provided:

Now we can form two equations:

Simplifying the equations gives us:

Further simplification and solving for x yields:

This means Jenya has 2 $1 bills, 2*2 = 4 $5 bills, and 2*2 + 2 = 6 $10 bills.

The better deal is the loan with the 600% APR.

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum).

Given that, Pete is borrowing the money for one week, the APR must be divided into a daily interest rate before we can figure out how much he'll pay for the loan.

There are 365 days in a year. Divide the APR by 365 to find the daily interest rate.

600/365 = 1.643

The daily interest rate of the loan will be 1.643%.

The following equation is used to find the total interest payment:

[tex]A = P(1+\frac{r}{365} )^{t} -P[/tex]

A represents the total amount paid in interest. P represents the amount borrowed for the loan. r represents the daily interest rate. t represents the amount of days the loan will last.

Plug in your values into the equation.

P = 380 r = 1.643 and t = 7

380(1+1.643/365)^7 - 380 = 12.136

Rounded to the nearest hundredths value, the total interest paid will be $12.14.

Compare the total amounts paid for both loans.

$12.14 < $45

Hence, The better deal is the loan with the 600% APR.

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Answer:

368

Step-by-step explanation:

B. 22 : 2. 22 : 2 is equivalent to 11 : 1.

C. 55 : 5. 55 : 5 is equivalent to 11 : 1.

E. 110 : 10. 110 : 10 is equivalent to 11 : 1.

In order to determine the ratios that are equivalent to the given ratio, we would evaluate by dividing each of them by their respective common multiple (numerator or denominator):

For 22 : 2, we would divide all through by 11;

22 : 2 = 11 : 1

For 55 : 5, we would divide all through by 5;

55 : 5 = 11 : 1

For 110 : 10, we would divide all through by 10;

110 : 10 = 11 : 1

Complete Question:

Select three ratios that are equivalent to 11 : 1.

Choose 3 answers:

1 :11

22 : 2

55 : 5

9 : 99

110 : 10

The limit of the sequence defined by an+1=1/2*(an+2an), as n approaches infinity, is 0. This is determined by setting a = limn→∞an and solving for 'a' in the equation a=1/2*(a+2a).

This question is about calculating the limit of a sequence, where the sequence, denoted as {an}, is defined recursively with a given formula, an+1=1/2*(an+2an).

To calculate the limit as n approaches infinity (limn→∞an), we first suppose a is this limit. This means as n grows very large, the values of an and an+1 converge to 'a'. Hence we can write the recursive formula of the sequence in terms of 'a': a=1/2*(a+2a).

By simplifying the equation, we get: a = 1/2 * (3a). This implies that 2a = 3a, and thus 'a' must be 0.

Therefore, the limit of the sequence as n tends to infinity is 0.

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