Determine the coordinates of the corners of the rectangle to compute the area of the rectangle using the distance formula (round to the nearest integer).

We find that there are 24 girls and 40 boys, leading to a total of 64 people in the group.

To solve for the total number of people in the group given the ratio of boys to girls and the information that there are 16 more boys than girls, we can set up a proportion based on the ratio 5:3. Let the number of girls be represented by x and the number of boys be represented by x + 16, as there are 16 more boys than girls. From the ratio 5:3, we know that for every 8 parts (5+3), there are 5 parts boys and 3 parts girls. This gives us two equations: 5/8 of the total is boys, and 3/8 of the total is girls.

From the information given:

(x + 16) / x = 5 / 3

Cross-multiplying gives us:

3(x + 16) = 5x

3x + 48 = 5x

48 = 5x - 3x

48 = 2x

x = 24

This means there are 24 girls. Since there are 16 more boys, this means there are 24 + 16 = 40 boys. Adding up the boys and girls gives us the total number of people in the group:

40 boys + 24 girls = 64 people in total.

Answer:

63 percent student scored below Jake.

Step-by-step explanation:

For finding the percentile

Step 1: Subtracting mean from Jake’s score

=520-500

=20

Step 2: Calculating z-score

The z-Score is found by dividing the difference obtained in step 1 by SD of the data

z-score=  20/60

z-score=0.333

Step 3: Converting the z-score to percentile

The z-score will be converted to percentile using the z-score to percentile conversion table, the value of percentile for 0.3333 is 63rd .  

So, 63 percent students scored below Jake.  

$437.25 ÷ $0.75 = 583 bottles of lemonade

Hope this helps :)

Answer:

[tex]\$10,833[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=1\ years\\ P=\$10,000\\ r=0.08[/tex]  

substitute in the formula above  

[tex]A=\$10,000(e)^{0.08*1}=\$10,833[/tex]  

Compound interest computed continuously after one year on a principal sum of $10,000 with an 8% interest rate will yield $10,833, rounded to the nearest dollar.

Your question relates to the mathematics topic of compound interest. When interest is compounded continuously, we use the formula A = P * e^(rt), where A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years.

In your case, you are looking to find how much $10,000, invested at a nominal 8% per year compounded continuously, would amount to at the end of one year. Substituting the given values into the formula, we have:
A = $10,000 * e^(0.08*1).

The value of 'e' is approximately 2.71828. Therefore, we calculate:
A = $10,000 * 2.71828^0.08 = $10,833.

So, the amount in the account at the end of one year, rounded to the nearest dollar, would be $10,833.

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The question is a little blurry. I can't read it.

Answer:

I believe the answer is c.

Step-by-step explanation:

Reducing the equation, we get:

3^(3-3a) = 3^(-2a)

So 3-3a = -2a, a = 3.

The value of the variable 'a' will be 3. Then the correct option is C.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

[tex]7 + 42 \cdot 3^{2 - 3a} = 14 \cdot 3^{-2a} + 7[/tex]

Simplify the equation, then we have

[tex]42 \cdot 3^{2 - 3a} = 14 \cdot 3^{-2a}\\\\3^{2 - 3a} = \dfrac{1}{3} \cdot 3^{-2a}\\\\\left (3 \right )^{2 - 3a } } = (3)^{-1 - 2a}[/tex]

Compare the power of the number 3, then we have

- 1 - 2a = 2 - 3a

3a - 2a = 2 + 1

a = 3

The value of the variable 'a' will be 3. Then the correct option is C.

More about the solution of the equation link is given below.

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Answer:

[tex]\large\boxed{9x^8,\ 25x^{12},\ 36x^{16}}[/tex]

Step-by-step explanation:

[tex]Use\\(\sqrt{s})^2=s\ for\ s\geq0\\(a^n)^m=a^{nm}\\(ab)^n=a^nb^n\\a^n\cdot a^m=a^{n+m}\\===========================\\6x^2=(\sqrt6)^2x^2=(x\sqrt6)^2\to\boxed{NOT}\\\\9x^8=3^2x^{4\cdot2}=3^2(x^4)^2=(3x^4)^2\to\boxed{YES}\\\\16x^9=4^2x^{8+1}=4^2x^{4\cdot2}\cdot x=4^2(x^4)^2x=(4x^4)^2x\to\boxed{NOT}\\\\25x^{12}=5^2x^{6\cdot2}=5^2(x^6)^2=(5x^6)^2\to\boxed{YES}\\\\36x^{16}=6^2x^{8\cdot2}=6^2(x^8)^2=(6x^8)^2\to\boxed{YES}[/tex]

Answer:

[verb] to allow someone to do; to allow something; to acquiesce on something; to concede something.

ANSWER

[tex]S_{30}= - 3390[/tex]

EXPLANATION

The given sequence is

3,-5,-13,.....-229.

The first term of this sequence is

a_1=3

There is a common difference of

[tex]d = - 5 - 3 = - 8[/tex]

The last term of this sequence is -229.

The nth term of this sequence is given by:

[tex]a_n=a_1+d(n-1)[/tex]

We use the last term to determine the number of terms in the sequence.

[tex] - 229 = 3 + - 8(n - 1)[/tex]

[tex]- 229 - 3= - 8(n - 1)[/tex]

[tex]- 232= - 8(n - 1)[/tex]

Divide through by -8;

[tex]29= (n - 1)[/tex]

[tex]n = 30[/tex]

Hence there are thirty terms in the sequence.

The sum of the first n terms is given by:

[tex]S_n= \frac{n}{2} ( a_{1} + l)[/tex]

The sum of the first 30 terms is given by:

[tex]S_{30}= \frac{30}{2} ( 3 + - 229)[/tex]

[tex]S_{30}=15( - 226)[/tex]

[tex]S_{30}= - 3390[/tex]

It would have to be C. point.

Since it says AB that marks two points and a line in between them. If only talking about A, it would be a point.

Option: C is the correct answer.

                c.)  Point

In the symbol AB:

AB represents a line segment which connects point A to point B.

If there would be an arrow over this with right arrow then it would represent a ray which originates at point A an it extends to infinity from the other direction.

Hence the letter A will represent a : Point.

Answer:

The domain is the interval [tex][-6,6][/tex]

The range is the interval [tex][-2,2][/tex]

Step-by-step explanation:

we know that

Observing the graph

The domain is the interval [tex][-6,6][/tex]

All real numbers greater than or equal to -6 and less than or equal to 6

The range is the interval [tex][-2,2][/tex]

All real numbers greater than or equal to -2 and less than or equal to 2

The graph's domain spans from -6 to 6, and the range extends from -2 to 2. In summary, the domain is [-6, 6], and the range is [-2, 2].

In the given graph, the domain represents all possible input values, and it spans from -6 to 6, inclusive. This is because the graph includes every real number greater than or equal to -6 and less than or equal to 6 along the horizontal axis.

The range, on the other hand, corresponds to the output values of the function and extends from -2 to 2, inclusive. This is derived from the observation that the graph encompasses all real numbers greater than or equal to -2 and less than or equal to 2 along the vertical axis.

The domain is [-6, 6], indicating all real numbers between -6 and 6, and the range is [-2, 2], signifying all real numbers between -2 and 2. The graph visually illustrates these intervals as the inclusive bounds for both domain and range.

To learn more about domain

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Answer:

b. [tex]y=3.9^x[/tex]

Step-by-step explanation:

Remember that the standard exponential function is [tex]y=ab^x[/tex]

where

[tex]a[/tex] is the coefficient

[tex]b[/tex] is the base

If [tex]b>0[/tex], the function is growing

If [tex]0<b<1[/tex] the graph is decaying

We can infer from the graph that the function is growing, so we can discard [tex]y=0.45^x[/tex] and [tex]y=0.73^x[/tex].

Now, to evaluate our tow remaining equations, we are using the test values [tex]x=0[/tex] and [tex]x=1[/tex]:

For [tex]y=1.8^x[/tex]

For [tex]x=0[/tex]

[tex]y=1.8^0[/tex]

[tex]y=0[/tex]

For [tex]x=1[/tex]

[tex]y=1.8^1[/tex]

[tex]y=1.8[/tex]

The graph passes through the points (0,1) and (1, 1.8)

For [tex]y=3.9^x[/tex]

[tex]x=0[/tex]

[tex]y=3.9^0[/tex]

[tex]y=0[/tex]

[tex]x=1[/tex]

[tex]y=3.9^1[/tex]

[tex]y=3.9[/tex]

The graph passes through the points (0,1) and (1, 3.9)

We can see in the graph when [tex]x=1[/tex], [tex]y[/tex] is almost 4, so we can conclude that the correct equation is [tex]y=3.9^x[/tex]

Answer:

Risk

More risky

Step-by-step explanation:

Got it right on edmunto

Different investments have different levels of - RISKS and offer different rates of return. For example, investing in property is MORE RISKY than investing in bonds.

The property rates can change drastically within a short period of time, while bonds are static in income. This is why investing in property is riskier than investing in bonds.

Number of pallets moved in 4.5 hours = 108

converting 4.5 hours in minutes we get,

4*60 + 0.5*60 = 240+30 = 270 minutes

So, 108 pallets were moved in = 270 minutes

1 pallet was moved in = [tex]\frac{270}{108}=2.5[/tex] minutes

As the tie will get over in 2 hours or 2*60 = 120 minutes, the number of pallets that can be moved will be = [tex]\frac{120}{2.5}= 48[/tex] pallets.

Hence, 48 pallets can be moved before quitting time.

Answer:

The answer is 2.5 minutes; 48 pallets

Step-by-step explanation:

Number of pallets worker moved in a warehouse = 108

Number of hours it takes to do so  = 4.5

Rate at which they require to move one pallet is given by

Number of pallets worker moved in a warehouse = 108

Number of hours it takes to do so  = 4.5

Rate at which they require to move one pallet is given by

4.5/108 x 60 minutes = 2.5 minutes

Now, if the worker will be off the clock in 2 hours ,

So, number of pallets he can move before quitting time is given by

In 4.5 hours, number of pallets they moved = 108

In 1 hour, number of pallets they moved = 108/4.5 = 24

In 2 hours, number of pallets they moved = 24 x 2 = 48

Answer:

x = 25

Step-by-step explanation:

To find the value of x we use the formula:

tan x° = opposite side /adjacent side

Opposite Side = 8

Adjacent Side = 17

tan x° = 8/17

tan x° = 0.4705882352941

[tex]Tan^{-1}[/tex] of [tex]0.4705882352941[/tex]

x° = 25

Answer:

D. They have the same value and the same sign.

Step-by-step explanation:

72 / 9 and -72/ (-9)

Answer:

D

Step-by-step explanation:

just took the test

Answer:

Your dew point would be at 10.

Step-by-step explanation:

The base of the middle triangle is 3 and the base of the larger one is 6, so the larger triangle is twice the size of the middle one.

Multiply the height of the middle one by 2 to get the height of the larger one, which is labeled n.

n = 5 x 2 = 10

Answer:

The answer would be around 3.7

Step-by-step explanation:

PARALLEL slopes always have the same slope no matter what because they are parallel

Answer:

[tex]y=47x-654[/tex]

Step-by-step explanation:

To find the line parallel to the given linear equation, we have to use the same slope, because the condition of parallelism is that they must have the same slope.

So, the slope of the given line is [tex]m=47[/tex], because it's expressed in slope-intercept form, where the coefficient of the variable x is the slope.

Now, we know that they new parallel lines must have a slope equal to 47, and must pass through (14,4). Using this data, we apply the point-slope formula to find the equation of the new line:

[tex]y-y_{1}=m(x-x_{1})\\y-4=47(x-14)\\y=47x-658+4\\y=47x-654[/tex]

The image attached shows the parallelism.

Therefore, the answer is [tex]y=47x-654[/tex]

4,12,16,22,32,45648383929282

Answer:

B.)  10, 6, 9, 14, 1, 6, 12, 7

&

D.)  6, 8, 11, 1, 7, 14, 10

Step-by-step explanation:

i got it right

Answer:

15.25

Step-by-step explanation:

Answer:

It is the sum of the initial amount and the additional amount after d days.

Step-by-step explanation:

It is the sum of the initial amount and the additional amount after d days.i have ttm

Answer:

Step-by-step explanation:

4×+3Y-15-3y+×

The equivalent expressions to 5x-15 are 5(x-3), 4x+3y-15-3y+x, and -20-3x+5+8x. These simplify to 5x-15 when combining like terms and distributing, matching the original expression.

The student is asking which expressions are equivalent to 5x-15. To find the equivalent expressions, we need to check each option to see if they simplify to the same form.

Therefore, the expressions 5(x-3), 4x+3y-15-3y+x, and -20-3x+5+8x are equivalent to 5x - 15.

Answer:

[tex]\$10,608[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=16\ years\\ P=\$6,800\\r=0.035[/tex]

substitute in the formula above

[tex]A=\$6,800(1+0.035*16)=\$10,608[/tex]

Answer: [tex]x=\frac{37}{9}[/tex]

Step-by-step explanation:

By the negative exponent rule, you have that:

[tex](\frac{1}{a})^n=a^{-n}[/tex]

By the exponents properties, you know that:

[tex](m^n)^l=m^{(nl)}[/tex]

[tex](m^n)(m^l)=m^{(n+l)}[/tex]

Rewrite 4, 8 and 32 as following:

4=2²

8=2³

32=2⁵

Rewrite the expression:

[tex](2^2)^{(x-7)}*(2^3)^{(2x-3)}=\frac{32}{2^{(x-9)}}[/tex]

Keeping on mind the exponents properties, you have:

[tex](2)^{2(x-7)}*(2)^{3(2x-3)}=32(2^{-(x-9)}[/tex]

[tex](2)^{2(x-7)}*(2)^{3(2x-3)}=(2^5)(2^{-(x-9)})\\\\(2)^{(2x-14)}*(2)^{(6x-9)}=(2^5)(2^{(-x+9)})\\\\2^{((2x-14)+(6x-9))}=2^{(5+(-x+9))}[/tex]

As the bases are equal, then:

[tex](2x-14)+(6x-9)=5+(-x+9)\\\\2x-14+6x-9=5-x+9\\\\8x-23=14-x\\9x=37[/tex]

[tex]x=\frac{37}{9}[/tex]

Answer:

[tex]x=4\frac{1}{9}[/tex]

Step-by-step explanation:

We are given the following linear equation and we are to solve it:

[tex] 4 ^ { x - 7 } \times 8 ^ { 2x - 3 } = \frac { 32 } { x ^ { x - 8 } } [/tex]

Changing the constants to the same base to make it easier to solve:

[tex] 2 ^ { 2 ( x - 7 ) } \times 2^ { 3 ( 2x - 3 ) } = \frac { 2 ^ 5 } { 2 ^ { x - 9 } } [/tex]

[tex]2^{2x-14} \times 2^{6x-9} = 2^{5}(2^{-x+9})[/tex]

[tex] 2 ^ { 2x - 14 + 6x - 9 } = 2 ^ { 5 - x + 9 } [/tex]

[tex] 2 x + 6x - 14 - 9 = 5 - x + 9 [/tex]

[tex]8x+x=14+9+5+9[/tex]

[tex]9x=37[/tex]

[tex]x=4\frac{1}{9}[/tex]

Answer:

See below  

Step-by-step explanation:

19)

  13² =  4² + AM²

 169 = 16  + AM ²

AM ² = 153

AM =√153 = √(9× 17) = 3√17

sinA = MT /AT  = 4/13

cosA = AM/AT  = (3√17)/13

tanA = MT/AM  = 4/(3√17)   = (4√17)/51

sinT = AM/AT  = (3√17)/13

cosT = MT/AT  = 4/13

tanT = AM/MT = (3√17)/4

20)

10² =  5² + AJ²

100 = 25  + AJ²

AJ² = 75

AJ = √75 = √(25×3) = 5√3

sinA = JT/AT  = 5/10       = ½

cosA = AJ/AT = (5√3)/10 = (√3)/2

tanA = AJ /AJ = 5/(5√3)  = (√3)/3

sinT = AJ/AT = (5√3)/10 = (√3)/2

cosT = AJ/AT = 5/10       = ½

tanT = AJ/JT  = (5√3)/5   = √3

Answer:

Step-by-step explanation:

Consecutive integer:

... -2, -1, 0, 1, 2, 3, ...

Difference between two consecutive integers is equal to 1.

Therefore two consecutive integers is x and x + 1.

Answer:

Step-by-step explanation:

Look at the picture.

R(x, y)

y - is the same as second coordinate of the point Q → y = b

x - is first coordinate of the point S reduced by distance a → x = c - a