A rectangle perimeter is 102 inches. The width of the rectangle is 9 inches more than half the length. What are the length and width of the rectangle?

Given :The scented burns [tex] \frac{1}{12} [/tex] inches in 20 minutes

The scented candle will burn [tex] \frac{1}{12} times 3 =\frac{1}{4} [/tex] inches in one hour.

The unscented candle burns [tex] \frac{1}{6} [/tex] inches in 30 minutes

In one hour it will burn [tex] \frac{1}{6} times 2=\frac{1}{3} [/tex] inches .

Burn rate of scented is [tex] \frac{1}{4} [/tex] inches per hour.

Burn rate of unscented is [tex] \frac{1}{3} [/tex] inches per hour.

Solution:

we are given that

water hose is leaking at a rate of 0.25 cups per hour.

We have been asked to find that

how many gallons did you hose leak in a full 24 hour day.

Since water hose is leaking at a rate of 0.25 cups per hour.

It mean the tank will leak by [tex] 0.25*4=1 \ Cup [/tex] in 4 Hours.

So in 24 Hours the tank will leak by [tex] \frac{24}{4}*1=6*1=6 \ Cups [/tex] .

As we know that 1 Gallon=16 Cups.

It mean in 24 Hours the tank leaked by [tex] \frac{1}{16}*6= 0.375 \ Gallon [/tex]

The inverse of a function is its opposite

The values of the unknown are: b = 1, c = 81 and d = 9

The function is given as:

[tex]y = x^2 - 18x[/tex]

Rewrite the equation in vertex form as:

[tex]y = (x - 9)^2 - 81[/tex]

Swap the positions of x and y

[tex]x = (y - 9)^2 - 81[/tex]

Add 81 to both sides

[tex](y - 9)^2 = x + 81[/tex]

take the square roots of both sides

[tex]y - 9 = \pm\sqrt{x + 81}[/tex]

Add 9 to both sides

[tex]y = \pm\sqrt{x + 81} + 9[/tex]

By comparison, the values of the unknown are:

b = 1, c = 81 and d = 9

Read more about inverse functions at:

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Answer: It took Sean 55 seconds to drink all the slushy

Solution:

Original Volume: Vo=275 milliliters

After t1=13 seconds, 210 milliliters remained: V1=210 milliliters

He drank the slushy at a constant rate: r

Sean drank V=Vo-V1=275 milliliters-210 milliliters→V=65 milliliters

r=V/t1

r=65 milliliters / 13 seconds

r=5 milliliters/second

Sean will drink the remained volumen in a time t2:

t2=V1/r

t2=210 milliliters / (5 milliliters/second)

t2=42 seconds

Total time to drink: t

t=t1+t2

t=13 seconds + 42 seconds

t=55 seconds

Answer:

Sean drank at a rate of 5 milliliters per second.

It took Sean 55 seconds to drink all the slushy.

Step-by-step explanation:

Hope it helps in the picture below.

The frequency of Dexter's fourth group (35-39) in his frequency distribution is 2. This was determined by counting the numbers within the 35-39 range from the provided data set.

Calculating the Frequency of the Fourth Group:

To calculate the frequency of the fourth group in Dexter's frequency distribution, let's first establish the groups.

Next, we'll count how many data points fall within each range:

Thus, there are 2 data points in the fourth group (35-39).

The radius of the circle with an area of 324π sq cm is  18 cm.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

We know, The area of a circle is πr².

So, We can equate the given area with the general formula,

324π = πr².

r² = 324.

r = 18 cm.

A clock can be thought of as a circle having 12 steps and we know that circle is 360°,

So, the measure of each integer step of a clock is 30°.

Also, If we want to find some portion(arc) of the circumference we use the formula, s = rФ.

learn more about circles here :

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Answer:  [tex]\frac{8}{17}[/tex] or 8:17

Step-by-step explanation:

For any angle x (other than right angle) in a right triangle ,the trigonometric ratio of sin x is given by :-

[tex]\sin x=\frac{\text{side opposite to x}}{\text{Hypotenuse}}[/tex]

Given: A right triangle with hypotenuse = 68 units

The side adjacent to S =  60

Let h be the side opposite to S, then using Pythagoras in the given right triangle, we get

[tex](68)^2=60^2+h^2\\\\\Rightarrow\ h^2=68^2-60^2\\\\\Rightarrow\ h^2=1024\\\\\Rightarrow\ h=\sqrt{1024}=32[/tex]

Thus, the side opposite to S = 32 units

Now,  the trigonometric ratio for sin S is given by :-

[tex]\sin S=\frac{\text{side opposite to S}}{\text{Hypotenuse}}\\\\\Rightarrow\sin S=\frac{32}{68}=\frac{8}{17}[/tex]

Hence, the  trigonometric ratio for sin S =[tex]\frac{8}{17}[/tex] or 8:17

Answer:

D

Step-by-step explanation:

To find f(1/4) when f(x)=2x^2+9x-7, substitute x=1/4 into the function and simplify.

To find f(1/4) when f(x) = 2x² + 9x - 7, we substitute x = 1/4 into the function.

Plugging in the value of x, we have f(1/4) = 2(1/4)² + 9(1/4) - 7.

Simplifying the expression, we get f(1/4) = 2/16 + 9/4 - 7. Evaluating the fractions and subtracting, we find that f(1/4) = -45/16.

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Answer:

The correct option is A.

Step-by-step explanation:

The vertices of △ABC are A(−7, 1) , B(−5, −3) , and C(−3, 2) . The vertices of △A′B′C′ are A′(−7, −1) , B′(−5, 3) , and C′(−3, −2) .

The relation between coordinates of preimage and image is defined as

[tex](x,y)\rightarrow (x,-y)[/tex]

Sign of y-coordinate changes but x-coordinate remains the same. It is possible it the figure is reflection across the x-axis.

Therefore the correct option is A.

Answer:

From the given problem statement of the this question,the amount of the gift is 1 dollar and sixty cents

x=60*B

Yes is it possible to have 60 pennies in $1.87

Answer with explanation:

Mean of this data set

[tex]=\frac{\text{sum of all the observation}}{\text{Total number of observation}}\\\\=\frac{30+37+37+41+22+69+45+64+51+22+63+31+64+65+25+51+26+48+28+49}{20}\\\\=43.4[/tex]

Arranging the data set in ascending order

22, 22,25, 26, 28,30,31,37,37,41,45,48,49,51,51,63,64,64,65,69

Median =Middle observation ,if number of terms is odd

and if number of terms is even, divide number of terms by ,2 and then follow the procedure

[tex]=\frac{10^{th term}+11^{th term}}{2}\\\\=\frac{41+45}{2}\\\\=43[/tex]

To find the Outlier

[tex]Q_{1}=\frac{28+30}{2}=29,Q_{3}=\frac{51+63}{2}=57[/tex]

Interquartile range = 57 - 29=28

Data values are approximately equally distributed on both sides of median.

That is, 43-22=21, and ,69 -43=26

So,we can say that there will be no outliers.

Graph will be positively skewed.

Mean > Median

So,mean will be better measure of central tendency because, 43.4-22=21.4, and 69-43.4=25.6

Option A: There are no outliers.

And, Option C: The Mean is good measure of central tendency.