water flows at a constant rate. Kian measures 8 cups in 6 seconds. whats the constant of proportionality of cups of water to minutes

Check the picture below.

[tex]\stackrel{\measuredangle N}{(5x-8)}~~ + ~~\stackrel{\measuredangle O}{(x-5)}~~ + ~~\stackrel{\measuredangle P}{(6x+1)}~~ = ~~180 \\\\\\ 12x-12=180\implies 12x=168\implies x=\cfrac{168}{12}\implies x=14 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle O}{(x-5)}\implies (14)-5\implies {\Large \begin{array}{llll} \stackrel{\measuredangle O}{9} \end{array}}[/tex]

Answer:

Step-by-step explanation:

2) What type of angle is 4 and 8?

I What is the special angle pair relationship between < 8 and < 4?

Angle 4 and angle 8 are also alternate interior angles. Alternate exterior angles: Pairs of exterior angles on opposite sides of the transversal. Angle 2 and angle 7 are alternate exterior angles.

3)Twos are generally thoughtful, people-oriented, and caring, while Threes are resourceful, energetic, and determined.

4) Do not use a protractor. Use the properties of straight and vertical angles to help you.

Answer:

y+3= 1/5 (x+2)

Step-by-step explanation:

The point slope form looks like this.

y - y1 = m (x - x1)

the m represent slope and (x1, y1) are the coordinates of the point that the line passes through.

The ordered pair that satisfies the inequality is (aₓ ,bₓ) .

In mathematics, an inequality is a link that compares two numbers or other mathematical expressions unfairly.

Therefore we can conclude that (aₓ, bₓ) satisfies the inequality.

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Answer:

Step-by-step explanation:

your answer along with the work is down below please go and check it out also sorry I'm wrong have nice day:)

The mean and the standard deviation for the population of products produced with this process are 2.0 and 0.3329

The population mean is given by

ц = [tex]\frac{L+U}{2}[/tex]

where L and U are the two given boundaries

Here, L = 1.9 and U = 2.1

⇒ ц = [tex]\frac{1.9+2.1}{2}[/tex]

⇒ ц = 2.0

Now, the z value when p =5%, from z table of probability will be

z = -1.645

Standard Deviation denoted by σ is a measure of how dispersed the data is in relation to the mean.

The Standard Deviation can be calculated by the z-score which is given as:

z = (x-ц) / (σ / [tex]\sqrt{n}[/tex])

where z is the Standard score, x is observed value, ц is mean of the sample, σ is standard deviation and n is sample size

-1.645 = (1.9 - 2.0) / (σ / [tex]\sqrt{30}[/tex])

-1.645 × (σ / [tex]\sqrt{30}[/tex]) = -0.1

1.645 × (σ / 5.477) = 0.1

σ = 0.3329

Therefore, the mean and the standard deviation for the population of products produced with this process are 2.0 and 0.3329

Complete Question: A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of 30 finished products and computes the sample mean product weights [tex]x^{-}[/tex]. If test results over a long period of time show that 5% of [tex]x^{-}[/tex] the values are over 2.1 pounds and are under 1.9 pounds, what are the mean and the standard deviation for the population of products produced with this process?

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Answer: 3.6

20

8.25

Step-by-step explanation:

7 - 10 = 3

-6 - -8 = 2

[tex]\sqrt{3^{2} +2^{2} } =3.6[/tex]

Answer: His slope should be positive because the trend line is slanted up to the right.

Step-by-step explanation:

This answer is correct because the third line is slanted up to the right, so it makes it positive.

Answer:

0.103 acres

Step-by-step explanation:

This question tests on the concept of Conversion.

Given from the question, we know that:

107 pounds of seed = 11 acre field

To find the acres of field we can plant per pound of seed, we simply divide both sides of the equation by 107.

(107 ÷ 107) pounds of seed = (11 ÷ 107) acres of fiels

1 pound of seed = 0.103 acres of field (Rounded off to 3 significant figures)

well, let's first check with the Bank

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$16000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &3 \end{cases} \\\\\\ A=16000[1+(0.08)(3)] \implies A = 19840~\hfill \underset{monthly~payment}{\stackrel{19840~\div \stackrel{months}{36}}{\approx \text{\LARGE 551.11}}}[/tex]

now let's check with the Credit Card

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$16000\\ r=rate\to 15\%\to \frac{15}{100}\dotfill &0.15\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &12\\ t=years\dotfill &7 \end{cases}[/tex]

[tex]A=16000\left(1+\frac{0.15}{12}\right)^{12\cdot 7} \implies A \approx 45425.81~\hfill \underset{monthly~payment}{\stackrel{45425.81~\div \stackrel{months}{84}}{\approx\text{\LARGE 540.78}}}[/tex]

well, seems the Credit Card is the better deal monthly wise, though in the long run is a lot of dough.

A plan which would give Genesis the lowest monthly payment is the monthly payment on a bank loan would be $317.50.

Mathematically, the simple interest earned can be calculated by using this formula:

A = P(1 + rt)

Where: A represents the future value.

P represents the principal or original value.

r represents the interest rate.

t represents the time.

Now Substituting the given parameters into the formula, we have,

A = 9000[1 + (0.09 × 3)]

A = 9000[1 + 0.27]

A = 9000 × 1.27

Future value, A = $11,430.

Next, we will calculate the monthly payment over a period of 36 months as follows:

Monthly payment = Future value/Time

Monthly payment = 11,430/36

Monthly payment = $317.50.

Similarly, we will calculate the compound interest earned on the credit card :

A = 9000[1 + (0.18/12)]⁽¹² ˣ ⁷⁾

A = 9000[1 + 0.015]⁸⁴

A = 9000 × 1.015⁸⁴

A = 9000 × 3.49258954

Future value, A = $31,433.31.

Next, we will calculate the monthly payment over a period of 84 months as follows;

Monthly payment = Future value/Time

Monthly payment = 31,433.31/84

Monthly payment = $372.21.

In this context, A plan which would give Genesis the lowest monthly payment is the monthly payment on a bank loan would be $317.50.

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Answer:

if x = -6, r = 180/pi and D = 360/pi

without knowing the actual D or r, one cannot truly solve for x.

Step-by-step explanation:

looking at the angle, [tex]125^o[/tex], it is part of two supplementary parts of the circle, let us call the angle between [tex]55^o\ \&\ 125^o[/tex] y. given that 125 is supplementary to y:

125+y=180

and so...

y=55

now, let us call the angle associated with the arc-length, x+76 z.

Knowing that y+55 and z are supplementary (given the length is a diameter), we can write the equation:

y + 55 + z = 180

substituting y=55 gives:

55 + 55 + z = 180

combining like terms gives:

110 + z = 180

further simplifying gives:

z = 70

x + 76 is the arc-length of the section of the circle, whose angle is now denoted by z = 70.

Arc-length = Circumference * percentage of circle

circumference is given as C = π * D OR C = 2r * π (because 2r = D)

percentage of circle is simply (number of degrees covered ÷ total degrees of a circle)

so, we have that the percentage = 70/360 [360 degrees in a circle, 70 degrees covered by the angle, z]

and the circumference is unknown without a radius or diameter length, so we will use the equation C = π * D

using the formula for arc-length:

Arc-length =  π * D * 70/360

Arc-length also happens to equal x + 76, so:

x + 76 =  π * D * 70/360

reduce:

x + 76 =  π * D * 7/36

simplify by getting x alone:

x =  π * D * 7/36 - 76

we can further simplify by creating one fraction:

[tex]x = \frac{7D\pi - 2736}{36}[/tex]

it can also be shown as:

[tex]x = \frac{7r\pi - 1368}{18}[/tex]

because, D = 2r and you could factor 2 from (7*2*r*pi - 2736) and then reduce by dividing top and bottom each by 2.

You can divide top and bottom by 2 because:

[tex]\frac{2}{36} = \frac{1}{18}[/tex]

which is because [tex]\frac{km}{ln}=\frac{k}{l} * \frac{m}{n}[/tex]

if we say km = 2 and ln = 36, then k = 2, m = 1 is the only options for k and m

and l and n can be any set of factors of 36, which include 2*18, 3*12, 6*6, 9*4.

if we choose l = 2 and n = 18, then k = l = 2 and:

[tex]\frac{k}l=\frac{2}2 = \frac{r}{r}[/tex]

which is to say that k = r = l = 2, which I only show to say generally that when k = l or you have r ÷ r, it is equal to 1.

1 * s = s

and if s =  m ÷ n, then [tex]\frac{km}{ln} = \frac{m}{n}\ whenever\ k = l[/tex]

given that the answer to what is x, is -6, the arc length is therefore 70. we can plug in this 70 now to find r and therefore, D.

[tex]70 = \pi * D * \frac{70}{360}\\\\multiply\ by\ \frac{360}{70}\ on\ both\ sides\ to\ get:\\360=\pi * D\\divide\ by\ \pi\ on\ both\ sides\ to\ get:\\360/\pi = D\ OR\ 180/\pi=r[/tex]

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{9}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-3 - 9~~)^2 + (~~-9 - (-6)~~)^2} \implies d=\sqrt{(-3 -9)^2 + (-9 +6)^2} \\\\\\ d=\sqrt{( -12 )^2 + ( -3 )^2} \implies d=\sqrt{ 144 + 9 } \implies d=\sqrt{ 153 }\implies \boxed{d\approx 12.37}[/tex]

Answer:

[tex]15u^{2}[/tex]

Step-by-step explanation:

let's say each square is = [tex]1u^{2}[/tex]

triangle A area: 2*5

[tex]\frac{2*5}{2}=5u^{2}[/tex]

----------------------------------

triangle B area: 2*2

[tex]\frac{2*2}{2}=2u^{2} \\Triangle A - B = 5 - 2= 3u^{2}[/tex]

----------------------------------

next figure

triangle C area 3*3

[tex]\frac{3/3}{2}=4.5u^{2}\\ -------------\\\\3u^{2}+4.5u^{2}=7.5u^{2}\\ -------------\\[/tex]

And since the other figure is a reflection *2

[tex]7.5u^{2}*2=15u^{2}[/tex]

Answer:

A = 15 units²

Step-by-step explanation:

the area (A) of the shaded triangle is calculated as

A = area of rectangle enclosing the triangle - area of white triangles on either side of shaded triangle and the one on top

area of rectangle = 10 × 5 = 50 units²

area of 2 congruent triangles = 2 × [tex]\frac{1}{2}[/tex] ×  5 × 5 = 5 × 5 = 25 units²

area of top triangle = [tex]\frac{1}{2}[/tex] × 10 × 2 = 5× 2 = 10 units²

A = 50 - 25 - 10= 15 units²

The number is (x/2)+15=5+3x if Half of Number augmented by 15 equals the sum of 5 and the product of 3 and the number.

A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.

Decimal Number System is one of the four popular forms of number systems and other 3 are -

System of binary numbers.

System of Octal Numbers.

System of Hexadecimal Numbers.

From the given question,

X is the number. first we have to halve it , then we add 15.

Next ,set it equal to the other side . the second side is 5+ ( because it is the sum)

3x( the product of 3 and x means multiply them)

Hence the number is (x/2)+15=5+3x

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Answer:

B

Step-by-step explanation:

The range of |x| is [tex]{y|0 \leq y <\infty\}[/tex]. Adding 3 to this yields option B.

From the given figure the value of angle x is 40 degrees

|AC| = | CD |

Δ ( ACD ) = Δ ( DCB )

< ( BAC ) = 70 degrees

Since |AC| = | CD | then the base angles are equal, hence

< ( ADC ) =  < ( BAC ) 70 degrees. ( base angles of isosceles triangle )

< ( ADC ) + < ( BAC ) + < ( ACD ) = 180 degree ( sum of angles in a triangle)

note < ( BAC ) = < ( DAC )

< ( ACD ) = 180 - 70 - 70

< ( ACD ) = 180 - 140

< ( ACD ) = 40 degrees

If Δ ( ACD ) = Δ ( DCB ) then the angles should be equal

Δ ( ACD ) has angles:

< ( ADC )  = 70

< ( DAC ) = 70

< ( ACD ) = 40

Then Δ ( DCB ) should have angles 70, 70, and 40. The figure did not give enough information to put the angles where it should be.

Comparing with the options, only angle 40 degrees is in the option, hence the correct answer

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It is impossible to give a value for f(-1) because -1 is not in the domain of the function f.

It is given in the question that function f(x) is defined by the set of coordinate pairs {(-3,8),(2,5),(7,-1),(11,3)}.

Here, the ordered pair (a,b) represents (x ,f(x))

Which means:-

f(-3) = 8 , f(2) = 5, f(7) = -1, f(11) = 3.

Here, the elements of domain are -3, 5, -1 and, 3 and the elements of range are 8, 5, -1 and, 3.

We cannot find the value of f(-1) because -1 is not present in the domain of the function.

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The simplified form of the exponential expression [tex]64^{\frac{1}{4} }[/tex] is  [tex]2\sqrt{2}[/tex]

The given expression = [tex]64^{\frac{1}{4} }[/tex]

The exponential function is the function in the form of f(x)= [tex]a^{x}[/tex], where x is the variable and a is the constant. The constant term is the base of the exponential function.

The given expression = [tex]64^{\frac{1}{4} }[/tex]

Here we have to use the power rule of the exponents

[tex](a^{m})^{n}=a^{mn}[/tex]

To increase a number with an exponent to the power, we have to multiply the exponent times the power

We know

64 = [tex]2^{6}[/tex]

Then

[tex]64^{\frac{1}{4} }[/tex] = [tex](2^{6})^{\frac{1}{4} }[/tex]

Apply the power rule of the exponent

[tex](2^{6})^{\frac{1}{4} }[/tex] = [tex]2^{(6)(\frac{1}{4} )}[/tex]

= [tex]2^{\frac{3}{2} }[/tex]

= [tex]2\sqrt{2}[/tex]

Hence, the simplified form of the exponential expression [tex]64^{\frac{1}{4} }[/tex] is  [tex]2\sqrt{2}[/tex]

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Answer:

$0

Step-by-step explanation:

Henry has $75 in his bank account. If he withdraws $75 from the account, how much money will be left in the account?

$75 beginning balance - $75 withdrawal = $0

The 146°, and the x and 58° which are vertical angles formed by the two intersecting lines where the x and 58° are formed by the ray gives the measure of x as 88°

Vertical angles or vertically opposite angles are the angles formed by two intersecting lines and which are on either side to each other

The description parameters are;

The objects in the figure includes; Two intersecting lines and a ray

The measure of one of the angles formed by the intersecting lines = 146°

The vertically opposite angle to the 146° angle is broken into = x and 58°

Required; The value of x

Solution; The vertical angles theorem states that vertically opposite angles that are formed when two lines intersect, are congruent.

In geometry, two figures are congruent when they exactly coincide when they are superimposed, which means that the two figures have the same measurement.

Given that 146° is congruent to x + 58°, we have;

146° = x + 58° Definition of congruency and angle addition postulate

x = 146° - 58° = 88°

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The height of the arch is about 6.71 feet when measured from its base at a distance of one foot.

This is further explained below.

Generally, An ellipse is a collection of points whose distances from a fixed point (focus) or fixed line (directrix) is constant and less than 1.

Depending on whether the transverse axis is horizontal or vertical, we may construct an equation for the ellipse. The main axis is located along the transverse axis. The ellipse may be represented using the following equations:

[tex]\begin{aligned}&\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1 \\&\frac{(y-k)^2}{a^2}+\frac{(x-h)^2}{b^2}=1\end{aligned}[/tex]

An elliptical arch is described as having a center height of 9 feet and a width of 6 feet. The precise height of the arch from the base has to be determined.

[tex]\frac{(y-k)^2}{a^2}+\frac{(x-h)^2}{b^2}=1[/tex]

The center (h, k) is where the graph is since we centered it at the origin (0,0). We only need to enter the numbers into the equation at this point.

[tex]\begin{aligned}\frac{(y-0)^2}{9^2}+\frac{(x-0)^2}{3^2} &=1 \\\frac{y^2}{81}+\frac{x^2}{9} &=1\end{aligned}[/tex]

Since we divided the arch in half, 0 [tex]\leq[/tex] 9 in this instance. All that is left to do is calculate the arch's height in feet from the base.

The height of 1 foot from each end of the arch must thus be determined. The locations of the arch's ends are x=-3 and x=3. Here, we have a choice between the two. We may choose x=3-1=2 for this. Therefore, all that is left to do is enter x=2 in our usual form and work out the value of y that results.

[tex]\frac{y^2}{81}+\frac{(2)^2}{9}=1[/tex]

y^2+36=81

y^2+36-36=81-36

y=3√5

Therefore, the height of the arch at 1ft from the base is 3 √5ft or approximately 6.71ft

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Answer:

c

Step-by-step explanation:

I have finished all my math classes

Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

[tex]24g - 16 \leqslant 24g + 12 \\ 24g - 24g \leqslant 12 + 16 \\ 0 \leqslant 28[/tex]

THAT IS WHERE THE INEQUALITY LEADS US THERE IS NO CERTAIN VALUE FOR g .

HOPE THIS HELPS

If C is the midpoint of AB then the length of CD is 11 units.

The midpoint of a line segment is referred to as the midpoint in geometry.

Given C is the midpoint of AB.

AD = 15 and BD = 7

Now AB = 15 - 7 = 8

Again AC = BC

Therefore = BC = 8 / 2 = 4

Now CD = BC + BD = 4 + 7 = 11

Therefore the length of CD is 11 units.

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Answer:

12

Step-by-step explanation:

Did you mean 7+5?

If so, then 7 + 5 = 12

Answer:

I don't understand the equation....pls rewrite it

Answer:

if x=4 y=12

if y=4 x=-4

Step-by-step explanation:

y=4+8 (add)

y=12

4=x+8 (subtract 8 from each side)

-4=x

Answer:

9. 178

Step-by-step explanation:

To find the complement subtract from 90

because complementary means sum of the angles is 90 degrees.

To find supplement, subtract from 180

because supplementary means sum of the angles is 180 degrees.