8x-5y=37 x=2y+6 substitution

On solving the provided question, we can say that by fraction, 4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

by fraction

4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.

16/12+9/12+8/12+9/12=42/12=3 and 1/2 cups.

20/3.5=5.7 or 6

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1)

The polynomial modelling this scenario is expressed as

P(t) = - 16t^2 + 300t

where

P(t) represents the height at time t

a) To find the height of the projectile when t = 1 second, we would substitute

t = 1 into the equation. Thus,

P(1) = - 16(1)^2 + 300(1)

P(1) = - 16 + 300 = 284

Height of projectile when t = 1 second is 284 feet

b) To find the height of the projectile when t = 5 second, we would substitute

t = 5 into the equation. Thus,

P(1) = - 16(5)^2 + 300(5)

P(1) = - 400 + 1500

Height of projectile when t = 5 second is 1100 feet

c) At the time when the object hits the ground, the height would be zero. This means that p(t) = 0

Thus, the equation would be

0 = - 16t^2 + 300t

Factoring out 4t from the right, we have

0 = - 4t(4t - 75)

- 4t = 0 or 4t - 75 = 0

t = 0/-4 or 4t = 75

t = 0 or t = 75/4

t = 0 or t = 18.75

It will take 18.75 seconds until the object hits the ground

Using the hypergeometric distribution, it is found that the probabilities are given as follows:

a) 0.2059 = 20.59%.

b) 0.5294 = 52.94%.

c) 0.2647 = 26.47%.

The formula is:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem, the parameters are as follows: N = 17, k = 8, n = 2.

Item a:

This probbility is P(X = 2), hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 2) = h(2,17,2,2) = \frac{C_{8,2}C_{9,0}}{C_{17,2}} = 0.2059\)

Item b:

This probbility is P(X = 1), hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 1) = h(1,17,2,2) = \frac{C_{8,1}C_{9,1}}{C_{17,2}} = 0.5294\)

Item c:

This probbility is P(X = 0), hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 0) = h(0,17,2,2) = \frac{C_{8,0}C_{9,2}}{C_{17,2}} = 0.2647\)

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Answer:

9750

Step-by-step explanation:

profit amount = 30% of R 7500

= 30/100 *R 7500

= 2250

now

sp = R 7500 + R 2250

= R 9750

Answer:

α = 0.01 ; 2 - tailed

χ² = 16.998

Pvalue = 0.1497

Fail to reject H0

Step-by-step explanation:

Given the data above :

Number of People Making Contribution

Ethnic Group $1-50 $51-100 $101-150 $151-200 Over $200 Row Total

A 77 63 54 39 18 251

B 90 48 76 26 24 264

C 73 67 59 37 30 266

D 108 82 70 50 30 340

Column Total 348 260 259 152 102 1121

1.) The level of significance, α/2 = 0.01/2

2.)

The hypothesis :

H0 : Contribution and Ethnic group are independent

H1 : Contribution and Ethnic group are not independent

The Chisquare statistic :

χ² = (Observed - Expected)²/ Expected

The expected value for each cell is calculated thus :

(Row total * column total) / sum total

The expected values :

77.9197 58.2159 57.992 34.0339 22.8385

81.9554 61.231 60.9955 35.7966 24.0214

82.5763 61.6949 61.4576 36.0678 24.2034

105.549 78.8582 78.5549 46.1017 30.9367

Using the χ² formula above ;

χ² values for each cell are :

0.010855 0.393154 0.274794 0.724635 1.02509

0.789645 2.85902 3.69099 2.68108 0.0000191

1.11055 0.456179 0.098278 0.0240936 1.38826

0.056933 0.125176 0.93165 0.32963 0.028359

Taking the sum :

0.010855+0.393154+0.274794+0.724635+1.02509+0.789645+2.85902+3.69099+2.68108+0.0000191+1.11055+0.456179+0.098278+0.0240936+1.38826+0.056933+0.125176+0.93165+0.3293+0.028359

χ² = 16.998

To obtain the Pvalue :

df = (Row - 1)(column - 1) = (5-1)*(4-1) = 4 * 3 = 12

Pvalue(16.998 ; 12) = 0.1497

If Pvalue < α ; Reject H0 ;

Since Pvalue > α ; WE fail to reject H0

Answer:

Approximately 68%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 1, standard deviation = 0.05.

Estimate the percent of pails with volumes between 0.95 gallons and 1.05 gallons.

0.95 = 1 - 0.05

1.05 = 1 + 0.05

So within 1 standard deviation of the mean, which by the Empirical Rule, is approximately 68% of values.

68.29% of pails have volumes between 0.95 gallons and 1.05 gallons.

Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

\(z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \sigma=standard\ deviation\)

Given that:

μ = 1, σ = 0.05

\(For\ x=0.95:\\\\z=\frac{0.95-1}{0.05} =-1\\\\For\ x=1.05:\\\\z=\frac{1.05-1}{0.05} =1\)

P(0.95 < x < 1.05) = P(-1 < z < 1) = P(z < 1) - P(z < -1) = 0.8413 - 0.1587 = 68.29%

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Answer:

Step-by-step explanation:

Okay, so you need to create an equation which shows that twice the sum of a number (n) and 7 is 3 times that number. So you need twice the sum of n + 7 and that will equal 3 times n.

2(n + 7) = 3n

Now, multiply

2n + 14 = 3n

2n + 14 -2n = 3n - 2n

14 = n

So the number is 14. Now you can check your answer

2(14 + 7) = 3(14)

2x21 = 42

42 = 42

Step-by-step explanation:

1. if to rewrite the given equation, then

y= -3(x+5)²+1;

2. the vertex of the parabola is (-5;1) and it is the highest point. Then

3. domain: x is any value, x∈(-∞;+∞);

range: y not greater than 1, y∈(-∞;1].

For the parabola f(x) = -3x² - 30x - 74, the domain is all real numbers (-∞, ∞), and the range is also all real numbers (-∞, ∞).

To determine the domain and range of the given parabola f(x) = -3x² - 30x - 74, we need to understand the behavior of parabolas.

The domain of a function represents all the possible x-values for which the function is defined. In this case, there are no restrictions on the x-values for the given quadratic function. Therefore, the domain is all real numbers, expressed as (-∞, ∞).

The range of a function represents all the possible y-values that the function can produce. For a parabola, if the coefficient of the squared term (in this case, -3) is negative, the parabola opens downward. Since the coefficient is negative, the parabola will have a maximum value. In this example, there is no minimum or maximum specified; thus, the range will also be all real numbers.

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If wheel on a scooter completes 124 revolutions and travels 22.4 meters then  diameter of the wheel is 57 mm

Each revolution of the wheel covers a distance equal to the circumference of the wheel.

The diameter of the wheel "d".

The distance covered in 124 revolutions is:

distance = 124 x circumference

= 124 x pi x d

= 124 x 3.14 x d

We know that this distance is equal to 22.4 meters, so we can set up an equation:

124 x 3.14 x d = 22.4

Simplifying and solving for d:

d = 22.4 / (124 x 3.14)

d = 0.057 meters

As we know that 1 meter is equal to thousand millimeters so multiply by 1000 to get in millimeters

d = 57 millimeters

Therefore, the diameter of the wheel is approximately 57 mm.

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Answer:

The first bottle holds 25 3/5 ounces of water.

Step-by-step explanation:

16 x 8/5

= 16/1 x 8/5

= 128/5

= 25 3/5

Answer:

10 ounces

Step-by-step explanation:

16=8/5

z=1

16*1=16

8/5*z=8/5z

16=8/5z

16/1.6z=10

z=10

Answer:

√221 is between 14 and 15.

√221 ≈ 14.86

Step-by-step explanation:

Perfect square:  A number made by squaring a whole number.

Perfect squares:  1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, ...

To find an approximate value of a square root, find the perfect squares above and below the number:

⇒ 196 < 221 < 225

Therefore:

\(\implies \sf \sqrt{196} < \sqrt{221} < \sqrt{225}\)

\(\implies \sf \sqrt{14^2} < \sqrt{221} < \sqrt{15^2}\)

\(\implies \sf 14 < \sqrt{221} < 15\)

Therefore, √221 is between 14 and 15 on a number line.

Drawing the number line

(see attachment 1)

Locate 221 on the number line. We can see that it is between 14.8 and 14.9.  Place a marker halfway between 14.8 and 14.9, then divide the second half into 5 equal increments (see attachment 2).

Therefore, an approx value of √221 is 14.86.

Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.

An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.

In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.

Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

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Answer:

Step-by-step explanation:

13-2x=4x+7                                                                                                          -2x+13=4x+7                                                                                                       (-2x+13)+(-13-4x)=(4x+7)+(-13-4x)                                                                        -2x+13-4x-13=4x+7-13-4x                                                                                

-2x-4x+13-13=4x-4x+7-13                                                                                                  -6x=-6                                                                                                               6x/6=6/6                                                                                                                 x=1                                                                                                    

The actual pressure when the gauge shows 33.58 would be 36.5.

Used the concept of the percentage that states,

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating the hundredth part of any quantity is called a percentage.

Given that,

Ali's tire pressure gauge shows a reading which is \(8 \%\)lower than the actual pressure.

And, the gauge shows \(33.58.\)

Let us assume that,

The actual pressure of Ali's tires = x

Hence, we can formulate the equation,

\(x \times (1 - 8\%) = 33.58\)

Solve the equation for x,

\(x \times (1 - \dfrac{8}{100} ) = 33.58\)

\(x \times (1 - 0.08) = 33.58\)

\(x \times 0.92 = 33.58\)

Divide both sides by 0.92;

\(x= \dfrac{33.58}{0.92}\)

\(x = 36.5\)

Therefore, The actual pressure of Ali's tires = 36.5

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The complete question is,

Ali's tire pressure gauge shows a reading which is 8% lower than the actual pressure.

What is the actual pressure of Ali's tires when the gauge shows 33.58?

Answer:

x = 4.5

Step-by-step explanation:

0.2(-3) + 5.1 = -0.6 + 5.1 = 4.5

Answer:

v = -12

Step-by-step explanation:

29 = -8v - 7 + 5v

Combine the 'like terms':  

29 = (-8v + 5v) - 7

29 = -3v -7

Add 7 to both sides:

29 + 7 = -3v -7 +7

36     =    -3v + 0

36      =    -3v

Divide both sides by the coefficient in front of the variable 'v' because we want to get 'v' all by itself. So, divide by -3.

36/-3 = -3v/-3

   -12  =  v

And that is the answer, v is negative twelve

Answer:

v=

Step-by-step explanation:

29= -8v- 7 + 5v

-8v + 5v - 7 = 29

-3v - 7 = 29

-3v - 7 + 7 = 29 + 7

-3v = 36

-3v ÷ -3 = 36 ÷ -3

v = -12

Answer:

The first is not equivalent, second is.

Step-by-step explanation:

2x-3.9x+7.5=5.9x+7.5

The first is not equivalent, second is.

Answer:

D

Step-by-step explanation:

Graph D has a y intercept of 3 and a slope of 6.25

let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said

\(\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill\)

\(\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}\)

Step-by-step explanation:

WX is parallel to YZ and WZ is also parallel to XY

Option C,D and E are correct.

Explanation:

In Euclidean geometry,a parallelogram is a simple quadrilateral with two pairs of parallel sides.The opposite or facing sides of a parallelogram are of equa length and the opposite angles of a parallelogram are of equal measure.

Hope this helps...

Good luck on your assignment..

Answer:

  A.  $25,888

  B.  $42,877

Step-by-step explanation:

The total cost is the product of the cost of each item and the number of items. The total profit will be the product of the profit on each item and the number of items.

The cost of 809 tires at $32 each is ...

  809 × $32 = $25,888 . . . . . total cost of the purchase

The profit the store makes on each tire is ...

  profit = selling price - cost = $85 -32 = $53

The gross profit on 809 tires at $53 each is ...

  total profit = 809 × $53 = $42,877 . . . . . gross profit

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The areas of the trapezoid is 50 units².

The trapezoid PQRS have bases 10 and 12 units respectively. The height of the trapezoid is unknown. Let's find the area of the trapezoid as follows:

area of trapezoid = 1 / 2 (a + b)h

where

Therefore,

a = 10 units

b = 15 units

Using Pythagoras's theorem,

5² - 3² = h²

h = √25 - 9

h = √16

h = 4 units

area of trapezoid = 1 / 2 (10 + 15)4

area of trapezoid = 1 / 2 × 25 × 4

area of trapezoid = 100 / 2

area of trapezoid = 50 units²

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Answer:

decimal: 13.33

mixed number: 13 1/3

Answer:

A(t) = π(8t)²

Step-by-step explanation:

Radius of a circular wave increases by 8 cm each second.

Every second radius of circular wave so the sequence of increase in radius will be,

8, 16, 24, 32.........(8t)

Here 't' = time

Since, area of a circle = πr²

Therefore, area of the circular wave after 't' seconds since the wave begins,

A(t) = π(8t)²

Answer:

Yes, the graph is a function because the lines do not overlap one another (vertical line test)

- I hope this helps have a great night

Slope of line is 1/2.

What is slope?

In arithmetic, the slope or gradient of a line is a range that describes each the direction and therefore the gradient of the road.

Main body:

to find the slope from a graph , we need to fix two co-ordinates at slope for axis

let point at x be = (40,40)

let point y = (80,60)

Formula for slope ,

m = y₂-y₁/x₂-x₁

m = 60-40/80-40

m = 20/40

m = 1/2

hence , slope of line is 1/2.

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The total number of coins that were in Kay's bank are 137 coins.

In order to determine the number of dimes and nickels, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Since she has 11 less dimes than nickels, an equation which models this situation is given by;

n = d + 11     ....equation 1.

Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.

Additionally, the coins are worth 10 dollars;

0.1d + 0.05n = 10 ....equation 2.

By solving both equations simultaneously, we have:

0.1d + 0.05(d + 11) = 10

0.1d + 0.05d + 0.55 = 10

0.15d = 9.45

d = 63 dimes.

For nickels, we have:

n = d + 11

n = 63 + 11

n = 74

Now, we can determine the total number of coins;

Total number of coins = n + d

Total number of coins = 74 + 63

Total number of coins = 137 coins.

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Using the Intersecting secants theorem, the length of JK in the given diagram is 17

From the question, we are to determine the length of JK in the given diagram.

The diagram shows a circle with intersecting secants.

From the Intersecting secants theorem which states that "if two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment".

Then,

We can write that

JK × KL = NM × ML

From the given diagram,

KL = 14

NM = 14

ML = 17

Substituting the values

JK × 14 = 14 × 17

JK = (14 × 17) / 14

JK = 17

Hence, the length of JK is 17

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