Jackson runs a farm stand that sells bananas and grapes. Each pound of bananas sells for $1 and each pound of grapes sells for $2.25. Jackson sold 15 more pounds of bananas than pounds of grapes and made $54 altogether. Graphically solve a system of equations in order to determine the number of pounds of bananas sold, x , x, and the number of pounds of grapes sold, y y

The angles that are 118 degrees are ∠1 , ∠3, ∠5 and ∠7.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles etc.

Therefore, let's find the angle relationship in the line and find the angles that are 118 degrees.

Hence,

∠3 = 180 - 62 = 118 degrees(angles on a straight line)

∠1 ≅ ∠3 (vertically opposite angles)

∠7 ≅ ∠3 (alternate interior angles)

∠5 ≅ ∠7 (vertically opposite angles)

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In order to achieve the shortest distance from starting vertex (A) to F on a network, utilize Dijkstra's algorithm following these steps:

Initiate every vertex with a tentative distance value: assign zero to the starting point and infinity to other vertices.

Establish the initiating vertex as the current vertex.

Analyze all neighboring vertices of the current vertex and determine their respective tentative path length via current vertex. Proceed to compare it with its already assigned value; upgrade such distance if shorter than before.

Subsequent to analyzing adjacent points of the present node, designate it as 'visited'. Futuristic reference will disregard this chosen and visited vertex altogether.

Examine unexplored vertices marked as having the most reduced tentative distances, declare them 'current' while formulating new calculations for other contenders until pertinent conclusion is reached.

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Answer:

330 approximately.

Step-by-step explanation:

The percentage lying between 2 standard deviations is 95%.

So we have 348 * 0.95 = 330 approximately.

The Distance will be  5.

The distance between two points is the length of the line segment connecting the two points on the plane. The formula for finding the distance between two points is usually d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on the coordinate or x-y plane.

Let point (7,5) be A and point (4,9) be B

Distance formula =

Ab  = √(x1- x2) ² + (y1 -y2) ²

Then Distance AB will be

Ab  = √(7-4) ² + (5 -9) ²

= √ 3² + 4²

= √ 9 + 16

= 5

Hence the distance  will be 5.

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The points \((7,5)\)  \((4,9)\) are separated by a distance of \(5\) units.

The distance between the two points is given by the length of the segment between them.

The Distance Formula is a helpful tool for figuring out how far apart two points are when they are arbitrarily represented on a coordinate plane as points A\((x_{1},y_{1})\) and B\((x_{2},y_{2})\).

The Pythagorean Theorem is essentially the source of the Distance Formula. Calculating the right triangle's hypotenuse's length is the fundamental purpose of the distance formula.

Use the distance formula to get the distance between two places.

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

In the posted query,

\((x_{1},y_{1})=(7,5)\\\\(x_{2},y_{2})=(4,9)\)

Distance formula,

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

\(d = \sqrt{ (4-7)^{2} +(9-5)^{2} }\)

\(d = \sqrt{ (-3)^{2} +(4)^{2} }\)

\(d = \sqrt{ 9+16 }\)

\(d = \sqrt{ 25 }\)

\(d = 5\)

Therefore, the points \((7,5)\)  \((4,9)\) are at a distance of \(5\) units.

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A set S spans R^2 if any element of R^2 can be written as linear combination of elements of S the set S spans R2.

(a) Given that S={ (1,-1),(2,1) }

Let (x,y) be the any element in R^2.

(x,y) = C1(1,-1)+C2(2,1)

(x,y) = (c1+2c2,-c1+c2)

x  =  c1+2c2

y  = -c1+c2

x+y = 3c2

c2= {x+y}/{3}

c1 = c2-y

= {x+y}/{3}-y

={x-2y}/{3}

So for any element (x,y) in R^{2} we have the constants c_1,c_2 so that (x,y) can be written as,

(x,y)= {(x-2y)}/{3}(1,-1) + {(x+y)}/{3}(2,1)

So S= { (1,-1),(2,1) } spans R^2.

(b) Given that S = { (1,1) }

Let (x,y) be the any element in R^2.

(x,y)=c_1(1,1)

(x,y)=(c_1,c_1)

x=c_1,y=c_1

If x,y are distinct then do not get a value of c_1 so that (x,y) = c_1(1,1).

So set S= { (1,1) } does not span R^2.

(c) Given that S= { (0,2),(1,4) }

Let (x,y) be the any element in R^2.

(x,y)=c_1(0,2)+c_2(1,4)

(x,y)=(c_2,2c_1+4c_2)

x=c_2

y=2c_1+4c_2

c_1={y-4c_2} / {2}

={y-4x} / {2}

So (x,y)= {(y-4x)}/{2}(0,2)+x(1,4)

So any element of R^2 can be written as written as linear combination of elements of Set S.

Hence set S={ (0,2),(1,4) } spans R^2.

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Answer:

80

Step-by-step explanation:

1 pizza has 8 \(\frac{1}{8}\)ths. 10 pizzas have 10 × 8 = 80 1/8ths. So 80.

Answer:

80 because if one student gets 1/8 that means 8 students get one slice out of the pizza multiply 8 by 10 and it equals 80

The number of months to reach 51 can be illustrated as 3060 - 100x = 51.

The expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both.

The farmer planted 3,060 tomato plants in his garden.

Let's assume there's a decrease of 100 monthly.

The number of months, x, it will take for the number of tomato plants in his crop to reach 51 = c

This will be:

3060 - 100x = 51.

This illustrates the equation for the number of months.

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Answer:

answer is 47.49 because tan theta is equals to 12 / 11 which is 1.09091.

So tan-¹(1.09091) = 47.49

Answer:

b. He should use the two-sample test of the mean to answer question one and the two-sample test of proportion to answer question two.

Step-by-step explanation:

Here we have two independent groups, Men and Women, therefore, to show if it is the Men or Women who performed better, this can be determined based the mean scores of each group. Therefore, use the two sample test of mean which is used to test whether the unknown mean of two independent population are equal or not.

In other to determine those who have the greater number of admissions between the two groups, this is determined by comparing the proportion of each group admitted. Hence, rather Than testing for the mean, we compare the proportion. Hence, we use the two sample test of proportion.

Check the picture below.

so hmm we have a 6x6 square atop and a triangle with base of 6 and a height of "h", let's get "h".

\(\sin( 42^o )=\cfrac{\stackrel{opposite}{h}}{\underset{hypotenuse}{2}} \implies 2\sin(42^o)=h \implies 1.34\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{6})(\underset{h}{1.34})}~~ + ~~\stackrel{ square }{(6)(6)}} ~~ \approx ~~ 4.02+36~~ \approx ~~ \text{\LARGE 40.0}\)

Check the picture below.

Answer:

A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.

Step-by-step explanation:

Answer:

A translation is converting another language into English

Step-by-step explanation:

Answer:

$800

Step-by-step explanation:

Let the original price be $x.

75% reduction ----- 100% -75%= 25%

25%x= 200

\( \frac{25}{100} x = 200 \\ x = 200 \div \frac{25}{100} \\ x = 200 \times \frac{100}{25} \\ x = 800\)

Thus, the original price of the clothes dryer is $800.

Answer:

$800

Step-by-step explanation:

Let the original price be x.

Final price=100%-75%

                  =25%

x-75%=200

x=200 x 100/75

x=8 x 100

x=800

Thank you!

Answer:

189

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(a)

perimeter (P) is calculated as

P = 2(l + b) ← l is the length and b the breadth

given l = x and P = 20 , then

2(x + b) = 20 ( divide both sides by 2 )

x + b = 10 ( subtract x from both sides )

b = 10 - x

Using Pythagoras' identity in the right triangle

x² + (10 - x)² = 8²

x² + 100 - 20x + x² = 64 ( subtract 64 from both sides )

2x² - 20x + 36 = 0 ( divide through by 2 )

x² - 10x + 18 = 0 ← as required

(b)

solve using the method of completing the square

x² - 10x + 18 = 0 ( subtract 18 from both sides )

x² - 10x = - 18

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 5)x + 25 = - 18 + 25

(x - 5)² = 7 ( take square root of both sides )

x - 5 = ± \(\sqrt{7}\) ( add 5 to both sides )

x = 5 ± \(\sqrt{7}\)

Then

x = 5 - \(\sqrt{7}\) ≈ 2.35 ( to 3 significant figures )

x = 5 + \(\sqrt{7}\) ≈ 7.65 ( to 3 significant figures )

Step-by-step explanation:

A=102cm2

A=Lengthxbreadth

102=Lengthx6

Length=17 cm

Answer:

refer to attachment

Step-by-step explanation:

The order of the given fractions will be 5/3>3/2>5/6.

What exactly is a fraction?

A fraction is a mathematical term that represents a portion or part of a whole. It represents the equal parts of the whole. A fraction has two components: the numerator and the denominator. The top number is referred to as the numerator, while the bottom number is referred to as the denominator. The denominator describes the total number of equal parts in a whole, whereas the numerator defines the number of equal parts taken.

5/10, for example, is a fraction.

In this case, 5 is the numerator and 10 is the denominator.

Now,

Given fractions are 5/6 ,5/3,  3/2

lets make the denominator same

Divide and multiply fraction 2 and 3 by 2 and 3 respectively

then fractions are 5/6, 10/6, 9/6

so, the order will be 10/6>9/6>5/6 i.e. 5/3>3/2>5/6

hence,

           The order of the given  fractions will be 5/3>3/2>5/6.

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The measures of angle 4 (m<4) and angle 7 (m<7) are 42° and 96°, respectively.

To find the measures of angles 4 and 7, we need to apply some geometric principles. Since the top and bottom pieces of the crib are parallel to each other, we can use the property of alternate interior angles.

Angle 4 (m<4) is formed by a transversal (the line connecting the top and bottom pieces of the crib) intersecting two parallel lines. Given that angle m<2 is 42°, we know that angle 4 is congruent to angle 2. Therefore, m<4 = m<2 = 42°.

Angle 7 (m<7) is formed by a transversal intersecting two parallel lines as well. However, in this case, angle 7 is an exterior angle, which is equal to the sum of the two remote interior angles. The remote interior angles are angles 2 and 4. We know that m<2 = 42° (as given) and m<4 = m<2 = 42° (as explained above). Therefore, the sum of angles 2 and 4 is 42° + 42° = 84°. Since angle 7 is an exterior angle, it is equal to 180° minus the sum of the remote interior angles. Thus, m<7 = 180° - 84° = 96°.

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Answer:

152 yards

Step-by-step explanation:

456 divided by 3 equals 152

Answer:

456 feet equal 152 yards

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I checked it and it’s right hope this helps!!

Answer:

150

Step-by-step explanation:

The IRA that is best is C. The Roth IRA is the best choice because the employee will pay more in taxes during employment than in retirement.

When contributing to a Roth IRA, one must use after-tax dollars, resulting in taxes being paid on the money prior to it being deposited into the account. Withdrawals made from a Roth IRA that meet the necessary qualifications are completely exempt from taxation, thus employees will not be required to pay any taxes on the amount withdrawn during their retirement period.

It is probable that an employee's retirement income tax bracket will be higher than their current bracket, given the anticipated increase in their income and tax rate.

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Step-by-step explanation:

The difference in overall loss or gain between sell at the current day's high price or low price is found tp be the difference in overall gain as $280.10

The third option is correct.

High price value: 115 shares * $105.19 per share = $12,084.85

Low price value: 115 shares * $103.25 per share = $11,858.75

High price value: 30 shares * $145.18 per share = $4,355.40

Low price value: 30 shares * $143.28 per share = $4,298.40

The overall value at high price:

$12,084.85 + $4,355.40

= $16,440.25

The overall value at low price:

$11,858.75 + $4,298.40

= $16,157.15

In conclusion, the difference in overall gain or loss:

$16,440.25 - $16,157.15 = $280.10

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The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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