Consider this system of equations 2/3 x + 3/5 y =12 (equation A) 5/2y - 3x = 6 (equations B)

Jim has to travel 26.82 miles more to reach Denver.

What is the equation of a line?

Let the first point be = (x₁ , y₁)

Let the second point be = (x₂ , y₂)

m(slope) = (y₂ - y₁) / (x₂ - x₁)

Equation of line = (y - y₁) = m(x - x₁)

Let the no. of miles be plotted on X-axis

Let the driving time be plotted on Y-axis

First point = (61 , 41)

Second point = (42.3 , 63)

Slope of the linear function = (63 - 41)/(42.3 - 61) = -1.17

Equation of the line = (y - 41) = -1.17(x - 61)

Given time of driving = 81 min

Number of miles = (81 - 41) = -1.17(x - 61)

40/-1.17 = x - 61

-34.18 + 61 = x

x = 26.82

Hence, Jim has to travel 26.82 miles more to reach Denver.

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It looks like the equation is

[tex]\dfrac{du}{dt} = 2t + \dfrac12 \sec^2(t) u[/tex]

with initial value [tex]u(0) = \frac\pi2[/tex].

Rearrange the equation to

[tex]\dfrac{du}{dt} - \dfrac12 \sec^2(t) u = 2t[/tex]

Multiply both sides by the integrating factor

[tex]\displaystyle \mu = \exp\left( \int -\frac12 \sec^2(t)\,dt\right) = \exp\left(-\frac12\tan(t)\right)[/tex]

and solve for [tex]u[/tex].

[tex]\implies e^{-\frac12 \tan(t)} \dfrac{du}{dt} - \dfrac12 \sec^2(t) e^{-\frac12 \tan(t)} u = 2t e^{-\frac12 \tan(t)}[/tex]

[tex]\implies \dfrac{d}{dt}\left[e^{-\frac12 \tan(t)} u\right] = 2t e^{-\frac12 \tan(t)}[/tex]

By the fundamental theorem of calculus, integrating both sides yields

[tex]e^{-\frac12\tan(t)} u = e^{-\frac12\tan(t)} u \bigg|_{t=0} + \displaystyle \int_{\xi=0}^{\xi=t} 2\xi e^{-\frac12 \tan(\xi)} \, d\xi[/tex]

[tex]\implies e^{-\frac12\tan(t)} u = 1\times\dfrac\pi2 + \displaystyle \int_{0}^{t} 2\xi e^{-\frac12 \tan(\xi)} \, d\xi[/tex]

[tex]\implies \boxed{\displaystyle u = \frac\pi2 e^{\frac12\tan(t)} + 2e^{\frac12\tan(t)} \int_0^t \xi e^{-\frac12 \tan(\xi)} \, d\xi}[/tex]

Answer:

[tex] \frac{6}{20} = \frac{3}{10?} [/tex]

Step-by-step explanation:

total amount of acts = 4+10+6 = 20

amount of dancers = 6

probability of picking a dancer = number of dancers / total number of talents = 6/20 = 3/10

The probability that a dancer performs first is 3/10.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

The acts in a talent competition consist of 4 instrumentalists, 10 singers, and 6 dancers.

Total participants = 4+ 10 +6 = 20

So, the probability that a dancer performs first

= 6 /20

= 3/10

Hence, the probability that a dancer performs first is 3/10.

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Answer:

d: y=5x

Step-by-step explanation:

Since we know a few points: (2,10), (3,15), (4,20), we can use two of them to first find the slope. The equation for the slope is (Increase in y)/(increase in x).

1. Slope between (2,10) and (3,15) is 5/1 which is 5. So the slope will be 5.

2. With the slope, we know that our equation will be: y=5x+b. To find b, we can replace x and y with another point. 20 = 5(4)+b. --> 20 = 20 +b. Now we know that b equals 0.

Our final equation will be y = 5x.

RECHECKING!

I'll recheck whether my answer is right or not using Desmos (A online graphing calculator).

I added an image down below, and I drew the points in blue. This shows that since the graph crosses all three points, it is correct.

WHY y=1/5x IS NOT CORRECT (based on your comments)

If you look at the points, the relationship between x and y is not 1/5. If you multiply something from x, it should become 10.

--> 2 times __ = 10

--> 3 times __ = 15

--> 4 times __ = 20

And clearly, __ will be 5. If it becomes 1/5, we won't get the right number of y.

This is why y=1/5 is not correct.

Hope this helps!

The money can be withdrawn from the account every two months for the next 6 years is $20, 625, 000

The formula for compound interest is given as;

[tex]A = P ( 1 + \frac{r}{n} )^n^t[/tex]

P = principal interest = $25, 000

r = rate = 4. 5%

n = 2 months

t = 6 years

A = [tex]25, 000 ( 1 + \frac{4. 5}{2} )^2 ^*^6[/tex]

A = [tex]25, 000(1 + 0. 75)^1^2[/tex]

A = [tex]25, 000( 825. 00)[/tex]

A = $20, 625, 000

Thus, the money can be withdrawn from the account every two months for the next 6 years is $20, 625, 000

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What is inequality?

In Algebra, inequality shows the relation between two expressions using the inequality symbol.

The graph shows the equation y<x^2+1 is attached

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The graph at option 1 shows the given inequality y < x² + 1. The domain and range of the given inequality is {x: x ∈ (-∞, ∞)} and {y: y ∈ [1, ∞)}.

The steps to graph an inequality equation are:

The given inequality is y < x² + 1

Finding points to graph the boundary line by taking y = x² + 1:

When x = -2,

y = (-2)² + 1 = 4 + 1 = 5

⇒ (-2, 5)

When x = -1,

y = (-1)² + 1 = 2

⇒ (-1, 2)

When x = 0,

y = (0)² + 1 = 1

⇒ (0, 1)

When x = 1,

y = (1)² + 1 = 2

⇒ (1, 2)

When x = 2,

y = (2)² + 1 = 5

⇒ (2, 5)

Plotting these points in the graph forms an upward-facing parabola.

So, all the points above the vertex of the parabola satisfy the given inequality. Thus, that part is shaded.

From this, the graph at option 1 is the required graph for the inequality y < x² + 1. The boundary line is dashed since the inequality symbol is " < ".

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Answer:

angle x equals 25

Step-by-step explanation:

130 + 25 = 155

180 - 155 = 25

Triangles always add up to 180°

Answer:

it is so easy the answer is 25

Step-by-step explanation:

The total sum of the traingle is 180 degree. So frist add both the numbers in the traingle and then subtract it by 180 degree

The proof to show that at least 80% of students who study both art and science, also study math is illustrated below.

From the information given, it was stated that at least 80% of students study both math and art and that at least 80% of students study both math and science.

Therefore, about (100 - 80) 20% doesn't study the combination of both subjects.

Here, those students who study both art and science, and also study math will be:

= 100% - 20%

= 80%

Therefore, at least 80% study the subjects.

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Answer:

Step-by-step explanation:

the area of a circle is πr²

r being the radius, which is equal to half the diameter

3.3/2= 1.65

π(1.65)²=8.6m

The probability would be 3/125 in the given conditions.

As there are 105 items, of which 30 are bats. The probability for that draw is 30/105.

There are now 104 items remaining, of which 15 are gloves. The probability of getting a glove now is 15/104.

There are now 103 items remaining, of which 60 are balls. The probability of getting a ball now is 60/103.

The probability of all three occurring = product of three

15/104* 30/105* 60/103

= 3/125

Hence the probability is 3/125.

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The question is an illustration of combination and there are 729 potential pass codes available

The given parameters are

Symbols available = 9

Length of pass code = 3

From the question, we understand that a symbol may be entered any number of times.

This means that each of the 9 available symbols can be used three times

So, the number of potential pass codes is

Passcodes = 9 * 9 * 9

Evaluate the product

Passcodes = 729

Hence, there are 729 potential pass codes available

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Given the 6 pound weight of the new seasoning having ingredients that cost $8, and $11, the amount she should charge for 1 ounce is $0.53125

The ingredients in the new seasoning are;

5 pounds of dried rose hips + 1 pounds of five-spice powder

Cost of the ingredients are;

1 pound of dried rose hips = $8

1 pound of five-spice powder = $11

The cost of combined spice, C, is therefore;

C = $8 × 5 + $11 × 1 = $51

The weight of the new combined seasoning = (5 + 1) pounds = 6 pounds

Cost of 1 pound of the new seasoning is therefore;

[tex]1 \: lb = \frac{51}{6} = 8.5[/tex]

Therefore;

[tex]1 \: ounce = \frac{8.5}{16} = \mathbf{0.53125}[/tex]

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Answer: $2.25

Step-by-step explanation:

5 lbs = 80 oz, so the mixture is worth

80(8/16) + 16(11) = 96x

x = $2.25/oz

Hope this helps!!

The least polynomial in standard form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.

Polynomials can be expressed as a product of binomials of the form (x - r) multiplied by a leading coefficient. The least polynomial contain the number of roots presented in statement, whose factor form is shown below:

f(x) = 1 · (x + 3)³ · x³ · (x - 3)

f(x) = (x + 3)³ · (x⁴ - 3 · x³)

f(x) = (x³ + 9 · x² + 27 · x + 27) · (x⁴ - 3 · x³)

f(x) = x⁷ + 9 · x⁶  + 27 · x⁵ + 27 · x⁴ - 3 · x⁶ - 27 · x⁵ - 81 · x⁴ - 81 · x³

f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³

The least polynomial in standard form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.

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Answer:

  Slope = 7/4

Step-by-step explanation:

You are given coordinate values and a formula that tells you what to do with them. All you need to do is put the values in the formula and do the arithmetic.

You are given points (2, -3) and (6, 4). The slope formula refers to the two points as (x1, y1) and (x2, y2). It does not matter which is which.

If we use the points in the same order they are given, then we can see that ...

Using these values in the given formula, we find the slope to be ...

  [tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-(-3)}{6-2}=\dfrac{7}{4}[/tex]

The slope of the line through the given points is 7/4.

The management salary is $19,429

What is ratio?

Ratio is the quantitative relationship between two numbers which shows the number of times an amount or a number is contained within the other amount or number.

In this case, a ratio  of 8:7 shows the number of times the management salaries is contained within the management trainee salary

The management salary has a  value of 8 whereas the management trainee salary has a value of 7 as shown below:

salary ratio=management salary/management trainee salary

salary ratio=8/7

management salary=unknown(assume it is X)

management trainee salary=$17,000

8/7=X/$17,000

cross multiply

8*$17,000=7*X

X=8*$17,000/7

X=$19,429

The fact that annual management trainee salary is $17,000 means that the management salary is $19,429 annually.

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Total of 1820 different kinds of banquets can be made.

Combinations are mathematical procedures that count how many different ways a collection of items could be arranged when the order in which they are chosen is immaterial. Combos' components can be chosen in any hierarchy.

[tex]$C_{12}(16)=\left(\begin{array}{l}16 \\ 12\end{array}\right)=\frac{16 !}{12 !(16-12) !}=\frac{16 \cdot 15 \cdot 14\cdot13}{4\cdot3 \cdot 2 \cdot 1}=1820[/tex]

[tex]$n=5$ $k=12$\\$x=\left(\begin{array}{c}n+k-1 \\ k\end{array}\right)=\left(\begin{array}{c}5+12-1 \\ 12\end{array}\right)=1820$[/tex]    

Total of 1820 different kinds of banquets can be made

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Answer:

[tex]\huge\boxed{\sf y = 1/3}[/tex]

Step-by-step explanation:

-4 + 3y = -3

Add 4 to both sides

3y = -3 + 4

3y = 1

Divide 3 to both sides

[tex]\rule[225]{225}{2}[/tex]

Answer:

h (1) = $140

Step-by-step explanation:

10x + 150

-10     -10

150-10

=140

so the answer must be $140

So it is definitely the first one

H(12)=$270

When it comes to resource allocation, it's not a one sentence answer. The explanation for how to go about this is given below. But first, lets look at what Profit Allocation means.

This simply means the process of distributing profit to various areas of the business such that all parts are (human and non-human  components) are satisfied and operating at equilibrium.

There are five steps to aligning your budget and resource demands when planning for support resource allocation.

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The statements that are true for the box plots are:

C. The median of Nadia’s data = median of Ben’s data.

D. Nadia had the highest score on a test

The median of a data set is the center value, which is indicated on a box plot by a vertical line that divides the box.

Given the two box plots, we can conclude that:

Median for the data of Nadia is 92, which is the same for Ben.

The extreme whisker to the right for Nadia is at 100, which is the highest value for Nadia while that of Ben is 99.

The true statements are:

C. The median of Nadia’s data = median of Ben’s data.

D. Nadia had the highest score on a test

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Answer:

"C" and "D"

Step-by-step explanation:

took test on edge 2023

Answer:

Area of parallelogram = 9600 m²

Step-by-step explanation:

• We can find the measure of angle x using the cos rule:

[tex]160^2 = 100^2 +100^2 -2(100)(100) \cdot cos (x)[/tex]

Make x the subject of the equation:

⇒  [tex]20000 \cdot cos(x) = 100^2 +100^2 - 160^2[/tex]

⇒  [tex]cos(x) = -0.28[/tex]

⇒  [tex]x = cos^{-1} (-0.28)[/tex]

⇒  [tex]x = 106.26 \textdegree[/tex]

• Now we can find the area of one the triangles formed using the formula:

[tex]Area =\frac{1}{2} ab \cdot sin \theta[/tex]

where a and b are two sides of a triangle, and θ is the angle between them (angle x).

Substituting the values:

Area of one triangle = [tex]\frac{1}{2}[/tex]  × (100)(100) × sin(106.26°)

                             = 4800 m²

• Since the parallelogram is formed by two such triangles, we have to double the area of the triangle to find the parallelogram's area:

Area of parallelogram = 2 × 4800

                                     = 9600 m²

Answer:

m=15

Step-by-step explanation:

Oh, I think I answered this question recently, but it's m=15c

The explanation for the question was written in my other response.

Answer:

d.  m = 15c

Step-by-step explanation:

Directly proportional means as one amount increases, another amount increases at the same rate.

Proportionality can be used to set up an equation.

Given variables:

If m is directly proportional to c then:  [tex]m \propto c[/tex]

Convert this to an equation by using a constant of proportionality, k:

[tex]\implies m=kc[/tex]

We are told that Paul washed 8 cars and earned $120.

Substitute these values into the found equation and solve for k:

[tex]\implies 120=8k[/tex]

[tex]\implies k=\dfrac{120}{8}[/tex]

[tex]\implies k=15[/tex]

Finally, substitute the found constant of proportionality (k) into the equation:

[tex]\implies m=15c[/tex]

A = 6 cm; B = 3 cm; C = 8 cm; D = 10 cm

The Surface area of the prism = 120 cm².

Surface area = Area of A + B + C + D

The side lengths are:

A = 6 cm

B = 3 cm

C = 8 cm

D = 10 cm

Surface area of the prism = 2(area of triangular face) + area of rectangle 1 + area of rectangle 2 + area of rectangle 3

Area of triangular face = 1/2(b)(h) = 1/2(8)(6) = 24 cm

Area of rectangle 1 = (length)(width) = (10)(3) = 30 cm²

Area of rectangle 2 = (length)(width) = (6)(3) = 18 cm²

Area of rectangle 3 = (length)(width) = (8)(3) = 24 cm²

Surface area of the prism = 2(24) + 30 + 18 + 24 = 120 cm².

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The ratio between the circle and triangle is described as 3:4.

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The the next step in the proof is D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem.

It should be noted that vertical angles are the angles that are opposite each other when the two line cross.

In this case, 7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem.

In conclusion, the correct option is D.

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Answer:

98

Step-by-step explanation:

m<KJU + m<UJI = m<KJI

this equation will help us find the value of x therefore the value of m<KJU

Rewrite the equation using the expressions

104 + x + x + 76 = 168 add like terms

180 + 2x = 168 subtract 180 from both sides

2x = -12 divide both sides by 2

x = -6 to find the value of m<KJU replace x with -6

104 + (-6) = 98