Doris and Miguel are saving money weekly but at different rates. Doris
and Miguel both write and graph equations to represent their savings. In
both equations y represents the amount in savings account after x
number of weeks. When the equations are graphed, the lines intersect at
the point (6,114). Which statement best explains the point of
intersection?

Miguel will have $114 more than Doris after 6 weeks.

Doris will have $114 more than Miguel after 6 weeks.

Doris and Miguel will have the same amount after 6 weeks.

Doris and Miguel will have the same amount after 114 weeks.

Answer:

y = -2x + 7

Step-by-step explanation:

The slopes of perpendicular lines are negative reciprocals.

That means that their product is -1.

If the slope of a line is m, then a perpendicular line has slope -1/m.

Given line slope: 1/2

Perpendicular slope: -2

Perpendicular line:

y = -2x + b

Point on new line: (0, 7)

7 = -2(0) + b

b = 7

Perpendicular line:

y = -2x + 7

Perpendicular lines have slopes that are negative reciprocals of each other.

We're given:

First, we must find the slope.

The y-intercept occurs when x=0. Therefore, given the point (0,7), we know that the y-intercept is 7:

[tex]y=-2x+7[/tex]

The values in the parallelogram figure are as follows

angle B = 74 degrees

x = 4

angle BCA = 49 degrees

Remembering that opposite angels of a parallelogram are equal will help us know that angel B is equal to angel D which is 74 degrees

The property that the two opposite sides of parallelogram is used to find x

4x = 16

x = 4

Applying alternate interior angles postulate, we can see that

angle BCA = angle DAC = 49 degrees

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The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.

A quadratic equation's roots are equal to the second term's coefficient negated, divided by the leading coefficient. The constant term (the third term), divided by the leading coefficient, is equivalent to the product of the roots of a quadratic equation.

According to the Product Rule, the derivative of a product of two functions is equal to the product of the first function times the second function's derivative plus the second function times the first function's derivative.

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Answer:

526.68

To find out how much the price went up, you first want to find what 32% of 399 is.

32% of 399 = 127.68

The price will go up $127.68.

Now, just add that to the original price:

127.68 + 399 = 526.68

The price of the game system will now be $526.68

Step-by-step explanation:

Hope it helps! =D

The equivalent expressions to t(-7.4s+3.8-4.5)-t are:

This expression can be simplified as follows:

t(-7.4s + 3.8 - 4.5) - t

= t(-7.4s - 0.7) - t

= -7.4st - 1.7t.

t(-7.4s+3.8-4.5)-t

= t(-3.6s-4.5)-t

-7.4s + 3.8 - 4.5t - t

= t(7.4s+3.8)-5.5t

Therefore the correct options are A, B, E.

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Answer:

B

Step-by-step explanation:

[tex]1. \: 5.1 \div - 2 \\ 2. \: - 2.55[/tex]

Answer:

y = 125°

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the interior angles and equate to 540°

y + 86° + 142° + 72° + 115° = 540°

y + 415° = 540° ( subtract 415° from both sides )

y = 125°

Answer:

125°

Step-by-step explanation:

First you find the value of total interior angles

Since it's a Pentagon

[tex](5- 2) \times 180[/tex]

Then you arrive at 540°

When you sum all the angles in the Pentagon together they should be equal to 540

[tex]540 = 86 + 142 + 72 + 115 + y[/tex]

[tex]540 = 415 + y[/tex]

[tex]540 - 415 = y[/tex]

[tex]y = 125[/tex]

Answer:

Ecuación: 59.53 - 6.49 = 53.04

53.04 / 8 = X

X = 6.63

Respuesta: X=6.63

Answer: 104

Step-by-step explanation:

To put it simply, let's say 100% is 160 dollars. When Christmas arrived, it was sold with a discount of 35%. This means we deduct 35% from 100% which is 65%. We then find 65% of 160 dollars, which is 104.

Hope that helps, if not, then please reply back :)

Answer:

5.6km

Step-by-step explanation:

1km = 1000 meters

5,600 meters = 5.6km

5600 divided by 1000 = 5.6km

So, Chen walked 5.6km today.

Probability that the event can happen = 1/2

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes

Given,

Total outcomes of event = 14

Outcomes, event can happen = 7

Probability

= Favorable Outcomes/Total Outcomes

= 7/14 = 1/2

Hence, 1/2 is Probability that the event occurs.

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Answer: 398 + 399 + 400 equals 1197 

Step-by-step explanation: The sum of three consecutive natural numbers is 1197, find the numbers X) + (X + 1) + (X + 2) = 1197 To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:X + X + 1 + X + 2 = 11973X + 3 = 11973X + 3 - 3 = 1197 - 33X = 11943X/3 = 1194/3X = 398Which means that the first number is 398, the second number is 398 + 1 and the third number is 398 + 2. Therefore, three consecutive integers that add up to 1197 are 398, 399, and 400. 

The solution is given below.

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have,

the reflection is with respect to y=x line,

so, the transformation will be,

(x,y)⇒(y,x)

so, we get,

X = (-3,8 ) ⇒ X' = (8,-3)

Y(2,5)⇒Y(5,2)

Z(-4,-1)⇒Z'(-1,-4)

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Answer:

0.43 cup of water

Step-by-step explanation:

We know

For every 1 1/8 cups of water, she uses 2 5/8 of flour.

1 1/8 = 9/8 = 1.125

2 5/8 = 21/8 = 2.625

How much water does Cindy need for each cup of flour?

1.125 divided by 2.625 = 0.43 cup of water

So, Cindy needs 0.43 cup of eater for each cup of flour

Answer: $252 for 120 ft

Step-by-step explanation: Divide the money by the feet value in order to find dollars per foot. Since 252/120 = 2.1 $/ft and 285/150 = 1.9 $/ft, it would be better value to go with the 1.9 $/ft option.

Noah, Preston, and Zach work for 26 hours, 24 hours and 44 hours respectively

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

Let N, P and Z represent the number of hours Noah, Preston, and Zach work respectively. Thus, we can write:

N = P + 2  ---- (1)

Z = 2P - 4  ---- (2)

N + P + Z = 94  ---- (3)

Put (1) and (2) in (3):

N + P + Z = 94

P+2 + P + 2P-4 = 94

4P -2 = 94

4P = 94 + 2

4P = 96

P = 96/4

P = 24

Since N = P + 2,

N = 24 + 2 = 26

Since Z = 2P - 4,

Z = 2(24) - 4 = 44

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Therefore , the solution of the given problem of ratio comes out to be

CD:DE = 1:2. and AB:BC = 2:1 .

Use the simple formula "a / b" to create a group of linked variables "a" and "b," where "b" may also be higher than zero. One ratio is created by combining two equation ratios. If there were only one man and three ladies, the ratio would be 1:1. There are 1/4 males and 3/4 girls in the group. A division between two or more objects, a number, or even a portion of a component's volume are all examples of parts.

Here,

Ratio 1: AB:BC = 2:1

Let's use the midpoint formula to find the coordinates of point C, which is the midpoint of line segment AB:

C = ((5+x)/2, (0+y)/2) = ((5+x)/2, y/2)

Since AB:BC = 2:1, we know that the distance from A to B is twice the distance from B to C. Using the distance formula, we can write:

2 * BC = AB

2 * √((x+1)² + y²) = √((x-5)^2 + y^2)

Simplifying this equation, we get:

4 * (x+1)² + 4y² = x² - 10x + 25 + y²

Simplifying further, we get:

3x²+ 8x - 16y² - 75 = 0

Ratio 2: CD:DE = 1:2

Let's use the midpoint formula to find the coordinates of point E, which is the midpoint of line segment CD:

E = ((p-1)/2, (q-4)/2)

Since CD:DE = 1:2.

Therefore , the solution of the given problem of ratio comes out to be

CD:DE = 1:2. and AB:BC = 2:1 .

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Answer:

(-4, 6) (-1, 0)

Source:

Took test. ✌

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{ -2 }{ 1 } \implies - 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- 2}(x-\stackrel{x_1}{0})\implies {\Large \begin{array}{llll} y=-2x+3 \end{array}}[/tex]

Consecuencia de 5^3 - 3 √(375 ÷ 3) + (7 + 2)^2 - 9^11 ÷ 9^9 es 91.46.

Potencias es una operación matemática para la multiplicación repetida de un número tanto como el rango. El rango de un número es un número que se escribe más pequeño y se ubica ligeramente hacia arriba. Basado en la semántica de escribir letras se llama superíndice, por ejemplo: 2², 3², 4³ y otros. En inglés, el exponencial se llama "potencia" o "exponente".

5³=125

3√(375:3) =3√125=3√5³= 3.5^3/2

(7+2) ²=9²=81

9¹¹÷9^9=9²=81

5³ - 3 √(375 ÷ 3) + (7 + 2)² - 9¹¹ ÷ 9^9= 5³-3.5^3/2+81-81 =125-3√125=125-(3(11.18) = 125- 33.54=91.46

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A. X is a discrete random variable

B. The conditions are satisfied.

C. The expected value of X is 15.25

A. X is a discrete random variable because it can only take on specific values (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16) and not any value in an interval.

B. To show that the probability distribution is valid, we need to check if the following conditions are satisfied:

1. P(X=x) ≥ 0 for all x in the set of possible values of X

2. The sum of all probabilities equals 1

From the information given, it appears that these conditions are satisfied.

C. The expected value of X can be calculated as the weighted average of all possible values of X, where the weights are their corresponding probabilities.

E(X) = Σ[x * P(X=x)]

E(X) = (14*0.15) + (15*0.55) + (16*0.20) + (17*0.10) = 15.25

The expected value of X, which is 15.25, represents the mean or average number of credits taken by a randomly selected first-year student at the large state university.

D. The standard deviation measures the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the values are close to the mean (expected value), while a high standard deviation indicates that the values are spread out over a wider range. In this context, a standard deviation of 0.829 means that the number of credits taken by first-year students at the university is spread out over a range of approximately 0.829 units on average.

E. The event "taking at least 16 credits" can be expressed as X ≥ 16. To find its probability, we can sum up the probabilities of all the values that are greater than or equal to 16.

P(X ≥ 16) = ΣP(X = x)

P(X ≥ 16) = 0.20 + 0.10 = 0.30

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The values of x and y​ are x = 5 and y = 5.

The subtraction of vectors a and b can be represented as the vector sum of a and the negative of b:

a - b = a + (-b)

To find the negative of b, simply multiply each component by -1:

-b = (-1) × (1, 2) = (-1, -2)

So,

a - b = a + (-b) = (6, 7) + (-1, -2) = (5, 5)

Therefore, the values of x and y are 5 and 5 respectively.

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Answer:

y = -2.5x + 6.5

Step-by-step explanation:

The equation of the line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

With a slope of -2.5 and a point (2,1.5) on the line, we can use the point-slope formula to find the equation of the line:

y - 1.5 = -2.5 (x - 2)

Expanding the right-hand side, we get:

y - 1.5 = -2.5x + 5

Adding 1.5 to both sides, we get:

y = -2.5x + 6.5

So the equation of the line in slope-intercept form is y = -2.5x + 6.5.

Answer: Young gentleman. Here are some things you can use.

Step-by-step explanation: Calculator, Desmos (this was a website) ruler, protractor, math dictionary.

The trigonometric function for the values in the table is defined as follows:

y = 3sin(π/4(x - π/2)) + 3.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

The function has a maximum value of 6 and a minimum value of 0, for a difference of 6 units, hence the amplitude is obtained as follows:

2A = 6

A = 3.

Without vertical shift, a function with amplitude of 3 would oscillate between -3 and 3, while this one oscillates between 0 and 6, hence the vertical shift is given as follows:

D = 3.

The shortest distance between repetitions can be given by 8 - 0, hence the period is of 8 units and the coefficient B is given as follows:

2π/B = 8

B = 2π/8.

B = π/4.

The function is at's minimum value at x = 0, meaning that the sine function has a phase shift of π/2 units right, thus the coefficient C is given as follows:

C = π/2.

Then the function is defined as follows:

y = 3sin(π/4(x - π/2)) + 3.

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Answer:

3404.9(1dp)

Step-by-step explanation:

The musical frequency of notes is decreasing between beat number 6 and 7.

Beats refer to the periodic variations in the loudness of a sound resulting from the interference between two waves of slightly different frequencies. When two waves of different frequencies overlap, they create an interference pattern that results in a waveform that varies in amplitude (loudness) over time. The resulting pattern of loud and soft sounds is known as beats.

The musical note frequency is in the given question is measured in Hz and it started decreasing from a frequency of 444 Hz to frequency of 392 Hz.

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Correlation is to "measurement of variables", as experimentation is to "manipulation of variables".

Correlation refers to the statistical relationship between two or more variables, where changes in one variable are related to changes in the other variable(s). It measures the strength and direction of the relationship, but it does not establish cause and effect.

Experimentation, on the other hand, involves the manipulation of variables to determine the cause-and-effect relationship between variables. The experimenter changes the independent variable and measures the effect it has on the dependent variable.

This method allows the experimenter to establish cause and effect and to control extraneous variables that might interfere with the relationship between the independent and dependent variables.

Therefore, the correct answer is D.

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--The given question is incomplete; the complete question is

"Correlation is to___as experimentation is to___.

A. manipulation of variables; measurement of variables

B. unobtrusiveness: correlation

C. single variables; multiple variables

D. measurement of variables; manipulation of variables"--

The value of k that makes the probability distribution valid is given as follows:

k = 4.

To obtain the value of k, we must consider that the integral assumes a value of 1 over it's entire domain, that is:

[tex]\int_{-1}^{1} F(x) dx = 1[/tex]

The function F(x) is given as follows:

F(x) = (x + 2)/k.

Considering 1/k as a constant, the integral is given as follows:

1/k[0.5x² + 2x].

At x = 1, the integral is given as follows:

0.5 + 2 = 2.5.

At x = -1, the integral is given as follows:

0.5 - 2 = -1.5.

Applying the Fundamental Theorem of Calculus, the result of the integral is given as follows:

1/k[2.5 - (-1.5)] = 4/k.

As the result of the integral must be of one, the value of k is obtained as follows:

4/k = 1

k = 4.

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Answer:X[tex]x^{2} +2x-15[/tex]

Step-by-step explanation:   you do it by multiplying  out the brackets and then you  simplify the result expression by collecting the like terms.