For each value of y , determine whether it is a solution to -5 = 9 - 7y

Step by Step Solution/ just copy and paste but if this is a test, the answer is 2.000

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    2*y-(4*x-5)=0

STEP

1

:Equation of a Straight Line

1.1     Solve   2y-4x+5  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  2y-4x+5  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is -5/2 so this line "cuts" the y axis at y=-2.50000

 y-intercept = -5/2  = -2.50000

Calculate the X-Intercept :

When y = 0 the value of x is 5/4 Our line therefore "cuts" the x axis at x= 1.25000

 x-intercept = 5/4  =  1.25000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.500 and for x=2.000, the value of y is 1.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.500 - (-2.500) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  4.000/2.000 =  2.000

Geometric figure: Straight Line

 Slope = 4.000/2.000 = 2.000

 x-intercept = 5/4 = 1.25000

 y-intercept = -5/2 = -2.50000

The z-score corresponding to a sample mean capacity for 20 tanks of 8550 is 2.238.

To find the z-score corresponding to a sample mean capacity for 20 tanks of 8550, we need to use the formula for the z-score:

z = (x - μ) / (σ / √n)

Where:

x = sample mean capacity

μ = population mean capacity

σ = population standard deviation

n = sample size

Given:

x = 8550, μ = 8544, σ = 12 and n = 20

Substituting these values into the formula:

z = (8550 - 8544) / (12 / √20)

z = 6 / (12 / √20)

z = 6 / (12 / 4.472)

z = 6 / 2.683

z = 2.238

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Answer:

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

Taking the inverse tangent (arctan) of the given ratio 7/9.

Use a calculator or trigonometric table to find:

The approximate value of θ is 37.9°.

To find the subtracted value, we need to calculate the multiplicative inverse of (4/3 - 4/9) and then subtract it from the sum of 7/12 and 7/8.

First, let's find the multiplicative inverse of (4/3 - 4/9):

Multiplicative inverse = 1 / (4/3 - 4/9)

To simplify the expression, we need a common denominator:

Multiplicative inverse = 1 / ((12/9) - (4/9))

= 1 / (8/9)

= 9/8

Now, we need to subtract the multiplicative inverse from the sum of 7/12 and 7/8:

Subtracted value = (7/12 + 7/8) - (9/8)

To perform this calculation, we need a common denominator:

Subtracted value = (7/12 * 2/2 + 7/8 * 3/3) - (9/8)

= (14/24 + 21/24) - (9/8)

= 35/24 - 9/8

To simplify further, we need a common denominator:

Subtracted value = (35/24 * 1/1) - (9/8 * 3/3)

= 35/24 - 27/24

= 8/24

= 1/3

Therefore, subtracting 1/3 from the sum of 7/12 and 7/8 will give you the multiplicative inverse of (4/3 - 4/9).

The coordinates of the focus obtained from the vertex form of the equation of the parabola is; (h, v) = (2, -7/4)

The vertex form of the equation of a parabola is; y = a·(x - h)² + k

The points on the parabola are;

(3, -1), and (2, -2)

The vertex of the parabola is; (2, -2)

Therefore, we get;

The vertex form of the equation of a parabola is; y = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex, therefore;

y = a·(x - 2)² - 2

y + 2 = a·(x - 2)²

The point (3, -1), indicates that we get;

-1 + 2 = a·(3 - 2)²

(-1 + 2)/((3 - 2)²) = 1 = a

The equation of the parabola in focus form is; (x - h)² = 4·p·(y - k)

Therefore; (x - 2)² = 4·p·(y + k)

We get; (x - 2)² = (y + k)

(x - 2)²/(4·p) = y + k

(4·p) = a = 1

p = 1/4

The y-coordinates of the focus, v = -2 + 1/4 = -1 3/4 = -7/4

The coordinates of the focus, (h, v) is therefore;

(h, v) = (2, -7/4)

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If Graph g(x) the transformation of f(x)=x² then the graph of function g(x) is x²+4

To graph the transformation of the function f(x) = x² translated up 4 units, we need to add 4 to the function.

The new function, g(x), can be defined as g(x) = f(x) + 4.

Start with the graph of the original function f(x) = x²

Shift the graph vertically upward by 4 units.

To do this, for each point (x, y) on the graph of f(x), plot a new point (x, y + 4) on the graph of g(x).

This means that every y-coordinate is increased by 4 units.

g(x)= x²+4

Hence, the red line in the graph represents f(x) and blue line in graph represents the g(x)

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Answer:

8[tex]\sqrt[3]{2}[/tex]

Step-by-step explanation:

The cube root of -2 to the power of 10 is;

(-2)^10=2^10

2^10=(2^3)*(2^3)*(2^3)*2

You can factor out 2^3=8 of the cube root

So you get 8 times the cube root of 2

12/13 is the value of cosA is  in the triangle ABC

ABC is a right angle triangle

Angle B has a angle of 90 degrees

We know that the cosine function is a ratio of adjacent side and hypotenuse

The adjacent side of angle A is AB which we have to find

hypotenuse is 26

Cos A =AB/26

Let us find AB by using pythagoras theorem

10²+AB²=26²

100+AB²=676

Subtract 100 from both sides

AB²=576

Take square root on both sides

AB=√576

=24

Now plug in this value in cosA

CosA = 24/26

=12/13

Hence, the value of cosA is 12/13 in the triangle ABC

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Answer:

The angles x, y, and z are 70 degrees, 110 degrees, and 110 degrees, respectively.

Step-by-step explanation:

If one angle is 70 degrees, then its corresponding angle will also be 70 degrees. Therefore, the two linear angle pairs with 70 degrees are:

70 degrees and its corresponding angle (also 70 degrees)

x degrees and y degrees, where x and y add up to 180 degrees (because they are linear angle pairs)

Since x is a vertical angle to 70 degrees, it is also equal to 70 degrees. Therefore:

x = 70 degrees

y = 180 - x = 180 - 70 = 110 degrees

To find the angle z, we can use the fact that the sum of the angles around a point is 360 degrees. Since the two lines intersect and create four angles, the angles around the point where they intersect must add up to 360 degrees. Therefore:

z + 70 + 70 + 110 = 360

z + 250 = 360

z = 110 degrees

Therefore, the angles x, y, and z are 70 degrees, 110 degrees, and 110 degrees, respectively.

Answer: To find the area of the region between the graph of y = x^2 + 1 and the x-axis on the interval [2, 4], we can integrate the function f(x) = x^2 + 1 with respect to x over the given interval. The definite integral represents the area under the curve between the specified x-values. Here's how to calculate it using integration:

∫[2,4] (x^2 + 1) dx

To integrate this function, we apply the power rule for integration. The power rule states that the integral of x^n with respect to x is (x^(n+1))/(n+1), where n is any real number except -1.

∫(x^2 + 1) dx = [(x^3)/3 + x] + C

Now, we can evaluate the definite integral over the interval [2, 4]:

[(4^3)/3 + 4] - [(2^3)/3 + 2]

= (64/3 + 4) - (8/3 + 2)

= (64/3 + 12/3) - (8/3 + 6/3)

= (76/3) - (14/3)

= 62/3

Therefore, the area of the region between the graph of y = x^2 + 1 and the x-axis on the interval [2, 4] is 62/3 square units.

Step-by-step explanation:

Answer:

[tex]slope_{UF}[/tex] = - [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = U (3, - 5 ) and ( x₂, y₂ ) = F (- 1, - 4 )

m = [tex]\frac{-4-(-5)}{-1-3}[/tex] = [tex]\frac{-4+5}{-4}[/tex] = [tex]\frac{1}{-4}[/tex] = - [tex]\frac{1}{4}[/tex]

The given numerical data should be ordered from least to greatest as follows;

-11, -9, -8, -7, -2, 4, 5, 6, |-11|.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals.

In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1).

Next, we would order or sort the given numerical data from least to greatest as follows;

-11, -9, -8, -7, -2, 4, 5, 6, |-11|.

Note: |-11| is an absolute value that equals to 11.

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(a) The joint probability distribution of X and Y is 3/70.

(b) The value of P[(X,Y) € A), where A is the region that is given is 3/35.

(a) To find the probabilities, we consider the total number of ways to select 4 fruits out of 8:

Total number of ways to select 4 fruits out of 8 = C(8, 4) = 70

The probabilities for each combination of X and Y are as follows:

P(X = 0, Y = 0) = C(3, 0) * C(2, 0) * C(3, 4) / 70

P(X = 0, Y = 0) = 1 / 70

P(X = 0, Y = 1) = C(3, 0) * C(2, 1) * C(3, 3) / 70

P(X = 0, Y = 1)  = 2 / 70

P(X = 1, Y = 0) = C(3, 1) * C(2, 0) * C(3, 3) / 70

P(X = 1, Y = 0) = 3 / 70

P(X = 1, Y = 1) = C(3, 1) * C(2, 1) * C(3, 2) / 70

P(X = 1, Y = 1) = 18 / 70

P(X = 2, Y = 0) = C(3, 2) * C(2, 0) * C(3, 2) / 70

P(X = 2, Y = 0) = 9 / 70

P(X = 2, Y = 1) = C(3, 2) * C(2, 1) * C(3, 1) / 70

P(X = 2, Y = 1) = 18 / 70

P(X = 3, Y = 0) = C(3, 3) * C(2, 0) * C(3, 1) / 70

P(X = 3, Y = 0) = 3 / 70

The joint probability distribution of X and Y is as follows:

X\Y  0   1

0 1/70  2/70

1 3/70 18/70

2 9/70 18/70

3 3/70 0

(b) P[(X,Y) ∈ A], where A is given by ((a + v) | a + y < 2):

From the joint probability distribution table, we can see that the combinations (0, 0), (0, 1), and (1, 0) satisfy this condition.

P[(X, Y) ∈ A] = P[(0, 0)] + P[(0, 1)] + P[(1, 0)] = 1/70 + 2/70 + 3/70

P[(X, Y) ∈ A] = 6/70 or 3/35

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The rewritten  statement : "It is not the case that there exists an x for which P(x) and Q(x) are true, and for all y, if R(y) is true, then P(y) is true."

The symbolic logic statement: ¬(∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y)).

The statement can be translated as: "There does not exist an x such that P(x) and Q(x) hold true, and for all y, if R(y) is true, then P(y) is true."

Potential ambiguities in this statement can arise from the unclear precedence of logical operators, specifically the negation operator "¬" in relation to the existential quantifier "∃".

To eliminate ambiguities while maintaining the original meaning, we can add parentheses to make the precedence explicit: (¬(∃x)(P(x) ∧ Q(x))) ∧ (∀y)(R(y) → P(y)).

This ensures that the negation applies only to the existential quantifier, not to the entire conjunction.

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Answer:

First find the sales tax: $160 \times 0.0785 = $12.56.

Then add the sales tax to the price of the purchase to find the total cost: $160 + $12.56 = $172.56.

Next find the daily interest rate: $0.042\% = 0.00042$.

Then multiply the daily interest rate by the total cost to find the interest per day: $0.00042 \times $172.56 = $0.0725752$.

Finally, multiply the interest per day by 30 days to find the total interest and add it to the total cost to find the final answer: $0.0725752 \times 30 = $2.177256 + $172.56 = $174.737256 \approx $174.74.

So the answer is b.

Answer:

0.0772 OR 0.95 OR 7.72

Step-by-step explanation:

A player makes 622 shots on goal and in that time scores 48 goals.

48 goals ÷ 622 shots = 0.0772.

This player’s shooting percentage is 0.0772, or 7.72%.

Answer:

Since 1 fluid ounce is equal to 0.03125 quarts, we can convert the volume of water poured into the jar from ounces to quarts:

114 ounces x 0.03125 quarts/ounce = 3.5625 quarts

Therefore, Kenna pours 3 x 3.5625 = 10.6875 quarts of water to fill the jar three times. Rounding to the nearest whole number, we get 11 quarts.

So it takes 11 quarts of water to fill the jar.

The interval notation of the number line is [-3, ∝) while that of the inequality is  called x >= 3

One can use interval notation to represent real numbers that are continuous by specifying the values that define their boundaries. Written intervals appear somewhat akin to ordered pairs.

The way to know the interval notation of the graph is:

Based on the number line in the question, one can see:

The rule that applies is that a closed line tells us that the number at that endpoint is one that is part of the solution set.

So this tells us that the interval notation of the number line is [-3, ∝). When depicted as an inequality, One can have x >= 3

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The total area covered by the roll of wrapping paper is 3.6 square meters.

To calculate the total area covered by the wrapping paper, we need to find the surface area of each cube and then multiply it by the number of cubes.

The formula for the surface area of a cube is:

Surface Area = 6 * (side length)^2

Given that the length of each side of the cube is 20 cm (which is equal to 0.2 meters), we can substitute this value into the formula:

Surface Area = 6 * (0.2)^2

Surface Area = 6 * 0.04

Surface Area = 0.24 square meters

Now, we know that 15 cubes can be covered by the roll of wrapping paper. Therefore, the total area covered by the wrapping paper is:

Total Area = Surface Area * Number of Cubes

Total Area = 0.24 * 15

Total Area = 3.6 square meters

Therefore, the total area covered by the roll of wrapping paper is 3.6 square meters.

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Hello !

1. A quadratic equation results in the form: ax² + bx + c

2. Calculate the discriminant: Δ = b² - 4ac

3. Calculate x with the dicriminant: (-b ± √Δ) / 2a

Example:

3x² + 7x - 2 = 0 is a quadratic equation.

x = (-b ± √(b² - 4ac)) / 2a

= (-7 ± √(7² - 4*3*(-2))) / (2*3)

= (-7 ± √73)/6

Answer:

Step-by-step explanation:

x=6/5,−4

Decimal Form:

x=1.2,−4

Mixed Number Form:

x=1  1/5,−4

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2496\\ P=\textit{original amount deposited}\dotfill & \pounds1600\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 2496 = 1600[1+(0.08)(t)]\implies \cfrac{2496}{1600}=1+0.08t\implies \cfrac{39}{25}=1+0.08t \\\\\\ \cfrac{39}{25}-1=0.08t \implies \cfrac{14}{25}=0.08t\implies \cfrac{14}{25(0.08)}=t\implies 7=t[/tex]

Answer: C

Step-by-step explanation:

For box and whiskers plot the box is where the majority of the data is.  the whiskers(the lines on both sides will tell you where the range of numbers lie)

The middle line in the box is the median number.

The question is worded oddly where they want least likely to be more than 30 which means which one will have less than 30. (Double negative question)

You want the majority of the data to be less than 30, which is subway.  C

Answer: 7.8

Step-by-step explanation: Identify the triangle as a 45-45-90 triangle.

Recognize that the sides of a 45-45-90 triangle are in a ratio of 1:1:√2.

Find the length of the hypotenuse of the triangle. In this case, the hypotenuse is 11 units.

Divide the length of the hypotenuse by √2 to find the length of the side opposite the 45-degree angle. In this case, the length of side x is 11/√2 = 7.77 units.

Round the length of side x to the nearest tenth. In this case, the length of side x is 7.8 units.

Answer:

= 10.4

Step-by-step explanation:

Here given is the right-angled triangle

For angle: = 60º

Perpendicular: = 9

Hypotenuse: =

Now using the trigonometry formula:

  = /

sin 60º = 9/

3√2 = 9/

= 18/3√

= 10.4(rounded to the nearest tenth)

Therefore required length is = 10.4

The correct answer is $28,100.

To calculate the difference between the costs of the accident and the premiums paid by the car owner, let's break down the expenses step by step:

(1) Annual Premium: The car owner pays an annual premium of $780 for automobile insurance. Over five years, the total premium paid is $780 * 5 = $3,900.

(2) Liability Coverage: The liability coverage provided by the insurance is up to $100,000. However, the other driver is claiming $32,000 in damages. Therefore, the insurance will cover the full amount of $32,000.

(3) Difference in Costs: To find the difference between the costs of the accident and the premiums paid, we subtract the insurance coverage from the total premium paid. In this case, the difference is $32,000 - $3,900 = $28,100.

Therefore, the costs of the accident were $28,100 more expensive than what the car owner paid in premiums.

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Given statement solution :-  Party A received the most votes with a total of 47, compared to Party B's total of 38 votes.

Let's calculate the number of votes each party received based on the given information.

Assuming there is a population of 100 people (this is an arbitrary number chosen for ease of calculation), we can determine the number of votes for each party.

Percentage of people who said they would vote for Party A = 33%

Number of people who said they would vote for Party A = 33/100 * 100 = 33

Percentage of people who said they would vote for Party B = 10%

Number of people who said they would vote for Party B = 10/100 * 100 = 10

Percentage of people who said they would not vote = 15%

Number of people who said they would not vote = 15/100 * 100 = 15

Now, let's calculate the votes from the rest of the population (those who didn't state their voting preference).

Percentage of people who voted for Party A from the rest of the population = 1/3

Number of people who voted for Party A from the rest of the population = (1/3) * (100 - (33 + 10 + 15)) = (1/3) * 42 = 14

Percentage of people who voted for Party B from the rest of the population = 2/3

Number of people who voted for Party B from the rest of the population = (2/3) * (100 - (33 + 10 + 15)) = (2/3) * 42 = 28

Now, let's calculate the total votes for each party:

Total votes for Party A = votes from those who stated their preference + votes from the rest of the population

= 33 + 14 = 47

Total votes for Party B = votes from those who stated their preference + votes from the rest of the population

= 10 + 28 = 38

Therefore, Party A received the most votes with a total of 47, compared to Party B's total of 38 votes.

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Answer:

[tex]\frac{6}{x+1}[/tex]

Step-by-step explanation:

I learned this like a month ago so I have notes abt it if you don't understand how it works. Just lmk if you need them

The class intervals to use for the given data is 10.

The class interval is the difference between the upper class limit and the lower class limit. Class interval represents the width of each class in a frequency distribution

The frequency of a class interval is the number of observations that occur in a particular predefined interval.

From the given data the prepare a table for age and frequency

[tex]\begin{tabular}{c | l} Age & Frequency \\ \cline{1-2} 0-10 & 4 \\ 11-20 & 5 \\ 21-30 & 5 \\ 31-40 & 5 \\ 41-50 & 0 \\ 51-60 & 2 \\ 61-70 & 1 \end{tabular}[/tex]

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Answer:

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If the middle number is x, the other numbers are x - 1 and x + 1.

They sum to 3x and it is equal to 51:

The numbers are 16, 17 and 18.