Solve the inequalities below. Write the solution set in interval notation and graph the solution.

−
3
2
x
>
−
14
-
3
2
x
>
-
14


Solution:

Interval notation for the solution:

Therefore, the distance across the river is approximately 283 feet (rounded to the nearest foot).

An equation is a mathematical statement that uses symbols, such as letters and numbers, to show that two expressions are equal. It typically consists of two sides separated by an equals sign. The expressions on both sides can contain variables, constants, functions, and operators, and the goal is often to solve for the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and many other fields to model real-world phenomena, make predictions, and solve problems.

Here,

Without a diagram, it is difficult to determine the exact location and orientation of the points and lines. However, based on the information provided, we can use the Law of Sines to find the length of PR.

In triangle ROC, we have:

sin(CEO) = RO/OC

sin(CEO) = 165/330

sin(CEO) = 0.5

CEO = sin⁻¹(0.5)

CEO = 30 degrees

In triangle REO, we have:

sin(ERO) = RO/RE

sin(ERO) = 165/210

sin(ERO) = 0.7857

ERO = sin⁻¹(0.7857)

ERO = 51.06 degrees

Now, in triangle PER, we have:

sin(PER) / 210 = sin(ERO) / PR

Therefore, we can solve for PR:

PR = 210 * sin(ERO) / sin(PER)

PR = 210 * sin(51.06) / sin(180 - CEO - ERO)

Plugging in the values, we get:

PR = 210 * sin(51.06) / sin(99.94)

PR ≈ 283.2 feet

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The coordinate of the other stop sign located will be (21, 3).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

Kelsey’s neighborhood has a straight road with stop signs at both ends and a fire hydrant at its midpoint. On a map, the fire hydrant is located at (12,7) and one of the stop signs is located at (3,11).

Then the coordinate of the other stop sign located is given as,

(12, 7) = [(x₁ + 3) / 2, (y₁ + 11) / 2]

(24, 14) = [x₁ + 3, y₁ + 11)

(21, 3) = (x₁, y₁)

(x₁, y₁) = (21, 3)

The coordinate of the other stop sign located will be (21, 3).

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An atom X has 3 protons in its nucleus. An atomic number of 3 corresponds to the element lithium (Li).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We can use Coulomb's law to predict the number of protons in X's nucleus. Coulomb's law states that the force of attraction between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

⇒ F = k (q₁ q₂) / r²

Where, F is the force of attraction, k is the Coulomb constant (8.99 x 10⁹ Nm²/C²), q₁ and q₂ are the magnitudes of the charges, and r is the distance between them.

We can rearrange the equation to solve for the charge:

⇒ q₂ = (F * r²) / (k * q₁)

In this case, q1 is the charge on the electron, which is -1.60 x 10⁻¹⁹ C. The radius of atom X, r, is given, and the force of attraction, F, is also given.

So, we have:

⇒ q₂ = (2.2 x 10⁻⁸ N * (1.02 x 10⁻¹⁰ m)²) / (8.99 x 10⁹ Nm²/C^2 * -1.60 x 10⁻¹⁹ C)

Solving for q₂, we find that;

q₂ = +5.4 x 10⁻¹⁹ C.

This is the charge on the nucleus of atom X. The number of protons in the nucleus of atom X can be found by dividing the charge by the charge of a proton:

⇒ N = q₂ / qp

Where N is the number of protons and qp is the charge on a proton, which is +1.60 x 10⁻¹⁹ C.

So, we have:

N = (5.4 x 10⁻¹⁹ C) / (1.60 x 10⁻¹⁹ C) = 3.375

Hence, the number of protons must be a whole number, the closest whole number to 3.375 is 3. This means that atom X has 3 protons in its nucleus. The identity of atom X can be determined based on its atomic number, which is equal to the number of protons in its nucleus. An atomic number of 3 corresponds to the element lithium (Li).

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The solution is, center = ( 0,0) & coefficient = 3

The act or action of enlarging, expanding, or widening : the state of being dilated: such as. : the act or process of expanding (such as in extent or volume)

here, we have,

from the given figure,

we get,

length of MQ = 8.48

length of M'Q' = 2.82

so, dilation factor = 8.48/2.82

                             = 3

and, we get, the center of dilation = (0,0)

Hence, The solution is, center = ( 0,0) & coefficient = 3

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For large samples, the sample proportion is approximately normally distributed, with mean μˆP=p. and standard deviation σˆP=√pqn

Taken from stats.libretexts.org btw^^

By using synthetic division and the Remainder Theorem, we have found that f(-2) = -14, f(-1) = -7, f(0) = 7, f(1) = -6 and f(2) = -6.

Synthetic Division: Synthetic division is a shorthand method for dividing polynomials. It is used to divide a polynomial by a binomial of the form x - k, where k is a real number. To perform synthetic division, the coefficients of the polynomial are written in a row and divided by the denominator of the binomial.

To calculate f(-2), f(-1), f(0), f(1), f(2):

We will use synthetic division with the binomial x - k, where k = -2, -1, 0, 1, 2.

First, we will write the coefficients of the polynomial in a row:

7, -6, 3

For k = -2:

7|-2  -1  3

-2|-14  0  0

4  1  3

Therefore, f(-2) = -14.

For k = -1:

7|-1  -2  3

-1|-7  0  0

7  1  3

Therefore, f(-1) = -7.

For k = 0:

7|0  -1  3

0|7  0  0

7  -1  3

Therefore, f(0) = 7.

For k = 1:

7|1  0  3

1|7  -6  0

Therefore, f(1) = -6.

For k = 2:

7|2  1  3

2|14  -6  0

Therefore, f(2) = -6.

By using synthetic division and the Remainder Theorem, we have found that f(-2) = -14, f(-1) = -7, f(0) = 7, f(1) = -6 and f(2) = -6.

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Step-by-step explanation:

a. Given a positive test result, the probability that a random patient has the disease is called the positive predictive value (PPV). The PPV can be calculated using the following formula:

PPV = Sensitivity * Prevalence / (Sensitivity * Prevalence + (1 - Specificity) * (1 - Prevalence))

Plugging in the values given in the question, we get:

PPV = 0.92 * 0.01 / (0.92 * 0.01 + (1 - 0.93) * (1 - 0.01)) = 0.087

So, the probability that a random patient has the disease given a positive test result is 0.087 or 8.7%.

b. A tree diagram for a typical sample of patients with a positive test result would look something like this:

+-----------+-----------------+

| Test Result| Positive (TP + FP) |

+-----------+-----------------+

| | TP (Disease) |

| | 0.92 * 0.01 |

| | FP (No Disease)|

| | 0.08 * 0.99 |

+-----------+-----------------+

c. If the prevalence is lower, the proportion of positive test results due to false positives (FP) increases compared to true positives (TP). This is because the positive predictive value (PPV) decreases as the prevalence decreases, meaning that a larger proportion of positive test results are due to false positives. This is why the proportion in error is larger if the prevalence is lower.

Answer:

It is graphed in the picture.

Step-by-step explanation:

Answer:

See the attached graph

Step-by-step explanation:

Take each inequality and isolate x for each

x+1 < 9
==> x + 1 - 1 < 9 -1  add 1 both sides

==> x < 8

4x ≤ 8

==> 4x/4 ≤ 8/4    divide by 4 both sides

==> x  ≤ 2

So we have two inequalities to satisfy

To graph,

To graph the first inequality, draw a vertical line at x = 9 parallel to the y-axis. This line should be dotted to show it is a < inequality. Everything to the left of this line satisfies x < 8

To graph the second inequality, x ≤ 2, draw a vertical line at x = 2 parallel to the y-axis. This line should be solid to show it is a ≤ inequality. Everything to the left of this line satisfies x ≤ 2

The common points for both lines are shown in dark purple in the graph where the two shaded areas overlap

If you just wanted it on the number line that would be the second image

Answer:

The figures are similar.

Step-by-step explanation:

The scale factor is 2.  The transformation is a a dilation.

The answer as a result of the numerical expression above is B) 1/36

This expression is rank number:

[tex]( {6}^{ - 4} ) {}^{ \frac{1}{2} } = 6 {}^{ - 2} = \frac{1}{ {6}^{2} } = \frac{1}{36}.

So the answer as a result of the numerical expression above is 1/36.

From these calculations it can be seen that the rank between what is inside the brackets and what is outside it can be multiplied.

In the question above the power of -4 multiplied by the power of ½ ( (-4×½) the result is -2.

So all that's left is 6⁻². Another form of 6⁻² is 1/6² or 1/36.

This refers to the exponential rule in mathematics, namely a⁻ⁿ can be written as 1/aⁿ.

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Answer:

Here are some fractions and equivalent percentages.

1/4 = 1/4 x 100 = 25%
1/8 = 1/8 x 100 = 12.5$
3/8 = 3/8 x 100 = 300/8 = 37.5%
3/4 = 3/4 x 100 = 75%
1/3 = 1/3 x 100 = 33.33% (rounded to 2 decimal places)
54% = 54/100 = 27/50

Here are some percentages and equivalent fractions:
54% = 54/100 = 27/50
36% = 36/100
45% = 9/20
20% = 1/5
30% = 3/10

Step-by-step explanation:

To convert a fraction to a percentage, multiply by 100

To convert a percentage to a fraction, divide by 100 and reduce to lowest fractional form

Examples:

1/4 = 1/4 x 100 = 25%

1/8 = 1/8 x 100 = 12.5$

3/8 = 3/8 x 100 = 300/8 = 37.5$

3/4 = 3/4 x 100 = 75%

1/3 = 1/3 x 100 = 33.33% (rounded to 2 decimal places)

Similarly,

54% = 54/100 = 27/50

36% = 36/100
dividing by 4 both numerator and denominator gives
36% = 36/100 = 9/20

45% = 45/100 = 9/20  (divide by 5)

20% = 20/100 = 1/5

Based on the given information:

From the case we know that the cost of rent a truck was charged by 2 rules:

Cost per truck = fixed cost = $22.95

Cost per miles distance = variable cost = $0.72 per mile

Both costs can be formulated as a linear equation:

C(d) = 22.95 + 0.72d

where we take the fixed cost of $22.95 as the y-intercept and the variable cost of $0.72 per mile as the slope of the line.

Based on our linear equation, we can try to find the cost needed to rent a truck and drive it for 15 miles:

C(15) = 22.95 + 0.72(15)

C(15) = 22.95 + 10.8

C(15) = $33.75

We can use the same approach to find the available distance for our budget of $110:

C(d) = 22.95 + 0.72d

110 = 22.95 + 0.72d

0.72d = 87.05

d = 120.9

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True, a contour line defines the outer edge or profile of an object, and can be used to suggest a volume in space.

It is the amount of space contained within the boundaries of an object and is typically represented by cubic units such as cubic centimeters (cm³), cubic meters (m³), or cubic inches (in³).

Volume can be calculated for various three-dimensional objects such as a cube, sphere, cylinder, or pyramid. The formula for finding the volume of an object depends on its shape. For example, the formula for the volume of a cube is V = s³, where s is the length of one of its sides. The formula for the volume of a cylinder is V = π²h, where r is the radius of the base, h is the height of the cylinder, and π is a mathematical constant approximately equal to 3.14.

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the value of x=17/9 and y=5 by solving the system of equations.

What is a System of Equations?

When two or more algebraic equations are solved together, they form a system of equations. A system of linear equations is a collection of equations that are all satisfied by a single set of variables. The first stage in resolving an equation system is determining the values of the variables used in the equation system. We determine the values of the unknown variables while keeping the equations' equality on both sides. The main purpose of solving an equation system is to identify a variable whose value makes the condition of each equation in the system true.

The given equation are

9x+2y = 27

y=-8x+31

9x+2y =27

16x+2y =62

7y = 62-27

7y = 35

y=5

x = 17/9

Hence the value of x=17/9 and y=5 by solving the system of equations.

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Based on the information, it can be inferred that the area of a surface with sides 23 yards and base 23 yards is 529 square yards.

To calculate the surface area of this figure we must perform the following procedure:

We know the side and the base of this figure measure 23 yards, so we must apply the following formula.

So we can infer that the area of this surface would be 534 square yards.

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Answer:

Step-by-step explanation:

You want the number of liters of 25%, 45%, and 65% acid solution required to make a mixture that is 224 L of a 35% acid solution, using 3 times as much of the 65% solution as of the 45% solution.

There are numerous ways this mixing problem can be formulated. The calculator display in the attachment shows one of them: 3 equations in 3 unknowns.

Here, we choose to use one variable. Let x represent the amount of 45% solution. Then 3x is the amount of 65% solution, and (224 -4x) is the amount of 25% solution. The amount of acid in the final mix is ...

  0.25(224 -4x) + 0.45x + 0.65(3x) = 0.35·224

The equation can be simplified to ...

  1.4x +56 = 78.4

  1.4x = 22.4

  x = 16 . . . . . . . . . liters of 45% solution

  3x = 48 . . . . . . . . liters of 65% solution

  224 -4x = 224 -64 = 160 . . . . liters of 25% solution

The chemist should use ...

<95141404393>

392

8630 divided by 22. = 392.272727... cant be decimal so round down

Jimmy  has five dollars more than three times Bethany has. Jimmy has $31.25.

A mathematical statement with two equal algebraic expressions is called an algebraic equation. Equations in algebra with only one variable are referred to as univariate equations, while equations with several variables are referred to as multivariate equations.

Let's say Jimmy has [tex]x[/tex] dollars.

Three times the amount of money Bethany has is [tex]3x[/tex].

Jimmy has 5 dollars more than three times what Bethany has,

so, [tex]x = 3x + 5[/tex]

The combined amount of money Jimmy and Bethany have is $130,

so, [tex]x + 3x +5= 130[/tex]

Combining like terms, [tex]4x = 125[/tex].

Dividing both sides by 4, [tex]x = 31.25[/tex]

So Jimmy has $31.25.

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Answer:

Jimmy have $98.75.

Step-by-step explanation:

let J=money Jimmy have

B= money Batheby have

therefore J = 5+3B.....................(1)

but J + B = $130.......................(2).

putting equation (1) into 2

5 + 3B + B = 130

4B = 130 - 5

4B = 125

4B/4 = 125/4

B = 31.25

therefore J = 5+ 3B = 5 + 3(31.25)

= 5 + 93.75

= $98.75.

therefore Jimmy have $98.75.

To graph the equation y = 12.3x, identify and locate the vertical and horizontal intercepts. To do this, set x equal to zero to find the vertical intercept, which is y = 12.3(0) = 0. Then, set y equal to zero to find the horizontal intercept, which is x = 0/12.3 = 0.

To graph the equation y = 12.3x, we need to identify and locate the vertical and horizontal intercepts. The vertical intercept is found by setting x equal to zero, which gives us y = 12.3(0) = 0. This means the vertical intercept is at the point (0,0). The horizontal intercept is found by setting y equal to zero, which gives us x = 0/12.3 = 0. This means the horizontal intercept is at the point (0,12.3). We can then plot these two points to graph the equation. Drawing a line through the points, we can see that the equation is a straight line that goes through the origin with a positive slope, meaning that as x increases, so does y. This line has a y-intercept of 0 and an x-intercept of 12.3.

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Answer:

x + 2y = 6

2y = -x -6

y = - 1/2 x - 3

From the equation, the y intercept is -3

Put y = 0,

-1/2 x -3 = 0

-1/2 x = 3

x = -6

Therefore, x intercept = -6

The capacity of her mixture in liters is 1.6 L

Capacity describes your ability to do something or the amount something can hold.

Given that, Jane mixes the juice in jug A with the water in jug B, we need to find that, what is the capacity of her mixture in liters,

We know that,

1 L = 1000 ml

Jug A = 400 × 1L / 1000 ml = 0.4 L

Jug B = 12 / 10 L = 1.2 L

Total = 0.4 + 1.2 = 1.6 L

Hence, the capacity of her mixture in liters is 1.6 L

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1. The diagonals bisect each other.

2. The diagonals of parallelogram are perpendicular and equal to each other.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

Given:

Using the theorem a quadrilateral whose diagonal bisect each other is a parallelogram.

Then, the diagonals bisect each other then the quadrilateral is a parallelogram.

As, the diagonals of parallelogram are perpendicular and equal to each other then , the parallelogram is a square.

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Answer:

4 laps

Step-by-step explanation:

A jogging trail has sides that measure

168 yards 2 feet,

175 yards, and

96 yards 1 foot.

total = 168+175+96 yards and 3 feet= 439 yd 3ft

1 yard = 3ft

so total 440yd

How many laps around the trail is equal to 1 mile (1,760 yards)?

1760/440 = 4laps

Answer:

Step-by-step explanation:

To solve this - determine how long it takes the acron to fall 12 feet.

At that point it will be 1 foot above ground.  13-1 = 12 so you are solving for how long it takes for the acorn to fall 12 feet.

Make a proportion:  

seconds    =    1     =        x

distance        4.8            12

If the acorn falls 4.8 feet every second, how long does it take to fall 12 feet, which is one foot above the ground.

Cross multiply:   4.8x= 12 (1)

                           4.8x = 12

divide each side by 4.8

                          4.8x/4.8 = 12/4.8

                              x       =   2.5

It takes 2.5 seconds to be one foot above the ground or fall 12 feet.

As a fraction, the probability of each sample point is 8/9.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms.

Here,

(a) The sample points in this experiment are:

V1V1, V1V2, V1V3, V2V1, V2V2, V2V3, V3V1, V3V2, V3V3

(b) Since the vendors are selected at random each day, each sample point has the same probability of occurrence. There are a total of 3 * 3 = 9 possible sample points, so each sample point has a probability of 1/9.

(c) Let A denote the event that the same vendor gets both orders, and let B denote the event that V2 gets at least one order.

P(A) is the probability that the same vendor gets both orders, so it is the sum of the probabilities of the sample points V1V1, V2V2, and V3V3. P(A) = 1/9 + 1/9 + 1/9 = 3/9.

P(B) is the probability that V2 gets at least one order, so it is the sum of the probabilities of the sample points V2V1, V2V2, and V2V3. P(B) = 1/9 + 1/9 + 1/9 = 3/9.

P(AUB) is the probability of either A or B occurring, so it is the sum of the probabilities of all 9 sample points. P(AUB) = 9/9 = 1.

P(ANB) is the probability of both A and B occurring, so it is the sum of the probabilities of the sample points V2V2. P(ANB) = 1/9.

So, P(AUB) - P(ANB) = 1 - 1/9 = 8/9.

The probability of each sample point as a fraction is 8/9.

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Answer:

The total of all three raises is $1,890. Jane's raise is $1,660 (4% of $41,400), John's raise is $1,980 (4.5% of $44,000), and Jack's raise is $1,250 (3% of $39,400).

[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ x = \sqrt{13^2+17^2~-~2(13)(17)\cos(98^o)} \implies x = \sqrt{ 458 - 442 \cos(98^o) } \\\\\\ x\approx\sqrt{519.51}\implies x\approx 22.8[/tex]

Make sure your calculator is in Degree mode.

Answer:

684π

Step-by-step explanation:

It is two parts: half of a sphere and one cylinder.

Sphere volume formula: V=4/3πR³, r=12/2=6, r³=216

                                      v=4/3π216

                                      v=288π

Half of sphere:  288π/2=144π

Cylinder volume: V=πr²h, r=12/2=6, r²=36, h=15,

                           V=π*36*15=540π

So, total is 144π+540π=684π

The exact length of the midsegment of the trapezoid is  √29 units.

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

The midsegment of a trapezoid is the line segment that connects the midpoints of the two non-parallel sides. Let's first find the midpoints of the sides SU and TV.

The midpoint of SU can be found as:

((Sx + Ux)/2, (Sy + Uy)/2) = ((-2 + 3)/2, (4 - 2)/2) = (1/2, 1)

Similarly, the midpoint of TV can be found as:

((Tx + Vx)/2, (Ty + Vy)/2) = ((-2 + 13)/2, (-4 + 10)/2) = (5.5, 3)

Now we can find the length of the midsegment that connects these two midpoints.

Distance=√(x₂-x₁)²+(y₂-y₁)²

So the length of the midsegment is:

d = √(5.5 -0.5)²+ (3 - 1)²)

= √25 + 4= = √29

Therefore, the exact length of the midsegment of the trapezoid is  √29 units.

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