Lorrie biked d miles in 2 hours. She traveled at an average speed of more than 8 miles per hour. To determine the distance she may have traveled, she uses the inequality 2d > 8. She then determines that she biked at most 4 miles. Analyze Lorrie’s inequality and solution.

Answer:

x ≥ 3

Step-by-step explanation:

The closed dot represents ≥ and ≤

The dot is located on the number "3"

The closed dot essentially shows that the solution is nothing more than 3 and up.

Let "x" be the variable we use.

x ≥ 3

Best of Luck!

The above never line shows the possible values of an variable in any expression.

Through Observation:

Hence, the required value of the variable can be equal to 3 or greater than 3 for that expression. This can be written as:

\( \large{ \boxed{ \rm{ x\geqslant 3}}}\)

Carry On learning !

Answer:

1.4%

Step-by-step explanation:

The total number of outcomes is 216

P= 3/216 * 100 = 1.4%

Answer:

The index of refraction of this medium is 1.4

Step-by-step explanation:

The refractive index, n, of a transparent medium is defined as the ratio of speed of light in vacuum to the speed of light in that medium.

Here the given speed of light in a certain medium is 2.2 x \(10^{8}\) and the speed of light is c= 3 x \(10^{8}\)

Refractive index = n= c/v

                                  =3 x \(10^{8}\)/2.2 x \(10^{8}\)

                                  = 1.36

                                  = 1.4

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The refractive index of this medium is 1.4 .

Here the given speed of light in a given medium is 2.2 x 10⁸ and the speed of light is c = 3 x 10⁸

Refractive index = n= c/v

                                 =3 x 10⁸ / 2.2 x 10⁸

                                 = 1.36

                                 = 1.4

The refractive index of this medium is 1.4 .

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Answer:

false

Step-by-step explanation:

it would be subtracting 6 units

Hey there! I'm happy to help!

To find the x value of the midpoint, add the x values and divide by 2.

-2+(-4)=-2-4=-6

-6/2=-3

For the y value, add the y values and divide by 2.

6+(-4)=6-4=2

2/2=1

So, our midpoint is (-3,1).

Have a wonderful day! :D

Answer:

182 apples

Step-by-step explanation:

x+2 times 10= 200 apples sold this month

×+2=200/10

×=18

200-18=182 apples

0.50 off of each

6 tubes bought

So, saved

0.50 * 6 = $3

Paid 25.80 total for 6 of them (after sale). Saved $3. So, regularly it costed:

25.8 + 3 = $28.80

6 cost 28.80, so 1 cost:

28.80/6 = $4.80

Regular Price of each tube = $4.80 (r)

Note: Equation >>>

Answer:

4 IS THE ANSWER MATE

Step-by-step explanation:

Absolutely, I can do that!

Let's take a look at each statement:

1) f(x) has a y-intercept at (0,2)

To find the y-intercept, we need to set x to 0 and solve for y. Plugging in x = 0 into the equation for f(x), we get:

f(0) = -log(0+4) + 2

f(0) = -log(4) + 2

f(0) = -0.602 + 2

f(0) = 1.398

Since the y-coordinate of the y-intercept is 1.398, not 2, this statement is false.

2) The function -f(x) has a y-intercept at (0,2)

Since the negative sign in front of f(x) reflects the graph of f(x) across the x-axis, we can determine the y-intercept of -f(x) by taking the opposite of the y-intercept of f(x). Since the y-intercept of f(x) is not 2, this statement is also false.

3) As x approaches positive infinity, the function f(x) approaches negative infinity.

The function f(x) is a logarithmic function with a negative coefficient, which means it approaches negative infinity as x approaches positive infinity. Therefore, this statement is true.

4) As x approaches -4 from the right, the function f(x) approaches negative infinity.

As x approaches -4 from the right, the value of f(x) becomes more and more negative without bound, which means that f(x) approaches negative infinity as x approaches -4 from the right. Therefore, this statement is also true.

In summary, statements (1) and (2) are false, while statements (3) and (4) are true.

The length of the microorganism in millimeters is 0.005 mm.

The theory behind converting length units from one unit to another is based on the conversion factor principle. In the International System of Units (SI), the conversion factor between two units of length can be obtained by comparing the number of meters represented by each unit. For example, 1 millimeter is equal to 0.001 meters, and 1 micrometer is equal to 0.000001 meters.

To convert from one unit of length to another, we multiply the length by the appropriate conversion factor. In this case, to convert from micrometers to millimeters, we multiply the length in micrometers by 0.001 to obtain the length in millimeters.

To convert the length of the microorganism from micrometers (μm) to millimeters (mm), we divide by 1000.

5 μm / 1000 = 0.005 mm

Therefore, the length of the microorganism in millimeters is 0.005 mm.

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A homogeneous linear system of 6 equations with 3 variables may have 0, 1, or infinitely many solutions depending on the properties of the equations.

A homogeneous linear system is a system of linear equations where the constant terms are all equal to zero. In general, the number of solutions depends on the relationship between the number of equations and the number of variables, as well as the properties of the equations themselves.

In your case, you have 6 equations with 3 variables. If the system is consistent, it will always have at least one solution, which is the trivial solution (all variables equal to zero). If the system is also linearly dependent, meaning some of the equations are multiples or linear combinations of others, then the system will have infinitely many solutions. However, if the system is inconsistent, meaning there is a contradiction among the equations, then there will be no solution.

To summarize, a homogeneous linear system of 6 equations with 3 variables may have 0, 1, or infinitely many solutions depending on the properties of the equations.

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Answer:

D.

Step-by-step explanation:

a1 = -8

a2 = -8 * 2.5

a3 = -8 * 2.5 * 2.5

a4 = -8 * 2.5^3

an = -8 * 2.5^(n - 1)

The first term is -8. Each subsequent term is 5/2 times the previous term.

Answer: D.

The value of ║5p-3q║=180°.

It is given that line l₁ & l₂ are parallel and l₂ & l₃ are transversal then

they must follow the property that the alternate exterior angles must be equal i.e. ∠ q = 135°.

Also ∠ p + ∠ q = 180°.

Therefore, ∠ p = 45°.

Now to solve ║5p-3q║, substituting the values of p & q in the given equation

║5*45 - 3*135║ = 180°.

Hence, ║5p-3q║=180°.

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The quilt's area is approximately 60.74 square feet.

To calculate the area of the quilt, we need to multiply the width by the length.

First, we need to convert the mixed numbers to improper fractions:

Width: 6 5/7 ft = (7 x 6 + 5)/7 = 47/7 ft

Length: 7 3/5 ft = (5 x 7 + 3)/5 = 38/5 ft

Now, we can multiply the width by the length:

Area = width x length

Area = (47/7) ft x (38/5) ft

Area = 2126/35 sq ft

Area ≈ 60.74 sq ft

Therefore, the area of the quilt is approximately 60.74 square feet.

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Answer:

$14.00

Step-by-step explanation:

So, the 20 peaches all weigh 4 oz, and there are 16 oz in 1 pound. 16 oz divided by 4 is also equal to 4 oz, so we need to divide $2.80 by 4, which would be $0.70. That means that a 4 oz peach would be $0.70, so we multiply that by 20, which gives us $14.00, so Stacey will need $14.00 to buy 20 peaches that each weigh 4 oz.

The calculated value of x in the similar triangles is 36

From the question, we have the following parameters that can be used in our computation:

The similar triangles (see attachment)

using the above as a guide, we have the following:

x : 45 = 28 : 35

Express the ratio as fraction

So, we have

x/45 = 28/35

Cross multiply the equation

x = 45 * 28/35

Evaluate

x = 36

Hence, the value of x is 36

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84q is the simplified value of the given expression.

\((3q*7)*4\) simplifies to \((21q)*4\)which equals 84q.

\((3q^7)^4\)can be simplified using the power rule of exponents, which states that raising a power to another power means you multiply the exponents. Applying this rule, we get:

\((3q^7)^4 = 3^4 * (q^7)^4 = 81q^28\)

Therefore, (3q*7)*4 simplifies to 84q and \((3q^7)^4\) simplifies to \(81q^{28\).

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Answer:

$65m + 125 = 1165

Step-by-step explanation:

Answer:

19.2

Step-by-step explanation:

4.8 x-4 = 19.2 meters

Answer:

19.2

Step-by-step explanation:

4.8 x 4

Answer:

∠ Y = 45°, ∠ X = 135°

Step-by-step explanation:

Since the 2 angles are supplementary, then

X + Y = 180 ← substitute X = 3Y

3Y + Y = 180, that is

4Y = 180 ( divide both sides by 4 )

Y = 45

and

X + Y = 180, so

X + 45 = 180 ( subtract 45 from both sides )

X = 135

Thus

∠ X = 135° and ∠ Y = 45°

Answer:

the answer is 135

Step-by-step explanation:

Answer:

i think B. the data is easily combined due to the closed questioning method.

Step-by-step explanation:

The advantage of a personal interview is that data is easily combined due to the closed questioning method

An interview is a discussion or conversation between a potential employer and a candidate.

Given is an advantage of personal interview.

A personal interview involves a face to face interaction between a recruiter and a candidate. The closed questioning method involves the selection of answers from the given multiple options for example - questions whose answers include a selection from yes or no. This helps in the easy collection of data since the answer given represents the direct and to the point idea about how an individual thinks.

Therefore, the advantage of a personal interview is that data is easily combined due to the closed questioning method

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Answer:

12w +8

Step-by-step explanation:

Romeo spent $256,000, Baxter spent $243000 and Hirsch spent $81000 as determined by mathematical equation.

What is a mathematical equation?

Suppose Romero spent x.

x-13000 = Baxter

Hirsch's expenses equal (x - 13000)3

Making a mathematical equation out of it,

Romero, Baxter, and Hirsch equal 580000

x + x - 13000 + [(x - 13000)3] = 580000

2x + [(x - 13000)3] = 580000 + 13000

6x + x - 13000 = 593000 x 3

7x = 1779000 + 13000

x = 17920007

X = 256000

Thus,

According to a mathematical equation,

Hirsch spent $81,000,

Romeo spent $256,000,

Baxter spent $243,000.

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The area of the triangle is 94.9 square inches

For given question,

We have been given triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches.

Let x be the third side of ΔRST

⇒ 22 + 13 + x = 50

⇒ x = 50 - 35

⇒ x = 15

Let s = sum of three sides of the triangle / 2

s = (22 + 13 + 15)/2

s = 25

Now using the formula for the area of the triangle,

A = √[s × (s-a) × (s-b) × (s-c)]

Let a = 22 inches, b = 13 inches, c = 15 inches

Substituting the values,

⇒ A = √[25 × (25 - 22) × (25 - 13) × (25 - 15)]

⇒ A = √(25 × 3 × 12 × 10)

⇒ A = √9000

⇒ A = 94.9 square inches

Therefore, the area of the triangle is 94.9 square inches

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The area of  triangle rst which have sides 22 inches and 13 inches with perimeter 50 inches is 95 square inches.

We are given that the two sides of the triangle rst are 22 inches and 13 inches respectively. Also perimeter of the triangle rst is 50 inches.

We have to find the area of  triangle to the nearest square inches.

Let the third side of the triangle rst be x.

Hence,

22 + 13 + x = 50 inch

35 + x = 50 inch

x = 50 - 35
x = 15 inches

Hence, the third side of the triangle is 15 inches.

We will use the Heron's formula here to find the area of the triangle.

Heron's formula = \(\sqrt{s(s-a)(s-b)(s-c)}\)
Here,

s = Semi- perimeter

a, b, and c are sides of the triangle.

Hence,

\(s=\frac{50}{2} \\\\s=25 inches\)

a = 22 inches

b = 13 inches

c = 15 inches

Hence,

Area of the triangle rst = \(\sqrt{25(25-22)(25-13)(25-15)}\\\\ \sqrt{25(3)(12)(10)} =\sqrt{5*5*3*3*2*2*5*2}=5*3*2\sqrt{5*2}=30\sqrt{10}\)

We know that,

\(\sqrt{10}\) ≈ 3.162277
Hence,

\(\sqrt{10} * 30\) ≈ 94.86831 ≈ 95 square inches.

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Answer:

(2) b is negative

Step-by-step explanation:

If b is negative then the result of a + b would actually be a - b, which is located to the left of a. For answer 1, the number would be located on the right and for 3 the answer would be in the same place. Finally, for answer 4, the number would still be located to the right of a, just a smaller distance than a away.

Answer: The order of rotational symmetry of a shape is the number of times it can be rotated around a full circle and still look the same. If the triangle is rotated a full 360°, it never looks the same except when it arrives back at its original starting position.

Step-by-step explanation:

The order of rotational symmetry of this drawing is 4.

Each point in a figure is transformed into a rotation by rotating it a certain amount of degrees around another point.

As this is not a regular octagon, the appearance after a 45° rotation is different:

It must be rotated 90 degrees before it appears the same.

As a result, it maintains its appearance following rotations of 90, 180, 270, and 360 degrees, when it returns to its initial position.

As a result, the rotational symmetry order is 4.

The image is given in the image below.

Therefore, the order of symmetry is 4.

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The complete question:

What is the order of rotational symmetry of this drawing?

The drawing image is given in the image below.

Step-by-step explanation:

.5 / 1.5    is  1/3       (1/3)^2  = 1/9

Answer: 0.09

Step-by-step explanation:

0.5 ÷ 1.5 = 0.3 0.3squared = 0.09

Answer:

$720

Step-by-step explanation:

I = Prt

I = (9000)(0.04)(2)

I = 720

Answer:

15 feet

Step-by-step explanation:

10 + 5 = 15

Answer:

I think it is 15 feet

Step-by-step explanation:

I mean add sorry

To evaluate each definite integral without using the Fundamental Theorem of Calculus.

Integrals -

(a) ∫(3 to -3) \(x^2 dx = 0\)

(b) ∫(0 to -3) \(x^2 dx = 9\)

(c) ∫(3 to 0) \(-8x^2 dx = -72\)

(d) ∫(3 to -3) \(5x^2 dx = 0\)

What is Integrals?

In mathematics, the integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise from combining infinitesimally small data. The process of finding integrals is called integration.

To evaluate the definite integrals without using the Fundamental Theorem of Calculus, we can make use of the given information:

∫(0 to x) \(x^2 dx = 9\)

(a) To evaluate the integral ∫(3 to -3) \(x^2 dx\):

We can rewrite this integral as the sum of two integrals: ∫(3 to 0) \(x^2 dx\) + ∫(0 to -3)\(x^2 dx.\)

Using the given information, we have:

∫(3 to 0) \(x^2 dx\) = -∫(0 to 3)\(x^2 dx\)\(x^2 dx\) = -9

∫(0 to -3) \(x^2 dx\) = 9

Thus, ∫(3 to -3) \(x^2 dx\) = ∫(3 to 0) \(x^2 dx\) + ∫(0 to -3) \(x^2 dx\) = -9 + 9 = 0.

(b) To evaluate the integral ∫(0 to -3) \(x^2 dx\):

We already have ∫(0 to -3) \(x^2 dx\) = 9.

(c) To evaluate the integral ∫(3 to 0) \(-8\)\(x^2 dx\):

Since the given information is in terms of positive values of x, we need to reverse the limits of integration and change the sign:

∫(3 to 0) \(-8x^2 dx\) = -∫(0 to 3) \(-8x^2 dx\) = -8 * ∫(0 to 3) \(x^2 dx\) = -8 * 9 = -72.

(d) To evaluate the integral ∫(3 to -3) \(5x^2 dx\):

Similar to part (a), we can split this integral into two parts:

∫(3 to 0) \(5x^2 dx\)  + ∫(0 to -3) \(5x^2 dx\).

Using the given information, we have:

∫(3 to 0)\(5x^2 dx\) = -∫(0 to 3) \(5x^2 dx\) = -5 * 9 = -45

∫(0 to -3)\(5x^2 dx\) = 5 * 9 = 45

Thus, ∫(3 to -3) \(5x^2 dx\)= ∫(3 to 0) \(5x^2 dx\) \(5x^2 dx\) + ∫(0 to -3)\(5x^2 dx\) = -45 + 45 = 0.

Therefore:

(a) ∫(3 to -3) \(x^2 dx\) = 0

(b) ∫(0 to -3)\(x^2 dx\) = 9

(c) ∫(3 to 0) \(-8x^2 dx\) = -72

(d) ∫(3 to -3) \(5x^2 dx\) = 0

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