Solve the following compound inequality: 0 ≤ 3x + 6 < 18

a. -2 ≤ x < 4
b. 0 ≤ x < 4
c. -2x ≤ x < 18
d. 2 ≤ x < 4​

Check the picture below.

7 pretzels he can buy the max . then he will be left with $3 which cant buy him anything.

Using the unitary approach, an issue can be resolved by first figuring out the value of a single unit, then multiplying that value by the number of units needed to solve the problem.

The term "unitary" describes a single or singular unit. The aim of this approach is to determine values in reference to a single unit. If a car travels 44 km on two litres of gas, for example, we can use the unitary technique to calculate how many kilometers it will drive on one litre of gas.

cost of one hotdog is = $7

total hotdogs he bought = 6

total money spent on hotdogs = 7*6=$42

therefore he is left with 80 - 42 = $38 with him to spend on pretzels

each pretzels cost = $ 5

max . number of pretzels he can buy is = 38/5 = 7 pretzels he can buy the max . then he will be left with $3 which cant buy him anything.

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Answer: The y-intercept is when y = -7/5

Step-by-step explanation:

The y-intercept is when x = 0, so plug that in

\(y = \frac{8}{7}x - \frac{7}{5} \\y = - \frac{7}{5}\)

Answer:

Median: 20

first quartile: 9.75

third quartile: 28.75

interquartile range: 19

Explanation:

First we arrange the data from least to greatest

If we know the 4 numbers used but do not know the order, there are 24 possible combinations to use to find the password.

When you have 4 distinct numbers and need to find the order, you are looking to determine the number of possible combinations.
A combination is an arrangement of items in a specific order. In your case, you are trying to find the possible arrangements for the 4 numbers you know, which can be used to unlock the password.
To calculate the number of combinations, you can use the formula for permutations, which is n!/(n-r)!, where n is the total number of items (numbers) and r is the number of items you want to arrange.
In this situation, n = 4 (the 4 numbers you know), and r = 4 (since you want to arrange all of the numbers). Applying the formula, you'll have:
4!/(4-4)!
4! (which is 4 x 3 x 2 x 1) divided by 0! (0! is equal to 1)
4! = 24
So, you have 24 different possible combinations for the order of the 4 numbers. To find the correct password, you would need to try each of these 24 combinations.

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Answer:

C

Step-by-step explanation:

Answer:

There are 28 marbles in the box. Some are red (12), others are yellow (6) and others are blue (10).

If in this box there 28 marbles and 6 of them are yellow, we substract to get the quantity of marbles that aren't yellow: 28-6 = 22

So 22 of the 28 marbles aren't yellow: 22/28, which we can simplify dividing the numerator and denominator by 2: 11/14

Answer:

3/16

Step-by-step explanation:

Answer:

x=2/5y+2/5

Step-by-step explanation:

Answer: The answer is 40 students

Step-by-step explanation:

Answer:

4 dollar for the first 3 lines

Step-by-step explanation:

f'(2) is equal to 11 calculated by using product rule of differentiation.

The product rule is a formula used to find the derivative of a product of two functions. It states that the derivative of the product of two functions u(x) and v(x) is equal to u(x) times the derivative of v(x) plus v(x) times the derivative of u(x), or mathematically:

d/dx(uv) = u(dv/dx) + v(du/dx)

To find f'(2), we need to use the product rule for differentiation:

f'(t) = u'(t)v(t) + u(t)v'(t)

Substituting the given values, we get:

f'(t) = 5t + 2t^2u(2) + 3t^3u(2)

Since u(2) = 1, 2, −2 and v(t) = t, t^2, t^3, we get:

f'(t) = 5t + 2t^2 + 3t^3

Substituting t = 2, we get:

f'(2) = 5(2) + 2(2^2) + 3(2^3) = 11

Therefore, the answer is f'(2) = 11.

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Step-by-step explanation:

Let's call the shorter base of the trapezoid "b1", the longer base "b2", and the height "h". We can use the formula for the surface area of a right prism to set up an equation:

Surface area of prism = 2(base area) + (lateral area) = 1280

The base area is the area of the trapezoid, which is given by:

(base area) = (1/2)(b1 + b2)h

The lateral area is the area of the four rectangular faces of the prism, which are all congruent. Each face has an area equal to the product of the height and the length of one of the legs of the trapezoid, so the lateral area is:

(lateral area) = 4hl

where l is the length of one of the legs of the trapezoid.

Substituting these expressions into the formula for the surface area of the prism, we get:

2[(1/2)(b1 + b2)h] + 4hl = 1280

Simplifying and rearranging, we get:

h(b1 + b2) + 2hl = 1280

We also know that the sum of the lengths of the legs of the trapezoid is 52 feet, which means:

l1 + l2 = 52

But we can express l1 and l2 in terms of b1 and b2 using the formula for the area of a trapezoid:

(base area) = (1/2)(b1 + b2)h = (1/2)(l1 + l2)h

Simplifying, we get:

b1 + b2 = (l1 + l2)h

Substituting this into the previous equation, we get:

h[(l1 + l2)h] + 2hl = 1280

Simplifying, we get:

h^2(l1 + l2) + 2hl = 1280

Substituting l1 + l2 = 52, we get:

h^2(52) + 2hl = 1280

This is a quadratic equation in h. We can solve it using the quadratic formula:

h = [-2l ± sqrt(4l^2 + 4h^2(52)(1280 - 2hl))] / 2(52)

Simplifying and factoring out a 2, we get:

h = [-l ± sqrt(l^2 + h^2(1280 - 2hl))] / 52

We have two possible solutions for h, but one of them is negative, which doesn't make sense in the context of the problem. So we can discard the negative solution and focus on the positive one:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

We don't know the exact value of h yet, but we can use this equation to set up a system of equations that we can solve for h. Specifically, we can use the fact that the legs of the trapezoid add up to 52 feet to solve for l in terms of b1 and b2:

l = 52 - (b1 + b2)

Substituting this into the equation for h, we get:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

h = [-52 + (b1 + b2) + sqrt((52 - (b1 + b2))^2 + h^2(1280 - 2h(b1 + b

The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.

The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).

To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.

Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.

Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.

Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.

Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.

Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.

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Answer:

a

Step-by-step explanation:

first step is to set up an equation : 3x-105+2x+10=180

second step is to add like terms : 5x-95=180

third step is to add 95 to both sides: 5x=275

last step is divide 275 ( 180 + 95 ) by 5

9514 1404 393

Answer:

  (2, 3)

Step-by-step explanation:

The coefficients of x are opposites, so the x-terms can be eliminated by adding the two equations together:

  (2x+3y) +(-2x+5y) = (13) +(11)

  8y = 24 . . . simpify

  y = 3 . . . . . divide by 8

Only one answer choice has y = 3: (x, y) = (2, 3).

__

If you like, you can finish the solution by substituting into one of the equations.

  2x +3(3) = 13

  2x = 4 . . . . . . . subtract 9

  x = 2 . . . . . . . . divide by 2

The solution is (x, y) = (2, 3).

_____

A graph confirms this solution.

P(above average grades/boy) = P(above average grades). The correct option is B

The likelihood that a male will have grades above average is 23/37, or roughly 62%. 38/75, or almost 51%, of students are expected to have grades above average.

Statement A is untrue since the two probabilities do not equal one another. The probability of a guy having above-average grades is not the same as the probability of a student having above-average grades, hence Statement C is also untrue. Statement D is untrue since a boy's chance of being chosen is not the same as his chance of earning above-average grades.

Given that he was chosen, the likelihood of a boy obtaining above-average grades is the same as the likelihood that he will. This is so that the likelihood that a boy will have above-average grades is unaffected by the selecting procedure.

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Answer:

wouldn't that just be -35?

Step-by-step explanation:

you just have to do -29-6

we have shown that p^2 = p by multiplying p = a(at a)^(-1)at by itself and canceling.

To show that p^2 = p by multiplying p = a(at a)^(-1)at by itself and canceling, let's proceed with the calculation:

p^2 = p * p

Substituting p = a(at a)^(-1)at:

p^2 = a(at a)^(-1)at * a(at a)^(-1)at

We can cancel the terms in the middle:

p^2 = a(at a)^(-1)at * (at a)^(-1)at

Now, let's simplify the expression. Since (at a)^(-1)at * (at a)^(-1)at is equivalent to the identity matrix, we have:

p^2 = a(at a)^(-1) * at

Next, we can apply the inverse property of a matrix to obtain:

p^2 = a * (at a)^(-1) * at

By using the property (AB)^(-1) = B^(-1)A^(-1), we can rewrite the expression as:

p^2 = a * (a^(-1))(at)^(-1) * at

Now, we can use the property (AB)^(-1) = B^(-1)A^(-1) again to rearrange the terms:

p^2 = a * (at)^(-1) * a^(-1) * at

Finally, using the property (A^(-1))^(-1) = A, we have:

p^2 = a * I * a^(-1) * at

Simplifying further, we obtain:

p^2 = aa^(-1) * at

Since aa^(-1) is equal to the identity matrix I, we have:

p^2 = I * at

Multiplying any matrix by the identity matrix results in the original matrix, so:

p^2 = at

Hence, we have shown that p^2 = p by multiplying p = a(at a)^(-1)at by itself and canceling.

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As a simplified fraction, we have 107/33

Note that fractions are simply described as the part of a whole number or variable.

There are different types of fractions;

From the information given, we get;

3. 24 repeating can be expressed as the sum of 3 and 0. 24

Let x be 3.24

Then, we have;

Multiplying 100 by a certain number results in a repeating decimal of 324. 24

100x = 324.24

After taking the difference between the two equations, we have;

99x = 321.

Make 'x' the subject of formula, we have;

x = 321/99

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\(\angle PYZ=116^{\circ}\) (angles on a line add to 180 degrees)

\(\angle ZYQ=58^{\circ}\) (angle bisector)

\(\angle XYQ=122^{\circ}\) (angle addition postulate)

\(\angle QYP=58^{\circ}\) (angle bisector)

Reflex \(\angle QYP=302^{\circ}\) (an angle and its reflex angle add to 360 degrees)

The graph of 2x - y = 5 does not represent a direct variation.

Direct variation is variation in which the quotient of the two variables is constant. A constant ratio of two quantities means that one quantity varies directly with the other or that the two quantities vary directly. In symbols, the direct variation formula is y=k*x or k=y/x.

k is known as the constant of variation or the constant of proportionality.

This means that as x increases, y increases, and as x decreases, y decreases, and their ratio is always the same.

The graph of the direct variation equation is a straight line through the origin.

The graph of 2x-y =5 does not pass through the origin, so it does not represent a direct variation. (consult the images attached below).

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Answer:

2:3

Step-by-step explanation:

2 : 3

divide both numbers by 14

The height in which the weight is lifted is given as h = (P x δt) / m

The work done in lifting a weight is given by:

W = F x d

where F is the force required to lift the weight and d is the distance through which the weight is lifted.

The force required to lift the weight is equal to its weight, which is given by:

F = m x g

where m is the mass of the weight and g is the acceleration due to gravity.

The distance through which the weight can be lifted is given by:

d = h

where h is the height to which the weight is lifted.

If the energy used to lift the weight is given by p, and δt is the time taken to lift the weight, then the power used is given by:

P = p / δt

We can use the formula for power to express the force in terms of p and δt:

P = F x v = F x d / δt

F = P x δt / d

Substituting the expressions for F and d into the formula for work, we get:

W = (m x g x h) = (P x δt x h) / d

Solving for h, we get:

h = (P x δt x d) / (m x g)

Substituting the expression for d (d = h), we get:

h = (P x δt x h) / (m x g)

Multiplying both sides by (m x g), we get:

h x m x g = P x δt x h

Dividing both sides by (m x g), we get the final equation:

h = (P x δt) / m

Therefore, the height to which the weight can be lifted (h) in terms of p, δt, and m is given by:

h = (P x δt) / m

where P is the power used to lift the weight, δt is the time taken to lift the weight, and m is the mass of the weight.

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The composition of function is g ( x ) f ( x ) = 5x⁴ - 40x

Given data ,

Let the first function be g ( x ) = x³ - 8

Let the second function be h ( x ) = 5x

So, the composition of functions , g(x) x h(x) would be:

(x³ - 8) (5x)

We can distribute the multiplication to get:

5x ( x³ ) - 5x ( 8 )

On simplifying , we get

A = 5x⁴ - 40x

Hence , the result of the operation g(x) x h(x) is 5x⁴ - 40x

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the number of faces, edges and vertices the shape below has is 4, 4 and 6 respectively.

It is important to note that according to Euler’s formula for any convex polyhedron, the number of Faces (F) and vertices (V) added together is exactly two more than the number of edges (E).

It is mathematically written as;

Face + vertices = 2 + edges

F + V = 2 + E

From the figure given, we can see that it is a kite

Number of vertices = 4

Number of faces = 4

2 + edges = faces + vertices

2 + edges = 4 + 4

2 + edges = 8

Edges = 8 - 2

Edges = 6

Thus, the number of faces, edges and vertices the shape below has is 4, 4 and 6 respectively.

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Based on the given parameters of the question the correct angles are as follows;

The measure of the large angle is 155°, and the measure of the small angle is 25°

The reasons the above values are correct are given as follows:

The given parameters are;

The properties of the two angles = Supplementary angles (sum of 180°)

The measure of the larger angle = 7 × The measure of smaller angle - 20°

Required:

To find the measure of each angle algebraically

Solution:

An algebraic equation can be described as a mathematical expression having an equal to sign that relates variables representing unknown values or quantities

Let L, represent the measure of the larger angle and let S, represent the measure of the smaller angle, we have;

L + S = 180°...(1)

L = 7 × S - 20°...(2)

Therefore;

Plugging in the value of L from equation (2) in equation (1) gives;

L + S = 7 × S - 20 + S = 180

7·S + S - 20 = 180

Adding 20 to both sides gives;

7·S + S - 20 + 20  = 180 + 20 (addition property of equality)

8·S =180 + 20 = 200

\(S = \dfrac{200}{8} = 25\)

The measure of the small angle, S = 25°

L = 7 × S - 20

∴ L = 7 × 25 - 20 = 155

The measure of the large angle, L = 155°

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The average rate of change, in simplest form, is -2/5.

What is average rate ?

Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.

The rate of change of the function is its gradient or slope.

The formula for calculating the gradient of a function is expressed as:

\(m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}$$\)

Using the coordinate points from the table (0,41) and (15,35)

Substitute the coordinate into the expression:

\($$\begin{aligned}& m=\frac{35-41}{15-0} \\& m=\frac{-6}{15} \\& m=\frac{-2}{5}\end{aligned}$$\)

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