Match the following expression 12(x-3)+18=4(3x-3) with the number of solutions below.
A.One solution?
B.No solution ?
Or
C.All solution?

Answer:

x=2

Step-by-step explanation:

x^3=8

x=2  (take the cubed root of both sides)

This can be solved by adding 8 to both sides, then taking the cubed root of both sides

Answer:

false

Step-by-step explanation:

Answer: False

Explanation:

f(x) = 0

3(x-3)(x+3) = 0

x-3 = 0 or x+3 = 0

x = 3 or x = -3

This shows that if x is equal to either -3 or 3, then f(x) is 0.

First, we need to count the number of boxes that we have in a layer

We can count the number of boxes fast

we count the number of boxes of the length (boxes with a red point) the length is equal to 6

then we count the number of boxes of the width (boxes with a blue point) the width is equal to 6

then we do the next operation

number of boxes = (l)x(w)=6x6=36

In total 36 boxes in one layer

We know that the volume of each box is 1 cubic foot therefore the volume of one layer, is 36 cubic foot

In order to know the volume of 8 layers (volume of the container), we need to multiply 36 cubic ft (volume of one layer) by 8

The volume of the container is

The answer is B

The required angles are :

corresponding angles:  ∠7=∠5

alternate interior angles: ∠4 = ∠2 and∠3 = ∠1

alternate exterior angles: ∠7 = ∠6

same side interior angles: ∠7 = ∠8

alternate interior angles

alternate exterior angles

same side interior angles

Corresponding angles:

one that hold the same relative position as another angle somewhere in figure.

Alternate interior angles:

Alternate interior angles are the angles formed on the opposite sides of the transversal.

Alternate exterior angles:

Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.

Same side interior angles:

The theorem states that the same-side interior angles must be supplementary given the lines intersected by the transversal line are parallel.

corresponding angles:

∠7=∠5

alternate interior angles:

∠4 = ∠2

∠3 = ∠1

alternate exterior angles:

∠7 = ∠6

same side interior angles:

∠7 = ∠8

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With the help of given table of data of travelling time to work for 50 people, the estimated mean travelling time is 24.8 minutes.

To estimate the mean travelling time from the given frequency table, we can use the midpoint method, where we calculate the midpoint of each class interval and multiply it by the frequency of that interval. We then sum up the products and divide by the total frequency to get the estimate of the mean travelling time. The midpoint of each interval can be calculated as the average of the lower and upper bounds of the interval. Using this method, we get:

Class interval 0 < t < 10 | 10 < t < 20 |  20 < t < 30 | 30 < t < 40 |  40 < t < 50

Midpoint (m)    5                     15               25                 35                  45

Frequency (f)    5                    15               13                  10                   7

Midpoint x Frequency 25      225            325               350               315

Total | | 50 | 1240

To estimate the mean travelling time, we can now calculate the sum of the products of the midpoint and frequency for each interval, which is 1240. We then divide this by the total frequency, which is 50. Therefore, the estimate of the mean travelling time for these 50 people is: Mean  travelling time = Sum of (midpoint x frequency) / Total frequency

Mean travelling time = 1240 / 50 = 24.8

Thus, the estimated mean travelling time is 24.8 minutes.

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Complete Question

The table shows the travelling time to work of 50 people.

-Travelling time (t)  in minutes- -Frequency-

0 <t<10                                           5

10 < t < 20                                     15  

20 < t < 30                                    13

30 < t < 40                                    10

40 < t < 50                                    7

Calculate an estimate of the mean travelling time

Answer:

\(y=-\frac{1}{4}x - \frac{2}{3}\)

Step-by-step explanation:

Hi there!

We are given the equation 3x + 12y = -8 and we want to convert it into slope-intercept form

The equation is currently in standard form, which is ax+by=c, where a, b, and c are free integer coefficients

Slope-intercept form is y=mx+b, where m is the slope and b is the y intercept

Notice that in standard form, the terms containing x and y are both on the same side, but in slope-intercept form, the expression is set equal to y (x is on the other side)

So first, we'll need to subtract 3x from both sides to remove it from the left side.

3x + 12y = -8

-3x            -3x

_______________

12y=-3x-8

Now divide both sides by 12, since we want to isolate y by itself (it's a bit like solving the equation for y)

12y=-3x-8

÷12   ÷12

___________

y=-3/12x -8/12

We can simplify the fractions to get:

\(y=-\frac{1}{4}x - \frac{2}{3}\)

This is our final answer.

Hope this helps!
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We are 95% confident that the true difference between the population means falls between 0.3 and 5.1.

(a) The point estimate of the difference between the two population means is:

x1 - x2 = 22.8 - 20.1 = 2.7

(b) The degrees of freedom for the t distribution is given by:

df = (s1^2/n1 + s2^2/n2)^2 / {[(s1^2/n1)^2 / (n1 - 1)] + [(s2^2/n2)^2 / (n2 - 1)]}

df = [(2.2^2/20) + (4.6^2/30)]^2 / {[(2.2^2/20)^2 / 19] + [(4.6^2/30)^2 / 29]}

df ≈ 39.49

Rounding down, the degrees of freedom is 39.

(c) The margin of error at 95% confidence is given by:

ME = t* * SE

where t* is the critical value for the t distribution with 39 degrees of freedom and a 95% confidence level, and SE is the standard error of the difference between the means.

SE = sqrt[s1^2/n1 + s2^2/n2]

SE = sqrt[(2.2^2/20) + (4.6^2/30)]

SE ≈ 1.1817

Using a t-table or calculator, the critical value for a two-tailed t-test with 39 degrees of freedom and a 95% confidence level is approximately 2.0244.

ME = 2.0244 * 1.1817 ≈ 2.3919

Rounding to one decimal place, the margin of error is 2.4.

(d) The 95% confidence interval for the difference between the two population means is given by:

(x1 - x2) ± ME

= 2.7 ± 2.4

= (0.3, 5.1)

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A randomized controlled trial in which each subject is assigned to a combination of at least two independent variables is an example of a Factorial Design.

In statistics, a full factorial experiment is one in which all potential combinations of the levels across all of the factors are taken into account by the experimental units. A full factorial experiment has two or more factors with discrete possible values or "levels" in its design. A fully crossed design is another name for a full factorial design. Using such an experiment, the researcher can examine how each element affects the response variable as well as how different factors interact with one another.

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Answer:

135°

Step-by-step explanation:

m<VSR = m<RST + m<VST

Each angle at the vertices of a square is equal to 90°. <RST is one of the vertices of square RSTU, therefore,

m<RST = 90°

also, m<VST = 90 - 45 = 45°

m<VSR = m<RST + m<VST

Thus:

m<VSR = \( 90 + 45 = 135 \)

Measure of angle VSR is 135°

The angle VSR will be equal to 135°.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

m∠VSR = m∠RST + m∠VST

Each angle at the vertices of a square is equal to 90°. ∠RST is one of the vertices of square RSTU, therefore,

m∠RST = 90°

also, m∠VST = 90 - 45 = 45°

m∠VSR = m∠RST + m∠VST

Thus:

m∠VSR = 135

Therefore the measure of angle VSR is 135°

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Answer:

Step-by-step explanation:

um

its still 2:6:7?

please elaborate I don't get the question

Answer:

its 2:1

Step-by-step explanation:

The derivative of f(x) = sinº (4x) is f '(x) = 4cos (4x).

To find the derivative of f(x) = sinº (4x), we can use the chain rule.

First, we need to find the derivative of the outer function, which is sinº (4x). This can be done using the derivative of the sine function:

f '(x) = cos (4x)

Next, we need to multiply this by the derivative of the inner function, which is 4.

f '(x) = cos (4x) * 4

Simplifying this expression, we get:

f '(x) = 4cos (4x)

Therefore, the derivative of f(x) = sinº (4x) is f '(x) = 4cos (4x).

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Step-by-step explanation:

\(5 \: mile = > 8km \\ 60 \: mile = > x \\ 5x = 60 \times 8 \\ 5x = 480 \\ x = \frac{480}{5} \\ x = 96 \\ thank \: you\)

I hope it will help you .

Thank you.

Tedybearlover

^ - ^

In the bag containing the combinations of coins, the number of ways in which the combination of two nickels, two dimes and a quarter can be obtained is 1960 ways.

The answer is Option (E).

For this question, we apply the concepts and principles of Combinations.

The main formula used in all combinatoric questions, which can also be used to obtain equations for special cases is:

If we want to choose 'x' objects from a total of 'n' objects in a bag, then the number of ways in which this can be done is denoted as ⁿCₓ. The expression for the above term is:

ⁿCₓ = n!/[ x! * (n - x)! ]

If we have more than one objects to be chosen, we just multiply the number of combinations of each object to obtain the totals.

We divide our question into three parts, Nickels, Dimes, and Quarters.

For Nickels:

We are asked to choose 2 nickels from the 5 in the bag.

So, the number of combinations will be:

⁵C₂ = 5!/2! (5 - 2)!

     = 5!/2!*3!

     = 120/2*6

     = 120/12

     = 10 possible combinations.

For Dimes:

We have to choose 2 dimes from the 8 dimes in the bag.

So, no. of combinations is

⁸C₂ = 8!/2!(8 - 2)!

      = 8!/2!*6!

      = 7*8/1*2

      = 56/2

      = 28 combinations

For Quarters:

We are supposed to choose a quarter from the 7 in the bag.

We can say even without writing the formula, that there 7 possible combinations.

So, finally, the total number of ways in which the selection can be made is simply the product of the values obtained.

T = 28*10*7

T = 1960 ways.

So, we can make the required selections in 1960 ways.

Question:

From a bag containing 5 nickels, 8 dimes, and 7 quarters, 5 Coins are drawn at random, and all at once. In how many ways can the desired selection be made such that we obtain 2 nickels, 2 dimes, and a quarter?

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Ordered pairs are also very well known as coordinates.

An ordered pair is a set of two numbers that are used to describe the position of a point on a coordinate plane.

The first number in the ordered pair is called the x-coordinate and the second number is called the y-coordinate. The x and y coordinates represent the horizontal and vertical positions, respectively, of a point on a coordinate plane.

For example, (3,4) is an ordered pair. Here, 3 is the x-coordinate and 4 is the y-coordinate. Point (3,4) is located 3 units to the right of the y-axis and 4 units above the x-axis on a coordinate plane.

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If you have three side lengths, you should find the angle opposite the smallest side to determine the lowest angle, the angle opposite the medium-sized side to determine the greatest angle, and the angle opposite the largest side to determine the greatest angle.

Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned.

Angles are also produced when two planes intersect.

These are what are known as dihedral angles.

Consequently, if you have three side lengths, you should discover the lowest angle by finding the angle that is opposite the smallest side, the medium-sized angle by finding the angle that is opposite the medium-sized side, and the greatest angle by finding the angle that is opposite the largest side.

Therefore, if you have three side lengths, you should find the angle opposite the smallest side to determine the lowest angle, the angle opposite the medium-sized side to determine the greatest angle, and the angle opposite the largest side to determine the greatest angle.

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Answer:

See below

Step-by-step explanation:

You can always plug in x's and solve for y.

Answer:

\(BD = 30\)

Step-by-step explanation:

Given

\(AB = 17\)

\(AC = 16\)

See attachment

Required

Find BD

If AC = 16, then:

\(AO = 16/2\) i.e. half the diagonal AC

\(AO = 8\)

The diagonals of a rhombus are perpendicular.

This implies that we can apply Pythagoras theorem.

Using Pythagoras theorem on triangle AOB, we have:

\(AB^2 = AO^2 + OB^2\)

\(17^2 = 8^2 + OB^2\)

\(289 = 64 + OB^2\)

Collect like terms

\(OB^2 = 289 - 64\)

\(OB^2 = 225\)

Take positive square roots of both sides

\(OB = 15\)

To solve for BD, we use:

\(OB = \frac{BD}{2}\) --- i.e. half the diagonal BD

\(BD = 2 * OB\)

\(BD = 2 * 15\)

\(BD = 30\)

Answer:

15%

Step-by-step explanation:

1.00-.85=15%

AnswerAnswer:

a= -2

Step-by-step explanation

\(\huge\underline{\purple {A}\purple{n}\purple {s}\purple {w}\purple {e}\purple {r} ➾}\)

Step-by-step explanation:

There are 100 pennies in 1 dollar, so Priya collected 2400/2.5=<<2400/2.5=960>>960 pennies.

This means Priya raised 960/100=$<<960/100=9.60>>9.60. Answer: \boxed{9.60}

The deductible mileage cost has reduced by 2.16%

What is a percentage change?

A percentage change  compares the difference between the new amount and the old amount to the old amount.

I mean the percentage change is the new deductible mileage cost minus the old deductible mileage cost divided by the old deductible mileage cost

New deductible mileage cost= 57.5 cents

Old deductible mileage cost= 56 cents

percentage decrease=(56-57.5)/57.5

percentage decrease=-2.61%

The negative sign in -2.61% means that there was a percentage decrease in deductible mileage cost by 2.61%

In essence, the deductible mileage cost has been reduced by 2.16%

Hundredth of a percent means two decimal places.

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The given equation states that this integral is equal to -2. However, this is not correct, as the integral represents the sum of the areas and should result in a positive value.

To evaluate the integral in terms of areas, we need to interpret it as the area under a curve. The integrand, 3 + √9-x^2, is the equation of a semi-circle with radius 3 and center at the origin.

Thus, we can interpret the integral as the area of this semi-circle from x = 0 to x = 3. We know that the area of a semi-circle with radius r is (1/2)πr^2, so the area of this semi-circle is (1/2)π(3)^2 = (9/2)π.

However, the integral is evaluated from x = 0 to x = 3, so we need to take half of the area to get the area under the curve from x = 0 to x = 3. Therefore, the area under the curve is (9/4)π.

We also know that the integral is equal to -2, so we can set the area equal to -2:

(9/4)π = -2

Solving for π, we get:

π = (-8/9)

This is not a possible value for π, so there must be an error in the problem statement or the solution method.
To evaluate the integral by interpreting it in terms of areas, follow these steps:

Step 1: Identify the given integral
0 ∫ (3 + √9-x^2) dx

Step 2: Break the integral into two parts
0 ∫ 3 dx + 0 ∫ √(9-x^2) dx

Step 3: Evaluate the first integral (0 ∫ 3 dx)
This represents the area of a rectangle with height 3 and width from 0 to x.
Integral = 3x

Step 4: Evaluate the second integral (0 ∫ √(9-x^2) dx)
This represents the area of a quarter-circle with radius 3 (because 9 = 3^2). The area of the quarter-circle can be found using the formula for the area of a circle (A = πr^2) divided by 4:
Integral = (1/4)π(3)^2 = (9/4)π

Step 5: Add the two integrals together
(3x) + (9/4)π

Step 6: Evaluate the integral at the given limits (0 to x)
At x=0, the integral is 0.
So the definite integral = (3x) + (9/4)π - 0

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Answer:

y=22-1

Step-by-step explanation:

ewaan di ako sure

Step-by-step explanation:

Given. m = 8 , n = 3

mn = 8 * 3 = 24

Hope it will help :)

Answer:

hello

Step-by-step explanation:

if "m" is equal to 8 and "n" is equal to 3

then mn=8×3=24

have a nice day

bye

Answer:

all real numbers

Step-by-step explanation:

-(2x + 4) + x = 3x − 4x − 4

Distribute the negative sign on the left side. It is the same as having a -1 to the left of the parentheses.

-1(2x + 4) + x = 3x − 4x − 4

-2x - 4 + x = 3x - 4x - 4

Combine like terms on the left side. Combine like terms on the right side.

-x - 4 = -x - 4

Add 4 to both sides.

-x = -x

Add x to both sides.

0 = 0

You end up with a true equation. Therefore, there is an infinite number of solutions. Every real number is a solution.

Answer: all real numbers

Answer: The answer is 14.55

Step-by-step explanation:

Answer:

1,164 ÷ 80 is equal to 14.55.