Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options

On solving the provided question, we can say that Frequency Percentage is equal to the relative frequency times one hundred.

In order to make the information easier to understand, frequencies are organized into frequency distributions, which are visual displays. The frequencies displayed in a frequency distribution can be absolute or relative, like ratios or percentages. Both a graph and a table of frequencies can be used to represent a frequency distribution. Both the exact number of observations and the proportion of observations falling within each range can be displayed in a frequency distribution. A relative frequency distribution is the name given to the distribution in the latter scenario. The frequency of an observation is the frequency with which it appears in the data. The frequency of the number 9 in the following list of numbers, for instance, is 5. (because it occurs 5 times). 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9.

25–29 is listed as the First Class Group.

Class size is 4 (29-25).

Maintain the same class size for reminders from 89 through 93.

Count the values and record the frequency next to the appropriate class.

Midpoint equals (higher class limit plus lower class limit) / 2.

Relative Frequency is equal to Frequency/total Values.

Cumulative Frequency equals the sum of the past and current frequencies.

Frequency Percentage is equal to the relative frequency times one hundred.

Class Recurrence Point Midway Frequency relative Frequency Added Up percentage of frequency 25-29 0 27 0 0 0.00% 1.25% 1 31 0.0125

%ile Rank for 48 = 12.5

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Answer: 0

Step-by-step explanation:

1/2x = -1/2x cannot be true for any other value of x except when x equals 0. In other words, we need the left and right sides to equal each other, but that would only happen when x=0.

If a poll is to be conducted in an elementary school by interviewing 50 students, the following samples have been described as either representative or not representative as follows:

a. The first 50 students leaving the cafeteria. Not representative

b. Fifty randomly chosen names from a computer-generated list of names of all students at the school. Representative

c. Ten students randomly chosen from each of the 5 areas of campus. Representative

d. Five students from 10 teachers' classes. Representative

A representative sample is a small collection from a larger group from which any information obtained will be as good as the larger group. While choosing a representative sample, the researcher should take care not to zone the participants from a given section of the population. This will cause the information to be skewed and not objective.

Selecting 50 students leaving a cafeteria will not be representative because this might only represent a section of the school that will be giving their response based on a certain mood.

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The solution is:  (A) y+4=-3(x+6), is the equation of the line in point-slope form.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

The point-slope form of the equation of a line whose slope is m and passes through the point (x1,y1) is:

y-y1 = m (x-x1)

Given the point:

(x1,y1) = (-6, -4)

Slope, m= -3

x1 = -6,

y1 =-4

Substituting these values into: y-y1 = m (x-x1) , we obtain the point slope form of the equation:

we get,

y+4=-3(x+6)

The correct option is A.

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complete question:

The graph of a line has a slope of -3 and passes through the point (-6,-4).

What is the equation of the line in point-slope form?

Oy + 4 = -3(x + 6)

y + 6 = -3(x + 4)

y-4 = -3(x-6)

y-6 = -3(x – 4)

The numbers can be arranged as follows

The math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

Applying the sequence the to make the expression 1 2 3 4 5 6 7 8 9 equal to 30 using addition and subtraction signs:

(1 - 1) + 2 - (3 + 4) + (5 + 6 + 7 + 8 + 9) = 30

You can use parentheses to group the numbers and then add or subtract the groups to get the desired result.

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Answer:

Length = 26 feet; Width = 8 feet

Step-by-step explanation:

Let:

x = Length of rectangle

y = Width of rectangle

4 times the width = 4y

∴ 6 less than 4 times the width = 4y - 6

Perimeter of a rectangle = 2 × [Length + Width]
                                     68 = 2 × [(4y - 6) + y]

Expand the brackets or parenthesis by applying the Distributive Law and bring the like terms together:

                                    68 = 2 × [4y - 6 + y]
                                    68 = 2 × [5y - 6]

                                    68 = 10y - 12

                             68 + 12 = 10y

Isolate y by making it the subject of the equation:

                                  80 = 10y

                                    y = [tex]\frac{80}{10}[/tex]

                            y = Width of rectangle: 8 feet

Substitute y into the equation to calculate x:

       x = 4(8) - 6

         x = Length of rectangle = [tex](32 - 6)[/tex] feet

                                               x = 26 feet

The company’s revenue (R) from a particular distributor that buys x units is R(x) = 8999.93x

Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

Given:

original price = $9000 per unit.

let the number units bought be x

then amount= 9000x.

If the price reduces the list price by seven cents times the number of units bought .

7cents= 0.07 dollar

Then,

R(x) = 9000x - 0.07x

R(x) = 8999.93x

Hence, R(x) = 8999.93x.

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Option A:  Both functions are positive and decreasing on the interval.

The table shows that f(x) decreases when x increases in the interval (0,7) and (0, 3)

All the values of f(x) are positive in the interval (0,3).

For the exponential function that passes through the points (0, 27) and (3, 0), we also see that f(x) is decreasing when x increases: when x goes from 0 to 3, f(x) goes from 27 to 0.

Also all the values of f(x) are positive in the interval.

Then, both functions are positive and decreasing in the interval.

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f is increasing on (-infty, -4) and (2,infty) since that's where you'd be walking uphill.

f is never decreasing.

f is constant on (-4,2), since that's where it's completely flat.

The equation of the line will be y = -3/4x + 1.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The slope of the line is -3/4 and the y-intercept is 1. The equation of the line can be written as:-

y = mx + c

y = -3/4x + 1

Therefore, the line will have the equation y = -3/4x + 1.

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The mean, variance, and standard deviation of this sample is 377.5, 7007.5 meters^2 and 83.7 metres respectively. The 95% confidence interval for the true mean skidding distance is (340.5, 414.5) meters. we find that the p-value for a t-statistic of -3.61 is less than 0.01.

To calculate the mean, variance, and standard deviation of this sample, we can use the following formulas:

Using the formulas, we get:

Mean = (365 + 350 + 380 + 400 + 395 + 375 + 385 + 380 + 390 + 370 + 360 + 370 + 380 + 370 + 400 + 385 + 375 + 385 + 380 + 375) / 20

= 377.5 meters

Variance = [(365-377.5)^2 + (350-377.5)^2 + (380-377.5)^2 + ... + (380-377.5)^2 + (375-377.5)^2] / (20-1)

= 7007.5 meters^2

Standard deviation = square root of variance = sqrt(7007.5) = 83.7 meters

Therefore, the mean skidding distance is 377.5 meters, the variance is 7007.5 meters^2, and the standard deviation is 83.7 meters.

To estimate the true mean skidding distance of the road with a 95% confidence interval, we can use the following formula:

Confidence interval = sample mean ± (t-value * (standard deviation / sqrt(sample size)))

Here, the sample mean is 377.5 meters, the standard deviation is 83.7 meters, and the sample size is 20. To find the t-value, we need to look it up in a t-distribution table with 19 degrees of freedom. From the table, we find that the t-value for a 95% confidence interval is 2.093.

substituting the values, we get:

Confidence interval = 377.5 ± (2.093 * (83.7 / sqrt(20)))

= 377.5 ± 37.0

Therefore, the 95% confidence interval for the true mean skidding distance is (340.5, 414.5) meters.

The assumptions needed for this inference to be valid are:

The sample is a random sample from the population of skidding distances along the road.

The skidding distances follow a normal distribution in the population.

The sample size is large enough (at least 30) or the population standard deviation is known.

To check these assumptions, we can use a normal probability plot to check for normality and calculate the sample size to see if it is large enough. We can also use previous studies or expert knowledge to check if the assumption of normality is reasonable.

To test the logger's claim that the mean skidding distance is at least 425 meters, we can perform a one-sample t-test. The null hypothesis is that the mean skidding distance is 425 meters, and the alternative hypothesis is that it is less than 425 meters.

Using the formula for the t-statistic, we get:

t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

= (377.5 - 425) / (83.7 / sqrt(20))

= -3.61

From a t-distribution table with 19 degrees of freedom, we find that the p-value for a t-statistic of -3.61 is less than 0.01. Therefore, we reject the null hypothesis and can conclude that there is not enough evidence to support the logger's claim. Therefore, we do not agree with the logger's claim.

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The length of the caple is √3125 cm. (option C)

The caple and the tower would form a right triangle. The caple would be the hypotenuse. The tower would be the length and the distance from the base of the tower would be the base.

In order to determine the length of the caple, Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where:

c² = 25²  + 50 ²

c² = 625 + 2500

c² = 3125

c= √3125 cm

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His equation correctly represents the total cost of his order is the statement describes Sheldon’s equation

Two or more expressions with an Equal sign is called as Equation.

Sheldon wants to buy two shirts at the store.

They were each originally $14.99, but one of the shirts is on sale this week for 10% off.

A 6% sales tax is applied to the total cost of the shirts.

0.90 • 14.99 + 14.99 • 1.06 = n

The first term in the equation, 0.90 • 14.99, represents the cost of the shirt that is on sale.

The 10% discount is applied to the original price of $14.99, which is why we multiply by 0.90.

This term calculates the discounted price of the first shirt.

The second term in the equation, 14.99 • 1.06, represents the cost of the second shirt, plus the 6% sales tax that is applied to both shirts.

This term calculates the total cost of the second shirt with sales tax.

Hence, His equation correctly represents the total cost of his order is the statement describes Sheldon’s equation

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No, the marked price of $73.25 is not correct.

To calculate the sale price, we start by multiplying the original price by the discount percentage:

$95.00 * 0.25 = $23.75

This means that the original price of $95.00 should be reduced by $23.75 to find the sale price:

$95.00 - $23.75 = $71.25

Since the marked price is $73.25, this means that the store made a mistake and overpriced the shoes by $2.00. The correct sale price should have been $71.25.

Answer:

Step-by-step explanation:

Here's a step-by-step explanation of the solution:

Calculate the government deposit: For every $1.00 you deposit, the government deposits $2.00. So if you deposit the maximum of $100.00 each month, the government deposit would be $100.00 * $2.00 = $200.00.

Calculate the total deposit each month: The total deposit each month is the sum of your deposit and the government deposit, so it would be $100.00 + $200.00 = $300.00.

Calculate the number of months: You started with $100.00 and made the maximum deposit of $100.00 each month for 5 years. Five years is 5 * 12 = 60 months.

Calculate the total deposit over 5 years: Over 5 years, you made 60 deposits of $300.00 each, so the total deposit over 5 years would be 60 * $300.00 = $18,000.00.

Calculate the final balance: Adding the initial deposit of $100.00 to the total deposit over 5 years, the final balance in your account after 5 years would be $18,000.00 + $100.00 = $18,100.00.

So, at the end of 5 years, if you deposited the maximum of $100.00 each month into the College Savings fund, you would have $18,100.00 in your account.

Answer:a rectangular prism has  height  4m, length 6m & width 5m

thus the surface consist of two  4*6 vertical surfaces

                                          two 4*5 vertical surfaces

                                        & two 6*5 top & bottom surfaces

that is

            2(4*6) =  48

            2(4*5) =  40

            2(6*5) =  60

total surface area =  48+40+60 = 148m²

Step-by-step explanation:

The volume of the given complex structure would be = 56 m³

The structure is made up of the big and small cubes.

The volume of the big cube = length × breadth × width = 7 × 3 × 4 = 84 m³

The volume of the small cube cut out = length * breadth * width = 4 × 7 × (4 - 3) = 28 m³

Volume of the complex figure = 84 m³ - 28 m³ = 56 m³

The volume of the complex figure shown in the diagram is 56 m³.

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The positive angle which is less than 360 degrees and is co-terminal with -305 as required is; 55°.

It follows from the task content that the position angle which is co-terminal with -305° as required is to be determined.

Let the positive angle in discuss be; x.

Therefore, the angle x = 360 + (-305)

Consequently, it can be calculated as follows;

x = 360 - 305.

x = 55°

Hence, the required value of the positive co-terminal angle is; 55°.

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The option that is true for the central limit theorem is;

C: For a large enough sample size, the Central Limit Theorem states that the sample means of repeated samples of a population are normally distributed

Let us look at all the given options to access which one clearly is correct about the central limit theorem;

a) This option is incorrect because the CLT theorem is based on ‘sample mean’ distribution.

b) This option is Incorrect because the theorem is true for any population distribution.

c) This option is correct because Irrespective of the population distribution, the sample means of repeated samples are normally distributed for larger n.

d) The “central limit theorem(CLT)” states that, the sample means of the repeated samples follows normal distribution for ‘large’ sample sizes. Thus, this option is incorrect.

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Jean purchased a snow thrower for $1,980 using an installment plan that required a 10% down payment of $198 and 18 monthly payments of $116. This allowed Jean to spread out the cost of the snow thrower over time, avoiding a large upfront cost.

Jean recently purchased a snow thrower for $1,980 using an installment plan. To start, Jean had to make a down payment of 10% of the total purchase price, which was $198. This down payment allowed Jean to spread the remaining cost of the snow thrower across 18 monthly payments of $116 each. After making all 18 payments, Jean will have paid the full purchase price of $1,980. This installment plan option is an excellent way for Jean to get the snow thrower he needs while avoiding a large upfront cost and spreading the payments out over a period of time. With this installment plan, Jean can pay off the purchase of the snow thrower while still having money left over each month to cover other expenses.

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Answer:

Step-by-step explanation:

To show that point O is the center of the circle that passes through points D, E, and F, we can use the property of perpendicular bisectors. The perpendicular bisectors of two chords of a circle bisect the chord and pass through the center of the circle. Since the perpendicular bisectors of DE and EF intersect at point O, it follows that O must be the center of the circle that passes through points D, E, and F.

This property can also be proven using the Pythagorean theorem. Let the radius of the circle be r and let the midpoints of DE and EF be M1 and M2, respectively. Then, OM1 = OM2 = r, and the distance between M1 and M2 is equal to the distance between D and F. By the Pythagorean theorem, the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse, so we have:

OM1^2 + (M1M2)^2 = r^2 + r^2 = 2r^2

Since OM1^2 + (M1M2)^2 is equal to 2r^2, it follows that the distance between M1 and M2 is equal to the diameter of the circle. This means that M1 and M2 are the midpoints of the diameter of the circle, so they must both lie on the circumference of the circle. This, in turn, means that O is the center of the circle that passes through points D, E, and F.

Answer:

The correct answer is D. 7 pounds.

Step-by-step explanation:

The weight of the baby when its born is 7 pounds.

Answer: god

Step-by-step explanation: god god god god god god god god

Answer:

range = 33

Step-by-step explanation:

the range of a data set is the difference between the largest and smallest values in the set.

largest value = 163 and smallest value = 130 ( from diagram ), then

range = 163 - 130 = 33

The position of G in the given line segment is at point 1, which is between points F and D and the line segment between F and D in the ratio 8:5.

What is meant by line segment?

Two unique points on a line define the boundaries of a line segment. A line segment is a section of the path a line takes to join two locations. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

Given, the locations of D  and F on the line segment.

D = -4

F = 9

Number of units between F and D = 9 - (-4) = 13

Point G partitions the line segment from F to D in the ratio 8:5.

So distance of G from F = [8/(8+5)] * 13 = 8

Distance of G from D =  [5/(8+5)] * 13 = 5

So from F, it is 8 units behind F = 9 - 8 = 1

from D, it is 5 units in front of D = -4 + 5 = 1

Therefore the position of G in the given line segment is at point 1.

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2016 is the year in which the average gas mileage is the greatest.

An equation contains one or more variables connected by an equal sign.

Example:

1x + 2 = 99 is an equation.

We have,

y = -0.4 (x - 3)² + 42

where x = the number of years since 2013.

y = average gas mileage

Now,

In 2016,

x = 3

y = -0.4 (3 - 3)² + 42

y = 0 + 42

y = 42

This is the greatest value for any x value.

Thus,

In 2016, the average gas mileage for new vehicles sold is the greatest.

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The distance from the apex, or top of the pyramid, to each vertex of base is 10.9.

A right rectangular pyramid is a pyramid, with four slant sides, and a rectangular base, such that all the sides are congruent and the vertex is atop of the midpoint of the base rectangle.

Suppose the base of the pyramid has length = l units, and width = w units.

Suppose that the height of the pyramid is of h units, then:

[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]

is the volume of that pyramid.

The base is a rectangle with length = L units, and width = W units, so its area is:

[tex]b = l \times w\: \rm unit^2[/tex]

Given that;

Altitude of pyramid= 10

Each side base of pyramid= 6

Now,

So using pythagorean theorem,

x2=y2+(10)2....1

with y half of the length of the diagonal of the base.

2y=length of the diagnol

and (2y)2 = 72

4y2=72

y = 3√2.

So substitute y in eq1 and get x

( 3√2)2+(10)2=(x)2

(x)2=118

x=10.86.

x≈10.9

Therefore, the side of  right square pyramid will be 10.9.

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Answer:

Step-by-step explanation:

(a) We can find the position vectors of the points L, M, and N by taking the average of the position vectors of the points they lie between.

The midpoint of AB is given by:

N = (A + B)/2 = (41 + (41 + 21))/2 = (41 + 62)/2 = 51.5i

The midpoint of AD is given by:

L = (A + D)/2 = (41 + 6k)/2 = 23i + 3k

The midpoint of BD is given by:

M = (B + D)/2 = (41 + 21 + 6k)/2 = 31i + 3.5k

Now, we can find the vector MN by subtracting the position vectors of M and N:

MN = M - N = (31i + 3.5k) - (51.5i) = -20.5i + 3.5k

The angle between the directions of MN and OB can be found using the dot product:

cos(θ) = (MN . OB) / (|MN| * |OB|)

where θ is the angle between the two vectors. We can find the dot product and the magnitudes of the vectors as follows:

MN . OB = -20.5i + 3.5k . 41i + 21j = -20.5 * 41 + 3.5 * 21 = -847.5

|MN| = √((-20.5)^2 + (3.5)^2) = 21

|OB| = √(41^2 + 21^2) = √(1764) = 42

Substituting these values into the formula for cos(θ), we get:

cos(θ) = (-847.5) / (21 * 42) = -0.5

The angle θ can be found from the cosine inverse:

θ = cos^-1(-0.5) = 120 degrees

So, the angle between the directions of MN and OB is 120 degrees.

(b) To find the value of p, we can use the intersection of the lines through P and B and the lines through C and L. Let's call the intersection point R.

The line through P and B can be represented as P + t(B - P) = R

where t is a scalar and R is the position vector of the intersection point. Similarly, the line through C and L can be represented as:

C + s(L - C) = R

where s is a scalar. Setting these two expressions equal to each other, we get:

P + t(B - P) = C + s(L - C)

Expanding and simplifying, we get:

P + t(41i + 21j + 6k) = 21i + 6s(23i + 3k)

Comparing the i, j, and k components, we get:

P + 41t = 21 + 6s * 23

t = (21 - P)/41

6s = (P - 21)/23

s = (P - 21)/138

Substituting s back into the equation for C + s(L - C), we get:

C + (P - 21)/138 * (L - C) = R

21i + 6k + (P - 21)/138 * (23i + 3k - 6k) = R

Expanding, we get:

21i + 6k + (23/138) * Pi + (3/138) * k = R

Comparing the i and k components, we get:

21 + (23/138) * P = Ri

6 + (3/138) * P = Rk

Solving for P, we get:

P = 138 * (Ri - 21)/23 = 138 * (Rk - 6)/3

So the value of p for which the line through P and B intersects the line through C and L is given by the above formula.

Step-by-step explanation:

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