given a non-negative integer numrows, generate the first numrows of pascal's triangle. in pascal's triangle, each number is the sum of the two numbers directly above it

The required expression for

[tex]log_5(\frac{x}{4} )^2[/tex] = 2 [tex]log_5[/tex] x - 2 [tex]log_5[/tex] 4.

Given,

In the question:

The expression is given as:

Log subscript 5 baseline (startfraction x over 4 endfraction) squared

To find the which expression is equivalent?

Now, According to the question:

The expression is given as:

[tex]log_5(\frac{x}{4} )^2[/tex].

We know that from the properties of logarithm, the following identities

[tex]log m^n = n log m...(1)\\\\log\frac{m}{n} = log m - log n .....(2)[/tex]

Now,  [tex]log_5(\frac{x}{4} )^2[/tex] = 2 log [tex]\frac{x}{4}[/tex] (using 1 identity)

Again, Using (2) identity we get,

[tex]log_5(\frac{x}{4} )^2[/tex] = 2 [tex]log_5[/tex] x - 2 [tex]log_5[/tex] 4.

Learn more about Logarithms at:

https://brainly.com/question/27037425

#SPJ4

The opportunity cost for the Congo to produce additional diamonds is; 4 thousand units of corn.

Opportunity costs are defined as the benefits of an alternative decision when the decision maker is made to reject the alternative.

For example, the opportunity cost of going to college would be the earnings forgone.

The opportunity cost is calculated as the lost benefit when an alternative decision is not followed up.

Fractionally, we can say that the opportunity cost of producing one product A) to another (B) = Units of B/Units of A.

From the attached table, we can deduce the following;

United States opportunity cost to produce diamonds = 60/10 = 6

United States opportunity cost to produce corns = 10/60 = 1/6

Congo's opportunity cost to produce diamonds = 20/5 = 4

Congo's opportunity cost to produce corn = 5/20 = 1/4

Read more about Opportunity cost at; https://brainly.com/question/481029

#SPJ1

The value of x will be;

⇒ x = 3

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown in figure.

Now,

All the sides are given in figure.

By definition of proportionality, we get;

⇒ 3 / (6x - 2 - 10) = (3 + 5) / (6x - 2)

Solve for x as;

⇒ 3 / (6x - 12) = 8 / (6x - 2)

⇒ 3 (6x - 2) = 8 (6x - 12)

⇒ 18x - 6 = 48x - 96

⇒ 96 - 6 = 48x - 18x

⇒ 90 = 30x

⇒ 30x = 90

⇒ x = 90/30

⇒ x = 3

Thus, The value of x will be;

⇒ x = 3

Learn more about the triangle visit:

https://brainly.com/question/1058720

#SPJ1

The 10 multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 when we can just write the table of 3 all terms.

Given that,

We have to find the 10 multiples of 3.

We know that,

We can find the multiples of a number by counting the digits. A multiple in mathematics refers to the outcome or output of multiplying two numbers together.

The Least Common Multiple is the smallest common multiple of two or more numbers (Least Common Multiple).

The 10 multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.

Therefore, The 10 multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 when we can just write the table of 3 all terms.

To learn more about multiple visit: https://brainly.com/question/5992872

#SPJ4

the answer is -6x and the equation is equivalent

The car travels 183 miles distance in 3 hours.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Distance travelled by car in 4/5 hour = 48⁴/₅ miles  or 244/5 miles.

To find distance travelled by car in 3 hours, use ratio property,

4/5 hours = 244/5 miles

⇒1 hour = 61 miles

⇒3 hours = 61×3 = 183 miles

The distance covered by car in 3 hours is 183 miles.

To know more about Ratio on:

https://brainly.com/question/23724140

#SPJ1

Strawberries, apples, cherries, spinach, nectarines, and grape samples were positive for residues of two or more pesticides in more than 90% of the cases. The most pesticides were found in kale, collard, mustard greens, spicy peppers, and bell peppers totaling 103 and 101 pesticides, respectively.

According to the Environmental Working Group's 2022 Shoppers Guide to Pesticides in Vegetables, strawberries and spinach continue to have the highest pesticide levels of any product categories.

According to the EWG, more than 70% of non-organic vegetables contained pesticide residue. Nearly all the produce had pesticide residue levels below limits set by U.S. regulators.

Know more about pesticides at:

https://brainly.com/question/12912926

#SPJ4

The correct answer is median.

The salary of 35 year olds would vary greatly, with significant variations. Undoubtedly, this type of data contains outliers. Because median is unaffected by outliers in the data set, it would be appropriate for the data that included outliers.

The observations are divided into two equal portions by the median. When observations are organised in order of magnitude, it reflects the middle value for the group of observations.

When data are input in ascending order, the median value is the middle value. In other words, the observation is in the middle.

If there are an even number of observations overall, the median is calculated as the average of the middle two observations.

The median is the middle observation in the arranged data if the total number of observations is an odd number.

To know more about 'median' related questions

visit- https://brainly.com/question/28060453

#SPJ4

You already got 4.2 averaged from 120 reviews. To get a 4.5 average, you need more 72 reviews with 5 ratings.

This problem can solved using average value approach.

Average value can be calculated using:

Average = sum of data value / number of data

Let p = number of required 5 ratings to get a 4.5 average.

Then,

sum of data value = 120 x 4.2 + p x 5

number of data = 120 + p

Hence,

Average = (120 x 4.2 + p x 5) / (120 + p)

4.5 = (504 + 5p) / (120 + p)

540 + 4.5p = 504 + 5p

0.5 p = 36

p = 72

Hence, you need 72 reviews with 5 ratings.

Learn more about average value here:

https://brainly.com/question/20118982

#SPJ4

When there was a large variance for a sample of difference scores in a repeated-measures t-test, then there is probably not a significant difference between treatment groups and the participant's scores would be predictable.

In a repeated measures t-test, the test statistic is given by

[tex]t = \frac{d}{s_{d} / \sqrt{n} }[/tex]

Since [tex]s_{d}[/tex] = the standard deviation of difference scores is large occurs in the denominator of the test statistic.

Thus, there probably is not a significant difference between treatment groups and the participant's scores would be predictable.

To read more about t-tests, visit https://brainly.com/question/15870238

#SPJ4

Answer:

x = 3

y = 2

Step-by-step explanation:

x + 2y = 7 and

13 - 5y = x

transfer x to the left side and 13 to the right side of the equation for the second equation:

-x - 5y = -13 now find the sum of both equations:

x + 2y - x - 5y = 7 - 13 add/subtract like terms

-3y = -6 divide both sides by -3

y = 2

To find the value of x replace y with 2:

x + 2*2 = 7

x + 4 = 7 subtract 4 from both sides

x = 3

Using its formula, it is found that Val's margin of error is 9.8 pounds.

What is the margin of error?

In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.

The margin of error formula:

The margin of error is given by the following equation:

M = 1.96(s/√n)

Where,

s is the standard deviation.

n is the sample size.

Here, we have

Given

The standard deviation is 50, hence s = 50

Val weighed 100 cows, hence n = 100

By applying the margin of error formula and we get

M = 1.96(50/√100)

M = 1.96(50/10)

M = 9.8

Hence, Using its formula, it is found that Val's margin of error is 9.8 pounds.

To learn more about the margin of error from the given link

https://brainly.com/question/14396648

#SPJ4

Therefore, the national population growth rate in the United States in 2017 was 0.72%.

Growth rate is a metric for determining how quickly a variable has changed over time. It is usually represented as a percentage and is frequently used to calculate the rate of change in economic indicators such as GDP or the rate of inflation. Growth rate may also be used to quantify the rate of change in biological or population processes, such as the growth of an organism's population or the expansion of the size of a tumour. In general, a high growth rate is positive and indicates that a variable is increasing quickly, whereas a low growth rate is considered negative and suggests that a variable is increasing more slowly or may even be decreasing.

How to solve?

Population growth rate = (CBR - CDR + net migration rate) / 10

Population growth rate = (11.8 - 8.5 + 3.9) / 10

Population growth rate = (11.8 - 8.5) + 3.9 / 10

Population growth rate = 3.3 + 3.9 / 10

Population growth rate = 3.3 + 3.9

Population growth rate = 7.2 / 10

Population growth rate = 0.72 %

Therefore, the national population growth rate in the United States in 2017 was 0.72%.

To learn more about the growth rate, visit:

https://brainly.com/question/20805057

#SPJ4

The line declines from the left to the right, therefore the slope is negative.

Slope = -1.

The slope of the line is the rise of a line over its run, which is given as:

Slope (m) = change in y / change in x.

If a line decreases or declines from the left to the right, then the slope is said to be a negative slope.

The line in the graph shows it is a declining from the left to the right, therefore, it is a negative slope.

Slope of the line = rise/run = -4/4

= -1.

Learn more about the slope on:

https://brainly.com/question/16949303

#SPJ1

The total amount of money that she borrowed would be= $227.

A credit union could be defined as the union that identifies am individual as their members and there offer financial assistance to such an individual.

The number of gifts bought by Mr Steven = 5 identical gifts.

The price for each gift = $80

The total money that Mr Steven spent on gift = 5×80 = $400.

The amount paid was 1/2 of total cost = 1/2×400 = $200

The amount of money she borrowed for her credit union is calculated using simple interest formula;

si = P*T*R/100

si = 200×1.5 × 9/100

si = 2700/100

si = $27

The amount borrowed= 200+27 = $227.

Learn more about credit price here:

https://brainly.com/question/26376004

#SPJ1

To solve a system of linear equations without graphing, you can use the substitution method.

How do you solve a system of equations without graphing?

To solve a system of linear equations without graphing, you can use the substitution method. This method works by solving one of the linear equations for one of the variables, then substituting this value for the same variable in the other linear equation and solving for the other variable.

learn more about of equation here

https://brainly.com/question/10413253

#SPJ4

The relationship that represents the given function is y = 0.6x + 208 and the graph is attached below.

The water level rises at the rate of 0.6 cm/min .

After 20 minutes the water level is 220 cm

let the initial water level be a.

∴ 220 = a + 0.6×20

or, 220 = a + 12

or, a = 208 cm

therefore the initial water level is at 208 cm.

Now we will find the relationship.

Let the water level is y and the level rises at the rate of 0.6 cm /min .

The require function will be :

y = 0.6x + 208

The graph of the function is attached .

The set of all pairings (x, f (x)) that singularly represent a function is known as the graph of both the function, which is a common technique for illuminating the function.

When the domain and/or the codomain are sets of real values, each such pair can be thought of as the Cartesian coordinates of a point in the plane.

To learn more about graph of a function visit:

https://brainly.com/question/11326051

#SPJ4

Cluster Sampling method , is the required method .

Because the population is split into two separate groups in two different ways.

In a given problem, a survey says that a sample is selected by dividing the population into the gifts of votes, and we need to figure out how to sample. This is called cluster sampling. Analysts are run using a sample her cluster.

Cluster Sampling Method:

In cluster sampling, researchers divide the population into smaller groups called clusters. Then randomly select from these clusters to form a sample. Cluster sampling is a probabilistic sampling technique commonly used to study large populations, especially those that are geographically dispersed.

How to cluster the samples

To learn more about Cluster Sampling, refer:

https://brainly.com/question/14510792

#SPJ4

The co-ordinates of point Y and Z are (-1,-1) and (5, 0).

What is co-ordinates?

In geometry, a coordinate system could be a system that uses one or additional numbers, or coordinates, to unambiguously confirm the position of the points or alternative geometric components on a manifold like Euclidean space

Main body:

According to given information:

X (0,2) is translated to the point X(1,-3).

so the translation is 1 to right and 5 below

A) y(-2,4)

as the translation is 1 to right and 5 below

hence Y is (-1,-1).

B) Z (4,5)

as the translation is 1 to right and 5 below,

Z = (5,0)

Hence, co-ordinates of point Y and Z are (-1,-1) and (5, 0).

to know more about co-ordinates , click on the link below

https://brainly.com/question/20362114

#SPJ4

The correct response is 110.

Consider two numbers that are inside 1000.

324 and 434 are these two numbers.

As a result, for any number abc, the terms a, b, and c each have a place value of 100, 10, and 1.

We will therefore add the corresponding digits and multiply them by their place value when adding the two numbers abc and def.

In order to add 324 and 434, we will

(3+4)×100 + (2+3)×10 + (4+4)×1

The solution is 700+50+8=758.

This is equivalent to (324 + 434 = 758)

Similar steps apply for subtraction; simply choose the larger number and continue the same procedures, changing the + sign in the inner bracket to a -.

(4-3)×100 + (3-2) (3-2)×10 + (4-4)×1

Therefore, the correct response is 110.

This equals (434-324) = 110.

To learn more about subtraction click here:

brainly.com/question/2346316

#SPJ4

Answer:

45 hotdogs

Step-by-step explanation:

if he eats 1 hot dog every 20 seconds he will eat 3 hotdogs in a minute (20x3=60seconds aka a minute) so you multiply that by 15 and you get 45

According to the Side-Angle-Side Theorem (SAS), two triangles are congruence if their two sides and the angle between them are equal to those of another triangle's two sides and angle.

Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.

If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.

Learn more about Congruency here:

brainly.com/question/7888063

#SPJ4

The true statement regarding statistical plan is Transaction-based plans better support the business need for data

The term statistical plan refers to the document that a statistical organization uses to specify the data items that must be provided to the organization as well as the format in which the data must be reported.

The statistical analysis plan SAP includes information on the scope, population definitions, and methodology of planned analyses. The SAP should be built before any such data analysis because it is essential for directing them.

Hence The statement that transaction-based plans better meet the business demand for data is true with relation to statistical plans.

Learn more about statistical plan at:

https://brainly.com/question/14724376

#SPJ1

If you have more than one quadratic predictor in your model, you can test them all at the same time using the partial F-test. This statement is True.

What is partial F-test?

A partial F-test is used to determine whether or not there is a statistically significant difference between a regression model and some nested version of the same model.

A nested model is simply one that contains a subset of the predictor variables in the overall regression model.

Partial F-test is a statistical analysis used in multivariate linear regression to determine independent variables are to be considered when fitting a multivariate linear regression mode.

This is necessary because if too many variables are considered, then the model would be too complex. On the other hand, if too few variables are used, then we may get a very weak fit.

Hence if you have more than one quadratic predictor in your model, you can test them all at the same time using the partial F-test.

The given statement is true.

To know more about partial F-test here

https://brainly.com/question/14338586

#SPJ4

When you do not recognize a power of 4 which it equals 128 then the proper technique to solve this equation 4x=128 is; Find intersections on the graph of y = 4ˣ and y = 128.

Consider the given equations;

y = 4ˣ and y = 128

Since, the power of 4 equals 128 is unknown.

Thus, draw the graph of equation  y = 128. and y = 4ˣ .

Consider the intersected point from the graph.

Thus, when you do not recognize a power of 4 which it equals 128 then the proper technique to solve this equation 4x=128 is;

Find intersections on the graph of y = 4ˣ and y = 128.

To know more about the mathematical equation, here

https://brainly.com/question/28338737

#SPJ4

The mean of the numbers means that it is average of the given numbers.

According to the question,

We have the following information:

Mean of the numbers

We know that the mean of a given data set means that we add all the numbers in data set and divide the obtained result by the total numbers.

For example, we have a following data set:

2,5 and 8

Total numbers in the set = 3

Now, the mean of these numbers will be:

Mean = (2+5+8)/3

Mean = 15/3

Mean of the numbers = 5

So, in other words, it can be expressed as the average of the numbers.

Hence, the mean of the numbers means that it is average of the given numbers.

To know more about mean here

https://brainly.com/question/21800892

#SPJ4

The function of the length 'x' in meters of the side parallel to the wall is A(x) = x/2(210 - x)

What are perimeter and area?

While area describes the space it occupies, perimeter describes how far the shape's edge extends. A shape's perimeter is its entire circumference. The region that an object's shape defines as its area.

Given, perimeter (P) = 210 meters ........... (i)

Let the length parallel to the wall be 'x' and the width be 'y'

So, the perimeter of the fence is

P = 2y + x ............... (ii)

From eq. (i) & (ii), we get

210 = 2y + x

or, y = 1/2(210 - x)

The area of the wall is calculated as:

A = xy

or, A = x * 1/2(210 - x)

or, A = x/2(210 - x)

Rewrite as

A(x) = x/2(210 - x)

Hence, the function of the length 'x' in meters of the side parallel to the wall is A(x) = x/2(210 - x)

To learn more about perimeter and area

https://brainly.com/question/397857

#SPJ4

The equation of the  circle , with diameter  DEis (x - 5)² + (y - 7)² = 80

An equation is an expression that appears as the relationship between two or more variables and numbers. since the  standard equation  for a circle  is (x - h)² + (y - k)² = r², where    (h, k)  is the center of the circle and r is the radius. It is given that the diameter of the circle is at D(-3, 3) and E(13, 11). So the coordinate of the center is:

h = (13 + (-3))/2 = 5

k = (3 + 11)/2 = 7

(h, k) = (5, 7) and the  Radius is diameter / 2 = 8√5 ÷ 2 = 4√5.

the equation will be : (x - 5)² + (y - 7)² = (4√5)² => (x - 5)² + (y - 7)² = 80

to know more about circle refer to the link https://brainly.com/question/11833983?referrer=searchResults.

#SPJ4

Answer:

(x - 5)² + (y - 7)² = 80

Step-by-step explanation:

The horizontal force exerted on the skater 1170 N.

The diameter of the semicircular portion of the track is 16 m.

Therefore its radius is

r = 8 m.

The tangential velocity of the skater is 12 m/s.

Therefore the angular speed is

ω = v/r = (12 m/s)/(8 m) = 1.5 rad/s

The horizontal force on the skater is due to centripetal acceleration of

a = r*ω² = (8 m)*(1.5 rad/s)² = 18 m/s².

The force acting on the 65-kg skater is

F = m*a = (65 kg)*(18 m/s²) = 1170 N

Therefore, the horizontal force exerted on the skater 1170 N. The correct answer is 1170 N.

To learn more about force, refer:

https://brainly.com/question/13191643

#SPJ4

The zeros of the polynomial P(x) = x³ + 7x² - x - 7  is  1 , - 1 , - 7 .

In algebraic expressions, exponents may have rational values. A polynomial, on the other hand, is an algebraic assertion with a whole number exponent on any variable. The places where a polynomial turns 0 are referred to as its zeros.

P(x) = x³ + 7x² - x - 7

Now we have to find one zero of given polynomial.

By hit and trial, we get

P(-7) = (-7)³ + 7 (-7)² - (-7) - 7

        = 0

Hence we get one zero = -7

So, -7 is the roots of the equation.

Now, by factorisation :

   P(x) = x³ + 7x² - x - 7

           = x² ( x+7 ) - 1 ( x+3 )

            = (x² - 1) ( x+7 )

            = ( x-1 )( x+1 )( x+7)

Hence the zeros of the polynomial is 1 , - 1 , - 7.

To learn more about polynomial, visit:

https://brainly.com/question/11536910

#SPJ4

All the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

P(x) = x3 + 7x2 − x − 7