(?) James is following this recipe to make flapjacks.
James uses 650 g of margarine.
How many flapjacks is James making?
Recipe: Makes 8 flapjacks
50 g sugar
100 ml syrup
125 g oats
130 g margarine
65 g sultanas

Option 2) the first set of data has values that are closer to the mean because the standard deviation is lower is correct

If two samples have the same mean, then it means that the two values in the two samples are centered around the same value. However, this does not mean that the data values in the samples vary equally around this center and thus the standard deviations may also differ.

It depends what the standard deviations are. The standard deviation is a measure of how close the results are to the mean, a low standard deviation means that the measurements are accurate, so close to the mean. A high standard deviation means that the measurements are more spread out.

We need to find that if two sets of data both have a mean of 76. however, the first set has a standard deviation of 1.4 and the second set has a standard deviation of 5.7. what must be true about the two sets

The first set of data has values that are closer to the mean because the standard deviation is lower because in first set standard deviation is 1.4 and in second set standard deviation is 5.7

The one with smaller standard deviation are least spead from the mean

Hence the first set of data has values that are closer to the mean because the standard deviation is lower.

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Mercury travels a distance of 153 461 500 kilometers on its orbit.

The statement indicates that Mercury has a circular orbit and indicates the central angle covered by translation. The distance traveled is found by definition of circular arc:

s = (2.65 rad) · (57 910 000 km)

s = 153 461 500 km

Please notice that the radius of translation is the distance from the Sun to Mercury.

Mercury travels a distance of 153 461 500 kilometers on its orbit.

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Yes, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the line of best fit

From the question, we are to determine if the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks

In the graph, we have a scatterplot.

The line drawn is the line of best fit

Hence,

Yes, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the line of best fit.

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The values of x and y that are solutions to the simultaneous equations are; x = -11 and y = -4

We are given the simultaneous equations;

4x - 6y = -20   -----(eq 1)

-2x + 4y = 6     -----(eq 2)

Multiply equation 2 by 2 and eq 1 by 1 to get;

-4x + 8y = 12     -----(eq 3)

Add eq 3 to eq 1 to get;

2y = -8

y = -4

Thus;

4x - 6(-4) = -20

4x + 24 = - 20

4x = -20 - 24

4x = -44

x = -44/4

x = -11

Thus, the values of x and y that are solutions to the simultaneous equations are; x = -11 and y = -4

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The average increase in the number of flowers pollinated per day between days 4 and 10 is 39, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].

In the question, we are asked for the average increase in the number of flowers pollinated per day between days 4 and 10, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].

To find the average increase in the number of flowers pollinated per day between days 4 and 10, we use the formula {f(10) - f(4)}/{10 - 4}.

First, we find the value of the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex], for f(10) and f(4).

[tex]f(x) = (3)^{\frac{x}{2} }\\\Rightarrow f(10) = (3)^{\frac{10}{2} }\\\Rightarrow f(10) = 3^5 = 243[/tex]

[tex]f(x) = (3)^{\frac{x}{2} }\\\Rightarrow f(4) = (3)^{\frac{4}{2} }\\\Rightarrow f(10) = 3^2 = 9[/tex]

Thus, the average increase

= {f(10) - f(4)}/{10 - 4},

= (243 - 9)/(10 - 4),

= 234/6

= 39.

Thus, the average increase in the number of flowers pollinated per day between days 4 and 10 is 39, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].

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For complete question, refer to the attachment.

Formula  [tex]\text { area }=1 / 2 \times \text { base } \times \text { height }=1 / 2 \times 2 \pi r \times r=\pi r^{2}[/tex]  for the circumference of a circle.

Archimedes stated in his Proposition that the area of a circle is equal to the area of a triangle with a base equal to the circumference and a height equal to the radius: (1/2)(r · 2πr) = πr2. Archimedes arrived at his approximation of the circumference of the circle by increasing the number of sides of the hexagon. Archimedes claimed that the area of any circle is equal to the area of a right triangle, where the radius of the circle is represented by one side and the circumference by the other.

Archimedes demonstrated using a similar method that the area of a circle of diameter D is equal to the area of a right-angled triangle with one side equal to the radius and the other to the circumference of the circle on the right angle.

Formula for the circumference of a circle:

A circle's area is equal to pi times the radius squared (A = r2). Discover how to apply this formula to determine a circle's area given its diameter.

The circumference is diameter x pi, or 2 x radius x pi.

[tex]\text { area }=1 / 2 \times \text { base } \times \text { height }=1 / 2 \times 2 \pi r \times r=\pi r^{2}[/tex].

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Option (A) - 4 is the correct answer.

The value of x for linear equation -6x + 4x = 8 is - 4.

If a variable's maximum power constantly equals 1, the equation is considered linear equation. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. Here, A is a coefficient, B is a constant, and x is a variable.

The given equation is -6x + 4x = 8.
Simplifying the above equation.
-2x = 8
Now, dividing both sides by -2.

x = -4
Therefore the value of x in equation -6x + 4x = 8 is -4.

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I understand that the question you are looking for is " Jorge wrote the equation -6x + 4x = 8. What is the value of x?

(A) –4

(B) –2

(C) 2

(D) 4  "

Answer: (A): -4            

Step-by-step explanation:

It's the correct option.

By inverse variation, the electric force between the two particles is 5 newtons when they are 20 centimeters apart.

Herein we should present a statement that represents a real life situation and solve that statement. Here is an example:

In accordance with the Coulomb's law, electric force is inversely proportional to the square of the distance between the two electrically charged particles. If you know that electric force is 20 N when the two particles are 10 cm apart, what is the electric force if the distance is doubled.

Based on the statement, we have the following relationship:

F ∝ 1/r²

Where:

From such relation, we can determine the resulting force by the following equation:

F/20 = 10²/20²

F = 20 × 10²/20²

F = 5 N

By inverse variation, the electric force between the two particles is 5 newtons when they are 20 centimeters apart.

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Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

We kindly invite to check the image attached below to see the representation of the exponential function. This function shows exponential growth.

In this occasion we must plot the graph of exponential functions of the form:

y = a · bˣ     (1)

Where:

First, we need to follow this procedure to create the graph of the curve on Cartesian plane:

Therefore, we build the exponential curve with the help of a graphing tool (i.e. Desmos), whose result is shown in the image attached below.

From (1) we must understand that exponential functions report growth for b > 1 and decay for 0 < b < 1. Thus, the exponential function y = 3ˣ shows exponential growth according to graphical and analytical findings.

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The reason that completes the proof for step 6 is (a) Definition of median

From the graph, point R' to be the midpoint of points M' and O'

Also, points P' and Q' are the midpoints of lines M'N' and N'O', respectively

This means that the three points are the median of the sides of the triangle

The line drawn through the three medians meet at point S

Hence, the reason that completes the proof for step 6 is (a) Definition of median

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Answer: median

Step-by-step explanation:

Use the rules of exponents to simplify the expression.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{g^{5}h^{4} }{g^{2}h^{3} } \end{gathered}$}[/tex]

To divide powers with the same base, subtract the exponent in the denominator from the exponent in the numerator.

Subtract 2 from 5.

Subtract 3 from 4.

For any term t, t¹ =t.

Therefore, the correct option is "B".

Answer:

44

Step-by-step explanation:

x + (22 - 13) = 53

x + 9 = 53

x = 44

Answer:

44

Step-by-step explanation:

x+(22-13)=53

x+22-13=53

x+9=53

x=44

By using Binomial Distribution the probability that exactly 6 workers take the bus to work is 0.001.

When every experiment shares the probability of achieving a given value, the number of trials or observations is summarised using the binomial distribution.

The likelihood of observing a specific percentage of successful occurrences in a specific number of trials is determined by the binomial distribution.

The formula for binomial distribution is-

[tex]P(X=x)={ }^{n} C_{k} p^{k}(1-p)^{n-k}[/tex]

'p' is the probability of success,

(1-p) is probability of failure,

'n' is the number of workers,

'k' is number of given workers.

According to the question,

Calculate the probability of success as;

[tex]p=\frac{15}{100}=0.15[/tex]

The, the probability of the failure becomes;

[tex](1-p)=1-0.15=0.85[/tex]

Put above two value in formula of binomial theorem to get the value.

[tex]{ }^{10} C_{6}(0.15)^{6}(0.85)^{4}=0.001[/tex]

Therefore, the probability that exactly 6 workers take the bus to work is 0.001.

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cos^-1(x) represents the inverse of cos(x).

Answer:

$142.5

Step-by-step explanation:

225-60=165

165/2=82.5

82.5+60=142.5

The measure of ∠6 is 54 degrees.

When parallel lines are cut by a transversal, angle relationship are formed. Therefore,

∠6 = 5x + 9 (vertically opposite angles)

∠6 = ∠2

Hence,

∠2 + 13x + 9 = 180

5x + 9  + 13x + 9 = 180

18x = 162

x = 162 / 18

x = 9

Hence,

∠6 = 5(9) + 9  54°

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The probability expression is [tex]\frac{^{6}C_2}{^{20}C_2}[/tex]

The given parameters are

The total number of people is

n = 20

2 of the 20 people are to be selected.

So, the number of selection is

[tex]n = ^nC_r[/tex]

This gives

[tex]n = ^{20}C_2[/tex]

The expression that represents both students being sophomore is

[tex]n = ^{6}C_2[/tex] --- i.e. 2 students selected from 6

The probability is then represented as:

[tex]\frac{^{6}C_2}{^{20}C_2}[/tex]

Hence, the probability expression is [tex]\frac{^{6}C_2}{^{20}C_2}[/tex]

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Answer:

a

Step-by-step explanation:

edge 2023

Answer:

5

Step-by-step explanation:

6x+4=34

6x=30

x=5

hope this helps <3

Answer:

Math = 97

English = 66

Step-by-step explanation:

Let the score of the Math test be x, and the score of the English text be y

Then we have the two equations

[tex]x+y = 163\\x-y = 31[/tex]

To solve for x and y there are multiple ways, one of the easy ways is just to add the two equations together because that would cancel out the y:

[tex]x + x + y -y = 163 +31\\2x = 194\\x = 97\\[/tex]

Then using the  x, we can find y by doing

[tex]x+y = 163\\97 + y = 163\\(97 + y) - 97 = (163) - 97\\y = 66[/tex]

Therefore, we have a math score of 97, and an English score of 66.

Answer:

1800(5/6)^t

Step-by-step explanation:

I don't see any answer choices, but this would be another form if it is listed. The negative exponent means that you get the reciprocal of the fraction (in this case 1.2). This turns 1.2 into (1/1.2), which is equivalent to 5/6.

The answers are:

Given that:

The perimeter of vegetable plot:

= 4m + 3.5m + 4m + 2m + (3.5 + 2m)

= 19m

Area of vegetable plot:

(1.3 x 5.5) + ( (4 - 1.3) x 3.5)

rounding up to one decimal place = 67.6m²

To know the numbers of meter fence that one can buy, the equation will be:

(perimeter of vegetable plot + the left plot)  - gates.

(19m + (6.5 + 4 + (6.5 - 2) ) )m  - (2.5ft x 2)

= 19m + 15m - 1.5424m

=32.476

=32.5m

Therefore, the answers are:

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In order to determine the number of different groups of three players that are possible for Coach Bennet to select from, we would use a mathematical model referred to as combination.

Mathematically, combination is given by this mathematical equation:

[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]

Where:

Substituting the given parameters into the formula, we have;

Number of groups = (⁶C₃ × ⁸C₀) + (⁶C₂ × ⁸C₁) + (⁶C₁ × ⁸C₂) + (⁶C₀ × ⁸C₃)

Number of groups = 20 + 120 + 168 + 56

Number of groups = 364 different groups.

Therefore, there are 364 different groups of three players possible for Coach Bennet to select.

In conclusion, we can infer and logically deduce that this is a combination because the order in which the players are selected isn't important.

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Complete Question:

In this activity, you will apply your understanding of permutations and combinations to calculate probabilities. Use the information in this scenario to answer the questions that follow. Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.

How many different groups of three players are possible for Coach Bennet to select?

The cutoffs from the left and right sides of normal distribution at a 95-percent confidence level are 1.96.

The confidence level, which is used in statistics, describes the likelihood that the estimation of a statistical parameter's location in a sample survey is also true for the population.

Confidence levels must be decided upon in advance when surveying since they affect the survey's essential scope and error margin. Confidence intervals of 90, 95, and 99 percent are widely employed in surveys.

If the confidence level were set at 95%, there is a very good likelihood that the population's arithmetic mean, as a statistical number, will fall within the survey's established margins of error.

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The piecewise function is

f(x) = 2, 0 < x ≤ 1/2

f(x) = 2 + 0.7x, x > 1/2

From the question, we have:

Fares = $2.00 ⇒ up to (and including) 1/2 miles

Fares = $0.70 increment ⇒ greater than 1/2 miles

Let x represent the number of miles, and f(x) the fares.

So, we have:

f(x) = 2, 0 < x ≤ 1/2

f(x) = 2 + 0.7x, x > 1/2

The above represents the piecewise function

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Answer:

See below

Step-by-step explanation:

y = -6x^2 + 24x-100

solve for 'x'

y + 100 =   -6x^2 + 24x   = -6(x^2-4x)    complete the square for x

(y+100) /(-6 ) =    (x-2)^2 -4                     add 4 to both sides

(y+100)/(-6) +4   = (x-2)^2                       sqrt both sides

sqrt [  ( y+100)/(-6) + 4  ]  + 2 = x           change  x and y

y = ± sqrt [ (x+100)/(-6) + 4 ] + 2            simplify (if needed)

y  = ± sqrt( -x/6 -12.666)  + 2

Answer:

75%

Step-by-step explanation:

The number of angles that are alternate exterior with angle 5 is one, which is angle 11.

Alternate exterior angles are formed on the outside of the two parallel lines that are intersected by a transversal, each being located on the opposite side of the transversal.

The alternate exterior angle pairs are two angles that are supplementary. This means they add up to give a sum of 180 degrees.

Considering transversal s and parallel lines t and u, the angle that is an alternate angle to angle 5 is angle 11.

Angle 11 is the only angle that is alternate exterior angles with angle 5. therefore, we can conclude that, the number of angles that are alternate exterior with angle 5 is just 1, which is angle 11.

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Answer:

FP is 70 degrees 35 times 2 so PD is 180 half a turn minus 70 = 110 degrees

Step-by-step explanation: