what is 4 × 10^2 in scientific notation?​

Answer:

First Graph: h(x) = 0.5x^2

Second Graph: f(x) = -2x^2

Third Graph: j(x) = 2x^2

Fourth Graph: g(x) = -x^2

Step-by-step explanation:

First Graph and the Third Graph both open upwards thus we know the coefficient will be positive. Using the point (2,2) as a guide on the first graph, we can see that the best option to fit the first graph would be \(h(x) = 0.5x^2\) as \(h(2) = 0.5 (2)^2 = 0.5(4) = 2\). From process of elimination, we can see that the third graph will be \(j(x) = 2x^2\). Another way to determine this is by looking at the shape of the curves. The first graph opens "wider" thus meaning the coefficient will be smaller.

Second Graph and the Fourth Graph both open downwards thus we know the coefficient will be negative. We only have the options of \(f(x) = -2x^2\) and \(g(x) = -x^2\). We can see that the fourth graph opens "wider" so the coefficient will be smaller thus second graph will be f(x) = -2x^2  and the fourth graph will be g(x) = -x^2. Another way to determine this is by checking a point on a graph. On the fourth graph, there is the point (-2,4). This matches with the equation as \(g(-2) = -x^2 = -(-2)^2 = -4\).

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Answer:

The answer is 277

Step-by-step explanation:

25 x 5 = 125 (Big rectangle)

25 - 12 = 13 (Small Rectangle)

6 x 8 = 48 (Both triangles)

Put together = 277

Answer:

Therefore any set of data that satisfies the 5-Number summary: 16,18,22,26 and 28 can be represented with the box plot.

Step-by-step explanation:

Interpreting Box Plots

We use a box plot to present the 5-Number summary of a set of data.

The values contained in the 5-Number summary are:

In the box plot, the following rules apply:

Using these, we interpret the given box plot

A left whisker extends from 16 to 18, therefore:

The box extends from 18 to 26 and is divided into 2 parts by a vertical line segment at 22.

The right whisker extends from 26 to 28.

Therefore any set of data that satisfies the 5-Number summary: 16,18,22,26 and 28 can be represented with the box plot.

Box plot has boxes with some lines ( called whiskers ).

Box plot on the graphical level tells about 5 points:

There is starting whisker or left whisker denoting point minimum (Q0) and extends from there the line to Q1 ( first quartile).

Then the box starts which starts from Q1 and touched Q3. In the middle it passes through Q2 ( The median of the data ), and thus has a line in it.

At last, there is end whisker or right whisker denoting end quantile or Q4 (the maximum point).

Given data:

Left whisker extends from 16 to 18.

     Thus Q0 = 16

              Q1 = 18

Box plot starts from 18 and extends to 26, and is split by a vertical line segment at 22.

    Thus Q2 = 22

             Q3 = 26

The right whisker or end whisker extends from 26 to 28

    Thus Q4 = 28.

Thus the description of data is given as:

\(Q_0 = Minimum = 16\\Q_1 = First\: quartile = 18\\Q_2 = Second \:quartile = Median= 22\\Q_3 = Third\: quartile = 26\\Q_4 = Maximum = 28\\\)

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Answer:

4.)

Radius: 2.4cm

Diameter: 4.8cm

Circumference: 15.072cm

5.)

Radius: 3.5cm

Diameter: 7cm

Circumference: 21.98cm

6.)

Radius: 7cm

Diameter: 14cm

Circumference: 43.96cm

Step-by-step explanation:

Radius: \(d\) ÷ \(2\)

Circumference: \(d\) × \(\pi\) or \(2\) × \(\pi\) × \(r\)

Have a great day <3

Answer:

3rd

Step-by-step explanation:

Y=1/2x+3

Answer:

\(y=3cos(\frac{1}{2} (x+}225)+4\)   phase shift in degrees

\(y=3cos(\frac{1}{2} (x+\frac{5\pi }{4}))+4\)   phase shift in pi radians

Step-by-step explanation:

Here is the equation for the graph of the cosine function.

y = A sin(B(x + C)) + D

A = amplitude

period is 2π/B

C = phase shift

D = vertical shift

Lets convert 1800° to Pi radians.

\(1800*\frac{\pi }{180}\)

\(180(10)*\frac{\pi }{180}\)

\(10*\frac{\pi }{180}\)

\(10\pi\) radians

A = 3

B=2π/ 10π  simplifies to \(\frac{1}{2}\)

C = phase shift

D = 4

\(y=3cos(\frac{1}{2} (x+}225)+4\)   phase shift in degrees

\(y=3cos(\frac{1}{2} (x+\frac{5\pi }{4}))+4\)   phase shift in pi radians

Answer:

x la 2

Step-by-step explanation:

when we multiply with powers the powers gather

Answer:

10

Step-by-step explanation:

\(7.2\\+\\2.8\\--\\10\)

10 is an integer, there is no way to express it in decimal form.

Answer: 10

Step-by-step explanation:

2.8+7.2=10

yup

The region of the solutions to the system is (d) Region B

From the question, we have the following parameters that can be used in our computation:

The graph

This point of intersection of the lines of the graph represent the solution to the system graphed

From the graph, we have the intersection point to be

(x, y) = (2, 3)

This is located in region B and it means that

x = 2 and y = 3

Hence, the region of the solutions to the system is (d) Region B

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Answer:

x = -4, -2

Step-by-step explanation:

Key skills needed: Quadratics, Factoring, Solving for Roots

1) We are given : \(x^2 + 6x + 8 = 0\) and we need to solve for the roots.

2) You have to factor.

You need to find what factors of 8 add up to 6.

The factors of 8 are --> 1,2,4,8

The 2 factors that add up to 6 and multiply to equal 8 are --> 2 & 4

3) This means it would become ---> \((x+4)(x+2) = 0\).

4) Set x + 4 = 0 and get x = -4 as one root

Set x + 2 = 0 and get x = -2 as another root.

The 2 roots are -4, and -2

Hope you understood and have a nice day!! :D

To test the hypothesis of mean differences in artificially sweetened drink consumption among BMI groups, assuming a normal distribution, the researcher might use a one-way ANOVA.

The one-way ANOVA compares the means of three or more independent groups and determines if there are statistically significant differences among them. In this case, the BMI groups (normal weight, overweight, and obese) represent the independent groups, and the number of artificially sweetened drinks consumed is the dependent variable. By conducting a one-way ANOVA, the researcher can assess if there are significant differences in mean consumption among the BMI groups and draw conclusions regarding their hypothesis.

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The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

Answer:

c. (1, -7).

Step-by-step explanation:

Substitute the given values to see which set fits:

y = -11x + 4

Try (0, -7):

-11(0) + 4  = 4 . Not this one as we are looking for the result -7.

Try (-1, -7):

-11(-1) + 4  = 11+4 = 15.   Not this one as we are looking for the result -7.

Try (1, -7):

-11(1) + 4  = -11+4 = -7.  This is correct.  

Answer: 10 dollars per week

Step-by-step explanation:

To get 40 dollars in 5 weeks you would need to get 8 dollars each week. If Andre donates 2 dollars to the food bank each week he would get 2 dollars subtracted each week so his neighbor would have to pay him 10 dollars because he needs 8 dollars per week and the food bank donation takes away 2 dollars per week.

Answer:

37.8 metre

Step-by-step explanation:

CHECK THE COMPLETE QUESTION BELOW;

Linda shoots an arrow at a target in an archery competition. The arc of the arrow can be modeled by the equation y= -0.02x to the power of 2 + 0.65+4 where x is the horizontal distance (in meters) from Linda and y is the height (in meters) of the arrow. How far from Linda does the arrow hit the ground? Round to the nearest tenth.

From the question, we are told that the equation that modelled the arc is

y=-0.02x²+0.65x+4

From the question, "x" in the equation=

the horizontal distance (in meters

While "y" in the equation = the height (in meters) of the arrow.

We can find the value of x and y by equating to zero(since arrow hits the ground when its height (y) is zero) then solve the quadratic equation using quadratic formula

y=-0.02x²+0.65x+4=0

We have, x=37.79 or -5.29

The negative x= -5.29 can be described as been at the back of Linda,

But the distance is of positive value, therefore, the arrow hit the ground at 37.8 metre from Linda after Rounded to the nearest tenth.

Answer:

here

Step-by-step explanation:

find the circumference of the lid (this is like a side length of a rectangle)

2*pi*2= 12.566in

Then multiply by 3 (the other side length)

12.566*3= 37.7in squared :)

Given, the fraction numerator 5 + 2√3 over denominator 2 + √2.What is the simplified form of the given fraction?Solution:The given fraction is:n = 5 + 2√3d

= 2 + √2Now, to simplify the fraction we need to eliminate the irrational number in the denominator. For that, we need to rationalize the denominator. To do that we need to multiply and divide the denominator by its conjugate. The conjugate of 2 + √2 is 2 - √2.(2 + √2)(2 - √2)

= 22 - 2√2 + 2√2 - (√2 × - √2)

= 4 - 2

= 2We multiply both the numerator and the denominator by 2 - √2.n(2 - √2) = (5 + 2√3)(2 - √2)

= 10 - 5√2 + 4√3 - 2√6d(2 - √2) = (2 + √2)(2 - √2)

= 2 - 2

= 0

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Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

In all these cases, no interaction means that the variables act independently on the response variable Y, and their combined effects are simply additive rather than multiplicative or otherwise interdependent.

No interaction in modeling response variable Y and explanatory variables X and Z means that the effect of each explanatory variable on the response variable is independent of the other explanatory variable. This can be illustrated using graphs or tables as follows:

a. When all variables are continuous (multiple regression), no interaction means that the slope of Y on X is constant regardless of the level of Z, and the slope of Y on Z is constant regardless of the level of X. In other words, the effect of X on Y is the same for all levels of Z, and the effect of Z on Y is the same for all levels of X.

b. When Y and X are continuous, and Z is categorical (analysis of covariance), no interaction means that the mean difference in Y between each level of Z is the same for all levels of X. In other words, the effect of Z on Y is the same for all levels of X.

c. When Y is continuous, and X and Z are categorical (two-way ANOVA), no interaction means that the mean difference in Y between each combination of X and Z is the same. In other words, the effect of X on Y is the same for all levels of Z, and the effect of Z on Y is the same for all levels of X.

d. When Y is binary, and X and Z are categorical (logistic regression), no interaction means that the odds ratio of Y on X is the same for all levels of Z, and the odds ratio of Y on Z is the same for all levels of X. In other words, the effect of X on the odds of Y is the same for all levels of Z, and the effect of Z on the odds of Y is the same for all levels of X.

a. Multiple regression (All variables are continuous): No interaction means that the effect of one explanatory variable (X) on the response variable (Y) does not depend on the value of the other explanatory variable (Z). In a graph, this would be represented by parallel lines or planes when plotting Y against X for different values of Z.

b. Analysis of covariance (Y and X are continuous, Z is categorical): No interaction suggests that the relationship between Y and X is consistent across different levels of the categorical variable Z. In a graph, this would appear as parallel regression lines for each category of Z.

c. Two-way ANOVA (Y is continuous, X and Z are categorical): No interaction means that the effect of one categorical variable (X) on the response variable (Y) is not influenced by the levels of the other categorical variable (Z). In a table, this would be evident by having similar differences between cell means across all combinations of X and Z.

d. Logistic regression (Y is binary, X and Z are categorical): No interaction implies that the odds of the binary response variable (Y) occurring do not depend on the combined effect of X and Z. In a table, the odds ratios for different levels of X and Z should be consistent, indicating no interaction between the two categorical variables.

In all these cases, no interaction means that the variables act independently on the response variable Y, and their combined effects are simply additive rather than multiplicative or otherwise interdependent.

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Answer:

24 ounces butter

20 ounces sugar

28 ounces of flour

12 eggs

8 tsps baking powder

Answer:

Step-by-step explanation:

r=4 m

slant height l=5 m

surface area=πr²+πrl=πr(r+l)=π×4(4+5)=36 π m²≈113.1 m²

We will see that the linear equations are:

Parallel line: x = -9

Perpendicular line: y = 3

Here we have the vertical line:

x = -2

A parallel line to this one will also be vertical, of the form:

x = a

And a perpendicular line to this one will be horizontal, of the form:

y = b

We want the parallel line to pass through (-9, 3)

So our line x = a needs to pass through that point, then:

x = -9

Is the parallel line.

And if the perpendicular line y = b needs to pass through that point, then:

y = 3

Is the perpendicular line.

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1. The base pay Carter makes regardless of computer sales is $100

2. The linear relationship that shows the sales will be P = 100 + 10x

From the information given, Carter is a salesperson who sells computers at an electronics store and he makes a base pay amount each day and then is paid a commission for every computer sale he makes.

The starting salary is $100. This is the base pay.

The commission given is $10 per good sold. Therefore, the expression will be:

= 100 + 10x

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Answer:

id have to see the chart to help you

i can see k which the answer for 19).is (0,-3)

but for 20 id have to see the chart

Step-by-step explanation:

if you add a picture of the chart i can help:)

Answer: 44000

Step-by-step explanation:

From the question, we are informed that the population of Queens increased by 16,075.

Brooklyn's population increased by 11,870 more than the population increase of Queens. This means that Brooklyn's population will be:

= 16075 + 11870

= 27945

The total combined population increase of Queens and Brooklyn from 2010 to 2011 will then be:

= 16075 + 27945

Estimating 16075 gives 16000

Estimating 27945 gives 28000

Adding then together equals

16000 + 28000 = 44000

The pair of systems of equations are not equivalent equations

From the question, we have the following equations that can be used in our computation:

4y+2x=-7 and 2y-6x=8

Rewrite them as

4y + 2x = -7

2y - 6x = 8

Divide the equation 4y + 2x = -7 by 2

So, we have

2y + x = -3.5

By comparing the equations 2y + x = -3.5 and 2y - 6x = 8, we can see that both equations are not the same

This means that the system of equations are not equivalent

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Answer:

\( \frac{7}{15} \)

Step-by-step explanation:

The question is asking us to find the difference between 4/5 and 1/3.

\( \frac{4}{5} - \frac{1}{3} \)

First we have to determine the LCM which is 15.

LCM is obtained by multiplying 5 and 3 from the denominators.

Then proceed as follows

\( \frac{4}{5} - \frac{1}{3} = \frac{12 - 5}{15} \\ = \frac{7}{15} \)

The solution is therefore

\( \frac{7}{15} \)

Answer: D) Groundwater collects only where the soil and geological features allow water to seep down into underground chambers.

In other words, as long as there are gaps to allow water through, then that would lead to underground aquifers. Another important component is the amount of rain water that happens. Sources such as rivers, lakes and streams are also a contributing factor.

Stuff like earthquakes, volcanic activity, and continental movement doesn't really have much an effect on where or how aquifers form. It's really all about the soil type and how the landscape is formed, and of course the other factors mentioned in the previous paragraph.