EACH OF THE GREEN EQUATIONS HAS A
SOLUTION THAT MATCHES THE
SOLUTION OF A BLUE EQUATION.
RECORD THE MATCHING PAIRS OF
EQUATIONS AND THEIR SOLUTIONS IN
THE PURPLE BOX AT THE RIGHT.
A
5(3x-2) = 4(2x + 1)
D
-x + 3 = 2(x + 15)
B
Cards A and
Cards B and
Cards C and
-4x=-(10x+18)
E
-3(x + 4) = 6(-x - 1)
C
f
are true when x =
are true when x=
are true when x =
2.5x = 5(4x+12)
4x-20= -2(-3x+22)

The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.

In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.

The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.

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The probability that a child chosen at random from the class has both a cat and a dog is 1/10.

Suppose b is the total number of kids that have both:

• children having a cat Only must be 14 - b

• children having a dog Only must be 19 - b

We also get:

We also know there are 30 kids, therefore

⇒ (14 - b) + b + (19 - b) = 30

⇒ 33 - b = 30

⇒ b = 3

Consequently, we now understand:

3/30 = 1/10

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Answer: 3a2b2+3a2b−6ab2+3ab

Step-by-step explanation:By simplifying,

6ab+2a2b+5a2b2−3ab−6ab2+a2b−2a2b2

= 3a2b2+3a2b−6ab2+3ab

Hope this help's You

David's speed in still water 2 mile per hour , using downstream and upstream concept in river .

What is downstream and upstream in river?

Downstream : Towards the river where flow ends

In this river speed get added in rowing boat speed.

Upstream : Opposite to the flow of river

In this river speed gets subtracted from rowing boat speed.

In given que , one time boat is rowed by David in upstream and got back to original place i.e. case of downstream.

Speed of river = 1mile per hour

Let speed of David = x mile per hour.

Total time taken = 4 hour

As we know time = total distance / speed

Total distance covered by David = 3+3 = 6 miles

In upstream speed = x-1

In downstream speed = x+1

So, time = 3/(x-1 )+ 3/(x+1)

            4/3 = 1/x-1  + 1/x+1

Solving this we get,

2x^2 - 3x - 2 = 0

Solution for this eq will be

x  = 2, -1/2

But speed can't be negative.

So, x= 2mile per hour.

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Answer:

LOL

Step-by-step explanation:

On solving the provided question we can say that - as the probability the result will be either a red- or green-colorblind individual.

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1.

In the US, there are more males than women who are colorblind to red and green  = 0.07adults

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The distance from point A(−9,−3) to the line y = x−6 is 8.5 units

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

step 1

Find the slope of the perpendicular line to the given line

y=x-6 ---> given line

The slope is m=1

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

m1*m2 = -1

we have

m1=1

substitute

(1)*m2 = -1

so

m2 = -1

step 2

Find the equation of the perpendicular line to the given line

The equation in point slope form is

y-y1=m(x-x1)

we have

m=-1

(x1,y1)=(−9,−3)

substitute

y+3=-1(x+9)--> equation in point slope form

y+3= -x-9

y= -x-12---> equation in slope intercept form

step 3

Find the intersection point between the given line and the perpendicular line to the given line

we have the system of equations

y = x−6.

y= -x-12

Solve the system by graphing

The intersection point is (-3,-9)

see the attached figure

step 4

we know that

The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6

the formula to calculate the distance between two points is equal to

d=√[(y2-y1)² + (x2-x1)²]

substitute the values

d=√[(-9+3)² + (-3+9)²]

d= √72 units

simplify

d= 6√2 = 8.5 units

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The rate of change in the profit for the five months earned by the given small business is $2750.

The rate of change explains the relationship between two quantities.

Consider two quantities such profit and time in a small business.

Then, the rate of change in the profit is calculated by the ratio of change in the profit for the particular period to the time. I.e.,

rate of change in the profit = (change in the profit)/time

or

r = (p2 - p1)/(t2 - t1)

Where p1 is the profit gained at time t1 and p2 is the profit gained at time t2.

Given that, a small business earns a profit of $6500 in January (the first month of the year) and $17,500 in May (the fifth month of the year).

So, here p1 = $6500; p2 = $17,500; t1 = 1; and t2 = 5

Then, the rate of change in the profit for this period is

r = (17,500 - 6500)/(5 - 1)

 = 11000/4

 = 2750

Therefore, the rate of change in the profit for the five months is $2750.

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The months when both of these plans would pay off the same amout of money for the new phone is 8 months.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario

Let the number of months be x

You can pay a one-time charge of 200$ and then an additional $15 per month. This will be 200 + 15x. The second option is not paying any money at this time and having a monthly bill of 40$ a month. This will be 40x.

The equation will be

200 + 15x = 40x

Collect like terms

40x - 15x = 200

25x = 200

Divide

x = 200/25

x = 8

The number of months is 8.

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When testing individual cofficients of a Multiple regression model, i.e y = β + β₁x₁ + β₂x₂ + ---+βₖxₖ + ε where β , β₁ , --- , βₖ are regression cofficients

the sampling distribution is tested by hypothesis testing.

Testing the Regression Coefficients:

An individual regression coefficient, if we want to test if there is a relationship between the dependent variable and the independent variable.

for the test and identify the significance level α.

The p-value is the sum of the area in the tails of the t -distribution. The t-score and degrees of freedom are t , df = n−k−1

Compare the p-value to the significance level and state the outcome of the test:

The results of the sample data are significant. There is sufficient evidence to conclude that the null hypothesis H₀ is an incorrect belief and that the alternative hypothesis. Hₐ is most likely correct.

The results of the sample data are not significant. There is not sufficient evidence to conclude that the alternative hypothesis Hₐ may be correct.

Write down a concluding sentence specific to the context of the question.

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The inverse function of f(x) = 4x + 12 is [tex]f^{-1}(x) = \frac{x}{4}-3[/tex] .

Option (A) is correct.

What is the inverse of a function?

The inverse of a function is a new function that "undoes" the original function. If f(x) is a function that takes in an input x and produces an output y, then the inverse function denoted as [tex]f^{-1}(x)[/tex], takes in an input y and produces an output x.

The inverse function of f(x) = 4x + 12 is denoted as [tex]f^{-1}(x)[/tex]. To find the inverse function, we can follow these steps:

Replace f(x) with y.

Interchange x and y.

Solve for y.

Following these steps, we get:

y = 4x + 12

x = 4y + 12

x - 12 = 4y

y = (x - 12)/4

Hence, the inverse function of f(x) = 4x + 12 is [tex]f^{-1}(x) = \frac{(x - 12)}{4}[/tex] = (x/4) - 3

Option (A) is correct.

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The value of 0.88 in the exponential function p(x) = 8500(0.88)ˣ is the rate of growth

An exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form

f(x) = aˣ

In the exponential function given;

p(x) = 8500(0.88)ˣ

Where;

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Gravitational potential energy depends on which two of the following weight and height.

The energy that an object can possess or acquire when its position changes as a result of a gravitational field is known as gravitational potential energy. The energy connected to gravity or gravity is what is known as gravitational potential energy.

The motion, position, and deformation of an object can all contribute to its energy storage. Gravity affects you constantly on Earth. There is a latent (stored) energy present in everyone on Earth's surface. the gravitational potential energy of this.

Answer is - The gravitational potential energy of an object depends upon its weight and height.

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The correct question is -

What two things does gravitational potential energy depend on?

Answer:

Step-by-step explanation:

balls

The final coordinates of the vertices of quadrilateral A'B'C'D';

A''(12, 9)

B''(16, 2)

C''(12, -2)

D''(13, 2)

The coordinates of the quadrilateral ABCD are;

A(-3, 4)

B(-7, -3)

C(-3, -7)

D(-4, -3)

Now, the first sequence of transformation is reflection across the y-axis. Now, the transformation rule for reflection across the y-axis is;

(x, y) → (−x, y) .

Thus, we now have;

A'(3, 4)

B'(7, -3)

C'(3, -7)

D'(4, -3)

It is now translated 9 units left and as such the transformation rule is;

((x + 9), y)

We now have;

A'(12, 4)

B'(16, -3)

C'(12, -7)

D'(13, -3)

It is now translated 5 units up and as such, the final coordinates are;

A''(12, 9)

B''(16, 2)

C''(12, -2)

D''(13, 2)

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Answer:

[tex]\left[\begin{array}{cc}x&y\\1&5\\2&7\\3&9\end{array}\right][/tex]

Step-by-step explanation:

Note that f(x) is typically used in replacement of y. So in reality, to make the question simple to understand, we will replace f(x) with y.

y = 2x + 3

Remember to follow PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

You are finding a table of value, which results in something similar to:

[tex]\left[\begin{array}{cc}x&y\\1&5\\2&7\\3&9\end{array}\right][/tex]

Proof 1:

Plug in 1 for x in the given equation:

y = 2x + 3

y = 2(1) + 3

y = 2 + 3

y = 5

Proof 2:

Plug in 2 for x in the given equation:

y = 2x + 3

y = 2(2) + 3

y = 4 + 3

y = 7

Proof 3:

Plug in 3 for x in the given equation:

y = 2(3) + 3

y = 6 + 3

y = 9

~

Do this for as much values as you need.

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Answer:

180

Step-by-step explanation:

xdcjuggggggggggggggggggggg

Answer:

75.

Step-by-step explanation:

We need to divide 375 by 5 since we are looking for 5 times a number. This will give us the answer, 75.

Answer:

75.

Step-by-step explanation:

We need to divide 375 by 5 since we are looking for 5 times a number. so the answer is 75

The amounts in each mutual fund are $500 and $1800. By using a system of equations, the required values are evaluated.

It is given that, an investor invested $2300 in two mutual funds.

Consider the amount invested in two mutual funds as fund1 = x and fund2 = y.

So, we can write the equation for the total investment is

x + y = 2300 ...(1)

The percentage of profit earned from the fund1 = 6% = 0.06

The percentage of profit earned from the fund2 = 4% = 0.04

The total profit for the investor = $102

Then, the equation from this statement is

0.06x + 0.04y = 102 ...(2)

Then the system of equations is

x + y = 2300 ...(1)

0.06x + 0.04y = 102 ...(2)

Applying the substitution method to solve the obtained system of equations.

So, from (1), we can write x = 2300 - y

Then, equation (2) becomes

0.06(2300 - y) + 0.04y = 102

⇒ 6(2300 - y) + 4y = 10200

⇒ 13800 - 6y + 4y = 10200

⇒ 13800 - 2y = 10200

⇒ 2y = 13800 - 10200 = 3600

∴ y = 3600/2 = $1800

So, the value of x is x = 2300 - 1800 = $500

Thus, the amount of investment in two mutual funds is $500 and $1800.

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Answer:

since a || b

<A = <ABb = 60°

in a triangle the sum of all angles is 180°

so,

30 + 60 + x = 180

x= 180-90

x= 90

The happening in the graph is that the speed of the roller skater increases and decreases with time

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

The graph

On the graph, we have the following axes

x-axis = Time

y-axis = Speed

The x-axis is continually increasing while the y-axis decreases and increases (as in a sine function)

This means that the speed increases and decreases with time

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Answer:

5.5 hours

Step-by-step explanation:

6, 12, 18

20, 18, 16, 14, 12, 10, 8, 6, 4, 2

Option D. parallelogram is the correct option of the given statement.

The parallelogram is a quadrilateral with two sets of opposing sides that are equally and parallel. The opposing angles are also equal in magnitude.

Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional shape. Concave and convex are the two most common forms. Additionally, there are numerous subgroups of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombus, and squares.

The significance of quadrilaterals Creating floor plans for new buildings, as well as engineering and designing buildings and spaces, all rely on the properties and mathematical rules regulating the geometric shape known as a quadrilateral.

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Theoretical centre-to-centre distance (C)=3.25 which is the distance between the centers of the pinion and gear

Given data:

No. of teeth on the pinion(TP)=17.

Diametral pitch(pd)=8 teeth/in.

The rotational speed of the pinion(NP)=1120 rev/min or 1120 rpm.

The rotational speed of the gear(NG)=544 rev/min or 544 rpm.

To calculate:

No. of teeth on gear(TG) & theoretical centre-to-centre distance(C).

We know that;

Diametral pitch(pd)=No. of teeth in the gear/Diameter of the gear

For pinion,

pd=TP/DP

Pittiong the values in above eq.

8 teeth/in =17/DP =>DP=17/8 in.

or DP=2.125 in.

Gear ratio(G)=(NP/NG)=(TG/TP)=(DG/DP)

(NP/NG)=(TG/TP)

1120/544 =TG/17 =>TG=35

therefore No. of teeth the gear(TG)=35 {Ans}

Also from gear ratio formula,

(NP/NG)=(DG/DP)

1120/544=DG/2.125

DG=4.375 in.

In figure I have drawn a rough diagram of the pinion and gear arrangement which will help you to understand how to calculate the centre-to-centre distance(C)

From fig.,

centre to centre distance,C=rP+rG {Where rP and rG are the radii of pinion and gear respectively}

C=(DP+DG)/2 {\large \because Diameter =2*radius}

C=(2.125+4.375)/2 in. =3.25 in.

therefore Theoretical centre to centre distance (C)=3.25

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Answer: 25 dogs

Step-by-step explanation:

We know that every 4 cats will be with 5 dogs

So

First, take 20 divided by 4 = 5

Then take 5 times 5 = 25 dogs

The rewritten summation is [tex]\sum_{m=1}^{n}m(m+1)+(n+1)(n+2)[/tex].

A recursive function is a function that calculates subsequent terms by repeating or using its own prior terms, creating a succession of terms. By definition, the recursive function can be used to write the summation by separating the final term of the summation and adding a final term to the summation.

Given, the function is [tex]\sum_{m=1}^{n+1}m(m+1)[/tex].

First, we have to separate the final term from the given summation. The final term is m = n+1 which is present above the summation. For this replace the n+1 with n.

Then, add the term m(m+1) with m in the given summation replaced by n+1.

The new summation is rewritten as,

[tex]\begin{aligned}\sum_{m=1}^{n+1}&=\sum_{m=1}^{n}m(m+1)+(n+1)((n+1)+1)\\&=\sum_{m=1}^{n}m(m+1)+(n+1)(n+2)\end{aligned}[/tex]

The new summation is rewritten.

The complete question is -

Rewrite by separating off the final term [tex]\sum_{m=1}^{n+1}m(m+1)[/tex]

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A university surveys its student-athletes about their experience in college sports. The survey only includes student-athletes with scholarships. This is an example of sampling bias.

In the field of statistics, sampling bias is a type of bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of the population where all individuals, or instances, were not equally likely to have been selected. If this is not corrected, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling. Here as the sample of the survey only includes the student athletes with scholarship, it becomes biased.

Therefore, sampling bias is the type of bias when a university surveys its student-athletes about their experience in college sports. the survey only includes student-athletes with scholarships.

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The required mean as calculated from the given data is 13.

To calculate the mean x + y

mean of x + mean of y

= 5 + 8

=13

In addition to the mode and median, the mean is one of the measurements of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.

The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the

Standard Deviation

The indicator of dispersion is the standard deviation. It denotes how widely apart the data values are from the mean value.

Formula: σ=∑i=1nxi-μ2n

NOTE :

Complete question:

A random variable X has a mean of 5 and a st. dev of 0.40. A random variable Y has a mean of 8 and a st. dev of 0.60. If both are independent, what is the mean of X + Y?

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Answer:

  see the attachment

Step-by-step explanation:

You want graphs of f(x -5) and f(x)+2 and their asymptotes, given exponential function f(x).

The subtraction of 5 from the argument x causes the graph to be shifted to the right 5 units. The horizontal asymptote at y=0 is unchanged.

The addition of 2 to every function value causes the graph to be shifted up 2 units. The horizontal asymptote is likewise shifted up 2 units to y=2.

The red and blue graphs are attached. The asymptotes are dashed lines.

[tex]\displaystyle\\\\ Answer: A=\frac{2P}{xV^3}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\P=\frac{1}{2} xAV^3\\[/tex]

Multiply both parts of the equation by 2:

[tex]2P=xAV^3[/tex]

Divide both parts of the equation by xV³:

[tex]\displaystyle\\\frac{2P}{xV^3} =A[/tex]

[tex]\displaystyle\\\\Thus,\ A=\frac{2P}{xV^3}[/tex]