The function y=f(x) is graphed below. Plot a line segment connecting the the points on f where x=5 and x=7. Use the line segment to determine the average rate of change of the function f(x) on the interval

CM is the perpendicular bisector of AB at M, it means that CM is perpendicular to AB, and AM=BM. Therefore, we have two right triangles, triangle AMC and triangle BMC, with a shared side CM, and AM=BM.

By the Pythagorean theorem, we know that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Applying this to triangles AMC and BMC, we have:

AC² = AM² + CM²

BC² = BM² + CM²

Since AM=BM, we can substitute AM for BM in the second equation, giving:

BC² = AM² + CM²

Since the left-hand sides of these two equations are equal (by the given that CM is the perpendicular bisector of AB), we can set their right-hand sides equal to each other and simplify:

AC² = BC²

Taking the square root of both sides gives us:

AC = BC

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Answer:

e

Step-by-step explanation:

The ratios of\(4\):\(5\) and \(40\):\(3\) are not equal, the initial ratios of \(12\):\(15\) and \(200:15\)are not proportionate.

When two or more numbers or values are compared, the outcome is the ratio, which is expressed as a fraction or a colon. It is used to describe how the relative magnitudes of two or more objects correlate. Ratios can be used to evaluate quantities of the same unit or of different units.

For instance, a ratio of \(3:1\) is used to compare three units to four, while a ratio of \(2:1\) is used to compare two units to one. Ratios can be expressed or simplified in a variety of methods.

The ratio \(6:9\) will become\(2:3\) if both parts are multiplied by\(3\). Ratios can also take the shape of decimals or percentages.

\(12:15 =200:15\)

multiplying both the left side  by\(3\) and right side by \(5\) we get

\(4:5= 40:3\)

Hence it shows that they are not equal so they are not proportionate

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Answer:

It is possible

The numbers are 2,5,8

Step-by-step explanation:

1320/6=220

1350/6=225

1380/6=230

These numbers are all divisible by 6.

The possible digits that would make the number divisible by 6 are 2 , 5 and 8.

We know that any number must be divisible by 6 if the number is an even number and divisible by 3.

Now the given number is 13...0.

Since the last digit is 0, hence it is an even number.

Now for the number divisible by 3, the sum of the digits must be divisible by 3.

let the missing digit be a such that 6 is factor of 13a0

Therefore the number is 13a0.

Sum of the digits = 1+3+a +0 = 4+a

Now the value of a can be 2 then sum is 6, hence divisible.

The value of a can be 5 then sum is 9, hence divisible.

Also the value can be 8 then sum is 12 hence divisible.

Therefore the required complete numbers are :

1320/6=220

1350/6=225

1380/6=230

Hence the required digits are 2,5 and 8.

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\(\\ \rm\Rrightarrow \dfrac{x}{2}=3\)

\(\\ \rm\Rrightarrow x=2(3)\)

\(\\ \rm\Rrightarrow x=6\)

And

\(\\ \rm\Rrightarrow \dfrac{y}{2}+1=3\)

\(\\ \rm\Rrightarrow \dfrac{y}{2}=3-1=2\)

\(\\ \rm\Rrightarrow y=2(2)\)

\(\\ \rm\Rrightarrow y=4\)

Answer:

x=6 y=4

Step-by-step explanation:

Equating corresponding terms , we get

x/2=3

or, x=6

Also,

y/2+1=3

or, (y+2/2)=3

or, y+2=6

or, y=6-2

y=4

Therefore, x=6 and y=4.

Answer:

Jack's fathers work is 1350 miles away from home

Step-by-step explanation:

Equation for trip 1:

Usual speed=x

Time=30 minutes

Formula for distance: d=st

d=30x

Equation for trip 2:

Speed= x-30

Time=90 minutes

d=90(x-30)

Now we solve for x using simultaneous equations:

30x=90(x-30)

x=45

Now to find d we sub in our new found value into one of the two equations (it doesn't matter which one)

d=30(45)

d=1350 miles

Answer:

1/4

Step-by-step explanation:

Coin 2 sides, 1/2 chance to get heads.

Spinner 10 numbers, 5 even, 1/2 change to get even.

1/2x1/2

1/4

Answer:

4 hours to paint all 4 of walls

Step-by-step explanation:

well is it takes her 20 minutes to paint 1/3 of a wall and there is 4 walls to 1/3 on each it would take her 20 minutes for 1/12(total of 4 walls) you would do 20x12 which is 240 then divided by 60 which is 4 so the answer is 4.

Answer:

x = 144

Step-by-step explanation:

3/4x + 24 = x - 12

3/4x - x = -12 - 24

3/4x - 4/4x = -36

-1/4x = -36

x = -36/-1/4

x = 144

Answer:

186

Step-by-step explanation:

math

Answer:

x = 46°

Step-by-step explanation:

64° + 70° + x = 180°

x = 180° - 64° - 70°

x = 46°

After doing the equitation the at rate of $15 per week.

How to do graph representation?

Graph representation is a way of visualizing data as a graph or chart. It is used to easily identify relationships between data points and to illustrate trends in the data. Graphs can be used to present data in a variety of ways, such as bar graphs, line graphs, pie charts, scatter plots and more. Graphs are especially useful when trying to compare two or more sets of data and to highlight any patterns or trends that may exist. Additionally, graphs are often used to represent numerical data in a more visually appealing way. By using graphs, it is easier to identify relationships, trends and outliers in the data. Graphs also help to make data easier to interpret and understand.

Carson owes = $110

At rate of $15 per week.

The graph representation will follows:

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The completing square form of the equation is  \((x+1)^2=-25\).

What is completing square method?

By altering the equation's form so that the left side is a perfect square trinomial, a quadratic equation can be solved using the "Completing the Square" approach. One approach to locating the roots of the given quadratic equation is to complete the square method.

Here the equation \(x^2+2x=-26\)

To completing the square of the equation add 1 on both sides then,

=> \(x^2+2x+1=-26+1\)

=> \(x^2+2.x.1+1^2=-25\)

=> \((x+1)^2=-25\)

Hence the completing square of the equation is  \((x+1)^2=-25\).

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Answer:

Step-by-step explanation:

No, this is not correct.

Step 1: Find the directional distance from every vertex on the blue image to  the center, Point C.

Point A is 1 unit left and 4 units upwards to Point C.

Point B is 4 units right and 5 units upwards to Point C.

Point C is the center of the dilation, so that point will not change.

Step 2: Apply the scale factor to the directional distances to know the distances of the new images.

The scale factor is 2 so

Point A' should be 2 units left and 8 units upwards to Point C.

Point B' should 8 units right and 10 units upwards to Point C.

Step 3:  Move the point in respect to Point C.

The new image should have the these points.

One point that is 2 units left and 8 units upwards to Point C.

Another point that is Point B' should 8 units right and 10 units upwards to Point C.

One point that coincides  with  Point C.

Answer:

C = 9.5 + 1.25t

Step-by-step explanation:

C = 9.5 + 1.25t

16 = 9.5 + 1.25t

6.5 = 1.25t

6.5/1.25 = t

5.2 = t

you cant have 0.2 toppings so 5 is the max number of toppings Jonas can have

Answer:

Approximately \(12.9\; \rm km \cdot h^{-1}\), assuming that this orbit is circular.

Step-by-step explanation:

The question is asking for a tangential velocity with the unit \(\rm km \cdot h^{-1}\). The unit of the given distance is already in \(\rm km\) as required. Convert the unit of the orbital period to hours:

\(\begin{aligned}T &= 1230\; \text{day} \times \frac{24\; \rm h}{1\; \text{day}}. = 29520\; \rm h\end{aligned}\).

Calculate the angular velocity \(\omega\) of this planet from its orbital period:

\(\begin{aligned}\omega &= \frac{2\, \pi}{T} \\ &= \frac{2\, \pi}{29520\; \rm h} \approx 2.1285 \times 10^{-4}\; \rm h^{-1}\end{aligned}\).

Given the radius \(r\) of the orbit of this planet, the tangential velocity \(v_{\perp}\) of this planet would be:

\(\begin{aligned}v_{\perp} &= \omega\, r \\ &\approx 2.1285 \times 10^{-4}\; \rm h^{-1} \times 2.22\times 10^{7}\; \rm km \\ &\approx 4.73 \times 10^{3}\; \rm km \cdot h^{-1}\end{aligned}\).

If the orbit of this planet is circular, the velocity of the planet would be equal to its tangential velocity: \(4.73\times 10^{3}\; \rm km \cdot h^{-1}\).

The propagated error in computing the volume of the cube is estimated to be 0.50 inch3, and the propagated error in computing the surface area of the cube is estimated to be 0.28 inch2, both rounded to two decimal places.

(a) Volume of the cube

= (17 inches + 0.02 inch)3

= 17.02 inches3

Propagated error

= (17.02 inches3 - 17 inches3)

= 0.02 inch3

(b) Surface area of the cube

= 6(17 inches + 0.02 inch)2

= 617.04 inches2

Propagated error

= (617.04 inches2 - 617 inches2)

= 0.04 inch2

The edge of the cube is measured to be 17 inches, with a possible error of 0.02 inch. By using differentials, the propagated error in computing the volume of the cube is estimated to be 0.02 inch3, and the propagated error in computing the surface area of the cube is estimated to be 0.04 inch2. Both of these errors were rounded to two decimal places, resulting in a propagated error in computing the volume of the cube being 0.50 inch3, and the propagated error in computing the surface area of the cube being 0.28 inch2.

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Answer:

1.  20 tins of milk

2.  Weight of the Carton = 8,4kg ot 8400g

Step-by-step explanation:

Given

Volume of a Tin = 77cm³

Weight of a tin = 5000g

Volume of Empty Carton = 1540cm³

Weight of Empty Carton = 5000g

Calculating the number of tins of milk

To do this, we have to make use of the given volumes;

And this is done as follows;

\(Number = \frac{Volume\ of\ Empty\ Carton}{Volume\ of\ a\ Tin}\)

Substitute  77cm³ for Volume of a Tin and 1540cm³ for Volume of an Empty Carton

\(Number = \frac{1540cm^3}{77cm^3}\)

\(Number = 20\)

Hence, 20 tins of milk will filled the empty carton

Calculating the weight of the Carton after filled with tins of milk

This is calculated as thus;

Total Weight = Weight of Empty Carton + Weight of Tins of Milk

Substitute 5000g for Weight of Empty Carton

Total Weight = 5000g + Weight of Tins of Milk

_________________________________________

Calculating Weight of Tins of Milk

Since 20 tins of milk will fill the empty carton, the

Weight of Tins of Milk = 20 * Weight of 1 Tin of Milk

Weight of Tins of Milk = 20 * 170g

Weight of Tins of Milk = 3400g

_________________________________________

Substitute 3400g for Weight of Tins of Milk

\(Total\ Weight = 5000g + 3400g\)

\(Total\ Weight = 8400g\)

In Kilograms:

\(Total\ Weight = 8.4kg\)

The interval for the inequality is (5, ∞].

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

-11m <= -55

Now, solving the inequality

-11m ≤ -55

Divide both side by 11

-11m/ 11 ≤ -55/ 11

-m ≤ -5

m≥ 5

Hence, the interval for the inequality is (5, ∞]

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Answer:

Lilly

Step-by-step explanation:

According to the literature, the length of a medium grain rice is between 5.3 and 5.9 mm. Let's take the average (5.6 mm) and convert it to meters to compare it with the estimations. We will use the conversion factor 1 m = 1000 mm.

5.6 mm × 1 m/1000 mm = 5.6 × 10⁻³ m

Jack answered 4.5 × 10⁻³ kilometers. We will convert it to meters using the conversion factor 1 km = 1000 m.

4.5 × 10⁻³ km × 1000 m/1 km = 4.5 m

Lilly answered 4.5 × 10⁻³ meters.

Diego answered 4.5 × 10⁻³ centimeters. We will convert it to meters using the conversion factor 1 m = 100 cm.

4.5 × 10⁻³ cm × 1 m/100 cm = 4.5 × 10⁻⁵ m

Willa answered 4.5 × 10⁻³ millimeters. We will convert it to meters using the conversion factor 1 m = 1000 mm.

4.5 × 10⁻³ mm × 1 m/1000 mm = 4.5 × 10⁻⁶ m

As we can see, Lilly gave the best answer (same order of magnitude).

The average user spends approximately $3.65 per year on toothpaste.

To determine whether US retail toothpaste demand looks like a D, we need to understand what a D-shaped demand curve represents. A D-shaped demand curve is characterized by a small number of consumers who are willing to pay a high price for a product, while the majority of consumers are only willing to pay a low price. This type of demand curve is often seen in luxury goods or products with high status value.

In the case of toothpaste, it is unlikely that the demand curve would be D-shaped. This is because toothpaste is a necessity item that is used by the vast majority of Americans on a daily basis.

According to the given information, 90% of Americans use an average of 0.5 grams per day, indicating that there is a large and consistent demand for toothpaste.

To estimate how much the average user spends on toothpaste per year, we can use the following formula:

Annual toothpaste expenditure = (Daily usage in grams) x (Price per gram) x (Days in a year)

Assuming an average price of $0.02 per gram of toothpaste, the annual expenditure for an individual who uses 0.5 grams per day would be:

Annual toothpaste expenditure = (0.5 g/day) x ($0.02/g) x (365 days/year) = $3.65

Therefore, the average user spends approximately $3.65 per year on toothpaste.

In conclusion, based on the fact that toothpaste is a necessity item with consistent and widespread usage among Americans, it is unlikely that US retail toothpaste demand looks like a D.

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This statement is True. In the null hypothesis will be rejected in favor of the alternative hypothesis only if sample evidence suggests that h0.

A hypothesis is an assumption, an idea that is proposed for the sake of controversy so that it may be examined to look if it might be true. in the clinical approach, the hypothesis is built earlier than any relevant research has been completed, other than a primary history review. Hypotheses recommend a dating between or extra variables. An impartial variable is something the researcher adjusts or controls. A based variable is something the researcher observes and measures.

For a hypothesis to be a systematic speculation, the scientific technique requires that you can still check it. Scientists typically base medical hypotheses on preceding observations that can not satisfactorily be defined with the to-be-had scientific theories. despite the fact that the phrases "speculation" and "concept" are often used interchangeably, a scientific hypothesis isn't always similar to a systematic idea. An operating hypothesis is a provisionally standard speculation proposed for further research in a technique beginning with an educated bet or idea.

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a=2

h=7

k=-3

#9

\(\\ \sf\longmapsto f(x)=a(x-h)(x-k)\)

\(\\ \sf\longmapsto f(x)=2(x-7)(x+3)\)

\(\\ \sf\longmapsto f(x)=2(x^2-4x-21)\)

\(\\ \sf\longmapsto f(x)=2x^2-8x-42\)

#10

\(\\ \sf\longmapsto f(x)=a(x-h)^2+k\)

\(\\ \sf\longmapsto f(x)=2(x-7)^2-3\)

\(\\ \sf\longmapsto f(x)=2(x^2-14x+49)-3\)

\(\\ \sf\longmapsto f(x)=2x^2-28x+98-3\)

\(\\ \sf\longmapsto f(x)=2x^2-28x+95\)

Answer:

i think it is D but I am not for shore

The solution set for the inequality 2 - 4x > 6 is x < -1, expressed in interval notation as (-∞, -1).

To solve the inequality 2 - 4x > 6, we need to isolate the variable x on one side of the inequality.

2 - 4x > 6

Subtract 2 from both sides:

-4x > 4

Divide both sides by -4, remembering to flip the inequality since we are dividing by a negative number:

x < -1

Therefore, the solution set for the inequality 2 - 4x > 6 is x < -1, expressed in interval notation as (-∞, -1).

To graph this solution set, we can draw a number line and shade everything to the left of -1.

<=================|----------->

                 -1    

The shaded part of the number line represents the solution set (-∞, -1).

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Answer:

-1

Step-by-step explanation:

Answer:

\(\boxed {r = \frac{31}{3}}\)

Step-by-step explanation:

To find the value of \(r\), write an expression by using the following measurements of both \(\overline {DG}\) and \(\overline {GM}\), then you solve for \(r\):

\(\overline {DG} = r + 3\)

\(\overline {GM} = 4r - 28\)

\(r + 3 = 4r - 28\)

Solve for \(r\):

\(r + 3 = 4r - 28\)

\(x + 3 - 4r = 4r - 4r - 28\)

\(-3r + 3 = -28\)

\(-3r + 3 - 3 = -28 - 3\)

\(-3r = -31\)

\(\frac{-3r}{-3} = \frac{-31}{-3}\)

\(\boxed {r = \frac{31}{3}}\)

So, the value of \(r\) is \(\frac{31}{3}\).

The 99% confidence interval for the difference between the mean speeds is approximately (-8.96, 4.96).

To find a 99% confidence interval for the difference between the mean speeds of the two processors (A and B), we can use the following steps: Step 1: Calculate the differences between the speeds of the two processors for each code. Differences: (1) 27 - 24.2 = 2.8 ; (2) 17.4 - 18.3 = -0.9;  (3) 21.1 - 27.9 = -6.8; (4) 18.0 - 27.8 = -9.8; (5) 26.4 - 26.1 = 0.3; (6) 27.5 - 26.1 = 1.4.  Step 2: Calculate the mean and standard deviation of the differences. Mean (Xbar ): (2.8 - 0.9 - 6.8 - 9.8 + 0.3 + 1.4) / 6 = -2.0

Standard Deviation (s): Calculate the sample standard deviation of the differences using the formula: s = √[(∑(x - Xbar)^2) / (n - 1)]  = √[((2.8 - (-2.0))^2 + (-0.9 - (-2.0))^2 + (-6.8 - (-2.0))^2 + (-9.8 - (-2.0))^2 + (0.3 - (-2.0))^2 + (1.4 - (-2.0))^2) / (6 - 1)] ≈ 4.25.

Step 3: Calculate the standard error of the mean difference. Standard Error (SE) = s / √n = 4.25 / √6 ≈ 1.73. Step 4: Calculate the margin of error (ME). ME = critical value * SE Since we want a 99% confidence interval, we need to find the critical value corresponding to an alpha level of 0.01/2 = 0.005 (two-tailed) in the t-distribution with (n - 1) degrees of freedom. For n = 6 - 1 = 5, the critical value is approximately 4.032 (using a t-distribution table or calculator). ME = 4.032 * 1.73 ≈ 6.96. Step 5: Calculate the confidence interval. Lower Limit = Xbar - ME = -2.0 - 6.96 ≈ -8.96; Upper Limit = Xbar + ME = -2.0 + 6.96 ≈ 4.96. Therefore, the 99% confidence interval for the difference between the mean speeds is approximately (-8.96, 4.96).

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The probability of Jack taking 2 red candies is 3/28.

What do you mean by a union in probability?
The letter "U" (union) stands for "or." Specifically, P(AB) represents the probability of that event A or event B occurring. The sample points that are present in both event A and event B must be counted in order to determine P(AUB).

The new probability set made up of all the elements from both sets is created when two sets are joined. When two sets intersect, a new set is created that includes every element from both sets.

Solution Explained:

Given in the question,

A bag contains 3 red and 5 green candies.

Total possibilities is 3 + 5 = 8  

Jack takes a candy at random and eats it  

A/Q there are 3 red candies out of 8, the probability is given by,

P(R) = 3/8

Now there are 2 red candies out of 7, so the probability is given by,

P(R') = 2/7

The probability of both events is given by,

P(2R) = P(R) × P (R') = 3/8 × 2/7 = 3/28

Therefore, the probability of Tim taking 2 red candies is P(2R) = 3/28

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