the central angle of the arc of 75

Step-by-step explanation:

hello : here is an solution

It takes 165 minutes per week if 10% increase in volume for an exercising client.

A client is exercising for 150 minutes per week. I.e., 30 minutes, 5 days per week.

So, 10% increase results,

30 minutes × 10% = 3

So, the increased minutes per day = 30 + 3 = 33 minutes/day.

After the 10% increase, the minutes per day = 33 minutes

Since 5 days a week, he does exercise, the total minutes per week

= 33 × 5 = 165 minutes.

So, a 10% increase in volume would result in 165 minutes total per week.

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3a) The coordinate of R after dilation is; R' = (-6, 21)

3b) The coordinate of T after dilation is; T' = (1, 3)

5) A dilation by a scale factor of 2 followed by a translation right 1 up 3.

3a) We are given the coordinates of the rectangle as;

Q(-2, -1), R(-2, 7), S(4, 7), T(4, -1)

Now, we are told that R(-2, 7) is dilated about the origin with a scale factor of 3. Thus;

R' = (-2 *3), (3 * 7)

R' = (-6, 21)

3b) We are now told that T(4, -1) is dilated by a scale factor of 1/2 with R as center of origin. R has a coordinate of (-2, 7). Thus;

Coordinate of T' = (-2, 7) + ¹/₂((4, -1) - (-2, 7))

Coordinate of T' = (-2, 7) + ¹/₂(6, -8)

Coordinate of T' = (-2, 7) + (3, -4)

Coordinate of T' =  (1, 3)

5) We can see that LN is 2 units while L'N' is 4 units and so we can say scale factor in the transformation of ΔLMN to ΔL'M'N' is 2.

Now, if we apply scale factor of 2 to coordinates of N before transformation, we will have; 2(3, 1) = (6, 2)

Comparing to N' which is (5, 5) we can say that it was shifted up by 3 units and right by 1 unit.

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Answer:

4. b) an angle

5. b) the angles of a triangle

6. b) opposite, hypotenuse and adjacent

Step-by-step explanation:

4. To find sine, cosine, tangent, you use the sin, cos, tan key of the calculator.

If you are given the value of the sin, cos, tan, and you are looking for the angle, then you use the second function of the calculator.

Answer: b) angle

5. angles of a triangle

6. The sides that form the right angle are the legs. In trig, there is an angle of interest, so to distinguish between the legs, one leg is called the adjacent leg, and the other leg is called the opposite leg. The side opposite the right angle is the hypotenuse.

Answer: opposite, hypotenuse and adjacent

The term for breaking a number into smaller sections and multiplying these numbers is factorization.

This is a common method used in math that implies breaking a big number into smaller ones and then multiplying the numbers. This multiplication should lead you to the original number.

120 can be broken as 12 and 10, then 12 × 10 = 120

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Answer:

3x-5=1

3x=5+1

3x=6

x=6/3

x=2

Answer:

a) x = 1.5 or x = -0.3

b) x = 5 or x = -8

Explanation:

Quadratic formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \:\: ax^2 + bx + c = 0[/tex]

Here given equation: 5x² - 6x  - 2 = 0

Identify variable constants: a = 5, b = -6, c = -2

Putting these values into equation:

[tex]\sf x = \dfrac{ -(-6) \pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}[/tex]

[tex]\sf x = \dfrac{ 6 \pm \sqrt{36 + 40}}{10}[/tex]

[tex]\sf x = \dfrac{ 6 \pm \sqrt{76}}{10}[/tex]

[tex]\sf x = \dfrac{ 3\pm \sqrt{76}}{5}[/tex]

[tex]\sf x = \dfrac{ 3+ \sqrt{76}}{5} \quad or \quad \dfrac{ 3- \sqrt{76}}{5}[/tex]

In one decimal point:

[tex]\sf x = 1.5 \quad or \quad -0.3[/tex]

b) Here use "middle term split" method

⇒ x² + 3x = 40

relocate

⇒ x² + 3x - 40 = 0

The factors of 40 are 8 and 5

⇒ x² + 8x - 5x - 40 = 0

factor common terms

⇒ x(x + 8) - 5(x + 8) = 0

collect into groups

⇒ (x - 5)(x + 8) = 0

set to zero

⇒ x - 5 = 0 or x + 8 = 0

relocate

⇒ x = 5 or x = -8

Step-by-step explanation:

a) The quadratic formula can help find answers to a quadratic equation when it is equal to 0. The formula is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] for a quadratic equation of the form [tex]ax^2+bx+c=0[/tex].

In this question, a is 5, b is -6, and c is -2. Let's put them in the equation and solve.

[tex]x=\frac{6\pm\sqrt{(-6)^2-4(5)(-2)}}{2(5)}\\x=\frac{6\pm\sqrt{36+40}}{10}\\x=\frac{6\pm\sqrt{76}}{10}\\x=\frac{6\pm2\sqrt{19}}{10}\\x=\frac{3\pm\sqrt{19}}{5}[/tex]

This means that the value of x is both [tex]\frac{3+\sqrt{19}}5[/tex] and [tex]\frac{3-\sqrt{19}}5[/tex], since both values make x equal to 0. Putting both into the calculator, we get that [tex]x=1.5[/tex] or [tex]x=-0.3[/tex].

b) We can easily solve this equation using factoring, which turns a quadratic into two factors, and finds the solutions by setting both to 0. This will only work if the quadratic is equal to 0.

[tex]x^2+3x-40=0[/tex]

Now, we have to find two numbers that add to 3 and multiply to -40. The numbers 8 and -5 work, as 8-5=3 and 8*-5 is -40.

we can now make our factors x+8 and x-5

[tex](x+8)(x-5)=0[/tex]

If two numbers, say A and B, are being multiplied and equal 0, then either A is 0, or b is 0, or both. Similarly, if x+8 and x-5 are being multiplied and equal 0, either x+8 = 0, or x-5=0.

[tex]x+8=0\\x=-8[/tex]    [tex]x-5=0\\x=5[/tex]

This makes our solutions x=-8 and x=5.

If you are not familiar with factoring or the process I have went through above, I highly recommend learning about it.

The data should be displayed using a line graph, as shown in the attached figure.

Definition of a Line Graph

In a line graph, also known as a line plot or a line chart, each data point is connected by its own line. A line graph displays numerical values across a chosen time span.

Why is a line graph the best choice in this situation?

A line graph would be the best option for showing the data for David's family's grocery spending over the previous 10 weeks because it would show us the trend in the data. This graph tells us of how we can recognize instances where there were significant expenses by analyzing the trend from the line graph.

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In a(n) reversal design, two or more treatments are alternated relatively quickly on a regular schedule.

Reversal designs are used to observe the impact of a remedy on the conduct of a single player. The participant is observed time and again previous to remedy to establish a baseline stage of behavior.

One ought to not use a reversal layout with behaviors that aren't reversible. For instance, if you train a person to fish, that man or woman is not probable to forget about how to fish, making a reversal design a negative preference for evaluating your fishing intervention.

Reversal layout: reversing among remedies (e.g., baseline, treatment, NCR, treatment, NCR, remedy, and many others.) Withdrawal design: reversing among treatment and no treatment (e.g., baseline, remedy, baseline, treatment, etc.)

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Since the sum of any two sides is greater than the third, hence the three sides for the sides of a triangle

A triangle is a 2-D shape with 3sides and angles. According to the question, we are to determine whether the given measures form sides of a triangle.

For the following measure to form the sides of a triangle, the sum of any two sides must be equal to the third as shown:

3 + 12  = 15 > 13

3 + 13 = 16 > 12

13 + 12 = 25 > 3

Since the sum of any two sides is greater than the third, hence the three sides for the sides of a triangle

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The linear inequality in standard form is: x + y < -2 or x + y + 2 < 0

To determine what sign to use, follow these rules:

The graph given has the following features:

Find the slope:

Slope (m)= rise/run = -(2 units) / (2 units).

Slope (m) = -1.

The y-intercept (b) = -2.

Substitute m = -1 and b = -2 into y < mx + b:

y < (-1)x + (-2)

y < -x - 2

Rewrite

x + y < -2

x + y + 2 < 0

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Answer:

Step-by-step explanation:

The correct answer would be C (-6,3).  The y axis is the bold line going up and down on the middle of the page.   If you were able to pick up triangle and flip it over the y axis.  Point C would land at (-6,3).

Also, you can see that point C is six spaces to the right of the y axis.  That means when we flipped it over the axis, it will now be six paces to the right of the y axis.  Since the point did not go up or down when you flipped it.  It is still 3 spaces above the x axis.

Answer:

D (-6, 3)

Step-by-step explanation:

the point C is originally (6, 3).

that means the x coordinate is 6, the y coordinate is 3.

now, if we reflect (= mirror) that point across the y axis, that means we mirror it to the other side of the y axis.

the y axis is the vertical coordinate axis in the middle of the graph.

so, what is going to happen to the point ?

will the y coordinate change ? no. the point will move over to the other side of the y line in the same "height" as before. nothing will move it higher or lower.

so, it will keep the same y coordinate : 3.

will the x coordinate change ? oh, yes. because the point will move from the right of the y axis to the left of the y axis. and it will be the same distance to the left as it was originally to the right.

so, +6 turns into -6 (as the y axis represents x=0).

Answer:

A) 1/9, 3, 27

Step-by-step explanation:

i think you mean 3^x (and not 3x).

because otherwise none of the answer options withdraw makes any sense.

3^-2 = 1/(3²) = 1/9

3¹ = 3

3³ = 27

The dot plot that could represent the same data as the frequency table is  the second plot. This is further explained below.

Generally, Data points are represented as dots on a graph with an x- and y-axis in a dot plot sometimes referred to as a strip plot or dot chart, which is a straightforward kind of data visualization.

The frequency table displays the number of ill patients in each age group. The first two plots are incorrect because the sum of the dots connecting the numbers 24, 25, 26, 27, 28, and 29 in the first two plots is 3, but not in the other two plots.

In conclusion, there are only 4 ill individuals when the dots from the 30-34 age range on the first plot are added together. There are a total of 6 cases in that age group on the second graph. As a result, the second dot plot is the one that matches the frequency table.

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Answer:

id b on edge

Answer:

Step-by-step explanation:

I got you  first you want to get some little ceasers

we conclude that the system of inequalities has more solutions than the system of equations.

We have the system of equations:

y = (-1/2)*x + 1

y = x - 5

And the system of inequalities:

y > (-1/2)*x + 1

y < x - 5

First, if you look at the first system you can see that we have two non-parallel lines, so that system has only one solution.

Now let's look at the system of inequalities, we can get solutions like:

x = 10

y = 1

1 > (-1/2)*10 + 1 = -4

1 < 10 - 5 = 5

So both inequalities are true, which means that the point (10, 1) is a solution.

And also is the point (11, 1), and (12, 1), and infinite other points.

Then we conclude that the system of inequalities has more solutions than the system of equations.

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The probability of getting two numbers whose sum is greater than 9 is [tex]\frac{5}{36}[/tex].

To find the probability of getting two numbers whose sum is greater than 9:

The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Set of numbers greater than 9:

{(5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}

Formula:

Favorable event / Total number of events = [tex]\frac{5}{36}[/tex]

Therefore, the probability of getting two numbers whose sum is greater than 9 is [tex]\frac{5}{36}[/tex].

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Step-by-step explanation:

[tex] {2}^{4n} \times {2}^{2n} = 512[/tex]

[tex] {2}^{4n} \times {2}^{2n} = {2}^{9} [/tex]

[tex] {2}^{4n + 2n} = {2}^{9} [/tex]

[tex]6n = 9[/tex]

[tex]n = \frac{3}{2} [/tex]

Answer:

5 units

Step-by-step explanation:

Given the following question:

To find the answer to this question we will use the formula to calculate distance.

(6, 5) = (x1, y1)
(-3, 1) = (x2, y2)

[tex]d=\sqrt{(x1-x2)^2+(y1-y2)^2}[/tex]
[tex]d=\sqrt{(-6-(-3))^2+(5-1)^2}[/tex]
[tex]-6+3=-3[/tex]
[tex]5-1=4[/tex]
[tex]d=\sqrt{(-3^2+4^2)}[/tex]
[tex]-3^2=-3\times-3=9[/tex]
[tex]4^4=4\times4=16[/tex]
[tex]d=\sqrt{9+16}[/tex]
[tex]9+16=25[/tex]
[tex]\sqrt{25}[/tex]
[tex]\sqrt{25} =5\times5=25[/tex]
[tex]=5[/tex]

Which means the distance between the two points is "5 units."

Hope this helps.

Answer:

D.10

Step-by-step explanation:

Mode is the number that is repeated the most as we can see the number 10 is there 3 times in the data. 13 isn't there, 14 is only there once and 16 is also not there

Answer:

4

Step-by-step explanation:

If the probability of drawing a yellow jelly beans is 1/4, the box is has 1/4 yellow jellybeans.

1/4b=6

b=24

14+6+x=24

20+x=24

x=4

Answer:

36 blue jelly beans

Step-by-step explanation:

We can find the total number of jelly beans by adding all red, yellow, and blue jelly beans together.

14+6+x

This simplifies to 20+x

For probability, it is (the number of things you want)/(the total number of things there are).

If the probably of drawing a yellow jelly bean is 1/4, we can set up this equation:

[tex]\frac{14}{20+x}=\frac{1}{4}[/tex]

We can cross multiply:

[tex]20+x=14(4)\\x+20+56\\x=36[/tex]

There are 36 blue jelly beans.

Answer:

c

Step-by-step explanation:

1) eliminate the negative answers since we need the amount of feet below a section and a negative number below a section doesn't make sense in this context and would result in a distance higher than the shallowest section.

Just find the absolute value or the difference between 135 and 50 resulting in 85

"Meta Analysis" is a quantitative statistical analysis that compares and combines the results of individual but similar studies.

A quantitative statistical analysis of numerous distinct but related experiments or research to assess the statistical significance of the pooled results.

Some characteristics of meta analysis are-

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The probability of matching six numbers is [tex]\frac{1}{47C_{6}}[/tex].

To find the probability, we have to divide the favorable events by the total number of events.

The total number of events is given by:

[tex]47C_{6}[/tex]

We use combinations since the order doesn't matter.

The total number of favorable events is given by:

[tex]6C_{6}[/tex]

The probability is given by:

[tex]\frac{\text{Favorable events}}{\text{Total events}}=\frac{6C_{6}}{47C_{6}} \\= \frac{1}{47C_{6}}[/tex]

We have found the probability of matching all six balls to be [tex]\frac{1}{47C_{6}}[/tex].

Therefore, we have found that the probability of matching six numbers is [tex]\frac{1}{47C_{6}}[/tex].

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Disclaimer: The question was incomplete, the complete question is attached below.

Question: In the Michigan lottery game, LOTTO 47, the state selects six balls randomly out of 47 numbered balls. The player selects six different numbers out of the first 47 positive integers. Prizes are given for matching all six numbers in any order (the jackpot) and matching five numbers ($2500). A ticket costs $1.00 and this dollar is not returned to the player. Find the probability of matching six numbers.

The measure of the acute angles are 62° and 28° .

Let x represent the measure of one of the acute angles of the right angle triangle.

Let y represent the measure of the other acute angle of the right angle triangle.

One of the acute angles in a right triangle measures 22 degrees less than 3 times the other acute angle. This means that

x = 3y - 22

The sum of two acute angles in a right triangle is 90 degrees.

We write as

x + y = 90 - - - - - - - (1)

Substituting x = 3y - 22 into equation 1, it becomes

3y - 22 + y = 90

4y = 90 + 22= 112

y = 112/4 = 28

x = 90 - y = 90 - 28

x = 62

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The polynomial is P(z) = 5z * (z - 1) and the equivalent forms are P(z) = 5z^2 - 5z and P(z) = -5z + 5z^2

The GCF is given as:

GCF = 5z

This means that the polynomial can be represented as:

P(z) = GCF * Another factor

We can make use of the following function

P(z) = 5z * (z - 1)

Expand

P(z) = 5z^2 - 5z

Rewrite as:

P(z) = -5z + 5z^2

Hence, the polynomial is P(z) = 5z * (z - 1) and the equivalent forms are P(z) = 5z^2 - 5z and P(z) = -5z + 5z^2

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Answer:

20 hrs

Step-by-step explanation:

growth per hour=5%

no of hrs to double=100/5=20

(it may be wrong)<3

The sum of two terms are:

The sum of two numbers is one that tells you to find the sum of two or more numbers, and as such, you have to add the numbers altogether.

t₅, ₃ =  5 + 3

= 8

t₁₁, ₂ = 11 + 2

= 13

t₁₅,₁₃ =  15 + 13

= 28.

Hence the correct sum of two terms are:

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