Which sequence follows the pattern add 5, subtract 3?


A. 5,3,5,3,5,3,5

B. 6,3,8,5,10,7

C. 0,5,8,13,16,21,24

D. 12,8,6,4,20

The measure of the complement of a 1-degree angle is 89 degrees.

The complement of an angle is defined as the angle that, when added to the given angle, results in a sum of 90 degrees. To find the measure of the complement of a 1-degree angle, we need to determine the angle that, when added to 1 degree, equals 90 degrees.

Let's denote the measure of the complement as x degrees. According to the definition, we can set up the equation:

1 degree + x degrees = 90 degrees.

To solve for x, we need to isolate it on one side of the equation. By subtracting 1 degree from both sides, we have:

x degrees = 90 degrees - 1 degree.

Simplifying the right side, we get:

x degrees = 89 degrees.

In summary, when an angle measures 1 degree, its complement measures 89 degrees. Complementary angles are pairs of angles that add up to 90 degrees. In this case, since the given angle measures only 1 degree, its complement is significantly larger, nearly forming a right angle. The concept of complementary angles is fundamental in geometry and can be applied to various problems involving angles and their relationships.

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\(\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=\cfrac{1}{2}nR^2\sin\left( \frac{360}{n} \right) ~~ \begin{cases} R=\stackrel{\textit{radius of}}{circumcircle}\\ n=\stackrel{\textit{number of}}{sides}\\[-0.5em] \hrulefill\\ n=8\\ R=6 \end{cases}\implies A=\cfrac{1}{2}(8)(6)^2\sin\left( \frac{360}{8} \right) \\\\\\ A=144\sin(45^o)\implies A=144\cdot \cfrac{\sqrt{2}}{2}\implies A=72\sqrt{2}\implies A\approx 101.8\)

Answer:

y = 87º

Step-by-step explanation:

Vertical angles are congruent

y = 87º

Answer:

87°

Step-by-step explanation:

y is vertical to 87° meaning that the two are congruent which makes them the same

So, the pairs of numbers that would represent the simple main effect of therapy (factor a) at the group setting (b2) in this example would be a1b2 (cognitive-behavioral therapy at the group setting) and a2b2 (relaxation therapy at the group setting).

In a 2x2 factorial design, there are two independent variables, each with two levels. This means that there are a total of four treatment conditions in the experiment. The simple main effect of one of the independent variables (in this case, factor a) at a specific level of the other independent variable (in this case, b2) refers to the effect of that independent variable on the dependent variable when the other independent variable is held constant at a specific level.

To understand this concept more clearly, let's consider an example. Suppose that in your experiment, factor a is the type of therapy (cognitive-behavioral therapy vs. relaxation therapy) and factor b is the type of treatment setting (individual vs. group). In this case, the simple main effect of therapy (factor a) at the group setting (b2) would refer to the effect of therapy on the dependent variable when the treatment setting is held constant at the group level.

The simple main effect of therapy (factor a) at the group setting (b2) would be calculated by comparing the mean response for the cognitive-behavioral therapy condition (a1b2) to the mean response for the relaxation therapy condition (a2b2). This would allow you to determine whether there is a significant difference in the mean response between the two therapy conditions when the treatment setting is held constant at the group level.

So, to answer your question, the pairs of numbers that would represent the simple main effect of therapy (factor a) at the group setting (b2) in this example would be a1b2 (cognitive-behavioral therapy at the group setting) and a2b2 (relaxation therapy at the group setting).

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Answer:

Hey there!

3^-8(3^4)=3^-4

The second option is correct.

Hope this helps :)

Answer:

1,769

Step-by-step explanation:

The computation of the sum is shown below:

Future value = Present value × (1 + rate of interest)^number of years

2,590 = Present value × (1 + 0.10)^4

2,590 = Present value × 1.10^4

So, the present value is

= 2,590 ÷ 1.10^4

= 2,590 ÷ 1.4641

= 1,769

Can you read my messages here?

Great.

For example, f (x) = 2x - 1

That is the original function

If we solve f (3) = 2 * 3 - 1

f (3) = 5

Perfect, Appreciate it.

Oh, that is a totally different case. :=)

Let me download the picture, please.

As you can see, this function is a parabola, and its vertex is (1,7)

For f (x) = 3, we have two values:

On the left, (-1, 3) and on the right, (3, 3).

In consequence,

x = -1 and 3, for f(x) = 3

Two solutions, EK.

Like you prefer. The important piece of information here is that x has two values for f (x) = 3.

Is it clear now?

If you don’t need any further explanation, I’ll go ahead and end our session. Feel free to let me know how I did by rating our session - all feedback is welcome and appreciated. Thanks for coming today!

Remember that the solutions from tutors are always available in your profile!

Answer:

A, because A is the answer(I have my reasons) so A.

Answer:

1975------ 4.8%

1990 ------ 11.48%

1985 ------ 8.51%

Step-by-step explanation:

Given

\(P(t) = 0.04t + 4.6\) if 0 ≤ t < 10

\(P(t) = -0.01005t^2 + 0.945t - 3.4\) if 10 ≤ t ≤ 30

Where

t:=0 implies year = 1970

Solving (a): Beginning of 1975.

First, we calculate the value of t

\(t = 1975 - 1970\)

\(t = 5\)

This falls in the range: 0 ≤ t < 10

So:

\(P(t) = 0.04t + 4.6\)

\(P(5) = 0.04 * 5 + 4.6\)

\(P(5) = 4.80\)

Solving (b): Beginning of 1990.

\(t = 1990 - 1970\)

\(t = 20\)

This falls in the range: 10 ≤ t ≤ 30

So:

\(P(t) = -0.01005t^2 + 0.945t - 3.4\)

\(P(20) = -0.01005*20^2 + 0.945*20 - 3.4\)

\(P(20) = 11.48\)

Solving (c): Beginning of 1985

\(t = 1985 - 1970\)

\(t = 15\)

This falls in the range: 10 ≤ t ≤ 30

So:

\(P(t) = -0.01005t^2 + 0.945t - 3.4\)

\(P(15) = -0.01005*15^2 + 0.945*15 - 3.4\)

\(P(15) = 8.51375\)

\(P(15) = 8.51\)

Answer:

C

Step-by-step explanation:

The interquartile range is the difference between the upper quartile Q₃ and the lower quartile Q₁

From the five- number summary , then

Q₃ = 24.5 and Q₁ = 11.1

interquartile range = 24.5 - 11.1 = 13.4 → C

Therefore, the volume of Prism B is 727/4 ft³ or 181 3/4 ft³ in mixed number form.

Subtract the denominator from the numerator. The quotient should be expressed as a whole number in step 2. Step 3: Enter the denominator and numerator, respectively, as the remainder and the divisor.

We can write: Using the formula for a prism's volume (V = Bh, where B is the base area):

We must determine Prism B's cross-sectional area in order to get the volume of Prism B. By dividing the height equation of prism A by its volume equation, the following result is obtained:

cross-sectional area of Prism A = (Volume of Prism A) / (height of Prism A) = (872/1 ft³) / (6 ft) = 218/3 ft²

Using the scale factor equation for height, we get:

k = (height of Prism A) / (height of Prism B) = (6 ft) / (31/12 ft) = 24/31

Using the scale factor equation for cross-sectional area, we get:

k² = (cross-sectional area of Prism A) / (cross-sectional area of Prism B) = (218/3 ft²) / (cross-sectional area of Prism B)

Solving for the cross-sectional area of Prism B, we get:

cross-sectional area of Prism B = \((218/3 ft^2) / k^2 = (218/3 ft^2) / (24/31)^2 = 59/3 ft^2\)

Finally, substituting the height and cross-sectional area of Prism B into the volume equation of Prism B, we get:

Volume of Prism B = (cross-sectional area of Prism B) * (height of Prism B) = \((59/3 ft^2) * (31/12 ft) = 727/4 ft^3.\)

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It depends on the number of variables, if the inequality has one variable, then it is graphed on a number line.

The type of diagram that we need to use depends on the number of variables that we have.

That is the main reason, for example:

x > 2

Is graphed on a number line.

y > 3x + 4

is graphed on a coordinate plane.

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The association of the scatterplot is a (b) No association

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be scattered and they do not follow a particular direction

Also, we can see that

As the x values change, the y values do not follow a pattern

This represents a no association.

Hence, the association is (b) No association

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Answer:

exponential. not linear functions because they change by equal differences not intervals.

Answer:

Any line where y=-5/2*x+z and z does not equal 4.

Step-by-step explanation:

Per the definition of a parallel line, any line with the same slope that doesn't intersect is parallel to the first. To solve for the slope, first solve for y: 5x+2y=8 2y=-5x+8 y=-5/2*x+4.

Therefore, anything with the slope -5/2 that doesn't have the y-intercept of 4 is parallel (as it would be the same line if it did). You can try any equation where y=-5/2*x+z and z does not equal 4 and it would be parallel.

Answer:

\(\frac{31}{50}-\frac{4i}{25}\)

Step-by-step explanation:

Step-by-step explanation:

I just did in the other posting. how often did you post it ?

this is a trick question. the triangle at the top is not an isoceles triangle.

we use Pythagoras for an the steps.

so, the left part of the baseline (split by the height) is calculated by

12² = 10² + part²

144 = 100 + part²

part = sqrt(44) = 6.633249581... ft

the other part is then

20 - 6.633249581... = 13.36675042... ft

and the second leg of the large triangle is

leg² = 10² + 13.36675042...² = 278.6700168...

leg = 16.69341238... ft

P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈

≈ 64.69 ft

please see the answer to the other posting for more details.

Answer:

price and quantity demanded

Step-by-step explanation:

It looks like the integral you want to find is

\(\displaystyle \int_C x^2y\,\mathrm dx - xy^2\,\mathrm dy\)

where C is the circle x ² + y ² = 4. By Green's theorem, the line integral is equivalent to a double integral over the disk x ² + y ² ≤ 4, namely

\(\displaystyle \iint\limits_{x^2+y^2\le4}\frac{\partial(-xy^2)}{\partial x}-\frac{\partial(x^2y)}{\partial y}\,\mathrm dx\,\mathrm dy = -\iint\limits_{x^2+y^2\le4}(x^2+y^2)\,\mathrm dx\,\mathrm dy\)

To compute the remaining integral, convert to polar coordinates. We take

x = r cos(t )

y = r sin(t )

x ² + y ² = r ²

dx dy = r dr dt

Then

\(\displaystyle \int_C x^2y\,\mathrm dx - xy^2\,\mathrm dy = -\int_0^{2\pi}\int_0^2 r^3\,\mathrm dr\,\mathrm dt \\\\ = -2\pi\int_0^2 r^3\,\mathrm dr \\\\ = -\frac\pi2 r^4\bigg|_{r=0}^{r=2} \\\\ = \boxed{-8\pi}\)

The equivalent distance of 60,000 centimetres in kilometers as required to be determined is; 0.6 km.

According to the task content and the metric system conversions;

1 m = 100 cm

Therefore, it follows from proportion that; 60,000 cm is equivalent to; 60,000 / 100 = 600 m.

Additionally, it follows that; 1 km = 1000 m, it therefore follows from proportion that; 600 m is equivalent to; 600 / 1000 = 0.6 km.

Ultimately, the equivalent distance of 60,000 centimetres in kilometers is; 0.6 km.

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The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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Step-by-step explanation:

1)

180-68-41= 71°

2)

180-47-16=117

5)

m<1= 180-68-77= 35°

m<2= 77°

m<3 = 180-90-41= 49°

m<4 = 180-41-62= 77°

m<5= 90-28= 62°

m<6= 180-49-103= 28°

The statements and Reasons to prove that the two triangles are congruent are explained below.

When the corresponding sides and angles of two or more triangles are equal, then they are said to be congruent. This implies that the triangles are the same in sides and measure of angles, and the relation can be expressed in required term.

The expected prove with statement and reasons that ΔLIT ≅ ΔTER is explained below:

             STATEMENT                                           REASON

1. LT ≅ TR                                                            Given

2. <ILT ≅ <ETR                                                    Given

3. IT II ER                                                             Definition of parallel lines

4. <LTI ≅ <ERT                                                 Corresponding Angles

5. ΔLIT ≅ ΔTER                                                Angle-Side-Angle (ASA)

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The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

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Answer:

Q = 40.6°

Explanation:

Given three sides: 9.6, 8.1, 6.3

Use the cosine rule:

c² = a² + b² - 2ab cos(C)

Insert following variables:

6.3² = 9.6² + 8.1² - 2(9.6)(8.1) cos(Q)

39.69 = 157.77 - 155.52 cos(Q)

cos(Q) = -118.08/-155.52

cos(Q) = 41/54

Q = cos⁻¹(41/54) = 40.6°

Given: The function representing the distance, in feet, between the rock and the ground X seconds after it is thrown as

To Determine: How long after the rock is thrown does it hit the ground

Solution

Please note that when the rock hits the ground, the vertical distance f(x) would be zero

Therefore

Solve for x in the equation using the quadratic formula

The quadratic formula is given as

An equation of this line in slope-intercept form is y = x - 1.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-1, -2) and a slope of -1, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-2) = -1(x - (-1))  

y + 2 = x + 1

y = x + 1 - 2

y = x - 1

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Complete Question:

Write an equation of a line through point (-1, -2) with a slope of -1.

Answer:

You have to finish the question.

Step-by-step explanation:

Answer:

$1.37 per pint

Step-by-step explanation:

3 gallon = 24 pints

What is the price per pint?

32.88 / 24 = $1.37 per pint

So, the price per pint is $1.37.