Translate and solve: 82 less than a is at least −82.

Give your answer in interval notation.

As Tan A=Perpendicular/Base, x has the value of 21.56. Tan 54 = x/32, or x = 21.56, in this case.

When two lines cross at a 90-degree angle, they are said to be perpendicular. The definition of a parallel line is a line with constant spacing. being perfectly vertical or upright: making a straight angle with one another or another given line or plane. Adverbial phrase meaning "perpendicularly"

As a result of two lines meeting at a right angle, the word "perpendicular" denotes "at right angles." Including up and down, across, and side to side, perpendicular lines can face in any direction. Additionally, they don't need to be standing straight up from the bottom or side of the page.

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The test statistic z = 0.84 and P-value is 0.2005 when there is a line of unassembled furniture produced by The Mean Corporation.

Given that,

There is a line of unassembled furniture produced by The Mean Corporation. The customer care manager is aware that 0.63 of customers have had no issues putting together their furniture at home based on past data.

The null and alternative hypotheses are:

H₀: π = 0.63

H₁: π > 0.63

We have to find

(a) Calculate the test statistic (z).

(b) Calculate the P-value.

We know that,

a) z = p - π / √(π(1-π)/n)

      = 0.67 - 0.63 / √(0.63×0.37/102)

      = 0.04 / 0.0478

      = 0.84

b) p value(one tailed) is 0.2005.

Therefore, The test statistic z = 0.84 and P-value is 0.2005 when there is a line of unassembled furniture produced by The Mean Corporation.

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The value of S4 for the given expression ♾️. n-1 Σ 1/4(-1/3) is -1/12.

The given expression ♾️. n-1 Σ 1/4(-1/3) represents a summation of the term 1/4(-1/3) over a range of values from 1 to n-1, where n is an unknown value. We need to find the value of S4, which represents the sum of this expression when n is equal to 4.

To find the value of S4, we substitute n = 4 into the expression and evaluate it.

♾️. n-1 Σ 1/4(-1/3) = ♾️. 4-1 Σ 1/4(-1/3)

Simplifying, we get:

♾️. 3 Σ 1/4(-1/3)

Since the term 1/4(-1/3) is constant, we can pull it out of the summation:

1/4(-1/3) ♾️. 3

Now, ♾️. 3 represents the sum of 3 terms. Multiplying 1/4(-1/3) by 3 gives:

1/4(-1/3) * 3 = -1/4 * 1/3 * 3 = -1/12

Therefore, the value of S4 for the given expression ♾️. n-1 Σ 1/4(-1/3) is -1/12.

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The probable question could be:

What is the value of s4 for expression ♾️. n-1 Σ 1/4(-1/3) ?

A) 1/9

B) 7/54

C) 5/27

D) 10/27

Answer: One root

Reason:

The term "root" refers to the x intercept.

We plug in y = 0 and solve for x to get the x intercept

y = 2x-12

0 = 2x-12

2x = 12

x = 12/2

x = 6

The root is 6.

The single x intercept is located at (6,0).

Answer:

Thank you this really helps!

Step-by-step explanation:

The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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The opposite angles are ∠LRE = ∠FRA and ∠TRF = ∠NRL. Then the correct options are A and D.

The complete question is attached below.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

The opposite angles are given below.

∠LRE = ∠FRA

∠TRF = ∠NRL

Then the correct options are A and D.

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This is an observational study because the researchers do not attempt to modify or apply a treatment to the individuals. Major problem with the study is A.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

This is a convenience sample with voluntary response, which has a high chance of leading to bias.

The survey relies on self-selection, meaning that only those who were interested in responding to the question chose to do so.

This can result in a biased sample that does not accurately represent the population of all internet users.

Additionally, the sample size is not known to be representative or sufficient for generalization, and there is no control group or experimental design to establish cause and effect.

Hence, this is an observational study because the researchers do not attempt to modify or apply a treatment to the individuals.

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Answer:

A

C

D

F

G

Step-by-step explanation:

You can pretty easily find the answer by just going through each statement and analyzing what it means.  For A it asks if AB is parallel to DC (parallel means the lines could go on for infinity without ever touching) Looking at the shape we can see that AB and DC are on opposite sides and are slanted in the same direction meaning that they are in fact parallel.  This could be correct.  The next asks about angle BCD and whether or not it is congruent to CDA (congruent is just another word for the same) Angle BCD is the top right angle and we know this by following the letters on the shape in the order they were asked in the question.  We can see that these two angles are not congruent just via observation as BCD is an acute angle (less than 90 degrees with a right angle as a reference) and CDA is an obtuse angle (greater than 90 degrees)  This answer choice is incorrect.  Next up we have BPC and APD and it asks whether or not they are congruent.  We can apply the same logic to the previous choice and find out that they are in fact congruent angles which is also backed up by the rule of vertical angles which states that all vertical angles are congruent.  This means C is also a correct option.  Next up is line BC compared with AD which are very obviously congruent just by looking at the image, but we also know that opposite sides of a parallelogram are always congruent.  This answer choice is correct also.  Next up it asks us about AC in comparison to BD which are NOT congruent because each line has a different length due to the fact of the angles they are coming from.  AP is in fact congruent to PC because it is just a continual of the original line which stems from halfway across the middle of the parallelogram.  This IS a correct choice.  Next up it asks about supplementary angles and it is important to understand what that is before you can accurately answer the question.  Supplementary angles are angles which will total 180 degrees and the question specifically asks in relation to angles BAD and ADC.  These angles are in fact supplementary because they are across from each other at the base of the parallelogram and we know from theories that these angles will always be supplementary in these shapes.  G is also a correct answer.  Last but not least we have a question asking us about APB and APD and whether or not they are vertical angles.  Vertical angles are angles which are across from each other either vertically as the name sake says or horizontally, but they have to be directly across from each other.  Looking at the image we can clearly see that these angles are NOT across from each other but instead are adjacent to each other (next to each other) meaning the last option is not correct.  This leaves A,C,D,F, and G as the correct answers.

Therefore , the solution of the given problem of angles comes out to be Greeks failed to demonstrate that tripling a square with only a straight edge and compass was also unachievable.

The highest and lowest walls of a skew are used to split the curved lines that make up its ends using Cartesian measurements. A collision between two poles at an intersection is a potential. Angle is another outcome of two things interacting. They resemble dihedral forms the most closely. A two-dimensional curve can be created by placing two line beams in various configurations between their ends.

Here,

The Greeks were unable to trisect a line section using only a straight edge and compass.

The Greeks proved that using only a straight edge and compass, it is impossible to trisect any angle or double a cube.

The Greeks failed to demonstrate that tripling a square with only a straight edge and compass was also unachievable.

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The true statement about a ladder is; the ladder has parallel line segments and perpendicular line segments.

Parallel lines are lines that never meet on the same plane which have equal distance apart from each other.

They are lines that intersect each other to form a right angle.

Therefore, the ladder has parallel line segments and perpendicular line segments.

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Question:

Write the exponential function y = 50e^-0.21t in the form y = Pa^t .

Solution:

Consider the following function:

this is equivalent to:

applying the properties of exponents, this is equivalent to:

this is equivalent to:

so that, we can conclude that

Answer:

(12+x)(10 1/2+x)

Step-by-step explanation:

Step-by-step explanation:

15+3+3=21

21+15=36

36*16= 576

576/2= 288cm^2

Area= B

How I got his:

Area of a trapezium= \(\frac{(a+b)*h}{2}\)

Hope this helped!

Answer:

\(A=288cm^{2}\)

Step-by-step explanation:

Formula to find area of trapezoid:

\(A=\frac{a+b}{2} h\)

Add the values in the formula:

\(A=\frac{15+(15+3+3)}{2} (16)\)

\(A=\frac{36}{2} (16)\)

\(A=18(16)\)

\(A=288cm^{2}\)

Hope this helps, have a good day ahead :)

Answer:

last one

Step-by-step explanation:

Answer:

My day has been very stress full and on top of that many times my teachers have been assigning more things then anyone could handle. On top of that none of them will be in zoom meetings bc of "a/b" tours. So.. being sarcastic- yes my day is fine.

Answer:

b

Step-by-step explanation:

becouase its b

Answer:

14 triangles

Step-by-step explanation:

Just make equilateral triangles

Answer:

I’m pretty sure it’s 12

Step-by-step explanation:

There are 12 equilateral triangles

Answer:

45 units

Step-by-step explanation:

Answer:

The functions are:

f(x) = $14.75*x + $2

s(x) = $12.25*x + $17

Both iSpice and Spice Magic charge $90.50 for 6 pounds of paprika.

Step-by-step explanation:

A linear equation has the general shape:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that the function passes through the points: (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Ok, knowing this, let's look at the first table, we need to work with only two points, so let's use the first one (1, $16.75) and the second one (2, $31.50)

Then the slope of the equation is:

a = ($31.50 - $16.75)/(2 - 1) = $14.75

Then the equation is something like:

y = f(x) = $14.75*x + b

To find the value of b, we can use one of the two points. For example, the point (1, $16.75) means that when x = 1, we must have y = $16.75

Replacing these values in the equation we get:

$16.75 = f(1) = $14.75*1 + b

$16.75 - $14.75 = b = $2

Then the function f(x) is:

f(x) = $14.75*x + $2

Now let's go to the other function, again we can choose two points, let's use the first one (1, $29.25) and the third one (3, $53,75).

Then the slope is:

a = ($53.75 - $29.25)/(3 - 1) = $12.25

Then the equation is something like:

y = s(x) = $12.25*x + b

To find the value of b we do the same as before, if we use the first point (1, $29.25) we get:

$29.25 = s(1) = $12.25*1 + b

$29.25 - $12.25 = b = $17

Then this equation is:

y = s(x) = $12.25*x + $17

The two equations are:

f(x) = $14.75*x + $2

s(x) = $12.25*x + $17

b) now we want to find the value x such that the price is the same in both cases, then we need to solve:

f(x) = g(x)

$14.75*x + $2 =  $12.25*x + $17

$14.75*x - $12.25*x = $17 - $2

$2.5*x = $15

x = $15/$2.5 = 6

This means that for 6 pounds of paprika the price is the same on both companies, and the price is:

f(6) = g(6) = $14.75*6 + $2 = $90.50

We know that for every one and two thirds cups of flour, we add one cup of chocolate chips. If we divide one cup of chocolate chips by one and two thirds cups, we're going to find the amount of chocolate chips for every cup of flour.

Now we know that for every cup of flour, we haev 3/5 cups of chocolate chips.

To find the amount of chocolate chips when one and one quarter cups of flour is used, we just need to multiply this new ratio by one and one quarter.

And this is our answer.

When one and one quarter cups of flour is used, three quarters(3/4) of chocolate chips are used.

Answer:

Step-by-step explanation:

15+5x=20x

   -5x  -5x  => Subtract 5x from each side

You get

15 = 15x

Divide both sides by 15

1=x

Answer:

(a) There is a significant relationship between y and \(x_1, x_2, x_3, x_4\)

(b) \(SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45\)

(c) \(SSE_{(x_2,x_3)} = 100\)

(d) \(x_1\) and \(x_4\) are significant

Step-by-step explanation:

Given

\(y = 17.6+3.8x_1 - 2.3x_2 +7.6x_3 +2.7x_4\) --- estimated regression equation

\(n = 30\)

\(p = 4\) --- independent variables i.e. x1 to x4

\(SSR = 1760\)

\(SST = 1805\)

\(\alpha = 0.05\)

Solving (a): Test of significance

We have:

\(H_o :\) There is no significant relationship between y and \(x_1, x_2, x_3, x_4\)

\(H_a :\) There is a significant relationship between y and \(x_1, x_2, x_3, x_4\)

First, we calculate the t-score using:

\(t = \frac{SSR}{p} \div \frac{SST - SSR}{n - p - 1}\)

\(t = \frac{1760}{4} \div \frac{1805- 1760}{30 - 4 - 1}\)

\(t = 440 \div \frac{45}{25}\)

\(t = 440 \div 1.8\)

\(t = 244.44\)

Next, we calculate the p value from the t score

Where:

\(df = n - p - 1\)

\(df = 30 -4 - 1=25\)

The p value when \(t = 244.44\) and \(df = 25\) is:

\(p =0\)

So:

\(p < \alpha\) i.e. \(0 < 0.05\)

Solving (b): \(SSE(x_1 ,x_2 ,x_3 ,x_4)\)

To calculate SSE, we use:

\(SSE = SST - SSR\)

Given that:

\(SSR = 1760\) ----------- \((x_1 ,x_2 ,x_3 ,x_4)\)

\(SST = 1805\)

So:

\(SSE_{(x_1 ,x_2 ,x_3 ,x_4)} = 1805 - 1760\)

\(SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45\)

Solving (c): \(SSE(x_2 ,x_3)\)

To calculate SSE, we use:

\(SSE = SST - SSR\)

Given that:

\(SSR = 1705\) ----------- \((x_2 ,x_3)\)

\(SST = 1805\)

So:

\(SSE_{(x_2,x_3)} = 1805 - 1705\)

\(SSE_{(x_2,x_3)} = 100\)

Solving (d): F test of significance

The null and alternate hypothesis are:

We have:

\(H_o :\) \(x_1\) and \(x_4\) are not significant

\(H_a :\) \(x_1\) and \(x_4\) are significant

For this model:

\(y =11.1 -3.6x_2+8.1x_3\)

\(SSE_{(x_2,x_3)} = 100\)

\(SST = 1805\)

\(SSR_{(x_2 ,x_3)} = 1705\)

\(SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45\)

\(p_{(x_2,x_3)} = 2\)

\(\alpha = 0.05\)

Calculate the t-score

\(t = \frac{SSE_{(x_2,x_3)}-SSE_{(x_1,x_2,x_3,x_4)}}{p_{(x_2,x_3)}} \div \frac{SSE_{(x_1,x_2,x_3,x_4)}}{n - p - 1}\)

\(t = \frac{100-45}{2} \div \frac{45}{30 - 4 - 1}\)

\(t = \frac{55}{2} \div \frac{45}{25}\)

\(t = 27.5 \div 1.8\)

\(t = 15.28\)

Next, we calculate the p value from the t score

Where:

\(df = n - p - 1\)

\(df = 30 -4 - 1=25\)

The p value when \(t = 15.28\) and \(df = 25\) is:

\(p =0\)

So:

\(p < \alpha\) i.e. \(0 < 0.05\)

Hence, we reject the null hypothesis

The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Using the distributive property of matrix multiplication A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.

We have given that Ax = 0, where A is an m × n matrix and x is an n-dimensional vector in Rn.

To show that A(cu) = 0 for any scalar c, we can use the distributive property of matrix multiplication, which states that A(B + C) = AB + AC for any matrices A, B, and C of appropriate dimensions.

Let us substitute cu for x in the equation Ax = 0, then we get:

A(cu) = A(c × u)

Using the distributive property, we can write:

A(c × u) = c × A(u)

Since u satisfies the equation Ax = 0, we have:

A(u) = 0

Substituting this into the above equation, we get:

c × A(u) = c × 0 = 0

Therefore, we have shown that A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.

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We know that a function has a discontinuity if the left hand limit and right hand limit of the function are there but they are not equal.

According to the question,

We have the following information:

A function is given and we need to find if the given function is discontinuous or not.

There are two situations to find this whether the function is discontinuous or not. First, we need to know that the function has both the left hand limit as well as the right hand limit.

Second condition is to check whether if the limits are equal or not. If they are not equal then the function is discontinuous.

Hence, we know that a function has a discontinuity if the left hand limit and right hand limit of the function are there but they are not equal.

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The algebraic rule for the transformation is B' = (Bx + 15, By - 12)

Given data ,

To determine the algebraic rule for the transformation from point B to point B', we need to find the equations that relate the coordinates of the preimage point B to the image point B'.

Let's denote the translation amounts in the x-direction and y-direction as (dx, dy). The coordinates of B' can be obtained by adding these translation amounts to the coordinates of B:

B' = (Bx + dx, By + dy)

Given that B is located at (5, -4) and B' is located at (20, -16), we can calculate the translation amounts:

dx = 20 - 5 = 15

dy = -16 - (-4) = -12

Hence , the algebraic rule for the transformation is B' = (Bx + 15, By - 12)

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Answer:

place the decimal point in the product so that the number of decimal places in product is the sum of decilal places in the factors. keep all zeros in the product when you place the decimal point. you can drop the zeros on the right once the decimal point has been placed in the product.