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The values of theta for which the trigonometric ratio sin theta is smaller than or equal to cos theta is; θ ≤ 45°

The six trigonometric ratios are;

sine, cosine, tangent, secant, cosecant and cotangent.

Now, we are told that the angle theta is greater than or equal to zero but less that or equal to 90 degrees. Expressing this as a form of inequality gives us; 0 ≤ θ ≤ 90°

Now, it is common knowledge that;

sin 45 = cos 45

Also that;

cos 0 = 1 but sin 0 = 0

Also; cos 90 = 0 but sin 90 = 1

This tells us that the output for cos theta decreases from 0 to 90 degrees but the opposite is the case for sin theta.

Thus, sin theta is smaller than or equal to cos theta for angles equal to or less than 45 degrees.

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Answer:

10.5

Step-by-step explanation:

These numbers are off by a little more than one power of ten:

[tex]1.2\times 10^6 \rightarrow 1.26 \times 10^7[/tex]

[tex]10^7 \div 10^6 = 10[/tex]   ← one power of ten

[tex]1.26 \div 1.2 = 1.05[/tex]   ← a little more

To find the exact scale factor between the numbers, simply multiply the values we just solved for:

[tex]10 \times 1.05 = 10.5[/tex]

So, [tex]1.2 \times 10^6[/tex] is 10.5 times smaller than [tex]1.26 \times 10^7[/tex].

Answer: 10.5

Step-by-step explanation:

The indicated angles in the parallel lines cut by the transversal are as follows:

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, linear angles, vertically opposite angles, alternate exterior angles etc.

Therefore, according to the diagram the two parallel lines are cut by a transversal. Let's use the angle relationships to find the m ∠1 and m∠3.

m ∠6 = 78 degrees.

m ∠1 = m ∠ 7 (alternate exterior angles)

Alternate exterior angles are congruent.

Hence,

m ∠7 = 180 - 78 = 102 degrees

m ∠ 1 = 102 degrees

m ∠ 1 = m ∠ 3 (vertically opposite angles)

vertically opposite angles are congruent.

m ∠ 3 = 102 degrees.

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There are 1260 eight-digit numbers that have 2 once, 3 twice, and 4 thrice.

There are 10 digits in the number system from 0 to 9.

Let the 8-digit number be represented by

_ _ _ _ _ _ _ _

Here the numbers will have a single 2, a doublet of 3, and a triplet of 4 hence we get

2 3 3 4 4 4 _ _

Now for the last 2 numbers, we have 0, 1, 5, 6, 7,  8, 9. Therefore the last 2 digits can be chosen in ⁷C₂ ways.

= 7!/(2 X 5!)

= 21 ways

There are 6 fixed numbers which can e arranged in 6! ways. Since there are numbers repeated twice and thrice, we can arrange them in

6!/(2! X 3!)

= 6 X 5 X 2

= 60 ways.

Therefore we get

60 X 21 numbers

= 1260 numbers.

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Based on the product of powers rule, the missing power in the given calculation is 2/3.

The product of powers rule is used in simplifying exponents. In a given term a^x, a number or variable raised to a power is called the base, while the superscript number is called the exponent, or power. According to the rule, if the bases are the same in the multiplication problem, it can be simplified by adding the exponents. Hence, for any number a and all integers m and n:

a^m * a^n = a^(m+n)

The given calculation is:

5^1/3*5^□ = 5

5^1/3*5^□ = 5^1

Hence, the sum of the powers would be one. Let the missing power be x. Therefore,

1/3 + x = 1

x = 1 - 1/3

x = 2/3

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Answer:

–6t

Step-by-step explanation:

f(t) = 2t

f(–3t) = 2( –3t )

= –6t

Antonella have a number of coins of quaters and nickels whose total value is 250.

The number of coins of nickel is 10 and the number of coins of quarters is 7.

Nickel and quarters are the coin based form of currency in the United States. The value of one nickel is 5 cents, while that of one quarter is 25 cents. We have given that

Antonella has 3 more quaters than nickles.

Let she has "x" number of quaters and "y" be number of nickels .

According to question,

y = 3+ x ---(1)

Combined value of all is 225 cents .

i.e 25 × x + y× 5 = 225 cents

plug the value of y from equation (1) to equation(2) we get,

25 x + 5(3+x) = 225

solve the equation

=> 25x + 15 + 5x = 225

=> 30x = 210

=> x = 7

put the value of x in equation (1)

y = x + 3 = 10

Hence, the number of nickels coins is 10 and numbers of quaters are 7.

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Internal validity explains the association between binge-watching tv and irritability.

In the context of a specific study, internal validity refers to how strongly a piece of evidence supports a claim regarding cause and effect. It is one of the most crucial characteristics of scientific research and a crucial idea when considering evidence more generally.

The extent to which alternative explanations for a study's findings (often, sources of systematic error or "bias") can be ruled out is a measure of its internal validity. In contrast, external validity measures how well data support judgments made regarding other situations (that is, the extent to which results can be generalized).

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In Herrnstein's matching equation, the letters and numbers to the left of the equals sign refer to behaviour.

THE MATCHING LAW

Herrnstein's Experiment Herrnstein (1961) conducted an experiment with pigeons in a room with two response buttons, red and white. Each key was assigned its own VI gain schedule. For example, under one condition, the left button pick was boosted on a VI 135 second schedule, and the right button pick was boosted on a VI 270 second schedule.

After the birds have learned as much as possible about this electoral situation, how do they distribute their responses? We trained them for days and then measured their reactions. As is often the case with VI schedules, birds returned many responses for each reinforcer received. Most interesting, however, is that in this condition, where two-thirds of the reinforcers came from the left button, the birds performed about two-thirds of the responses with the left button. That is, the proportion of left button responses equaled or matched the proportion of reinforcers delivered by the left button. In another condition, two birds received only about 15% of reinforcers from the left key and responded about 15% to that key.

Based on these results, Herrnstein proposed the following general principle for individual behavior when presented with alternative sequences. So, what you think makes sense rather than other options available at that particular moment.

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Answer:x=-1

Step-by-step explanation:

-x-2(7)=-13

-x-14=-13

(Add 14 on both sides)

-x=1

(-1x is the same as -x)

-1x=1

(Divide both sides by -1)

X=-1

the formula for y after a 15 percentage of increase will be y=1.15x

What is the Percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term per cent signifies. The letter "%" stands for it.

Example percentages include:

There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we imply that it is 50% of everything.

As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any topic are calculated in terms of percentages in academics.

if there is a 15 percent increase in the initial value then the value will be y = 1.15x

y is the price after the  increase

x is the price before the increase

so the increase in the price will be x+ 15 percentage  of x

y= x+15/100 x

y=x+0.15x

y=1.15x

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Answer:

Reflection across the X axis, translate to the right by 7 points

Step-by-step explanation:

A reflection would move ABC to quadrant 3, and the translation of +7 would put point C where point S is.

The length of DB, AD and AC are 24 m, 32 m, 42 m respectively. The measurement of ∠C = 67.38°.

What is a right angle triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

Given that, in △BCD

BD = 24 m

DC = 10 m

BC = 26 m

△BCD is a right angle triangle.

The trigonometry ratio of sine is ratio of height to hypothenuse.

With respect to C, the height of △BCD is 24m and hypothenuse is 26m.

sin C = height/hypothenuse

sin C = 24/26

C = 67.38°

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Answer:

[tex]\frac{5}{2}[/tex]

Step-by-step explanation:

[tex]\frac{9}{4} +\frac{2}{8}[/tex]

1. Since the denominators (bottom numbers) are different, you have to find the lowest common denominator
Your denominators are 4 and 8. The goal is to find the least common multiple. (LCM) this is the lowest number that both 4 and 8 can go into. Here that is 8.

[tex]\frac{9}{4} +\frac{2}{8}[/tex]

To find the LCM you can write out the multiples like this

4: 4,8,12,16...

8: 8,16,24

Since they both have 8, this is your lcm

2. Now look at the difference between the denominators in the original problem.

 [tex]\frac{9}{4} +\frac{2}{8}[/tex]

The other bottom number is 4 so you need to see how many times you'd have to multiply 4 to get 8. Here that is 2. Because 4x2 is 8.

3. Now multiply both numbers on the left by 2. (because of step 2)

9x2= 19 and 4x2=8

Now you have [tex]\frac{18}{8} +\frac{2}{8}[/tex]

4. Now do the other side. The denominator is already 8 so you don't have to change anything. (this is because you would just do everything times 1 like you did 2 in the last step.)

5. Now you can just add the 2 fractions across.

[tex]\frac{18}{8} +\frac{2}{8}[/tex] 18+2= 20 and 8+8=16

This gives you: [tex]\frac{20}{8}[/tex]

6. Now simplify. To simplify, find the highest common factor (HCF). to do that you find the highest number that goes into both 20 and 8.

20: 1,2,4,5,20

8: 1,2,4,8

The highest number that goes into both is 4.

Noe divide both numbers of [tex]\frac{20}{8}[/tex] by 4.

This gives you

[tex]\frac{5}{2}[/tex]

28° & 62° are the measure of each acute angle.

What is acute angle and example?

Acute angles are defined as those that are less than 90 degrees. Compared to the right angle, this angle is smaller (which is equal to 90 degrees).

            For instance, acute angles include 30°, 45°, 60°, 75°, 33°, 55°, and 85°, among others.

In a right triangle we know that one of the angles is 90°. We also know that the 3 angles must add up to 180°.

Let x = acute angle 1

     y = acute angle 2

We have 2 unknowns, therefore we must have 2 equations to solve this.

Eq. I                                                       Eq. II

90 + x + y = 180                                  

x + y = 180 - 90                                    

x + y = 90

Using the value for x in terms of y from Eq. II in Eq. I we can solve for y:

x = 2y + 6                

x + y = 90                

2y + 6 + y =90        

3y = 90 - 6                

3y = 84                  

y = 84/3                    

y = 28                      

Using this value for y in Eq. II we can solve for x:

x = 2y + 6                

x = 2(28) + 6            

x = 56 + 6              

x = 62                      

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The complete question is -

In a right triangle, the measure of one acute angle is 2 times the sum of the measure of the other acute angle and 3. Find the measure of each acute angle

The rate at which the angle between the ladder and the wall of the house is changing is ≈ 0.083 deg/s when the base of the ladder is 7 feet from the wall.

Trigonometric The values of all trigonometric functions based on the ratio of sides in a right-angled triangle are defined as ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

sine, cosine, tangent, cotangent, secant, and cosecant are all trigonometric ratios.

Given:

Length of ladder = 25 feet

The base of the ladder pulled at the rate of = 2 feet per sec

Distance of the base of the ladder from the wall =7 feets

According to the question,

By using trigonometric ratios - sine ratio

[tex]sine = \frac{opposite}{hypotenuse} \\[/tex]

from the position of A, the opposite side is x and the hypotenuse is 25. hence

[tex]sin A = \frac{x}{25}[/tex]

Differentiating it with respect to the time t we have,

[tex]cos A= \frac{dA}{dt} = \frac{1}{25} \frac{dx}{dt} ...... (3)[/tex]

at x = 7

[tex]sin A = \frac{7}{25}\\cos A = \frac{24}{25}[/tex]

plugging in [tex]\frac{dx}{dt} = 2, cos A = \frac{24}{25}\\[/tex] into eq no (3) gives us rate of change

[tex]\frac{24}{25} \frac{dA}{dt} = \frac{1}{25} (2)\\\frac{dA}{dt} = \frac{25}{25} \frac{1}{25} (2)\\\frac{dA}{dt} = \frac{1}{12}\\[/tex]

[tex]\frac{dA}{dt}[/tex] ≈ 0.083

Therefore, the rate at which the angle between the ladder and the wall of the house is changing is ≈ 0.083 deg/s when the base of the ladder is 7 feet from the wall.

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A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall.

The solution of the equation is -2.

What is the solution of an equation?

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

What is distributive property?

The distributive Property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.

Given equation is 2(4x+3)+4=3x-(2x+4).

Apply distributive property in 2(4x+3):

8x + 6 + 4 = 3x - (2x+4)

8x + 10 = 3x - (2x+4)

Open parenthesis on the right side:

8x + 10 = 3x - 2x - 4

Combine like terms:

8x - 3x + 2x = -4 -10

7x = -14

Divide both sides by 7:

x = -14/7

x = -2

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Check the picture below.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+160}x\stackrel{\stackrel{c}{\downarrow }}{+20} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 160}{2(-16)}~~~~ ,~~~~ 20-\cfrac{ (160)^2}{4(-16)}\right) \implies \left( - \cfrac{ 160 }{ -32 }~~,~~20 - \cfrac{ 25600 }{ -64 } \right) \\\\\\ \left( 5 ~~~~ ,~~~~ 20 +400 \right)\implies (\stackrel{seconds}{5}~~,~~\stackrel{feet}{420})[/tex]

Answer:

0.0000010

Step-by-step explanation:

divide it by 10 6 times

The mean, variance and the standard deviation for the distance travelled by 10 students is computed as-

Mean  = 3.12; standard deviation = 1.8232; variance = 3.324

Total students n = 10 .

Given the information, 1, 5, 2, 3, 5, 4, 8, 1, 2, 2, 5, 1.5, and 0.8

To determine the mean, we must first add up all the information provided and divide it by the number of students.

X = 1.1 + 5.2 + 3.6 + 5.0 + 4.8 + 1.8 + 2.2 + 5.2 + 1.5 + 0.8

X = 31.2

Mean  = X/n

Mean  = 31.2/10

Mean  = 3.12

Now the standard deviation is estimated as-

S = √∑x² - [(∑x)²/n] / (n-1)

Putting the values-

s = 1.8232

standard deviation = 1.8232

The variance is estimated by -

variance = S²

S² = 1.8232²

variance = 3.324

Thus, the mean, variance and the standard deviation for the distance travelled by 10 students is computed.

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The complete question is-

In a random sample, 10 students were asked to compute the distance they travel one way to school to the nearest tenth of a mile. Compute the sample mean, standard mean, standard deviation and variance of the data:1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8 Mean = ?, Variance = ?; Standard Deviation= ?

Question:

To find :

solution:

[tex] ln\dfrac{1}{\sqrt{e^{3}}}=x\\\\ e^{^{({ln\dfrac{1}{\sqrt{e^{3}}}})}}=e^{x}\\\\ \dfrac{1}{\sqrt{e^{3}}}=e^{x} \\\\ (\dfrac{1}{\sqrt{e^{3}}})^{2}=e^{2x}\\\\ \dfrac{1}{e^{3}}=e^{2x}\\\\ e^{-3}=e^{2x}\\\\ -3=2x \\\\\sf{x=\dfrac{-3}{2}} [/tex]

final answer:

If there are 60 apples in total, then green are 15 .

Given:

in a basket of red and green apples, green apples are only 1/3 as common as red apples.

if there are 60 apples in total, how many are green = ?

x is the number of red apples

y is the number of green apples

x/3= y;

x=3y

x+y= 60

3y+y=60;

4y=60;

that means y=60/4

y = 15

Hence there are 15 green apples.

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Answer: 68 seconds

Step-by-step explanation:

Answer: 68sec

Step-by-step explanation:

The correct statement regarding the sign of the residuals in the table is given as follows:

3 negative residuals and 5 positive residuals.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

Hence the residuals are classified as either positive or negative as follows:

Thus the residuals in this problem are classified follows:

Hence the third statement is correct.

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The answer choice which correctly represents the vertex and range of y as given in the task content is; (−2, −6); −6 ≤ y < ∞.

It follows from the task content that the given absolute function is; y = | x + 2 | − 6.

Since the vertex form equation of an absolute function is given as;

y = a | x - h | + k.

where the vertex is; ( h, k ).

By observation, it follows that in the given equation;

a = 1, h = -2, and K = -6.

Therefore, since a > 0, it follows that the function opens upwards and the minimum is; 6.

Ultimately, the vertex of the given function, y is; (-2, -6) and the range is; −6 ≤ y < ∞.

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Doing factorization, we know that the factors of the given equation are ±√5 and ±10i.

In mathematics, factorization or factoring consists of writing a number or any mathematical item as a product of several factors, typically small or easier objects of the same.

For example, 3 × 5 is a factorization of an integer 15 and is a factorization of an equation x² – 4.

So, we have the equation:

x⁴ + 95x² – 500 = 0

Factorizing the above equation:

x⁴ + 100x² - 5x² - 500 = 0

x²(x² + 100) - 5(x² + 100) = 0

(x² - 5)(x² + 100) = 0

Solving further:

x² = 5

x² = -100

x = ±√5

x = √-100

Factors: ±√5 and ±10i

Therefore, doing factorization, we know that the factors of the given equation are ±√5 and ±10i.

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Complete question:
What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.

x=+- sqrt 5 and x = ±10

x=+- sqrt i5 and x = ±10i

x=+- sqrt 5 and x = ±10i

x=+- sqrt i5 and x = ±10

Answer:

D

Step-by-step explanation:

|x+2|<2

|x+2|<2 --> split abs. value equations into two parts. Flip the sign for the negative value

x+2<2 and x+2>-2

x+2<2 --> x<0

x+2>-2. --> x>-4

solituon. -4<x<0

To solve the given quadratic equation,  [tex]\frac{81}{4}[/tex] must be added to complete the square

What is quadratic equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A two degree equation is known as quadratic equation.

[tex]x^2+9x+7=0\\x^2+9x = -7\\x^2+2\times x \times \frac{9}{2} + (\frac{9}{2})^2 = -7 + (\frac{9}{2})^2\\x^2+2\times x \times \frac{9}{2} + \frac{81}{4}= -7 + \frac{81}{4}\\(x+ \frac{9}{2})^2 = \frac{53}{4}[/tex]

So, [tex]\frac{81}{4}[/tex] must be added to complete the square for solving the given quadratic equation

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The image after the sequence of transformations is (30, -14)

We start with the point (9, 4), first we need to translate it up 3 units, then right 6 units, dilate it by a scale factor of 2, and finally reflect it across the x-axis.

Let's write all these transformations in a general way and then let's apply them.

For a general point (x, y)

A vertical translation up of 3 units gives: (x, y + 3)

A horizontal translation of 6 units to the right gives: (x + 6, y)

A dilation of scale factor 2 gives: (2x, 2y)

A reflection across the x-axis gives: (x, -y)

Then if we apply all that to our point (9, 4) we will get:

A vertical translation up of 3 units gives: (9, 4 + 3) = (9, 7)

A horizontal translation of 6 units to the right gives: (9 + 6, 7) = (15, 7)

A dilation of scale factor 2 gives: (2*15, 2*7) = (30, 14)

A reflection across the x-axis gives: (30, -14)

That is the image after the sequence of transformations.

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