consider the inequality x 36>x4 1. which value of x is a solution to the inequality?

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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The true or false values of the statements are:

From the question, we have the graph which represents the given parameters that can be used in our computation

Analysing the graph, we have:

The graph crosses the y-axis at y = 18

This means that the y-intercept of the graph is

y-intercept  = 18

This in other word mean that:

The cost of the book is $18

So, (a) is true

Also, the graph crosses the x-axis at x = 90

This means that the x-intercept of the graph is

x-intercept  = 90

This in other word mean that:

Giselle gets $18 if she pulls all the weed (i.e. 90 weeds) in the garden

So, (b) and (d) are true

The amount paid by her grandma is calculated as

Amount = 18/90

Amount = 1/5

So, (c) is true

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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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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 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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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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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]

Answer:rise over rub

Step-by-step explanation:

Answer:

3.444 repeating on

Step-by-step explanation:

Answer:

/x/=3 then x value has 3 and -3

Answer:

The required equation has only two solution x = 3 and x = -3 is x2 -9

Step-by-step explanation:

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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The value of the definite integral is [tex]\frac{\pi }{4} - \frac{1}{2}[/tex]

Using microscopic slivers or stripes of the region, a definite integral is a formal estimate of the area beneath a function. Integrals can reflect a region's (signed) area, the total value of a function that changes over time, or the amount of a given thing given its density.

Definite Integral helps to find the area of a curve in a graph. It has limits, which are the start and the endpoints, within which the area under a curve is calculated. The limit points can be taken as [a, b], to find the area of the curve f(x), with respect to the x-axis.

Given,

[tex]\int\limits^\frac{1}{2} _0 {\frac{\sqrt{x} }{\sqrt{1-x} } } \, dx = \int\limits^\frac{\pi }{4} _0 {2sin^{2}y } \, dy[/tex]

[tex]\int\limits^\frac{1}{2} _0 {\frac{\sqrt{x} }{\sqrt{1-x} } } \, dx = \frac{\pi }{4} - \frac{1}{2}[/tex]

[tex]\int\limits^\frac{\pi }{4} _0 {2sin^{2}y } \, dy = \frac{\pi }{4} -\frac{1}{2}[/tex]

∴[tex]\frac{\pi }{4} - \frac{1}{2}[/tex] = [tex](\frac{\pi }{4} - \frac{1}{2})[/tex]

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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.

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]

The probability that they have an average weight of greater than 10 pounds and less than 15 pounds is 0.84134

In this question we have been given there are 250 dogs at a dog show who weigh an average of 15 pounds, with a standard deviation of 6 pounds. of 10 dogs are chosen at random.

We need to find the probability that they have an average weight of greater than 10 pounds and less than 15 pounds.

Given, μ = 12, σ = 8, n = 4

P(X > 8)

= P(z > (8 - 12 / 8/√4))

= P(z > -1)

= 1 - P(z ≤ -1)

= 1 - [1 - P(z ≤ 1)]

=  P(z ≤ 1)

= 0.84134

Therefore, the required probability is 0.84134

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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:

Answer:

–6t

Step-by-step explanation:

f(t) = 2t

f(–3t) = 2( –3t )

= –6t

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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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

The series in question converges.

If a series converges to a value as its terms approach to infinity, it is said to be convergent. If a series does not converge to a value but instead keeps on rising or dropping as the terms of the series go to infinity, it is said to be divergent.

The geometric sequence is as follows:

10 - 4 + 1.6 - 0.64 +...

If the common ratio of the series is between -1 and 1, then a geometric progression will be convergent.

The common ratio in this case is

r = -4/10

r = -0.4, or -1 -0.4 1.

The presented series is hence convergent.

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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 probability that a customer shops at za in week 0 will shop at za in week 2 = 57.76%

In this question, we have been given wb and za are two competing grocery stores in a particular region. the probability that a customer who shops this week at wb will shop again at wb next week is 64% whereas the probability that a za customer will shop next week at za is 76%.

We need to find the probability that a customer who shops at za in week 0 will shop at za in week 2.

Let  in week 0, 100 customers shop at za.

The probability that a za customer will shop next week at za is 76%.

This means, in week 1, 76 customers shop at za.

And in week 2, 76% of 76 customers will shop at za.

76 percent of 76 = 57.76

Therefore, the required probability is 57.76%

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Answer:

You are 110 feet under the sea and then you rise 120 feet.  How many feet are you now above the sea lever?  10.

Step-by-step explanation:

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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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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if the island is 10 miles long, it would take you 5 hours to walk the length of the island (10 miles/30 minutes = 5 hours).This depends on the length of the island.

First, you would need to know the length of the island. You can look up the exact distance of the island online. After you have the length, divide that number by the amount of time it takes you to walk a mile (30 minutes). That will give you the amount of time it takes to walk the length of the island.

To figure out how long it would take you to walk the length of this island, you need to know the exact length of the island first. You can look up its length online, or you can measure it on a map. Once you have the length, divide that number by the amount of time it takes you to walk a mile (30 minutes). That will give you the total amount of time it takes to walk the length of the island. For example, if the island is 10 miles long, it would take you 5 hours to walk the length of the island (10 miles/30 minutes = 5 hours).

If the island is 10 miles long, it would take you 5 hours to walk the length of the island (10 miles/30 minutes = 5 hours).

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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 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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Answer: $1632 is his total annual premium for health insurance

Step-by-step explanation:

85*.60=$51

His employer pays $51 per month

you would multiply 51 by 12 to get the employers amount and them multiply 85 by twelve then you would add the two to get the total which should be his annual premium amount

$51*12 months=612

$85*12=1020

1020+612=1632