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Use tests for symmetry to determine which graphs from the lists below are symmetric with respect to the y-axis, the x-axis, and the origin. (Select all that apply)

a. symmetric with respect to the y-axis

The only possible solution is x = 2. Therefore, the three consecutive integers that form the sides of the right triangle are 2, 3, and 4.

Since they are consecutive integers, let's assume that the hypotenuse, which is the longest side of the right triangle, is x+2, as it is three units longer than the shortest side.

In a right triangle, the hypotenuse's square is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem. We can thus write:

[tex](x+2)^2 = x^2 + (x+1)^2[/tex]

Expanding the squares, we get:

[tex]x^2 + 4x + 4 = x^2 + x^2 + 2x + 1[/tex]

Simplifying and rearranging terms, we get:

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

We can solve this quadratic equation by using the quadratic formula:

x = (-b ± [tex]\sqrt{b^2 - 4ac}[/tex]) / 2a

where a = 2, b = -2, and c = -3.

Plugging in these values, we get:

x = (-(-2) ± [tex]\sqrt{((-2)^2 - 4(2)(-3)))[/tex] / 2(2)

x = (2 ± [tex]\sqrt{(4 + 24))[/tex] / 4

x = (2 ± [tex]\sqrt28}[/tex] / 4

x = (2 ± [tex]2\sqrt{7}[/tex]) / 4

x = 1/2 ± [tex]\sqrt{7}[/tex]/2

The only option is x = 2, since x must be an integer. As a result, the numbers 2, 3, and 4 are the three consecutive integers that make up the sides of the right triangle.

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The volume of the block of wood is 104.7634 cm³ and the total surface area is 186.4502 cm².

Volume is the measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³).

The volume of the block of wood will be;

V = l x w x h = 4.55 cm x 9.1 cm x 2.54 cm

= 104.7634 cm³

Therefore, the volume of the block of wood is 104.7634 cm³.

The total surface area of the block of wood will be;

SA = 2lh + 2wh + 2lw

= 2(4.55 cm x 2.54 cm) + 2(9.1 cm x 2.54 cm) + 2(4.55 cm x 9.1 cm)

= 58.0094 cm² + 46.4314 cm² + 82.0094 cm²

= 186.4502 cm²

Therefore, the total surface area is 186.4502 cm².

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Answer: It is 1.24x smaller.

Step-by-step explanation:

1.2(106)= 127.2

1.47(107)= 157.3

157.3/127.2 = 1.24x smaller

The firm expects replacing around 734 batteries out of the 32,200 produced.

using the normal distribution formula z = (x - )

When z denotes the z-score,

x denotes the battery life of interest, is the mean battery life, and is the standard deviation.

For x = 100, use the z-score: z = (100 - 120) / 10 z = -2

Calculate the area under the normal curve to the left of z = -2.

0.0228 is the approximate value.

The number of batteries expected to be replaced by the manufacturer is equal to the proportion of batteries with a battery life of less than 100 hours multiplied by the total number of batteries produced:

Number of batteries to be replaced = 0.0228 x 32,200

734.16 batteries are expected to be replaced.

As a result, the firm anticipates replacing around 734 batteries out of the 32,200 produced.

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Answer is down below!

Step-by-step explanation:

This is of the form h = a + b cos ct, where: a = 40 m. This is the height of the axle of the Ferris wheel. b = -30 m. The magnitude of this number is the radius of the wheel.

Answer:

n + 8

M - x

z - 12

c + d

2f + 20 or 20 + 2f

(x + y)^2 or (x + y) × (x + y)

2mn or 2 × m × n

2b - 6 or 6 - 2b

u^2 + v^2 or v^2 + u^2

(xy)/2 or xy/2

The surface area of the figure is 344 m².

Area is the region bounded by a plane shape.

To calculate the surface area of the figure, we use the formula below.

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 2

Hence, the area is 344 m².

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Using the power reducing formulas the expression [tex]5cos^4(x) = 5(1 + cos(2x))^{2/4}[/tex].

We can define higher powers of a trigonometric function in terms of lower powers of the same function using the power-reducing formulas, which are trigonometric identities. Higher powers of cosine can be expressed using this formula in terms of sine and cosine's initial powers. For the other trigonometric functions, such as sine and tangent, there are equivalent formulas. These formulas can be used to solve trigonometric equations and to simplify trigonometric expressions.

The given function is 5cos^4(x).

Now, the power reducing formulas are given by:

[tex]cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1\\cos^2(x) = (1 + cos(2x))/2[/tex]

Substituting the value of second equation in 1 we have:

cos(2x) = 2(1 + cos(2x))/4 - 1

[tex]cos(2x) = (2cos^2(x) - 1) = cos^2(x) - sin^2(x)[/tex]

Now we have:

[tex]cos^2(x) = (1 + cos(2x))/2[/tex]

Thus,

[tex]cos^4(x) = (1 + cos(2x))/2)^2[/tex]

Now multiplying by 5:

[tex]5cos^4(x) = 5(1 + cos(2x))^{2/4}[/tex]

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The surface area of the square pyramid given above would be = 400ft²

To calculate the surface area of the given figure, the formula that should be used would be = b² +2bs

where B = base length= 10ft

s = slant height= 15ft

Surface area = 100+2(10×15)

= 100+300

= 400ft²

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We can see here that from the available information it is clear that imports of Benin were:

While the exports are:

A locally produced commodity or service that is sold to another nation is referred to as an export. To put it another way, it's a good or service that is sold or sent to another nation to be utilized or consumed there.

Exports may help a nation's economy expand by bringing in money and creating jobs.

Imports are actually known to be goods and services that are brought into a country/nation.

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This shows that the two circles intersect at a point P, and that the distance between their centers, OP1OP2, is less than the sum of their radii, r1 + r2. Thus, the two circles touch each other internally at point P.

You must calculate each circle's radius and centre in order to accomplish this. The circles will externally touch if the total of the radii and the space between the centres are identical. The circles will internally touch if the variations in radii and the separation between their centres are equal.

Let C1 and C2 stand for the two circles, with O1 and O2 serving as their respective centres. Let r1 and r2 represent the radius of C1 and C2, respectively.

Let's say that point P is where the two circles converge. The Pythagorean Theorem thus gives us:

OP1² = r1²

OP2² = r2²

OP1² + OP2² = (r1 + r2)²

Simplifying the third equation, we get:

OP1² + OP2² = r1² + 2r1r2 + r2²

The left half of this equation can be rewritten as (OP1 + OP2)2 - 2OP1OP2. When we simplify the equation above and substitute this, we get:

(OP1 + OP2)² = (r1 + r2)² + 2OP1OP2

Since OP1 and OP2 are both positive, we have:

(OP1 + OP2)²> (r1 + r2)²

Therefore, we must have:

OP1OP2 < r1 + r2

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The probability that the randomly selected person is taking a sunbath is 7/22.

Science uses a figure called the probability of occurrence to quantify how likely an event is to occur.

It is written as a number between 0 and 1, or between 0% and 100% when represented as a percentage.

The possibility of an event occurring increases as it gets higher.

So, the probability formula is:

P(E) = Favourable events/Total events

Now, insert values in the formula as follows:

P(E) = Favourable events/Total events

P(E) = 28/88

P(E) = 14/44

P(E) = 7/22

Therefore, the probability that the randomly selected person is taking a sunbath is 7/22.

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The difference between 6 5/6 and 5 1/2 is 4/3 .

To subtract these mixed numbers, we need to first convert them into improper fractions:

6 5/6 = (6 x 6 + 5)/6 = 41/6

5 1/2 = (5 x 2 + 1)/2 = 11/2

Now we can subtract:

41/6 - 11/2

To deduct divisions with various denominators, we really want to track down a shared factor. 6 is the smallest common multiple of 6 and 2 in this instance. Therefore, we can use denominator 6 to convert 11/2 into an equivalent fraction:

11/2 = (11 x 3)/(2 x 3) = 33/6

Now we can subtract the fractions with the same denominator:

41/6 - 33/6 = 8/6

Working on the portion by partitioning both the numerator and denominator by their most prominent normal component, we get:

8/6 = 4/3

As a result, in mixed numbers, the difference between 6 5/6 and 5 1/2 is 4/3, or 1 1/3..

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The complete question is:

What is the rule for the sequence

5/6, 1 1/2, 2 1/6, 2 5/6.....

The equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level is 11400

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

q = 20,000 − 2p

q = 8,500 + 0.5p

The equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level is when q = q

So, we have

20,000 − 2p = 8,500 + 0.5p

Evaluate the like terms

2.5p = 28500

Divide by 2.5

p = 28500/2.5

Evaluate

p = 11400

Hence, the equilibrium tuition price p is 11400

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the guests arrived for dinner at 6:39 P.M.which is solved by according to given question.

How to solve the question?

To solve this problem, we need to first convert the fraction of an hour that Miss Johnson's guests were late into minutes. We know that 1 hour is equal to 60 minutes, so we can find the number of minutes the guests were late by multiplying 2/5 by 60:

2/5 hour * 60 minutes/hour = 24 minutes

So the guests were 24 minutes late. To find out what time they arrived, we need to add 24 minutes to the original arrival time of 6:15 P.M.:

6:15 P.M. + 24 minutes = 6:39 P.M.

Therefore, the guests arrived for dinner at 6:39 P.M.

It's important to note that fractions can often be confusing when dealing with time calculations. In this case, we converted the fraction of an hour to minutes to make the calculation easier. Additionally, it's always a good idea to double-check your work to ensure that your answer makes sense in the context of the problem.

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The amount of time it would take to drain the swimming pool is equal to 75 minutes..

Generally speaking, a mathematical model for any quantity (water) that decreases by r percent per unit of time is an exponential function of this form:

[tex]P(t) = I(1 - r)^t[/tex]

Where:

Next, we would determine the amount of time it would take to have 0 gallons in the swimming pool:

20 gallons = 3 minutes

5,000 gallons = x minutes

20x = 1500

x = 1500/20

x = 75 minutes.

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Answer:

66 because 10 percent of 60 is 6 so add 60 and 6

The appropriate domain for the function h(t) = −3t^2 + 9t + 12 is [0, 3.08].

The domain of a function is the set of all possible input values for which the function is defined. In this case, the function h(t) gives the height of the ball above the ground as a function of time t.

The ball is thrown from the tree house at some initial time, and it continues to travel until it hits the ground. The height of the ball is defined for all values of t between the time it is thrown and the time it hits the ground.

To find the domain of h(t), we need to determine the range of values of t for which the function is defined. The ball cannot have a negative height, so the function is undefined for values of t that would make h(t) negative.

To find the time at which the ball hits the ground, we need to set h(t) equal to zero and solve for t:

h(t) = -3t^2 + 9t + 12 = 0

Using the quadratic formula, we get:

t = (-9 ± √(9^2 - 4(-3)(12)))/(2(-3))

t = (-9 ± √(105))/(-6)

t ≈ -0.41 or t ≈ 3.08

Since the ball cannot have a negative height, the domain of the function is the interval [0, 3.08]. Therefore, the appropriate domain for the function h(t) = −3t^2 + 9t + 12 is [0, 3.08].

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By sample distribution, (0.431,0.487) is Complete parts​ (a) through​ (d) below.

What does a statistical sample distribution mean?

An accurate probability distribution of a statistic is known as a sampling distribution, and it is created by repeatedly sampling a certain population. It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.

Given

Favourable cases (X)=?

Sample size(n)=510

Sample proportion (p_hat)=X/n=0.459

X=np_hat=510*0.459=234.09=234

Confidence level(1-α)=99%=0.99

α=0.0

The critical value for  α=0.01 is Zc=2.576

The margin of error is E=Zc* √((p_hat(1-p_hat)/n))

E=2.576* √((0.459(1-0.459)/510))=0.0568

The 99% confidence interval for p

CI=(p_hat-E,p_hat+E)

CI=(0.459-0.0568,0.458+0.0568)

CI=(0.402,0.516)

Confidence level(1-α)=80%=0.80

α=0.20

The critical value for  α=0.2 is Zc=1.282

The margin of error is E=Zc* √((p_hat(1-p_hat)/n))

E=1.282* √((0.459(1-0.459)/510))=0.0283

The 80 % confidence interval for p

CI=(p_hat-E,p_hat+E)

CI=(0.459-0.0283,0.458+0.0283)

CI=(0.431,0.487)

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Answer:

13

Step-by-step explanation:

First of all riley saved 200.73$ she needs 1,290.78$ so,

1290.78$-200.73$=1090.95$

she earns 83.85$ a week

then, 1090.95÷83.85= 13

13 weeks

The only option given that has a variable raised to the third power is D. -2x³, so the correct answer is D.

In algebra, a monomial is an expression that consists of a single term, which is a product of a constant coefficient and one or more variables raised to non-negative integer powers. In each of these expressions, there is only one term, and each term is a product of a constant coefficient and one or more variables raised to non-negative integer powers. Monomials are important in algebra because they can be combined using various operations such as addition, subtraction, multiplication, and division, to form more complex expressions.

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The equation that  matches this problem is 15 + 3p = 117

Let the cost of one pair of pants be represented by the variable p.

Then, the cost of three pairs of pants is 3p.

We are also given that the cost of a t-shirt is $15.

The total cost of Amelia's purchase is $117.

Therefore, the equation that matches this problem is:

15 + 3p = 117

This equation represents the total cost of Amelia's purchase, which includes the cost of one t-shirt and three pairs of pants.

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Thus, the statement  -3 to the -3 power written without using exponents is -1/27.

A number's power or exponent, in other words, tells how many times it must be multiplied by itself. Any integer, fraction, or decimal can serve as the basis in this situation. Moreover, the exponent might have either a positive or negative value.

Given that-

-3 to the -3 power

This can written as:

= (-3)⁻³

Now using the property of exponents,taking reciprocal of the number will remove the negative number.

= (1 /-3)³

= (1)³ / (-3)³

= 1/(-27)

= - 1/ 27

Thus, the statement  -3 to the -3 power written without using exponents is -1/27.

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The height is 230 feet after 9.125 seconds.

We have the  equation that describes the height of the object as a function of time as:

h(t) = -16t^2 + 145t + 2

We input the values and simplify:

-16t^2 + 145t + 2 = 230

-16t^2 + 145t - 228 = 0

we can use the quadratic formula, to solve this quadratic equation,

t = (-b ± √(b^2 - 4ac)) / 2a

where a = -16, b = 145, and c = -228.

t = (-145 ± √(145^2 - 4(-16)(-228))) / 2(-16)

t = (-145 ± √ (21025)) / (-32)

t = (-145 ± 145) / (-32)

t = 0.625 seconds or t = 9.125 seconds

In conclusion, the height is 230 feet after 9.125 seconds.

#complete question:

An object is thrown upward at a speed of 145 feet per second by a machine from a height of 2 feet off the ground. The height h of the object after t seconds can be found using the equation

When will the height be 230 feet?

Answer:

  D.  9 clubs

Step-by-step explanation:

Given a stem-and-leaf plot of the number of members in clubs, you want to know the number of clubs with 30 or more members.

The plot shows the club membership to be ...

  {10, 13, 15, 24, 26, 30, 36, 39, 50, 55, 59, 61, 66, 78}

The 9 clubs whose member numbers are in bold have at least 30 members.

The number of clubs with at least 30 members is ...

  D.  9 clubs

<95141404393>

Using the method of mathematical induction, we show that the inequality σ(n) > H(n) holds for all n≥1. Thus, the inequality n≥1 is true for all n≥1.

It is a  a technique used in mathematics to prove that a statement is true for every positive integer or natural number. It consists of two steps:

We can calculate like this:

Base case: Show that the inequality holds for n=1.

Inductive hypothesis: Assume that the inequality holds for some arbitrary positive integer k, i.e., k ≤ 2^(σ(k)/Hk).

Inductive step: Show that the inequality also holds for k+1. Consider σ(k+1) and H(k+1). We can express them as σ(k+1) = σ(k) + k+1 and H(k+1) = H(k) + 1/(k+1).

Using the inductive hypothesis, we have:

So, we can raise both sides to the power of (k+1)/(kH(k+1)) to get:

By the AM-GM inequality, we know that σ(k+1)/k+1 ≥ H(k+1), so we can replace the denominator (kH(k+1)) with H(k+1) and simplify to get

Therefore, we have shown that k+1 ≤ 2^(σ(k+1)/H(k+1)), which means the inequality holds for all positive integers n by mathematical induction.

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The measure of ∠DOT is equal to 58°

The measure of ∠TOU is equal to 32°.

In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).

Mathematically, a complementary angle can be calculated by using this mathematical equation:

Q + R = 90°

Where:

Q and R are measure of the angles subtended.

By substituting the given parameters into the complementary angle formula, the sum of the angles is given by;

(7x + 2) + 4x = 90.

11x + 2 = 90

11x = 90 - 2

x = 88/11

x = 8.

For the measure of ∠DOT, we have;

∠DOT = (7x + 2)

∠DOT = 7(8) + 2

∠DOT = 58°

For the measure of ∠TOU, we have;

∠TOU = 4x

∠TOU = 4(8)

∠DOT = 32°.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.