For the x-values 1, 2, 3, and so on, the yvalues of a function form a geometric
sequence that decreases in value. What type of function is it?​

The closest to the value of x is option A = 5.8cm

According to the Pythagorean theorem, the square on the hypotenuse of a right-angled triangle equals the sum of the squares on the other two sides.

To determine the value of x in centimeters, we can use the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is known as the triangle inequality.

so,we can use Pythagorean theorem we get,

x² = (8)² - (6)²

x²= 64 - 36

x² = 28

x = \(\sqrt28\)

x = 5.8 cm

Therefore,the value of x is 5.8 cm

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9514 1404 393

Answer:

  1. ΔOMN≅ΔMOP ∴ ∠OMN≅∠MOP by CPCTC

  2. ΔOSP≅ΔORP ∴ SP≅RP by CPCTC

Step-by-step explanation:

1 and 2

A properly constituted congruence statement lists the congruent vertices of the figures in the same order. That is, the sequence of vertices that make up one angle or segment in one of the figures will match the sequence of vertices that make up the congruent angle or segment in the other figure. The rule that lets you list congruent parts this way is ...

   Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

In problem 1, the vertices making up the congruent angles are listed 1st, 2nd, and 3rd in the triangle congruence statement: ΔOMN≅ΔMOP.

In problem 2, the vertices identifying the congruent segments are listed 2nd and 3rd in the triangle congruence statement: ΔOSP≅ΔORP.

Answer:

Gretta's Contribution = $52,500

Interest = $125,588.79

Step-by-step explanation:

Gretta contributes $125 each month, for 35 years. Therefore, to find the amount she contributed, we multiply those pieces together (12 months in each year).

125 x 12 x 35 = $52,500

Therefore, over the 35 years, Gretta contributed $52,500.

If there was $178,088.79 in her account, and she contributed $52,500, then the rest is interest.

$178,088.79 − $52,500 = $125,588.79

There was $125,588.79 in interest earned on Gretta's account.

Step-by-step explanation:

Check the attachment for answer

Answer:

\(\bold{-\dfrac{1}{2\sqrt{4-x}}}\)

Step-by-step explanation:

This can also be solved without using limits

Let  \(y = \sqrt{4-x}\)

The power rule of derivatives says that if we have a function

\(y = a.x^n,\)

then the first derivative given by \(\frac{dy}{dx}\) or abbreviated as \(y'\) is given by \(n(ax^{n-1})\)

We can use this in combination with the substitution rule of calculus

Let u = 4-x

Then we have \(\frac{du}{dx} = \frac{d(4)}{dx} - \frac{d(x)}{dx} = 0 -1 = -1\)

(First differential of a constant is 0 and first differential of x  is 1)

Substituting for u in the original expression \(\sqrt{4-x}\) we get \(\frac{dy}{du} = \frac{d}{du} (\sqrt{u}) = \frac{d}{du}(u^{1/2}) = \frac{1}{2} u^{\frac{1}{2} -1} = \frac{1}{2} u^{-1/2} =\frac{1}{2} \frac{1}{\sqrt{u} }\)

The substitution rule states \(\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}\)

So

\(\frac{dy}{dx} = \frac{1}{2\sqrt{u} } . (-1)\)

Substituting for u in terms of x we get
\(\frac{dy}{dx} = \frac{1}{2\sqrt{4-x} } . (-1) = -\frac{1}{2\sqrt{4-x}}\)

Answer: D

Step-by-step explanation:

The test statistic is t = 1.14.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean  and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean  and standard deviation .

here, we have,

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean  and standard deviation

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

From a random sample of 35 customers at Store M, the average amount spent was $300 with standard deviation $40.

This means that , μ_m = 6.761

From a random sample of 40 customers at Store V, the average amount spent was $290 with standard deviation $35.

This means that , μ_v = 5.534

Assuming a null hypothesis of no difference in population means

At the null hypothesis, we test that there is no difference, that is, the subtraction of the means is 0. So

H₀ = 0

At the alternate hypothesis, we test if there is difference, that is, the subtraction of the means is different of 0. So

H₁ ≠ 0

The test statistic is:

t = X - μ / s

In which X is the sample mean,  is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that μ= 0

From the samples:

X = 10

s = 8.737

The test statistic is t = 1.14.

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Complete question:

A two-sample t-test for a difference in means will be conducted to investigate whether the average amount of money spent per customer at Department Store M is different from that at Department Store V. From a random sample of 35 customers at Store M, the average amount spent was $300 with standard deviation $40. From a random sample of 40 customers at Store V, the average amount spent was $290 with standard deviation $35. Assuming a null hypothesis of no difference in population means, what is the test statistic for the appropriate test to investigate whether there is a difference in population means?

Answer: 7725.5775

Step-by-step explanation:

d=27

r=d/2=27/2=13.5

the volume of the spherical balloon= 3.14*r^3

                                                       = 3.14*(13.5)^3

                                                       = 7725.5775

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Answer:

The interest will be $30, the total amount she pays will be $530.

Step-by-step explanation:

500 x 0.06

30 = the interest rate cost

500 + 30 = $530

$530 is the total amount Victoria needs to pay, and the interest rate cost is $30.

The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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Answer:

18

Step-by-step explanation:

PEMDAS

I hope this helped

Answer:

33 , 39

Step-by-step explanation:

given

9 , 15 , 21 , 27

there is a common difference between consecutive terms, that is

15 - 9 = 21 - 15 = 27 - 21 = 6

to obtain terms in the sequence add 6 to the preceding term

27 + 6 = 33

33 + 6 = 39

the next two terms are 33 and 39

Answer:

10

Step-by-step explanation:

the formula you use to find the distance between two points is

square root of (x1-x2)^2+(y1-y2)^2

Answer:

Step-by-step explanation:

The relevant relation is that the product of distances from the point of intersection of secants to the two points of intersection of each with the circle is a constant. The point of tangency counts as both points of intersection.

__

By way of example, the product of distances to the circle for the tangent segment is 10·10 = 100

This is also the product of the distances on the secant that intersects the tangent:

  100 = 5(5+x+9)

  20 = x +14 . . . . . divide by 5

  x = 6 . . . . . . . . . . subtract 14

__

The same is true when the secants intersect inside the circle:

  6·9 = y·3

  y = 18 . . . . . . divide by 3

Step-by-step explanation:

given,

\( log_{7}(4) = 0.712 \\ log_{7}(12) = 1.277 \\ to \: find \: log_{7}( \frac{1}{3} ) \\ log_{7}( \frac{1}{3} ) = log_{7}( \frac{4}{12} ) \\ by \: logarithmic \: result \: log( \frac{a}{b} ) = log(a) - log(b) \\ implies \\ log_{7}( \frac{1}{3} ) \: = log_{7}(4) - log_{7}(12) \\ = 0.712 - 1.277 \\ = −0.565\)

I hope this is the answer.

pls mrk me brainliest, i rly worked hard on this i need to get the next rank

Answer:

Following are the solution to this question:

Step-by-step explanation:

For this set, the correlation coefficient is = -0.015.

It shows that financial variables have trust issues. Once a price rises, the other one is decreasing the value of -0,015 shows, that there are several fewer associations in the set of data among x and y and between y values. This interaction also can range between -1 to 1, to 0 being completely unrelated. But you'd never be sure, in this situation, 0.015 is very similar to 0.

It means that your prediction is nothing better than just a wild choice. Its odds of an estimated value being relatively close to the actual result are therefore much smaller as the points are it's hardly the best match.

Answer:

Step-by-step explanation:

The events are not independentd) The events are not mutually exclusiveStep-by-step explanation:Hi!Lets call: Gar = {homes with garage}Pool

Answer:

.91

Step-by-step explanation:

P(AUB) = 50/55 = .91 .

9514 1404 393

Answer:

  -(√2)/2

Step-by-step explanation:

The expression evaluated at n=a gives the indeterminate form 0/0, so L'Hopital's rule can be used to find the limit. The second expression comes from differentiating numerator and denominator. Then the form with n=a is no longer indeterminate.

  \(\displaystyle\lim_{n\to a}{\frac{\sqrt{2n}-\sqrt{3n-a}}{\sqrt{n}-\sqrt{a}}}=\lim_{n\to a}{\frac{\frac{2}{2\sqrt{2n}}-\frac{3}{2\sqrt{3n-a}}}{\frac{1}{2\sqrt{n}}-0}}\\\\=\sqrt{a}\left(\frac{2}{\sqrt{2a}}-\frac{3}{\sqrt{3a-a}}}\right)=\boxed{-\frac{1}{\sqrt{2}}}\)

1 : you would use a graduated cylinder . 2 : , you would use a yard stick or maybe a ruler if you are not able to find one. You can also use a meter stick.

Answer:

18.

Step-by-step explanation:

If the tens digit is x^3 the unit digit is x^3 + 7

So 10 * x^3 + x^3 + 7 < 100    (as its a 2 digit number).

11x^3 < 93

x^3 < 8 5/11

x <  2.04

As x must be an integer it is either 1 or 2.

It cannot be 2 as 2^3 = 8 and 8+7 = 15 which cannot be the tens digit so it must be 1.

The answer is 1  and (1+7)  = 18.

Answer:  

18.  

Step-by-step explanation:  

If the tens digit is x^3 the unit digit is x^3 + 7  

So 10 * x^3 + x^3 + 7 < 100    (as its a 2 digit number).  

11x^3 < 93  

x^3 < 8 5/11  

x <  2.04  

As x must be an integer it is either 1 or 2.  

It cannot be 2 as 2^3 = 8 and 8+7 = 15 which cannot be the tens digit so it must be 1.  

The answer is 1  and (1+7)  = 18.

The amount that Fatima will pay each month for the student loan of $15,000 for 10 years at 8.25% interest is $183.98.

The monthly payment can be computed using an online finance calculator below.

The monthly payment shows the periodic amount that the borrower repays the financier to settle the student loan, including accumulated interest.

N (# of periods) = 120 months (10 years x 12)

I/Y (Interest per year) = 8.25%

PV (Present Value) = $15,000

FV (Future Value) = $0

Results:

Monthly payment (PMT) = $-183.98

Sum of all periodic payments = $-22,077.47

Total Interest = $7,077.47

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Answer:

I think its 10 mi

Step-by-step explanation:

Please let me know if I'm wrong!

The sample size and sample proportion have a more significant impact on whether a sample proportion shows significance, while the number of simulated samples in the randomization distribution mainly affects the accuracy and stability of the p-value.

To find the p-value using StatKey with 5,000 simulated samples and determine if there is evidence that the coin is biased at a 5% significance level, follow these steps:
1. Open StatKey and choose the appropriate tool for proportions (you can find this under "Randomization Tests").
2. Enter the sample size, the sample proportion, and the number of simulated samples (5,000) in the given fields.
3. Click "Calculate" or "Simulate" to generate the randomization distribution.
4. Observe the p-value displayed by StatKey.

If the p-value is less than or equal to 0.05 (5% significance level), there is evidence that the coin is biased.

If the p-value is greater than 0.05, there is not enough evidence to conclude that the coin is biased.
Now, let's discuss the impact of each factor on the sample proportion's significance:
1. Sample size:

A larger sample size increases the power of the test, making it more likely to detect a biased coin if it exists. This is because larger sample sizes reduce sampling variability, leading to narrower confidence intervals and more precise estimates.
2. Sample proportion:

A sample proportion that deviates more from the expected proportion (0.5 for a fair coin) increases the likelihood of finding significance, as it indicates a stronger departure from the null hypothesis of no bias.
3. Number of simulated samples in the randomization distribution:

Increasing the number of simulated samples makes the p-value more accurate and stable.

However, the impact of this factor is generally smaller than the other two factors, as the p-value will often converge to a stable value after a certain number of simulations.

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The given table does not represent a function. The correct answer is D. No, because one x-value corresponds to two different y-values.

To determine if the table represents a function, we need to check if every x-value corresponds to exactly one y-value. Let's analyze the given table:

x | y

-------

O | 1

X | 4

2 | 3

3 | 2

3 | 5

4 |

5 |

From the table, we can see that the x-values are not unique. Both the values 3 and 4 appear twice in the x-column, but they have different corresponding y-values.

This violates the definition of a function, which states that each input (x-value) should have only one output (y-value).

Therefore, the given table does not represent a function.

The correct answer is D. No, because one x-value corresponds to two different y-values.

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ANSWER:

Isabella speed = 0.064 mi/min

Speed of current = 0.019 mi/min

STEP-BY-STEP EXPLANATION:

Let i = Isabella's speed rowing in still water

Let c = the speed of the current

i - c= her speed rowing against the current

i + c = her speed rowing with the current

We can propose the following system of equations:

We solve by means of the substitution method, we substitute the first equation in the second, like this:

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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