translate the sentence into an equation. Three times the sum of a number and 4 is 8 .

Answer:

HA:A hypotenuse and an acute angle define congruence

HL:A hypotenuse and a leg define congruence

LL: Two legs define congruence

LA:A leg and an acute angle define congruence

Step-by-step explanation:

HA theorem:

                     When hypotenuse and one acute angle of a triangle is congruent to hypotenuse and one acute angle of a other triangle, then the triangles are congruent

HL theorem:

                     When hypotenuse and one leg of a triangle is congruent to hypotenuse and one leg of other triangle, then the triangles are congruent

LL theorem:

                    When two legs of a triangle is congruent to the two legs of other triangle, then the triangles are congruent

LA theorem:

                    When one leg and one acute angle of a triangle is congruent to one leg and one acute angle of other triangle, then the triangle are congruent

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The exact expression for the cosine function is given as follows:

h(x) = 7.5cos(2π/7(x + 0.5)) - 1.5.

The definition of the cosine function is given as follows:

h(x) = acos(b(x - c)) + d.

The parameters of the function are given as follows:

The difference between the maximum value and the minimum value is of 6 - (-9) = 15, hence the amplitude is obtained as follows:

a = 15/2 = 7.5.

From the graph given at the end of the answer, the period is of 7 units, hence:

2π/b = 7

7b = 2π

b = 2π/7.

The minimum value should be at x = 0, however it is at x = -0.5, hence the phase shift is given as follows:

c = -0.5.

Considering the amplitude of 7.5, without vertical shift the function would oscillate between -7.5 and 7.5, however is oscillates between -9 and 6, hence the vertical shift is given as follows:

d = -1.5.

Thus the function is defined as follows:

h(x) = 7.5cos(2π/7(x + 0.5)) - 1.5.

The graph of the function is given by the image shown at the end of the answer.

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By using the properties of angle, it can be concluded that

[tex]\angle QPS[/tex] and [tex]\angle TSP[/tex] are consecutive interior angle

What is angle?

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

[tex]\angle QPS[/tex] and [tex]\angle TSU[/tex] are not consecutive interior angle as [tex]\angle PST[/tex] falls in between

[tex]\angle QPS[/tex] and [tex]\angle RSU[/tex] are not consecutive interior angle as [tex]\angle RSU[/tex] is an exterior angle

[tex]\angle QPS[/tex] and [tex]\angle TSP[/tex] are consecutive interior angle

[tex]\angle QPS[/tex] and [tex]\angle OPN[/tex] are not consecutive interior angle as [tex]\angle OPN[/tex] is an exterior angle

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The equation y = - 2 · x⁷ is not an exponential function because the independent variable x is the base of the formula instead of being its exponent. (Correct choice: A)

In this problem we need to determine whether the equation y = - 2 · x⁷ represent an exponential function or not. Exponential functions are expressions of the form:

y = b · aˣ

Where:

By direct comparison we notice that the given equation is not an exponential function as the independent variable x is not the exponent of the expression and it is the base instead. The expression y = - 2 · x⁷ is a power function, not an exponential function.

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The radius of convergence R of the given function f(x) = (-1)^n(1 - x)² be,

R = 1/2.

Given, a function f(x)

f(x) = (-1)^n(1 - x)²

we have to find the radius of convergence R of the given function,

first will find the (n+1)th term of the given function

as, an = (-1)^n(1 - x)²

then an+1 = (-1)^(n+1)(1 - x)²

to find the radius of convergence, we will find

lim x->∞ an+1/an

lim x->∞ ((-1)^(n+1)(1 - x)²)/((-1)^n(1 - x)²)

On solving the limits, we get

lim x->∞ an+1/an = 2x

then R = 1/2

as, -1/2 < x < 1/2

so, the radius of the convergence be, 1/2

Hence, the radius of the convergence be, 1/2

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This distribution has no shape parameter as it has only one shape, (i.e., the exponential, and the only parameter it has is the failure rate, \lambda \,\!).

The exponential distribution can be simulated in R with rexp(n,λ) where λ is the rate parameter. The mean or expected value of an exponential distribution is 1/λ and the standard deviation is also 1/λ. The variance of an exponential distribution is given by 1/λ2.

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If Diana averages 6 mph walking to school. The distance from  the school to her home is 5.4 miles.

Distance can be defined as how far an object is from another object.

Formula for Distance

Distance = Speed × Time

Solving for t (time) to walk to school

6t = 35 (t-.75)              

6t = 35t - 26.25

Collect like terms

29t= 26.25

Divide both side by  29t

t = 26.25/29

t=  .9

t=54 minutes

Solving for Distance (d)

d = 6× .9

d = 5.4 miles

Therefore the distance is 5.4 miles.

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The complete question is:

Diane averages 6 mph walking to school. Averaging 35 mph on the way back home by car, she takes 3/4 hour less time. How far is the school from her home?

Option- A is correct that is event a and b are independent when consider some events a and b rearranging the multiplication rule will result in.

Given that,

If and only if, two events, a and b, are independent. Remember that rearranging the multiplication rule will result in. Consider some events a and b.

We have to find which of the following claims about a and b is true.

We know that,

We have if the occurrence of event A has no bearing on the probability that event B will also occur, then the two events A and B are said to be independent.

P(A and B) = P(A) P(B) can be used to numerically describe the probability of two separate events.

As a result, we can draw the conclusion that two events, a and b, are independent if and only if they are.

Therefore, Option- A is correct that is event a and b are independent when consider some events a and b rearranging the multiplication rule will result in.

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Answer:

it's 0.25 for the first one

Answer:

OptionB)

Step-by-step explanation:

→→When you are talking about sample proportion You are considering a Single ,set of same kind of Data,Like body weight of  Students in a class, from which you are taking out samples for Observation.

For example, A colony is being studied whether each human in that colony is healthy or not by checking their body mass index.

→→When we are investigating or considering Sampling Distribution we consider two different sets or kinds of Data set Possessing Similar Characteristics because we have to compare these two sets of Data.

For example , Take two colonies A and B , Check their honesty by observing how many floors they have made in their Plot.Whether they care or don't care about their Surrounding or Mother Earth by looking, if number of floors exceeds than 2 i.e ground floor and first floor , it means Dishonest , if maximum number of floor =2 ,it means honest.

A spherical balloon is being filled with helium at the rate of 9 ft^3/min. the surface area of the balloon is increasing at a rate of approximately 37.1 ft^2/min.

Generally, To find the rate at which the surface area is increasing, we need to use the formula for the surface area of a sphere, which is 4πr^2, where r is the radius of the sphere. We also know that the volume of a sphere is (4/3)πr^3.

Since we know the volume of the balloon, we can set up the following equation:

(4/3)πr^3 = 26*π ft^3

Solving for r, we find that the radius of the sphere is approximately 2.15 ft. Plugging this value back into the formula for the surface area, we find that the surface area of the sphere is approximately 28.9 ft^2.

To find the rate at which the surface area is increasing, we need to find the d/dx surface area formula with respect to time. Since the radius of the sphere is changing at a constant rate (9 ft^3/min), we can use the chain rule to find the d/dx surface area.

The d/dx 4πr^2 with respect to r is 8pir, and the d/dx r with respect to time (which we'll call t) is 9 ft^3/min. Therefore, the d/dx surface area with respect to time is:

(d/dx 4πr^2 with respect to r) * (d/dx r with respect to t) = (8πr) * (9 ft^3/min)

Plugging in the value of r that we found earlier (2.15 ft), we get:

(8π2.15 ft) * (9 ft^3/min) = 37.1 ft^2/min

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The volume of the figure can be calculated by adding the volumes of the two rectangular prisms. The first rectangular prism has dimensions 12 in x 10 in x 2 in, so its volume is 12102 = 240 in^3. The second rectangular prism has dimensions 10 in x 7 in x 21 in, so its volume is 10721 = 1540 in^3. The total volume of the figure is 240 in^3 + 1540 in^3 = 1780 in^3.

Answer: y = 5x - 4

Step-by-step explanation: The equation of a linear function can be found by using the slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept (i.e., the point at which the line crosses the y-axis).

To find the equation of the linear function represented by the table, we can use the values from the table to calculate the slope. The slope is calculated as the change in y over the change in x, or (y2 - y1)/(x2 - x1). Using the values from the table, we can calculate the slope as (6 - 1)/(2 - 1) = 5/1 = 5.

Next, we can use the slope and one of the points from the table to find the y-intercept. If we use the point (1,1), we can substitute the values into the slope-intercept form to get 1 = 5*1 + b, so b = -4.

Therefore, the equation of the linear function represented by the table is y = 5x - 4.

They collected $134.45 and we can find this using percentage.

Travis = $43

Jessica = 43 - (43 × 20%) = $34.4

Robin = 43 + (43 × 35%) = $58.05

Percentage (%):

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Answer: the function is nonlinear

Step-by-step explanation:

y = x2 + 1 is a nonlinear equation because for it to be an linear question it must be the following

Linear:

2x-1=y 

y=2x-1

nonlinear

y = x2 + 1 

C. H2 1,96

To establish whether there is a significant difference between treatments using the Kruskal-Wallis test, the calculated value of H should be compared to the critical values ​​in the table of H values. The critical value of H to use depends on the significance level chosen for the test (0.05 in this case).

Using a significance level of 0.05, the critical value of H for a sample size of n-8 for each treatment is approximately H2 1.96. That is, if the calculated H value is greater than 1.96, we can conclude that there is a significant difference between the treatments.

Hence, the correct answer in this case is c. H2 1,96

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Answer:

C. 296 R3

Step-by-step explanation:

In order to find the quotient, lets use long division:

            296 R 3

      _________

7    |    2075

        - 14

          __

            67   ==> drop 7 from 2075

          - 63

            __

              45     ==> drop 5 from 2075

            - 42

              __

                3

The final value of company x sold price is; $22,000,500

The final value of company y sold price is; $21,999,500

Let the amount of sold out products in company x and company y be denoted by a

Now, we are told that sum of both the two companies salaries are $44,000,000.

Now, the sold price of company x is 1000 more than the other.

Thus;

Sold price of company y = y

Sold price of company x = 1000 + y

Thus;

1000 + y + y = 44000000

1000 + 2y = 44000000

2y = 44000000 - 1000

2y = 43,999,000

y = 43,999,000/2

y = $21,999,500

Thus;

Sold price of company x = $21,999,500 + $1000 = $22,000,500

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Answer:

  125 -v³ = (5 -v)(v² +5v +25)

Step-by-step explanation:

You want to factor the expression 125 -v³.

From your knowledge of the cubes of small integers, you recognize that 125 = 5³. That lets you see this expression is the difference of cubes, which has a factor pattern:

  a³ -b³ = (a -b)(a² +ab +b²)

Your difference factors as ...

  5³ -v³ = (5 -v)(5² +5v +v²)

  125 -v³ = (5 -v)(v² +5v +25)

To find Kaitlyn's original body weight, we need to determine how much weight she lost and add that amount back to her current weight.

Kaitlyn lost 8% of her body weight, which is equal to 8/100 * 222 pounds = <<8/100*222=17.76>>17.76 pounds.

Therefore, Kaitlyn's original body weight was 222 pounds + 17.76 pounds = <<222+17.76=239.76>>239.76 pounds.

The contrapositive is true

Proving a contraposition involves proving that the contrapositive of a statement is true. The opposite of "if m n is even then m is even or n is even" is "if m is not even and n is not even then m n is not even".

To prove this statement by a proof by contrast, first assume that m is not even and neither is n. This means that both m and n are odd.

Since m and n are odd, m n is also odd. This can be expressed as:

If m and n are odd, we can write m as;

2k + 1 and n as 2l + 1 for integers k and l.

Then mn = (2k + 1)(2l + 1) = 4kl + 2k + 2l + 1 = 2(2kl + k + l) + 1,

which is odd. Therefore, m n is not even if m is not even and n is not even.

It turns out that the opposite of the original statement is true, so the original statement must also be true. Therefore, if m n is even, then we can say that   that m is even or n is even using a proof by contrast.

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The length of DE is 6.3

Similar triangles are triangles that have a similar appearance but differ in size.

Two triangles are similar if their angles are the same (corresponding angles) and their sides have the same ratio or proportion (corresponding sides)

The " ~ " symbol is used to represent similarity.

According to the question,

In ΔABC and ΔDBE,

(1) ∠B = ∠B (common)

(2) ∠ACB = ∠DEB (opposite sides are equal)

(2) ∠CAB = ∠ECB

Therefore , ΔABC ~ ΔDBE

By using similar triangle property

The ratio of correspond sides are equal ,

AB/BD = BC/BE = AC/DE

=> 2/1 = AC/DE

=> 12.6 / DE = 2/1

=> DE =  12.6/2

=> DE = 6.3

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The sample variance is 2.976 , which means it's lesser than 6.25. We calculate this using the standard method.

Given:

Sample data is 0.05

The sample size is 20.

And ,

The hypotheses are:

H0: sigma^2 = 6.25 (>=)

Ha: sigma^2 < 6.25

The critical value is 10.117. If the test statistic is less than this value, we'll reject the null hypothesis. We Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go.

The test statistic is:

2.976 * 19 / 6.25 = 9.047.

So we reject the null hypothesis. The variance is not 6.25, which means it is lesser then 6.25

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The tri-linear inequality with the required 80% confidence interval of 54.1 to 57.7 shows the genuine mean value by which the drug decreases the average patient's systolic blood pressure.

A confidence interval expresses the likelihood that a population parameter will fall between a range of values a predetermined percentage of the time. It is the estimate's mean plus or minus the estimate's range of values.

Given the confidence level is 80%, the significance level α=100-80=20% = 0.20. The sample mean [tex]\overline{x}[/tex] is 55.9, the sample standard deviation s is 7.4, and the sample size n is 29.

We are using t-distribution to population standard deviation first. For that first find the degree of freedom and critical value of t.

Degree of freedom,

df = n - 1

df = 29 - 1

df = 28.

The critical value of t calculated from the t-distribution table is,

[tex]\begin{aligned}t_{\text{critical}}&=t_{\alpha/2,df}\\&=t_{0.10,28}\\&=\pm1.3125 \end{aligned}[/tex]

Then, an 80% confidence interval is,

[tex]\begin{aligned}\mu&=\overline{x}\pm\frac{t\cdot s}{\sqrt{n}}\\&=55.9\pm\frac{1.3125\times7.4}{\sqrt{29}}\\&=55.9\pm1.80\end{aligned}[/tex]

Then, the interval is written as

55.9 - 1.80 < μ < 55.9 + 1.80

54.1 < μ < 57.7

The required interval is 54.1 < μ < 57.7.

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Answer:

f⁻¹ [tex](x)[/tex] = [tex]3(x+2)[/tex]

Step-by-step explanation:

The first step to finding the inverse of a function is to let [tex]y=f(x)[/tex].

This would mean [tex]y=\frac{x}{3}-2[/tex].

Then we swap [tex]x[/tex] and [tex]y[/tex] in the formula.

[tex]x = \frac{y}{3} -2[/tex]

Then rearrange for [tex]y[/tex]:

[tex]x=\frac{y}{3}-2 \\\\x+2=\frac{y}{3}\\\\3(x+2)=y[/tex]

This new equation of [tex]y[/tex] is the inverse function.

f⁻¹ [tex](x)[/tex] = [tex]3(x+2)[/tex]

Therefore the value of K is -11

The range of 90% confidence will be: (0.5305,0.5695)

What is percentage?

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Given,

Sample percentage equals 0.55

z = 1.645 for 90% confidence.

Therefore, the range of 90% confidence will be:

(0.5305,0.5695)

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The probability of a Type I error is the probability of incorrectly rejecting the null hypothesis. When the probability of a Type I error decreases, the probability of a Type II error, It decreases the likelihood of choosing the null hypothesis wrongly.

When conducting a hypothesis test for a given sample size, a Type I error is the probability of incorrectly rejecting the null hypothesis. This means that the null hypothesis is true, but the hypothesis test incorrectly rejects it. A Type II error is the probability of incorrectly accepting the null hypothesis. This means that the null hypothesis is false, but the hypothesis test incorrectly accepts it. When the probability of a Type I error decreases, it means that the hypothesis test is more accurate in correctly rejecting the null hypothesis when it is false. This in turn means that the probability of a Type II error also decreases, as the test is more accurate in correctly accepting the null hypothesis when it is true. In other words, when the probability of a Type I error decreases, the probability of a Type II error decreases as well.

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