In the 30-60-90 triangle below, side s has a length of.
length of
30
90⁰
S
10
60"
A. 5.2: 5.2
B. 5,10,3
and side q has a

a) The test statistic is given as t = [tex]\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}[/tex]= 2.315

b) The pa value will be P = P( t₂₄ > 2.315 ) = 0.015

c) If we compare the p-value and the significance level is given we see that  so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance

In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

X= represents the sample mean

s = represent the sample standard deviation

n = 25 sample size  

[tex]\mu_o[/tex] = 12 represent the value that we want to test

[tex]\alpha[/tex] = 0.05 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p-value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is higher than 12, the system of hypothesis would be:  

Null hypothesis:  ≤ 12

Alternative hypothesis: > 12

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better to apply a t-test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\dfrac{X-\mu_o}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to a specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]\dfrac {14-12}{\dfrac{4.32}{\sqrt25}}}[/tex]= 2.315    

P-value:-

The first step is calculate the degrees of freedom, on this case:  

 df = n - 1 =25 - 1 = 2

Since is a one side right tailed test the p value would be:  

[tex]p_v[/tex] =  P( t₂₄ > 2.315 ) = 0.015

Conclusion  

If we compare the p-value and the significance level is given [tex]\alpha[/tex]= 0.05  we see that [tex]p_v < \alpha[/tex]  so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 1% of significance.

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The y-intercept of the quadratic equation is -47.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Here, given quadratic equation;

    f(i) = i² + 10i - 22

or, y = i² + 10i - 22

     y = i² + 2.5x - (47-25)    

    y = i² + 2.5x + 25 - 47

    y = (i+5)² - 47

Thus, the y-intercept of the quadratic equation is -47.

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Answer:

m<1 OR m>7

Step-by-step explanation:

3m<5-2

3m<3

m<1

m+1>8

m>8-1

m>7

Answer:

m<1 or m>7

Step-by-step explanation:

3m + 2 < 5

3m + 2-2 < 5-2

3m < 3

[tex]\frac{3m}{3}[/tex] < [tex]\frac{3}{3}[/tex]

m < 1

[tex]\frac{m+1}{2}[/tex] > 4

[tex]\frac{m+1}{2}[/tex]*2 > 4*2

m +1 > 8

m +1 -1 > 8 -1

m > 7

Answer:

Answer D

Step-by-step explanation:

It says to divide f(x)/g(x), which is displayed in D and if we find the domain it would be x is not equal to -1/4

Answer:

325

Step-by-step explanation:

10 is 3^2 + 1

37 is 6^2 + 1

82 is 9^2 + 1

145 is 12^2 +  1

226 is 15^2 + 1

325 is 18^2 + 1

325 is the next number in the sequence and is also the answer.

Answer:

6.5 seconds

Step-by-step explanation:

Ok so the equation you gave is -16T^2 + 676 in the comments which is what I'll be using for this problem. The problem is really just asking you to find the zeroes of the equation excluding any negative solutions since that doesn't really represent anything in this context since T is time.

So the first step is to set the equation equal to 0

[tex]0 = -16t^2 + 676[/tex].

Subtract 676 from both equations.

[tex]-676 = -16t^2[/tex]

Divide both sides by -16

[tex]42.25 = t^2[/tex]

Take the square root of both sides

[tex]\pm6.5 = t[/tex]

Ignore the negative and take only the positive solution, since in this context it doesn't make much sense. So after 6.5 seconds the height is 0, meaning it hits the ground after 6.5 seconds.

[tex]4x + 7 - (x + 6) = 68 \\ \\ 4x + 7 - x - 6 = 68 \\ \\ 3x + 1 = 68 \\ \\ 3x = 68 - 1 \\ \\ 3x = 67 \\ \\ x = \frac{67}{3} \\ \\ x = 22.3[/tex]

The value of x is 67/3 or 22.3 .

Hi!

__________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

x=

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

First let's distribute the minus sign.

[tex]\twoheadrightarrow\sf 4x+7-x-6=68[/tex]

[tex]\bullet[/tex] Add 6 to both sides

[tex]\twoheadrightarrow\sf 4x+7-x=74[/tex]

[tex]\bullet[/tex] Subtract the x's

[tex]\twoheadrightarrow\sf 3x+7=74[/tex]

[tex]\bullet[/tex] Subtract 7 from both sides

[tex]\twoheadrightarrow\sf3x=67[/tex]

[tex]\bullet[/tex] Divide both sides by 3

[tex]\twoheadrightarrow\sf x=\cfrac{67}{3}[/tex]

[tex]\bullet[/tex] Great job! We solved for the variable

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

--

In the case above about Samuel, one can say that Samuel's calculator has display option A.  2.5 E (- 13)

The function was  [tex]\frac{5E (-9) }{2E(4) }[/tex] :

We know that, E implies 10 to rise to power.

So, The equation above is Converted from scientific notation into standard form.

 [tex]\frac{5 x 10^-9 }{2 x 10^ 4 }[/tex]

= 5/2  x 10 ⁻⁹⁻⁴

=2.5 x 10⁻¹³

Therefore, In the case above about Samuel, one can say that Samuel's calculator has display option A.  2.5 E (- 13)

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According to law of cosines the length of RQ can be written as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].

Given the length PR is 6 , the length of RQ is p, the length of PQ is 8 and the angle RPQ is 39 degrees.

A length of the triangle can be written as according to law of cosines if sides are given and one angle is [tex]a^{2} =b^{2} +c^{2} -2bccos(A)[/tex]

We have to just put the values in the above equation.

as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].

p is the side opposite to angle given , the length of other sides are 6 and 8 and angle is 39 degrees.

Hence the side can be written as according to law of cosines if the angle is 39 degrees is  as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].

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Answer: OPTION B

Step-by-step explanation:

edge22

Answer:

4/7

Step-by-step explanation:

2/3 × 6

7

4/7

and bro that's really it

Answer:

35.1% chance of going sledding

Step-by-step explanation:

45% chance of snow on Friday

Convert percentage to decimal form (divide by 100)

45% = 0.45

78% chance of sledding if it snows

Convert percentage to decimal form (divide by 100) to multiply

78% = 0.78

Multiply to find the probability of both occurring

0.78 * 0.45 = 0.351

Convert back into a percentage (multiply by 100)

0.351 = 35.1% chance of sledding

Let me know if you have any questions!

Answer: B

Step-by-step explanation:

The maximum is 100 and the minimum is 27.

Answer: it's A, B, and D

Step-by-step explanation:

The interest which has to be paid is $28.

Simple Interest amount can be estimated by the product of principal amount, rate of interest, and time in year.

Simple Interest= S.I. =p*t*r/100

where p is the principal amount,

r: interest rate (%)

t: the time (in year).

Here, given,

Margo has taken borrowed $600 with an annual interest of 7% which has to be paid within 8 months.

principal amount P = $600

rate of interest= r=7%

time=t=8 months= 2/3 year

using the above-mentioned formula,

Simple Interest S.I.= p*t*r/100= (600*(2/3)*7)/100= $28

Therefore the interest which has to be paid is $28.

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Arc AB measures 3(16) = 48 degrees.

Arc BC measures 2(16) + 5 = 41 degrees.

By using the remainder theorem we found that ( x - 5 ) is the factor of function  f(x) = x³ – 5x² + 7x – 35.

Factorization is defined as splitting the polynomial into its most simplified form. This factor satisfies the polynomials from which it is extracted.

The factorization by using the Remainder theorem.

x - 5 )   x³ – 5x² + 7x – 35.( x ² + 7

             x³  -  5x²

             ______________

                00         7x - 35

                             7x - 35

              -------------------------

                                     00

Here the function is completely divided by the factor x - 5 therefore

by using the remainder theorem we found that ( x - 5 ) is the factor of function  f(x) = x³ – 5x² + 7x – 35.

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Answer:

A = 60 ft²

Step-by-step explanation:

the area (A) of the shaded sector is calculated as

A = area of circle × fraction of circle

   = 90 × [tex]\frac{240}{360}[/tex]

   = 90 × [tex]\frac{2}{3}[/tex]

    = 30 × 2

    = 60 ft²

Answer:

58.83 ft^2

Step-by-step explanation:

Finding the radius:

A = πr^2

90 = πr^2

90/π = r^2

28.6 = r^2

5.3 = r

Using the area of a sector of a circle formula:

θ/360 x πr^2

240/360 x π(5.3)^2

= 58.83 ft^2

Answer: Vikram is not incorrect because he found the sum by adding the numerators and denominators

Step-by-step explanation:  The first blank doesn't have a word so I answer it

Answer: (1+2a)^2 or (1+2a)(1+2a)

Step-by-step explanation:

Answer:

[tex](2a +1)( 2a + 1)[/tex]

Step-by-step explanation:

Answer:

  B.  2x = y; 2x +1.5y = 20

Step-by-step explanation:

The two given relations can be written as two equations, one for the numbers of fish, and one for their cost.

__

The number of goldfish (y) is twice the number of tetras (x), so one equation can be ...

  2x = y

The tetras (x) are $2 each, and the goldfish (y) are $1.50 each. Their total cost is the sum of products of the number of fish and the cost of each. That total is given as $20, so the other equation could be ...

  2x +1.5y = 20

Then the appropriate system of equations is ...

_____

Additional comment

The solution can be found by substituting for 2x to get ...

  y +1.5y = 20 . . . . . . substitute for 2x

  y = 20/2.5 = 8 . . . . divide by the coefficient of y

  x = y/2 = 4 . . . . . . . find the number of tetras

Rick bought 4 tetras and 8 goldfish.

__

The wording "twice as many goldfish as tetras" easily causes confusion. It is helpful to reword it as "goldfish were twice the number of tetras."

Answer:

3.8918

round the 1 from the 8 to get 2

3.892

Answer:

1. 8

2. 3

Step-by-step explanation:

[tex]f(g(3)) \\= f(2(3)-3))\\=f(3)\\=3^2-1\\= 9-1\\=8\\\\g(f(-2))\\= g((-2)^2-1)\\=g(4-1)\\=g(3)\\=2*3-3\\=3[/tex]

Answer:

B. y = (x+1)(x+5)

Step-by-step explanation:

If the x-intercepts are (-1,0) and (-5,0), then the solutions (also called zeros and x-intercepts) are

x = -1 and x = -5

This is a "working backwards" kind of problem. If you were solving the equation, right before the final step, x=-1 would have been:

x + 1 = 0

Right before x=-5

would have been,

x + 5 = 0.

These two: x+1 and x+5 are called the linear factors. You multiply them back together to find the equation.

y = (x+1)(x+5)

Answer: 5

Step-by-step explanation:

As all radii of a circle are congruent, [tex]\overline{OX} \cong \overline{OY}[/tex], it follows that [tex]\angle OXY \cong \angle OYX[/tex].

Because arc XY measures 60 degrees, we also know that [tex]m\angle XOY=60^{\circ}[/tex], and thus triangle OXY is equilateral.

Hence, XY=5 because all sides of an equilateral triangle are congruent.

Answer:

See below

Step-by-step explanation:

Not sure what you are asking....do you want to know what y is when x = -2   and the equation = 6 ?

3 xy^2 + 4x = 6         or is that    3 xy^(-2) + 4x = 6

Could use some serious editing of your question if you are able ....

If the function is reflected over the y-axis and then translated down 2 units. the resulting function will be -∛x - 2

Transformation is a technique used to change the position of an object on an xy-plane.

Given the function y = ∛x

If the function is reflected over the y-axis and then translated down 2 units to form f(x), the resulting function f(x) will be:

f(x) = -∛x - 2

The graph of the resulting function is attached

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Answer:

B

Edge 2023

The other answer is incorrect!!!

Step-by-step explanation:

please mark me as brainlest

Answer:

Parallel lines have the same slope, so the slope would be 1/3. It would need a different y intercept though or it would be the same line.

The line y = 12 has a slope of 0 because it is a horizontal line, meaning that for any change in x, there is no change in y. Ths means the slope of a line parallel to it would be 0 (since parallel lines have the same slope), and the slope of a line perpendicular to it would be undefined (since perpendicular lines have slopes that are negative reciprocals of each other, and when you divide by 0, you get an undefined result).