ABCD is a rhombus. If AB = 2x + 12 , AC = 7x - 3, ∠=12°, and ∠ = (4y - 1)°.m ∠BAC = __ .

Answer:

3, 7, 14

Step-by-step explanation:

Answer:

Hey Desmariesin7587, the median of the data set that you gave is  15.9

Step-by-step explanation:

Since the amount of values in the data set was not even, I could not find a middle number. Instead, I added up all of the values and divided the total sum by the amount of values that there were; in this case, 10.

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Have a great day,

Nish

The new dimensions of the flower bed are 4√2 and 6√2

The dimensions of the initial rectangular flower bed are given as:

Length = 4ft

Width = 6 ft

The area of the new flower bed is twice the area of the old one.

This means that

New Area = Old Area * 2

Substitute the dimensions of the old area in the above equation

New Area = 4 * 6 * 2

Express 2 as √2 * √2

This gives

New Area = 4 * 6 * √2 * √2

Rewrite the above equation as:

New Area = 4√2 * 6√2

The area of a rectangle is

Area = Length * Width

This means that:

Length = 4√2 ft

Width = 6√2 ft

Hence, the new dimensions of the flower bed are 4√2 and 6√2

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Answer: 6x8

Step-by-step explanation:

(4+x)(6+x)=2*24

x^2+10x+24=48

subtract 48 on both sides

x^2+10x-24=0

Solve using the quadratic formula

-10±√(100+96)÷2

simplifies to

-(10±14)÷2 = 2, -12

-12 doesn't work though because the sides can't be negative.

So x=2

To check, add both sides by 2:

2(4x6)=6x8=48

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Given:

f(x) = ln(x)

n = 4

c = 3

nth Taylor polynomial for the function, centered at c

The Taylor series for f(x) = ln x centered at 5 is:

[tex]P_{n}(x)=f(c)+\frac{f^{'} (c)}{1!}(x-c)+ \frac{f^{''} (c)}{2!}(x-c)^{2} +\frac{f^{'''} (c)}{3!}(x-c)^{3}+.....+\frac{f^{n} (c)}{n!}(x-c)^{n}[/tex]

Since, c = 5 so,

[tex]P_{4}(x)=f(5)+\frac{f^{'} (5)}{1!}(x-5)+ \frac{f^{''} (5)}{2!}(x-5)^{2} +\frac{f^{'''} (5)}{3!}(x-5)^{3}+.....+\frac{f^{n} (5)}{n!}(x-5)^{n}[/tex]

Now

f(5) = ln 5

f'(x) = 1/x ⇒ f'(5) = 1/5

f''(x) = -1/x² ⇒ f''(5) = -1/5² = -1/25

f'''(x) = 2/x³  ⇒ f'''(5) = 2/5³ = 2/125

f''''(x) = -6/x⁴ ⇒ f (5) = -6/5⁴ = -6/625

So Taylor polynomial for n = 4 is:

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Hence,

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

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The 45th term of the arithmetic sequence is 178. Option C

Given the arithmetic sequence formula as;

an = 2 + 4(n − 1)

we have n = 45

Let's substitute the value of 'n' into the formula;

a = 2 + 4( 45 - 1)

expand the bracket

a = 2 + 4(44)

a = 2 + 176

a = 178

The 45th term is 178

Thus, the 45th term of the arithmetic sequence is 178. Option C

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Answer:

3.75

Step-by-step explanation:

3/4 times 5 =3 3/4

The required reserve ratio is 0.226 or 22.6%.

Given that a depository institution holds $164 million in required reserves and $9 million in excess reserves and Its remaining assets include $417 million in loans and $137 million in securities.

The following equality always holds.

Total liabilities=Total assets

It is given that the institution's only liabilities are transaction deposits.

This means:

Total transaction deposits=Total assets

Total transaction deposits=Required reserves + Excess reserves + Loans + Securities

Total transaction deposits=$164+$9+$417+$137

Total transaction deposits=$727

Calculate the required reserve ratio as follows:

Required reserve ratio=(Required reserves)/(Total transaction deposits)

Required reserve ratio=($164 million)/($727 million)

Required reserve ratio=0.226 or 22.6%.

Hence, the required reserve ratio when a depository institution holds $164 million in required reserves and $9 million in excess reserves and Its remaining assets include $417 million in loans and $137 million in securities is 0.226 or 22.6%.

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The two positive numbers satisfying the given requirements are 15.56 and 15.56

For given question,

Let x and y be  two positive numbers satisfying the given requirements.

⇒ xy = 242             .............(1)

The sum of given two positive numbers is a minimum.

Let the sum of given two positive numbers is S.

⇒ x + y = S             ............(2)

From equation(1),

⇒ y = 242/x

Substitute above value of y in equation (2),

⇒ x + y = S  

⇒ S = x + (242 / x)    

Now, for above equation we find the derivative of x with respect to x.

⇒ 0 = 1 - [tex]\frac{242}{x^{2} }[/tex]

⇒ 242/x² = 1

⇒ x² = 242

⇒ x = ±15.56

Since the numbers are positive, x = 15.56

For x = 15.56

⇒ y = 15.56

Therefore, the two positive numbers satisfying the given requirements are 15.56 and 15.56

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The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

To find the probability that at least 1 ball was​ red, given that the first ball was replaced before the second draw. Not replaced before the second draw:

Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

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The complete question is given below:

Two balls are drawn in succession out of a box containing 2 red and 5 white balls. Find the probability that at least 1 ball was​ red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw.

Step-by-step explanation:

31) the answer is (98765x9) +3=888888

why if u look at the equation is descending and if u verify the cinjecture u will find out is correct

41)½+¼+⅛+1/16+1/32=1-1/32

just d same reason with (31)

The last one because the other ones only go to the positive side and not the negative too since the cube root

Answer:

12

Step-by-step explanation:

6*6 = 36

36/3 = 12

Answer:

12

Step-by-step explanation:

Given expression:

  [tex]\dfrac{1}{3}x^2[/tex]

To evaluate the given expression for x = 6, substitute x = 6 into the expression and simplify:

[tex]\begin{aligned}x=6 \implies \dfrac{1}{3}(6)^2 & = \dfrac{1}{3}(6 \cdot 6)\\\\& = \dfrac{1}{3}(36)\\\\& = \dfrac{36}{3}\\\\& = \dfrac{3 \cdot 12}{3}\\\\& = \dfrac{\diagup\!\!\!\!3 \cdot 12}{\diagup\!\!\!\!3}\\\\& = 12\end{aligned}[/tex]

Answer:

Step-by-step explanation:

800-160=640

640/800=64/80

64/80=16/20

16/20=4/5

Answer=4/5

The fraction of his original money does he have left = 4/5 .

What is a fraction in math?

A boy has = 800 and spends = 160

800-160=640

640/800=64/80

64/80=16/20

16/20=4/5

Therefore, his original money left =4/5

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concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.

Now, we know that there are 52 cards in a normal deck, if we only keep the ones with real numbers, there are 40.

These numbers go from 1 to 10.

5.5 is the average real number in the cards, so, having a 6 or more in a card is what we expect.

This means that if the card that we turn up is smaller than 6, we discard it.

If the card has the value 6 or larger, we keep it.

In this case, the probability of losing is if one of the other cards has a value larger than 6.

The probability that a random card has a value larger than 6 is:

p = (number of cards with a value larger than 6)/(total number of cards)

p = (16/39)

(The quotient is 39 instead of 40, because we already know one of the cards)

This means that if keep the 6, the probability of winning is:

1 - 16/39 = 0.59

If instead, we got a 7, obviously we keep it, in that case the probability of winning is:

1 - 12/39 = 0.69

And so on, concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.

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Answer:

d. 9

Step-by-step explanation:

y= 0.22x^2 - 1.76x +4.75

x is the time in months so we should replace x by 10

y = 0.22 (10)^2 - 1.76(10) + 4.75

0.22 (100) - 17.6 + 4.75

22 - 17.6 + 4.75

9.15

So the number of laptops that will be sold during month 10 is 9. (you can't have 0.15 of a computer)

Answer:

d. 9

Step-by-step explanation:

The equation: y = 0.22x^2 - 1.76x + 4.75

x: Time in months

y: Number of laptops sold

Since we need to predict the number of laptops that will be sold during month 10, we can replace the x with 10.

The new equation will be: y = 22 - 17.6 + 4.75

Then y will be 9.15

Since there cannot be 0.15 of a laptop, we round the number 9.15 to a whole number, which is 9.

D) 9 is our final answer to this question.

The amount of variance for y that is predicted by its relationship with x is 64%.

Variance measures the rate of dispersion of a data point around the dataset. It can be calculated by finding the square of the standard deviation of a dataset. Variance measures the variation of a data set.

Correlation is a statistical measure used to measure the linear relationship that exists between two variables. The greater the correlation coefficient is closer to one, the greater the linear relationship that exists between the two variables. A positive correlation occurs when the two variables move in the same direction.

Variance = (correlation coefficient²) x 100

(0.80²) x 100

0.64 x 100 = 64%

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Answer:

17 hours

Step-by-step explanation:

We first want to figure out how much money shes making per hour.

We can simply divide 176 by 8 getting us 22

Since we know she makes 22 dollars an hour we can divide 374 by 22 getting us 17.

Now we know it would take 17 hours to make 374 dollars

If you want to double check you can simply multiply 17 by 22 which would get you 374

Answer: 17 hours

Step-by-step explanation

Answer:

Height = 6m

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] × 36 = 12

72 ÷ 12 = 6

Answer: 60.

Step-by-step explanation:

Let in a right triangle one of the legs is 25, and the hypotenuse is 65.

Hence, the other leg is:  [tex]\sqrt{65^2-25^2}=\sqrt{4225-625}=\sqrt{3600}=60.[/tex]

The equivalent numbers of 12/20 are 60% and 0.60

The fraction expression is given as:

12/20

Multiply the fraction expression by 100%

So, the expression becomes

12/20 * 100%

Evaluate the product

60%

Express as fraction, again

60/100

Evaluate the quotient

0.60

Hence, the equivalent numbers of 12/20 are 60% and 0.60

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Answer:

x-int: (4, 0)

Step-by-step explanation:

First, we need to find the equation of the line.

The equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

Thus, we need to find the slope first by using the slope formula:

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } \\[/tex] or change in y / change in x

So we have: [tex]\frac{3-2}{1-2}=\frac{1}{-1}=-1=m[/tex]

We must plug in the slope to find the y-intercept:

[tex]3=-1(1)+b\\3=-1+b\\4=b[/tex]

So the equation of the line is y = -x + 4

The x-intercept means that the y coordinate is 0 so we can use the equation:

[tex]0=-x+4\\-4=-x\\4=x[/tex]

The expression of the equation will be:

x² - 8x = x(x - 8)

x² - 10x = x(x - 10)

x² - 5x = x(x - 5)

x² - 3x = x(x - 3)

It should be noted that an equation simply means the expression of the variables that are given.

In this case, the following can be represented:

x² - 8x = x(x - 8)

x² - 10x = x(x - 10)

x² - 5x = x(x - 5)

x² - 3x = x(x - 3)

This is illustrated above.

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Answer:

1.2 meters long

Step-by-step explanation:

3(4/5)m=3.8m

5m-3.8m=1.2m

Answer:

-1

Step-by-step explanation:

n^2+2n = -1

n(n+2) = -1

Using the normal distribution, there is a 0.3228 = 32.28% probability that at least 90 cars pass inspection.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution are given by:

n = 100, p = 0.88.

Hence the mean and the standard deviation for the approximation are:

The probability that at least 90 cars pass inspection, using continuity correction, is P(X > 89.5), which is one subtracted by the p-value of Z when X = 89.5, hence:

Z = (89.5 - 88)/3.25

Z = 0.46

Z = 0.46 has a p-value of 0.6772.

1 - 0.6772 = 0.3228.

0.3228 = 32.28% probability that at least 90 cars pass inspection.

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Answer:

Step-by-step explanation:

The equation will be in standard form when terms are listed in order of decreasing degree, and the right side of the equation is 0.

We can subtract the right-side expression from both sides to get standard form.

  -3x² -8 -(5x -7) = 5x -7 -(5x -7)

  -3x² -8 -5x +7 = 0 . . . . . . . simplify a bit

  -3x² -5x -1 = 0 . . . . . . . . . collect terms

The standard form equation can be written ...

  -3x² -5x -1 = 0

The quadratic coefficient is the coefficient of the term with degree 2. The quadratic coefficient is -3.

The linear coefficient is the coefficient of the term with degree 1. The linear coefficient is -5.

The constant coefficient is the coefficient of the term with no variables. The constant is -1.

__

Additional comment

We can make the leading coefficient positive by multiplying the equation by -1. This gives ...

  3x² +5x +1 = 0

with quadratic, linear, and constant coefficients 3, 5, 1.

This is a legitimate answer to this question. In the case of linear equations, the "standard form" has the constant on the right side of the equal sign, and the leading coefficient is required to be positive. A negative leading coefficient can sometimes lead to errors (when the sign is overlooked), so having a positive leading coefficient is often preferred.

Applying the Midpoint Formula, the midpoint of the line segment whose endpoints are the library and the museum is calculated as: D. (2.5, 5.5).

To find the coordinates of the midpoint between two endpoints on a coordinate plane, the midpoint formula that is used is expressed as: M[(x2 + x1)/2, (y2 + y1)/2].

Given the following coordinates:

The library is located at point (-3, 9)

The museum is located at point (8, 2), therefore, let:

(-3, 9) = (x1, y1)

(8, 2) = (x2, y2)

Midpoint = M(x, y)

Substitute the values into M[(x2 + x1)/2, (y2 + y1)/2]:

M(x, y) = [(8 + (-3))/2, (2 + 9)/2]

M(x, y) = (5/2, 11/2)

M(x, y) = (2.5, 5.5)

Thus, the midpoint of the line segment whose endpoints are the library and the museum is calculated as: D. (2.5, 5.5).

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Answer:

Its D (2.5, 5.5) On Edg 2022-23

Step-by-step explanation:

Hope This Helps:))

The volume of the triangular prism as described is; 15 cubic foot.

A triangular pyramid simply refers to any geometric solid with a triangular base, and all three lateral faces are also triangles with a common vertex

It follows from the formula for calculating the volume of a triangular prism that;

Volume = (1/3) × base area × height.

Consequently,

volume of the prism is; = (1/3) ×9 × 5

Volume = 15 cubic foot

Therefore, volume of the triangular prism as described is; 15 cubic foot.

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The reflection of the word DAD across the y-axis is not the same

The statement is given as:

MOM, when reflected over the y-axis = MOM

The above is true because the letters M and O have reflectional symmetry across the y-axis

However, the letter D do not have a reflectional symmetry across the y-axis

So, the letters would not remain the same when reflected

Hence, the reflection of the word DAD across the y-axis is not the same

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