Question 6 of 35
At the beginning of the day, the sum of the stocks in the Dow Jones was
$26,111.98. At the end of the ay, the sum of the stocks in the Dow Jones
was $25,972.44. What was the rate of change of the Dow Jones on this day?
O A. -5,3%
-
O B. 5.3%
O c. -0,53%
O D. 0.53%

Answer:

\(x=-11\)

Step-by-step explanation:

So we have the equation:

\(5+(x-2)=-8\)

Let's subtract 5 from both sides:

\((5+(x-2))-5=(-8)-5\)

The left side will cancel. Subtract on the right:

\(x-2=-13\)

Now, add 2 to both sides:

\((x-2)+2=(-13)+2\)

Again, the left side will cancel. Add the right:

\(x=-11\)

And we're done!

Answer:

it should be x=5

Step-by-step explanation:

5+(x-2)= -8

3+x=8

-3    -3

answer is x=5

The probability that the 5th child is a girl = 1/2

Before the first birth, the probability that the woman would give birth to 5 girls in a row = 0.03125

Step - by - Step expalanation

What to find?

• The probability that the 5th child is a girl.

• Before the first birth, the probability that the woman would give birth to 5 girls in a row.

Probability = required outcome / all possible outcome.

For the first part of the question, the 5th child could either be a boy or girl.

So, all possible outcome = 2 and the required outcome = 1

Hence, the probability that the fifth child is a girl = 1/2

For the second part of the question,

Before, the first birth, the probabilty that the woman would give birth to 5 girls in a row will simply =(probability of given birth to a girl)^no. of times she will give birth.

That is;

Answer:

10

Step-by-step explanation:

Answer:

The correct answer is: 2. t=0.45a

Step-by-step explanation:

Let t be the price of apples

and a be the number of apples

The price and quantity are directly proportional

\(t \propto a\)

Removing the proportionality symbol introduces a proportionality constant in the equation

\(t = ka\)

So far we know that cost of 6 apples is $2.70

Putting in the equation

\(2.70 = k (6)\\k = \frac{2.70}{6}\\k = 0.45\)

Putting the values of k will give us:

\(t = 0.45a\)

Hence,

The correct answer is: 2. t=0.45a

Answer:

y = 3x + 4

Step-by-step explanation:

Given:

Coordinates

(-3 , -5)

Slope m = 3

Find;

Equation of slope

Computation:

Given, x1 = -3 and y1 = -5

Equation of slope = y - y1 = m(x - x1)

Equation of slope = y - (-5) = 3(x + 3)

Equation of slope = y + 5 = 3x + 9

Equation of slope = y = 3x + 9 - 5

Equation of slope = y = 3x + 4

y = 3x + 4

The exact area of the region bounded by the curve is 0 for the t element of [0,2] by using the corollary to Green's theorem.

To find the exact area of the region bounded by the curve defined by the parametric equations:

x = 4t - t^3

y = 2sin(π/2 t)

for t ∈ [0, 2], we can use the corollary to Green's theorem, which relates the area of a planar region to a line integral.

The corollary states that if we have a vector field F = (M, N) and its partial derivatives Mx and Ny are continuous on a simply connected region R, then the area A of R is given by:

A = ∬<R> (Ny - Mx) dA

In this case, we can treat the curve defined by the parametric equations as a closed curve C. We can express the curve C as a vector function r(t) = (x(t), y(t)), where r'(t) = (x'(t), y'(t)) represents the derivative of r(t) with respect to t.

Let's calculate the partial derivatives of M = y and N = -x:

My = 0

Nx = 0

Since My and Nx are both zero, we can apply the corollary of Green's theorem and simplify the equation for the area:

A = ∬<R> (Ny - Mx) dA

= ∬<R> (0 - 0) dA

= 0

Therefore, the area of the region bounded by the curve is 0.

The complete question must be:

Find the exact area of the region bounded by the curve ~r = d 4t − t 3, 2 sin π 2 t, for the t element of [0,2] by using the corollary to Green's theorem.

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The following can be answered by the concept of Trigonometry.

The rearranged functions for each case, using appropriate mathematical techniques and identities:

(a) For 1 - cos(x) / x², we can use the identity sin²(x) + cos²(x) = 1 and rearrange as follows:
1 - cos(x) = sin²(x) / (1 + cos(x))
Then, divide by x² to get the rearranged function:
(sin²(x) / (1 + cos(x))) / x²

(b) For log(x + 1) - log(x) with x being large, we can use the logarithmic property of subtraction to combine the logs:
log((x + 1) / x)
As x is large, the expression simplifies to:
log(1 + (1/x))

(c) For sin(a + x) - sin(a), we can use the angle sum identity for sine:
sin(a + x) - sin(a) = (sin(a)cos(x) + cos(a)sin(x)) - sin(a)
Rearrange to get:
cos(a)sin(x) + sin(a)(cos(x) - 1)

(d) For √(1 + x - 1), we can simplify by removing the 1 and -1 inside the square root:
√(x)

(e) For √(4 + x - 2) / x, we can first simplify inside the square root:
√(2 + x) / x

These rearranged functions help avoid loss-of-significance errors in each of the given cases.

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Answer:

\(\huge\boxed{\sf x = 85}\)

Step-by-step explanation:

0.2x - 6 = 11

0.2x = 11 + 6

0.2x = 17

x = 17/0.2

\(\rule[225]{225}{2}\)

Given:-

\( \: \)

Solution:-

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \purple {━━━━━━━━━━━━━━━━━━━━━━━━━━━━}\)

hope it helps!

Answer:

Y,O,Q

Step-by-step explanation:

The range is 250 calories and the standard deviation is 57.5 calories.

In a neighbourhood donut shop, one type of donut has 440 calories, five types of donuts have 350 calories, seven types of donuts have 530 calories, five types of donuts have 330 calories, and five types of donuts have 580 calories

The formula for the range is given by;`

range = maximum value - minimum value`

The minimum value in this case is 330 and the maximum value is 580Therefore, `range = 580 - 330 = 250`

The formula for standard deviation is given by;`s = sqrt [Σ(x - µ)² / N]`

where Σ is a symbol of summation, x is the value, µ is the mean, N is the number of data and s is the standard deviation.

Calculate the mean (µ)`µ = Σ fx / N = 11960 / 23 ≈ 520.87`Substitute the values in the formula above and calculate;

Calories (x)fx(x - µ)² 3301750(-190.87)² 3501750(-170.87)² 440440(-80.87)² 5303710(9.13)² 5802900(59.13)²Total = 352191.55`s = sqrt (352191.55 / 23)≈ 57.5 calories

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Answer:

​3x−1

Step-by-step explanation:

1 Split the second term in 6{x}^{2}+x-16x

​2

​​ +x−1 into two terms.

\frac{6{x}^{2}+3x-2x-1}{4{x}^{2}-1}

​4x

​2

​​ −1

​

​6x

​2

​​ +3x−2x−1

​​  

2 Factor out common terms in the first two terms, then in the last two terms.

\frac{3x(2x+1)-(2x+1)}{4{x}^{2}-1}

​4x

​2

​​ −1

​

​3x(2x+1)−(2x+1)

​​  

3 Factor out the common term 2x+12x+1.

\frac{(2x+1)(3x-1)}{4{x}^{2}-1}

​4x

​2

​​ −1

​

​(2x+1)(3x−1)

​​  

4 Rewrite 4{x}^{2}-14x

​2

​​ −1 in the form {a}^{2}-{b}^{2}a

​2

​​ −b

​2

​​ , where a=2xa=2x and b=1b=1.

\frac{(2x+1)(3x-1)}{{(2x)}^{2}-{1}^{2}}

​(2x)

​2

​​ −1

​2

​​  

​

​(2x+1)(3x−1)

​​  

5 Use Difference of Squares: {a}^{2}-{b}^{2}=(a+b)(a-b)a

​2

​​ −b

​2

​​ =(a+b)(a−b).

\frac{(2x+1)(3x-1)}{(2x+1)(2x-1)}

​(2x+1)(2x−1)

​

​(2x+1)(3x−1)

​​  

6 Cancel 2x+12x+1.

\frac{3x-1}{2x-1}

​2x−1

​

​3x−1

​​  

Answer:

Y=mx+ b

Solve for slope and b

then plug in a point x1 and y1

Then solve for the final form

Completing squares we can rewrite the expression as:

(4x + 12)^2 + (2y - 2)^2 = 56

We know that the perfect square trinomial is:

(a + b)^2 = a^2 + 2ab + b^2

Here we have the expression:

16x^2 + 4y^2 + 96x - 8y + 84 = 0

We can rewrite this as:

(16x^2 + 96x) + (4y^2 - 8y) + 84 = 0

((4x)^2 + 2*12*(4x)) + ((2y)^2 - 2*2*(2y)) + 84 = 0

Then we need to add 12^2 and 2^2 in both sides, then we will get:

((4x)^2 + 2*12*(4x) + 12^2) + ((2y)^2 - 2*2*(2y) + 2^2) + 84 = 12^2 + 2^2

(4x + 12)^2 + (2y - 2)^2 = 144 + 4 - 84

(4x + 12)^2 + (2y - 2)^2 = 56

The squares are complete.

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The required time for Andrew to accumulate $6412 would be 2.37 years.

Given that Andrew has $5747 and wants to accumulate $6412. The interest rate on the investment is 4.1% compounded quarterly.

Let the required time be t, and the quarterly rate be r. We have to solve for t.In the compounded quarterly situation, the effective interest rate per quarter, r, is given as:

r = (1 + 4.1%/4) = 1.01025%

Let us find out the value of $5747 after t quarters of compounding at this rate using the formula for compound interest:

A = P(1 + r/n)^nt

Where: A = the accumulated value of the investment (future value), P = the principal (present value), r = the annual interest rate (as a decimal) = 0.041/n = the number of times compounded per year, = 4 for quarterly

t = the number of years

4.1% per annum compounded quarterly= 1.01025% per quarter

5747 * (1 + 0.041/4)^(4t) = 6412

Dividing by $5747, we get:(1 + 0.01025)^4t = 1.11622

Taking the logarithm base 10 on both sides, we get:

log 1.11622 = 4t log (1.01025)t = log 1.11622 / (4 log 1.01025) = 2.37 years, to 2 decimal places.

Therefore, the required time for Andrew to accumulate $6412 would be 2.37 years.

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The probability that a student has a GPA under 2.0 given that he has skipped many classes is 8/11.

From the table we see that,

The student who have a GPA under 2.0 = 80

The student who has skipped many classes = 80 + 25 + 5

The student who has skipped many classes = 110

Hence, the probability that a student has a GPA under 2.0 given that he has skipped many classes = The student who have a GPA under 2.0/The student who has skipped many classes

The probability that a student has a GPA under 2.0 given that he has skipped many classes = 80/110

The probability that a student has a GPA under 2.0 given that he has skipped many classes = 8/11

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The complete question is:

One thousand students at a city high school were classified both according to GPA and whether or not they consistently skipped classes.

What is the probability that a student has a GPA under 2.0 given that he has skipped many classes?

A. 0.080

B. 0.281

C. 0.285

D. 0.314

E. 0.727

Answer:

4 months

Step-by-step explanation:

The first planet we know grow 3 inches per month and starts at 6 inches. While the second plant is 2 inches and grows 4 inches per month, as 50-2 (the start of the inches) = 48. 48/12 months = 4 inches per month.

With this information we can slowly add up the time.

1st Month

Planet 1: 9 inches

Planet 2: 6 inches

2nd Month

Planet 1: 12 inches

Planet 2: 10 inches

3rd Month

Planet 1: 15 inches

Planet 2: 14 inches

4th Month

Planet 1: 18 inches

Planet 2: 18 inches

Answer:

8.4-16.2n²

Step-by-step explanation:

2.4-5.4n3n+6

= 2.4-16.2n²+6

= 8.4-16.2n²

Step-by-step explanation:

i. Looking at the table, he got 3 odd numbers out of 9 scored so the probability is 33% or 3/9 or 1/3

ii. He got 4 square numbers so the probability is 4/9( remeber 0 is a square number).

iii. Only two number are multiples of 5 so the probability is 2/9.

iv. No number is greater than 15 so the answer is 0%

v. 5 numbers are less than zero so the answer is 5/9

The cost of both plans when the cost is the same will be $68.8.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's suppose the number of minutes is x

Now,

The total cost of plan A ⇒

25 + 0.14x

The total cost of plan b ⇒

9 + 0.19x

Now, if the total cost is the same

25 + 0.14x = 9 + 0.19x

0.19x - 0.14x = 25 - 9

0.05x = 16

x = 320

Hence "The cost of both plans when the cost is the same will be $68.8".

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Answer:

3p - 145w ≥ 50

Step-by-step explanation:

w = number of winners

p = number of plays of carnival game

Profits = 3p - 145w

3p - 145w ≥ 50

Answer: Choice A) Alternate exterior angles are congruent

This is due to the alternate exterior angles theorem.

A more in depth answer would involve a multiple number of paths to take. One such path could have us noticing the following two properties

Both congruences are due to the vertical angle theorem.

Furthermore,

angle 4 = angle 5

because they are alternate interior angles

Then by the transitive property, we effectively connect the dots or the chain links to get to angle 1 = angle 8. We can also use the substitution property as well.

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

Side note: angles 1 and 8 are outside the parallel lines 'a' and m, so they are considered exterior angles. Also, they are on alternating sides of the transversal line t. These two facts lead to angles 1 and 8 being alternate exterior angles.

Answer:

interior angles are congruent

If Ridgewood Savings Bank charges a $27 per check overdraft protection fee. The amount she will owe the bank after July 12 is: $1,071.42.

Total obligation can be defined as the amount a person owe another person or the debt amount a borrower  is expected to payback to a lender.

Balance $1,400

July 9 check ($1,380.15)

Balance $19.85

July 10 check ($765.67)

($670 + $95.67)

Balance -$745.82 (Overdraft)

Now let find the amount she owe

Balance -$745.82

July 11 check $130

Balance -$875.82

July 12 check $87.60

Ending balance -$963.42

Overdraft fee $108

($27 ×4)

Total obligation -$1,071.42

Therefore her total obligation is $1,071.42.

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Answer:

Cluster analysis is used to identify groups of entities that have similar characteristics is a true statement.

Step-by-step explanation:

Cluster analysis is a statistical technique used to identify groups or clusters of entities that exhibit similar characteristics or behaviors. It is a common method employed in data mining, machine learning, and exploratory data analysis.

The goal of cluster analysis is to group data points or entities in a way that maximizes the similarity within each cluster and minimizes the similarity between different clusters. The similarity or dissimilarity between data points is typically measured using a distance or similarity metric, such as Euclidean distance or correlation coefficient.

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Answer:

m<A = 35

m<B = 55

Step-by-step explanation:

Complementary angles mean the 2 angles add up to 90 so:

y - 16 + y + 4 = 90

2y - 12 = 90

2y = 102

y = 51

m<A:

y - 16

51 - 16

35

m<B:

y + 4

51 + 4

55

The transformation from f(x) to g(x) is a vertical stretch by a factor of m

The functions are given as:

f(x) = x

g(x) = mx

Substitute f(x) = x in g(x) = mx

g(x) = mf(x)

From the question, we understand that:

m > 1

This means that;

The transformation from f(x) to g(x) is a vertical stretch by a factor of m

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True. The Pearson's linear correlation coefficient is a measure of the strength and direction of the linear relationship between two continuous random variables.

It ranges from -1 to 1, with values closer to -1 or 1 indicating a stronger linear correlation. If the value is near ±1, then the association between the variables is quasi perfectly linear. However, it is important to note that correlation does not imply causation and that other types of relationships between variables may exist beyond linear associations. In conclusion, the Pearson's linear correlation coefficient is a useful tool for assessing the strength and direction of linear relationships between continuous variables.

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Answer:

Trevor, Julio, Chantal, Vern, Danica, Andre, August, Maximus

Step-by-step explanation:

$964

$1,010

$1,165

$1,286

$1,425

$1,430

$1,530

$1,575

Answer:

$964

$1,010

$1,165

$1,286

$1,425

$1,430

$1,530

$1,575

Step-by-step explanation: