Last year Salma opened an investment account with $8200. At the end of the year the amount in the account had increased by 6.5%. How much money was in her account at the end of the year?

Answer:

A, y = -40x+300

Step-by-step explanation:

y=180

x=3

180=-40(3)+300

180=300-120

Answer:

Step-by-step explanation:

27 + D + 2A + C = 25 + D + B + C + A

subtract D, A, C on both sides

=> 27 + A = 25 + B

=> B = A + 2

3D + A + 29 = 2B + D + A + 27

=> 2D + 29 = 2B + 27

=> 2D = 2B + 27 - 29

=> D = B - 1

substitute:

27 + (B - 1) + 2(A + 2) + A = 2A + B + 30

substitute again:

2A + (A + 2) + 30 = 3A + 32

Answer:

Midpoint: (6, - 2)

Step-by-step explanation:

G (4,2) and H (8, -6)

Midpoint: (4+8)/2 = 6 and (2 +-6)/2 = -2

= (6, - 2)

Answer:

true

Step-by-step explanation:

got it right

Two consecutive whole numbers representing the estimated square root of 50 are 7 and 8.

Number need to estimate square root  = 50

To estimate √50,

Neal found that the two perfect squares nearest 50 are 49 and 64.

Since 50 is closer to 49 than to 64,

Square root of 49 is equal to 7

Square root of 64 is equal to 8.

We know that √50 is closer to the square root of 49 which is 7.

Estimated two consecutive whole numbers are 7 and 8.

Therefore, estimated √50 is between the two consecutive whole numbers 7 and 8.

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The above question is incomplete, the complete question is:

Neal estimated √50 by determining that the two perfect squares nearest 50 are 49 and 64. Select the two consecutive whole numbers that the √50 is between to complete the sentence.

Answer:

Its the second choice.

Step-by-step explanation:

x does not have a value of -2 so is not in the domain

The range does not have values  greater than 1 and less than or equal to 4.

The correct statement is: 'A standard normal distribution has a mean of 0 and a standard deviation of 1 '

The correct answer is an option (b)

In this question, we need to complete given statement.

We know that the normal distribution is a symmetrical and bell-shaped distribution.

In standard normal distribution the mean, median and mode are all equal. Also, it always has a mean of zero and a standard deviation of one.

So,  A standard normal distribution has a mean of 0 and a standard deviation of 1 .

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Step-by-step explanation:

b can be used to check her score

Answer:

3/4

Step-by-step explanation:

a. The Red Sea trough refers to a dip in the upper-level height originating over the eastern Mediterranean moving southeastward, and deepening over the Red Sea.

b. This weather phenomenon manifests itself as it causes a sudden drop in temperatures, thunderstorms, and dust storms.

c. The Red Sea trough presents a challenge to weather forecasting as it is hard to predict when the trough will develop.

d. The Red Sea trough presents several hazards as causes heavy rainfall, strong winds, and a sudden drop in temperatures.

The Red Sea trough is one of the familiar weather patterns in Jordan. It is seen both in spring and fall.

a. The Red Sea trough is a dip in the upper-level height that originates over the eastern Mediterranean, advances southeastward, and deepens over the Red Sea. During the fall and spring seasons, this trough becomes more profound and generates a shallow low-pressure system over the Levant region, resulting in a northwesterly to northeasterly wind.

b. This weather phenomenon manifests itself in terms of weather in several ways. They are as follows:

c. The Red Sea trough presents a significant challenge to weather forecasting. It is difficult to predict when the trough will develop and the magnitude of its impacts on weather. The weather forecasters struggle to estimate the movement of the trough, its depth, and intensity, and the amount of rain and wind it will produce. As a result, the meteorological department often issues warnings and alerts, but the severity and impact of the weather are not always accurately forecasted.

d. The Red Sea trough presents several hazards. They are as follows:

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Answer:

Not sure

Step-by-step explanation:

Still not sure

The binomial probability formula is used to calculate the probability of a specific number of successes in a fixed number of independent trials, where each trial can only result in success or failure. It is used to model situations where there are only two possible outcomes for each trial, and where the trials are independent and identically distributed.

The formula for binomial probability is:

\(P(x) = (n choose x) * p^x * (1 - p)^{n-x}\\\)

where P(x) is the probability of x successes in n trials, p is the probability of success on each trial, (n choose x) is the binomial coefficient which gives the number of ways to choose x successes from n trials, and (1 - p) is the probability of failure on each trial.

The binomial probability formula can be used in a variety of applications, such as:

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Let us first understand what is meant by the term probability of happening of an event. The term probability of an event happening tells us about the extent or how many times it is likely to happen in a given number of tries. For example, if we throw a die of six faces, then the probability of a number to come on the top of the dice tells us about the extent to which that is likely to occur.

The probability of an event to occur in an experiment is equal to the ratio of the outcomes in which this event happens to the total number of outcomes of the experiment. A pack of cards contains 52 total cards. Therefore, when we pick a card from the set there can be 52 different outcomes.

(i) A pack of cards contains 13 red cards. Therefore, out of those 52 outcomes, 13 outcomes are required. Hence, the probability of getting a red card is 1352=14.

(ii) A pack of cards contains 13 black cards. Therefore, out of those 52 outcomes, 13 outcomes are required. Hence, the probability of getting a black card is 1352=14

(iii) A pack of cards contains 4 black cards. Therefore, out of those 52 outcomes, 4 outcomes are required. Hence, the probability of getting an ace is 452=113.

Note: Note that probability is not always sure or it doesn’t guarantee that the specific event will surely happen in those number of trials. This means that the probability of getting an ace card does not mean that in four tries we will surely get an ace. Probability just tells us how likely the event may happen.

Answer:

C. -336

Step-by-step explanation:

1. Substitute 25 for x as g(25) simply means x = 25

2. Now that the equation is g(x) = 24(25 - 39), solve what's within the parenthesis first due to PEMDAS or subtract 25 - 39.

3. Now that the equation is g(x) = 24(-14) due to subtracting 25 and 39, multiply 24 by -14 since there is no sign. And a parenthesis with a number in it besides a number with no parenthesis signifies multiplication.

4. Now the answer found is -336.

Answer:

48 units

Step-by-step explanation:

The length of line segment DB is 48 units

Parallelograms are shapes with opposite parallel sides

Start by calculating the measure of t using:

AE = CE --- the diagonals

So, we have

3t - 14 = t + 2

Collect like terms

3t - t = 14 + 2

Evaluate

t = 8

The length of segment DB is calculated as;

DB = 2 * DE

So, we have:

DB = 2 * (2t + 8)

Substitute 8 for t

DB = 2 * (2* 8 + 8)

Evaluate

DB = 48

Hence, the length of line segment DB is 48 units

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Answer:

You wouldd say Steve is the better buy but if you look at it closely Steve has a 3lb bag for $2.25. But Martha has 5lb bag for $3.80 If I were in the market and I had to say which is a better buy I would say Martha's

Step-by-step explanation:

Steve's apples are the better buy, as they cost $0.75 per pound compared to Martha's apples, which cost $0.76 per pound.

A division is a process of splitting a specific amount into equal parts.

To determine which option is the better buy, we need to calculate the cost per pound of each option.

For Martha's apples, the cost per pound is:

$3.80 ÷ 5 lb. = $0.76/lb.

For Steve's apples, the cost per pound is:

$2.25 ÷ 3 lb. = $0.75/lb.

Therefore, Steve's apples are the better buy, as they cost $0.75 per pound compared to Martha's apples, which cost $0.76 per pound.

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Answer:

61

Step-by-step explanation:

160-99 = 61

Answer:

Solution,

160-99=61

Hence, 160 is more than by 61

Step-by-step explanation:

The expression for the area under the curve y = x^3 from 0 to 1, as a limit, is A = 1/4.

(a) To find an expression for the area under the curve y = x^3 from 0 to 1 using Definition 2, we need to approximate the area using a sum and then take the limit as the number of approximating rectangles approaches infinity.

Let's divide the interval [0, 1] into n equal subintervals. The width of each subinterval will be Δx = 1/n. We can choose any point within each subinterval as the representative x-value for that subinterval. Let's choose the right endpoint of each subinterval as our representative x-value.

The right endpoint of the ith subinterval will be x_i = iΔx = i/n, where i ranges from 1 to n. The corresponding y-value for each x_i is y_i = (i/n)^3.

The area of each rectangle can be approximated as the product of the width and height of the rectangle, which is ΔA_i = Δx  y_i = (1/n)  (i/n)^3.

The total area under the curve can be approximated by summing up the areas of all the rectangles:

A = Σ(ΔA_i) = Σ[(1/n)  (i/n)^3] for i = 1 to n.

(b) The formula given in Appendix E states that the sum of the cubes of the first n integers is [n(n+1)/2]^2. Therefore, we have:

1^3 + 2^3 + 3^3 + ... + n^3 = [n(n+1)/2]^2.

Using this formula, we can rewrite the expression for the area under the curve as a limit:

A ≈ Σ[(1/n)  (i/n)^3] for i = 1 to n

= (1/n^4)  [1^3 + 2^3 + 3^3 + ... + n^3]

= (1/n^4)  [n(n+1)/2]^2.

Taking the limit as n approaches infinity, we have:

A = lim(n→∞) [(1/n^4) [n(n+1)/2]^2]

= lim(n→∞) [(n^2(n+1)/2)^2 / n^4]

= lim(n→∞) [(n^4 + 2n^3 + n^2) / 4n^2]

= lim(n→∞) [(1 + 2/n + 1/n^2) / 4]

= (1 + 0 + 0) / 4

= 1/4.

Therefore, the expression for the area under the curve y = x^3 from 0 to 1, as a limit, is A = 1/4.

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Answer:

the value of x is 5/7 which is in fraction

Answer:  x = 5/7

Step-by-step explanation:  2x/3 + x/2 =5/6

To use a least common denominator, divide LCD by the original denominator and multiply the original numerator by the result.

for 2x/3  6÷3=2  2×2x=4x so that becomes 4x/6

for x/2    6÷2=3  3× (invisible) 1 = 3x, so that becomes 3x/6

combine 4x/6 + 3x/6 = 7x/6  

Back to the original equation, substituting the calculated term:

7x/6 = 5/6   Multiply both sides by 6 to simplify (6)(7x/6) = (6)(5/6) 6's "cancel"

7x = 5 .  Divide both sides by 7 to solve for x  7x/7 = 5/7

x = 5/7

Answer:

Step-by-step explanation:

The segments of the triangles are proportional.

Add all the measurements on the left to get the complete length of the

left side - 9 + 3 + 12 = 24

Form a proportion with a smaller triangle still using the left side,

this time 9 + 3 = 12

Use the bottom measurement of 22 to complete the proportion:

You have:

24/22 = 12/x

cross multiply - 12 × 22 = 264

divide by 24 = 11

x = 11

The sampling distribution of x for a sample size of 30 is N(16642, 423.27), for a sample size of 50 is N(16642, 328.08), for a sample size of 100 is N(16642, 232.00), and for a sample size of 400 is N(16642, 116.00).

The sampling distribution of x for itemized deductions for this population of taxpayers for each of the following sample sizes: 30, 50, 100, and 400 can be determined using the formula for the standard error of the mean (SEM):

SEM = σ / √n

where σ is the standard deviation and n is the sample size.

For a sample size of 30:

SEM = 2320 / √30 = 423.27

For a sample size of 50:

SEM = 2320 / √50 = 328.08

For a sample size of 100:

SEM = 2320 / √100 = 232.00

For a sample size of 400:

SEM = 2320 / √400 = 116.00

The sampling distributions of x for itemized deductions for this population of taxpayers for each of the sample sizes are normal distributions with a mean of $16,642 and the corresponding SEM values calculated above.

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Conducting multiple t-tests can be time-consuming and requires a larger sample size to ensure sufficient power to detect differences between the groups. This may increase the cost and resources required for the study.

What is analysis in mathematics?

The analysis is a branch of mathematics that deals with the study of functions, sequences, and limits. It is concerned with understanding how functions behave, how they change and grow, and how they can be approximated and analyzed.

There are several difficulties in conducting a multiple two-sample t-test analysis to compare four diets pairwise in the described study.

One difficulty is that the multiple t-tests increase the risk of Type I errors, which are false positive findings. When multiple tests are conducted, the overall probability of making at least one Type I error increases. This can lead to the conclusion that a difference exists between two groups when in fact there is no real difference. To control for this risk, the researchers would need to use a stricter significance level or adjust the p-values using a method such as the Bonferroni correction.

Another difficulty is that the multiple t-tests do not take into account the relationships between the different groups being compared. For example, if the low-carb diet group has significantly different outcomes from the control group, this may also affect the results of the comparison between the low-carb diet and the other diet groups. A more comprehensive analysis method, such as a one-way ANOVA or a multivariate analysis, would be needed to account for these relationships.

Hence, conducting multiple t-tests can be time-consuming and requires a larger sample size to ensure sufficient power to detect differences between the groups. This may increase the cost and resources required for the study.

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The code sorts the skill array in ascending order.

It then creates a HashMap to store the number of occurrences of each skill level. The left and right pointers are initialized to point to the first and last elements of the skill array. The result variable is used to store the sum of the effectiveness of all teams that can be created. The code then iterates through the skill array using the left and right pointers. If both pointers point to skills that have more than one occurrence, then two of each skill are used to create the team, and effectiveness is added to the result.

If only one pointer points to a skill with more than one occurrence, then one instance of that skill is paired with one instance of the other skill to form a team. Otherwise, if both pointers point to skills that have only one occurrence, then one instance of each skill is used to create the team. In any case, when a team is created, the HashMap is updated accordingly.

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In order to find out what g is equal too,u must subtract 19 from both sides of the equation to get

g +19-19=38-19

the nineteens cancel out getting

g=38 -19

g=19

Answer:

2) D

4) A

Step-by-step explanation:

y=3(x-1)

multiply

3(x-1)

then y=3x-3

y+1=4/3(x+3)

multiply 4/3(x+3)

y=4/3x+3

Answer:

1) D. y = 3x-3

2) A. y = 4/3 x+3

Step-by-step explanation:

1)

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : y-(3*x-3)=0

Step 1:

Equation of a Straight Line

Solve   y-3x+3  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  y-3x+3  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is -3/1 so this line "cuts" the y axis at y=-3.00000

 y-intercept = -3/1  = -3.00000  

Calculate the X-Intercept :

When y = 0 the value of x is 1/1 Our line therefore "cuts" the x axis at x= 1.00000

 x-intercept = 3/3  =  1  

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -3.000 and for x=2.000, the value of y is 3.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 3.000 - (-3.000) = 6.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  6.000/2.000 =  3.000  

Geometric figure: Straight Line

 Slope = 6.000/2.000 = 3.000

 x-intercept = 3/3 = 1

 y-intercept = -3/1 = -3.00000

2)

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    y-(4/3*x+3)=0

Step 1:

Simplify   4/3

Equation at the end of step  1:

y -  ((4/3 • x) +  3)  = 0

Step 2: Rewriting the whole as an Equivalent Fraction

Adding a whole to a fraction

Rewrite the whole as a fraction using  3  as the denominator :

3 = 3/1 = 3 · 3/3

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

4x + 3 · 3/3 = 4x+9/3

Equation at the end of step  2:

y - (4x+9)/3=0

Step 3:

Rewriting the whole as an Equivalent Fraction :

Subtracting a fraction from a whole

Rewrite the whole as a fraction using  3  as the denominator :

y = y/1 = y · 3/3

Adding fractions that have a common denominator :

Adding up the two equivalent fractions

y • 3 - ((4x+9))     3y - 4x - 9

————————————————  =  ———————————

       3                  3      

Equation at the end of step

3

:

 3y - 4x - 9

 ———————————  = 0  

      3      

STEP

4

:

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 3y-4x-9

 ——————— • 3 = 0 • 3

    3    

Now, on the left hand side, the  3  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  3y-4x-9  = 0

Equation of a Straight Line

4.2     Solve   3y-4x-9  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  3y-4x-9  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 3/1 so this line "cuts" the y axis at y= 3.00000

 y-intercept = 9/3  =  3  

Calculate the X-Intercept :

When y = 0 the value of x is 9/-4 Our line therefore "cuts" the x axis at x=-2.25000

 x-intercept = 9/-4  = -2.25000  

Calculate the Slope :

    Slope     =  2.667/2.000 =  1.333  

Geometric figure: Straight Line

 Slope = 2.667/2.000 = 1.333

 x-intercept = 9/-4 = -2.25000

 y-intercept = 9/3 = 3

Let x be the number

\(\small\bold\red{→}\small\bold{(\frac{1}{2} )x + 5 = 11}\)

\(\small\bold\red{→}\small\bold{(\frac{1}{2})x + 5 - 5 = 11 - 5}\)

\(\small\bold\red{→}\small\bold{(\frac{1}{2})x = 6}\)

\(\small\bold\red{→}\small\bold{2 × (\frac{1}{2})x = 6 × 2 }\)

\(\small\bold\red{→}\small\bold{x = 12}\)

Hello.

First, "half a number" means we divide that number by 2.

Let's say the number is z.

Divide z by 2:

\(\displaystyle\frac{z}{2}\)

Add 5 to it:

\(\displaystyle\frac{z}{2} +5\)

Now, this expression equals 11:

\(\displaystyle\frac{z}{2} +5=11\)

Subtract 5 from both sides:

\(\displaystyle\frac{z}{2} =11-5\)

\(\displaystyle\frac{z}{2} =6\)

Now, in order to get rid of the fraction, we should multiply the entire equation by 2:

\(\displaystyle\frac{z}{2} *2=6*2\)

\(z=6*2\)

\(\Large\boxed{z=12}\)

I hope it helps.

Have an outstanding day. :)

\(\boxed{imperturbability}\)

(a) Divergence at the indicated point is positive. (b) Divergence at the indicated point is zero. (c) Divergence at the indicated point is negative.

To find the divergence of each vector field at the indicated point, we will first calculate the divergence of each field and then evaluate it at the given point.
(a) The vector field is given as F = xi + yj.
The divergence of a 2D vector field F = P(x,y)i + Q(x,y)j is calculated as:
div(F) = (∂P/∂x) + (∂Q/∂y)
For this vector field, P(x,y) = x and Q(x,y) = y. So:
div(F) = (∂x/∂x) + (∂y/∂y) = 1 + 1 = 2
The divergence at the indicated point is positive.
(b) The vector field is given as F = yi.
For this vector field, P(x,y) = y and Q(x,y) = 0. So:
div(F) = (∂y/∂x) + (∂0/∂y) = 0 + 0 = 0
The divergence at the indicated point is zero.
(c) The vector field is given as F = yi - yj.
For this vector field, P(x,y) = y and Q(x,y) = -y. So:
div(F) = (∂y/∂x) + (∂(-y)/∂y) = 0 - 1 = -1
The divergence at the indicated point is negative.

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