Bank account C starts with $10 and doubles each week, represented by the equation LaTeX: B\left(c\right)=10\left(2\right)^xB ( c ) = 10 ( 2 ) x. Bank account D starts with $1,000 and grows by $500 each week, represented by the equation LaTeX: B\left(d\right)=1000+500xB ( d ) = 1000 + 500 x.




When will account C contain more money than account D?

Answer:

14,857.37

Step-by-step explanation:

15,890.23 - Percentage decrease =

15,890.23 - (6.5% × 15,890.23) =

15,890.23 - 6.5% × 15,890.23 =

(1 - 6.5%) × 15,890.23 =

(100% - 6.5%) × 15,890.23 =

93.5% × 15,890.23 =

93.5 ÷ 100 × 15,890.23 =

93.5 × 15,890.23 ÷ 100 =

1,485,736.505 ÷ 100 =

14,857.36505 ≈ 14,857.37

A sample size of approximately 4,148 newborns is required to obtain a 99% confidence interval for the proportion of all newborns who are breast-fed exclusively in the first two months of life to within 2 percentage points.

To calculate the required sample size for a 99% confidence interval with a margin of error (precision) of 2 percentage points for the proportion of newborns breast-fed exclusively in the first two months of life,

we will use the following formula:
\(n = (Z^2 * p * (1-p)) / E^2)\)
where:
n = required sample size
Z = Z-score for the desired confidence level (in this case, 99%)
p = estimated proportion (since we don't have this value, we will use 0.5 for the most conservative estimate)
E = margin of error (2 percentage points, or 0.02 in decimal form)
For a 99% confidence interval, the Z-score is 2.576.

Now, let's plug these values into the formula:
\(n = (2.576^2 * 0.5 * (1-0.5)) / 0.02^2\)
n = (6.635776 * 0.5 * 0.5) / 0.0004
n = 1.658944 / 0.0004
n ≈ 4147.36
Since we cannot have a fraction of a person, we will round up to the nearest whole number.

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Answer:

w = 39°

Step-by-step explanation:

108° and y° are suplementary angles

111° 69°and x° are suplemantary angles

then:

108 + y = 180

y = 180 - 108

y = 72°

111 + x = 180

x = 180 - 111

x = 69°

Internal angles of a triangle sum 180°

then:

x + y + w = 180

69 + 72 + w = 180

141 + w = 180

w = 180 - 141

w = 39°

Factoring a quadratic in two variables with a leading coefficient of 1 involves finding two binomial factors that, when multiplied, produce the quadratic expression. The factors can be determined by identifying the common factors of the quadratic terms and arranging them appropriately.

To factor a quadratic expression in two variables with a leading coefficient of 1, we need to look for common factors among the terms. The goal is to rewrite the quadratic expression as a product of two binomial factors. For example, if we have the quadratic expression x^2 + 5xy + 6y^2, we can factor it as (x + 2y)(x + 3y) by identifying the common factors and arranging them in the binomial factors.

The process of factoring a quadratic in two variables may involve trial and error, testing different combinations of factors to find the correct factorization. Additionally, factoring methods such as grouping or using the quadratic formula can also be applied depending on the specific quadratic expression.

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Answer:

15 cm squared

area =l x w

so 3 x 5= 15

Step-by-step explanation:

Answer:

15cm

Step-by-step explanation:

Answer:

Option 'b' i.e. -11/20 is the correct option.

Thus,

\(\frac{1}{5}-\frac{3}{4}=-\frac{11}{20}\)

Step-by-step explanation:

Given the expression

\(\frac{1}{5}-\frac{3}{4}\)

Determining the difference of the fractions

\(\frac{1}{5}-\frac{3}{4}\)

The Least Common Multiplier of 5, 4 is 20. Thus, adjust the fractions based on the L.C.M.

\(\frac{1}{5}-\frac{3}{4}=\frac{4}{20}-\frac{15}{20}\)

Apply the fraction rule:  \(\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}\)

          \(=\frac{4-15}{20}\)

Add the number: 4-15 = -11

           \(=\frac{-11}{20}\)

Apply the fraction rule:  \(\frac{-a}{b}=-\frac{a}{b}\)

            \(=-\frac{11}{20}\)

Please check the attached figure, where the pointing-down arrow is representing the correct answer which is -11/20.

Therefore, option 'b' i.e. -11/20 is the correct option.

Thus,

\(\frac{1}{5}-\frac{3}{4}=-\frac{11}{20}\)

The approximate length of the minor arc AB is given as follows:

B. 15.7 cm.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The radius for this problem is given as follows:

r = 10 cm.

Hence the circumference for the entire circle is given as follows:

C = 2π x 10

C = 62.8 cm.

The minor arc AB has an angle of 90º, which is 90/360 = one fourth of the circle, hence the length is given as follows:

62.8/4 = 15.7 cm.

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However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

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Answer:

Herb-Catherine-Amy

Step-by-step explanation:

Answer:

Herb-Catherine-Amy

Step-by-step explanation:

The minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts

Let x represent the number of Pi Day T-shirts sold.

They are selling Pi Day T-shirts for $7.50 each, So to raise $500:

7.5x > 500

Dividing through by 7.5:

7.5x / 7.5 > 500 / 7.5

x > 66.7

Hence, the minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts

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The mean weight of a randomly chosen vehicle can be calculated by taking the average of the minimum and maximum weights:

Mean = (2,180 + 4,449) / 2 = 3,314.5 pounds

The standard deviation of a uniformly distributed random variable can be calculated using the following formula:

Standard Deviation = (Max - Min) / √12

Standard Deviation = (4,449 - 2,180) / √12 ≈ 652.48 pounds

To find the probability that a vehicle will weigh less than 2,389 pounds, we need to calculate the proportion of the total range that falls below 2,389 pounds:

Probability = (2,389 - 2,180) / (4,449 - 2,180) ≈ 0.317

To find the probability that a vehicle will weigh more than 3,672 pounds, we need to calculate the proportion of the total range that exceeds 3,672 pounds:

Probability = (4,449 - 3,672) / (4,449 - 2,180) ≈ 0.361

To find the probability that a vehicle will weigh between 2,389 and 3,672 pounds, we need to calculate the proportion of the total range that falls within this interval:

Probability = (3,672 - 2,389) / (4,449 - 2,180) ≈ 0.322

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Type I error refers to rejecting a true null hypothesis, while Type II error refers to failing to reject a false null hypothesis. Types of statistical analyses include descriptive statistics, inferential statistics, correlation analysis, regression analysis, etc.

Type I error is a false positive, and Type II error is a false negative. Examples of Type I errors include convicting an innocent person in a criminal trial and rejecting a new drug that is actually effective. Examples of Type II errors include failing to convict a guilty person in a criminal trial and accepting a new drug that is actually ineffective.

Various statistical analyses can be applied to the data collected in research studies, depending on the research question and the type of data. Some common types of statistical analyses include descriptive statistics, inferential statistics, correlation analysis, regression analysis, t-tests, analysis of variance (ANOVA), and chi-square tests. Descriptive statistics are used to summarize and describe the characteristics of the data, while inferential statistics are used to draw conclusions and make inferences about the population based on sample data. Correlation analysis examines the relationship between two or more variables, regression analysis explores the relationship between a dependent variable and one or more independent variables, t-tests compare means between two groups, ANOVA analyzes differences among three or more groups, and chi-square tests examine the association between categorical variables.

Type I error, also known as a false positive, occurs when we reject a null hypothesis that is actually true. This means we conclude that there is a significant effect or relationship when there is none in reality. For example, in a criminal trial, a Type I error would be convicting an innocent person. Another example is rejecting a new drug that is actually effective, leading to the rejection of a potentially beneficial treatment.

On the other hand, a Type II error, also known as a false negative, occurs when we fail to reject a null hypothesis that is actually false. In this case, we fail to detect a significant effect or relationship when one exists. For instance, in a criminal trial, a Type II error would be failing to convict a guilty person. In the context of medical testing, a Type II error would occur if we accept a new drug as ineffective when it is actually effective, resulting in the approval of an ineffective treatment.

Various statistical analyses can be applied to research study data depending on the research question and the type of data collected. Descriptive statistics are used to summarize and describe the characteristics of the data, such as measures of central tendency (e.g., mean, median) and variability (e.g., standard deviation, range). Inferential statistics are used to make inferences and draw conclusions about the population based on sample data, such as hypothesis testing and confidence interval estimation.

Correlation analysis examines the relationship between two or more variables and determines the strength and direction of their association. Regression analysis explores the relationship between a dependent variable and one or more independent variables, allowing us to predict the value of the dependent variable based on the independent variables.

T-tests are used to compare means between two groups, such as comparing the average test scores of students who received a specific intervention versus those who did not. Analysis of variance (ANOVA) analyzes differences among three or more groups, such as comparing the performance of students across different grade levels.

Chi-square tests examine the association between categorical variables, such as analyzing whether there is a relationship between gender and voting preference. These are just a few examples of the statistical analyses commonly applied to research study data, and the specific choice of analysis depends on the research question and the nature of the data.

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Answer:

= -48

Step-by-step explanation:

3x^3 - 8y^2

3 ( 2 )^3 - 8 ( -3 )^2

first you solve the exponents

3 ( 8 ) - 8 ( 9 )

multiply

24 - 72

subtract

= - 48

hope this helps

The requried cost is $8995 when the two companies charge the same for transporting 20 tons of sugar.

To estimate the amount of sugar for which the two companies charge the same,

4995 + 200.50x = 6500 + 125.25x

Simplifying and solving for x, we get:

74.75x = 1505

x = 20

Therefore, the two companies charge the same when transporting 20 tons of sugar. To estimate the cost at this point, we can substitute x=20 into either equation:

For the first company:

cost = 4995 + 200.50(20) = $8995

For the second company:

cost = 6500 + 125.25(20) = $8995

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Answer:

3(tan 50°)

Step-by-step explanation:

I don't really get the question tho...

Hopefully it helps, tho!

Answer:  the absolute value of -5, 0.25, 0.25, -2.5, -1 1/5, -4

Step-by-step explanation:

3.14 is the answer aaaa

Answer:

3.14

Step-by-step explanation:

Answer:

5/9

step by step follow up

Answer:

\( \boxed{c = -17} \)

Step-by-step explanation:

\( = > 3 - 7c - 20c = 7( - 7c - 19) + 14c \\ \\ = > 3 - 27c = ( - 7c \times 7) - (7 \times 19) + 14c \\ \\ = > 3 - 27c = - 49c - 133 + 14c \\ \\ = > 3 - 27c = - 35c - 133 \\ \\ = > 3 - 27c + 35c = - 133 \\ \\ = > 3 + 8c = - 133 \\ \\ = > 8c = - 133 - 3 \\ \\ = > 8c = - 136 \\ \\ = > c = - \frac{136}{8} \\ \\ = > c = - 17\)

Answer:

c = -17

Step-by-step explanation:

→Distribute the 7 to (-7c - 19):

3 - 7c - 20c = -49c - 133 + 14c

→Add like terms (-7c and -20c, -49c and 14c):

3 - 27c = -35c - 133

→Add 35c to both sides:

3 + 8c = -133

→Subtract 3 from both sides:

8c = -136

→Divide both sides by 8:

c = -17

Answer:

C

Step-by-step explanation:

His dog casts a shadow of 6ft at 6 pm if it casts a 2ft shadow at noon.

A man casts a 3 ft shadow at noon and a 9 ft shadow at 6 pm.

His dog casts a 2 ft shadow at noon.

Therefore we can find the length of shadow casts by his dog at 6 pm as follows:

Length of the shadow of a man at noon/length of the shadow of a man at 6 pm = length of the shadow of his dog at noon/length of the shadow of his dog at 6 pm

⇒3/9 = 2/length of the shadow of his dog at 6 pm

⇒length of the shadow of his dog at 6 pm = (2 × 9)/3

⇒length of the shadow of his dog at 6 pm = 6 ft

Hence, the shadow cast by his dog at 6 pm will be 6 ft.

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x = -1 and y = 3 in equations (i) and (ii):x + y = 2-1 + 3 = 2 (satisfied)3x + y = 0-3 + 3 = 0 (satisfied)

a) Solving the system using substitution:

We know that: x+y=2 (i)3x+y=0 (ii)We will solve equation (i) for y:y=2-x

Now, substitute this value of y in equation (ii):3x + (2-x) = 03x+2-x=0 2x = -2 x = -1

Substitute the value of x in equation (i):x + y = 2-1 + y = 2y = 3b)

Solving the system using elimination (linear combination) :

We know that: x+y=2 (i)3x+y=0 (ii)

We will subtract equation (i) from equation (ii):3x + y - (x + y) = 0 2x = 0 x = 0

Substitute the value of x in equation (i):0 + y = 2y = 2c)

Solving the system by graphing:We know that: x+y=2 (i)3x+y=0 (ii)

Let us plot the graph for both the equations on the same plane:

                                graph{x+2=-y [-10, 10, -5, 5]}

                                 graph{y=-3x [-10, 10, -5, 5]}

From the graph, we can see that the intersection point is (-1, 3)d)

We calculated the value of x and y in parts a, b, and c and the solutions are as follows:

Substitution: x = -1, y = 3

Elimination: x = 0, y = 2

Graphing: x = -1, y = 3

We can see that the value of x is different in parts a and b but the value of y is the same.

The value of x is the same in parts a and c but the value of y is different.

However, the value of x and y in part c is the same as in part a.

Therefore, we can say that the solutions of parts a, b, and c are not the same.

However, we can check if these solutions satisfy the original equations or not. We will substitute these values in the original equations and check:

Substituting x = -1 and y = 3 in equations (i) and (ii):x + y = 2-1 + 3 = 2 (satisfied)3x + y = 0-3 + 3 = 0 (satisfied)

Therefore, the values we obtained for x and y are the correct solutions.

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a) To develop a complete probability model for the given scenario, we need to consider all possible outcomes of flipping the coin and selecting a golf ball.

Let's denote H for Heads, T for Tails, Y for Yellow ball, and W for White ball. Sample space: HHY, HHW,  HTY, HTW, THY, THW,TTY, TTW. b) To find the probability that the coin lands tails up and a white golf ball is selected, we need to determine the favorable outcomes and divide it by the total number of outcomes. Favorable outcomes: TTW (Tails up and White ball selected). Total outcomes: 8 (as listed in the sample space)

Probability = Favorable outcomes / Total outcomes

Probability = 1 (since there is only 1 favorable outcome) / 8

Probability = 1/8

Therefore, the probability that the coin lands tails up and a white golf ball is selected is 1/8.

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The 99% confidence interval for the mean math SAT score for this district is [468.80, 531.20]. We can be 99% confident that the true mean math SAT score for the district is within this interval.

To calculate the confidence interval, we will use the formula:

CI =\(\bar x\) ± zα/2 × (σ/√n)

where:

\(\bar x\) is the sample mean (500)

zα/2 is the z-score for the desired confidence level (99%, which corresponds to a z-score of 2.576 for a two-tailed test)

σ is the population standard deviation (100)

n is the sample size (68)

Plugging in the values, we get:

CI = 500 ± 2.576 × (100/√68)

CI = 500 ± 2.576 × 12.11

CI = 500 ± 31.20

Therefore, the 99% confidence interval for the mean math SAT score for this district is [468.80, 531.20]. We can be 99% confident that the true mean math SAT score for the district is within this interval.

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Answer:

  16.6°

Step-by-step explanation:

The triangle can be solved using the Law of Cosines to find the side opposite the given angle, then the Law of Sines to find the missing angle from the given sides.

__

We choose to use a=10, b=4, C=29°.

  c² = a² +b² -2ab·cos(C) . . . . . law of cosines

  c² = 10² +4² -2·10·4·cos(29°) ≈ 46.0304

  c ≈ √46.0304 ≈ 6.78457

Then angle B (opposite side b) is ...

  sin(B)/b = sin(C)/c . . . . . . . . . law of sines

  sin(B)/4 = sin(29°)/6.78457

  B = arcsin(4/6.78457×sin(29°)) ≈ 16.6085°

The missing acute angle is about 16.6°.

Answer:

Step-by-step explanation:

Use the Law of Sines for this. Set it up as follows:

\(\frac{sin(x)}{6}=\frac{sin(61)}{6.2}\)  Cross multiply:

6.2sin(x) = 6sin(61) and solve for the term with the unknown in it:

\(sin(x)=\frac{6sin(61)}{6.2}\)

Work on the right side first. Plug that into your calculator to get

sin(x) = .8464061682

Now the problem comes down to "what angle has a sine of .8464061682?" This requires the use of the inverse button on your calculator. Hit 2nd, then sin, and you will see on your screen:

\(sin^{-1}(\)

After that open parenthesis enter that big long decimal and hit equals. You should get an angle measure of 57.822 degrees. Not sure what you are rounding to.

Answer:

Step-by-step explanation:

Since ∠S and ∠Y are complementary, we have:

∠S + ∠Y = 90°

We also know that:

m∠S = 2(m∠Y) − 30°

Substituting the second equation into the first equation, we get:

2(m∠Y) − 30° + ∠Y = 90°

Combining like terms:

3(m∠Y) = 120°

Dividing both sides by 3:

m∠Y = 40°

Therefore, m∠Y is 40 degrees.

Answer:

7.96 ft

Step-by-step explanation:

Given;

Length of ramp L = 8 ft

Angle with the horizontal (ground) = 6°

Applying trigonometry;

With the length of ramp as the hypothenuse,

The horizontal distance d as the adjacent to angle 6°

Since we want to calculate the adjacent and we have the hypothenuse and the angle. We can apply cosine;

Cosθ = adjacent/hypothenuse

Substituting the values;

Cos6° = d/8

d = 8cos6°

d = 7.956175162946

d = 7.96 ft

The building is 7.96ft away from the entry point of the ramp.