What is one tenth seven hundredths three thousandths in standard form?​

Answer:

3,750

Step-by-step explanation:

2500+1250+625+625=5000

2500/5000=.50 or 50%

7500X.50=3750

Answer:

840

Step-by-step explanation:

7000×2×6 ÷ 100. since it is 2%

= 840

The cake has a cylindrical format, and the outside of the cake will be frosted, which means that the total surface area has to be found, and doing this, we find that she will need 298.5 square inches of frosting.

Surface area of a cylinder:  

The surface area of a cylinder of radius r and height h is given by:

\(S = 2\pi r^2 + 2\pi rh\)

The cake is 10 inches in  diameter and 4.5 inches tall.

Radius is half the diameter, so \(r = \frac{10}{2} = 5\).

The height is \(h = 4.5\).

How many square inches of frosting  will she need?

This is the surface area, so:

\(S = 2\pi(5)^2 + 2\pi(5)(4.5) = 50\pi + 45\pi = 95\pi = 298.5\)

She will need 298.5 square inches of frosting.

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Answer:

Step-by-step explanation:

First of all, we need the formula of a cylinder which is: 2\(\pi\)rh + 2\(\pi\)\(r^{2}\)

BUT also remember we are solving for one base since we do not count the bottom of the tray. That formula would look like this: 2\(\pi\)rh + \(\pi\)\(r^{2}\) since we are using 1 base instead of 2.

Now input the missing values into the formula and solve:

2\(\pi\)rh + \(\pi\)\(r^{2}\)

2\(\pi\)(5)(4.5) + \(\pi\)\((5^{2})\)

45\(\pi\) + 25\(\pi\) = 70\(\pi\)

Our Answer is 70\(\pi\), or 219.91 \(in^{2}\)

The mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

Given data values are 55, 56, 70, 61, 53, 57, 50, 73, 52, 69, and 2. We need to calculate the mean, median, and mode of this sample.So, let's first arrange the data values in ascending order:2, 50, 52, 53, 55, 56, 57, 61, 69, 70, 73

Mean:The mean is the sum of all the data values divided by the total number of data values. So, we can use the following formula to calculate the mean:

Mean = (sum of all the data values) / (total number of data values)Sum of all the data values = 55 + 56 + 70 + 61 + 53 + 57 + 50 + 73 + 52 + 69 + 2 = 598Total number of data values = 11

Therefore,Mean = (sum of all the data values) / (total number of data values) = 598 / 11 = 54.36 (rounded to two decimal places)Therefore, the mean of the given data values is 54.36.

Median:The median is the middle value of a sorted data set. Since the data set has 11 data values, the median is the average of the 6th and 7th values (counting from smallest to largest).

Therefore, the median is :Median = (55 + 56) / 2 = 55.5Therefore, the median of the given data values is 55.5.

Mode:The mode is the data value that appears most frequently in the data set. In this case, there is no data value that appears more than once. So, there is no mode.

Therefore, the mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

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Answer:

Step-by-step explanation:

? = 1/2(230)

A  115°

The probability of getting a false positive result is 0.01.

We have,

From the given conditions,

P(B|A) = 0.96 (the test gives a positive result when the tree has the disease)

P(B|A') = 0.97 (the test gives a positive result when the tree does not have the disease)

P(A) = Probability of a randomly selected tree having the disease

P(A'|B) = the probability that the tree does not have the disease (A') given that the test gives a positive result (B).

Using Bayes' theorem:

P(A'|B) = (P(B|A') * P(A')) / P(B)

And,

P(A') = 1 - P(A) (the probability of the tree not having the disease)

Now, calculate P(B):

P(B) = P(B|A) * P(A) + P(B|A') * P(A')

P(B) = 0.96 * P(A) + 0.97 * (1 - P(A))

Since the disease is assumed to be rare, P(A) is very small, approximate it as close to zero.

Thus, ignore the term 0.96 * P(A) in the equation for P(B).

P(B) ≈ 0.97 * (1 - P(A))

Now, calculate P(A'|B):

P(A'|B) = (P(B|A') * P(A')) / P(B)

P(A'|B) = (0.97 * (1 - P(A))) / (0.97 * (1 - P(A)))

P(A'|B) = 1 - P(A)

Given that the probability of getting a false positive result (not having the disease given a positive test result), P(A'|B) is equal to 1 - P(A).

Now,

The probability of getting a false positive result is 1 - P(A).

Assume P(A) is very small (as mentioned earlier), then 1 - P(A) is approximately 0.01 or 1%.

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The complete question:

Arborists use a test to detect the presence of a certain pathogen in fruit trees. The test gives a positive result 96% of the time for trees that have the disease, and it is 97% accurate for trees that do not have the disease.

What is the probability of getting a false positive result (that is, the tree tests positive for the pathogen but does not actually have it)?

0.04

0.07

0.01

0.03

The solutions using the square property are x = ±√3, x = -2 ± √2.

To solve 4x² - 1 = 47 using the square property, we first isolate the variable terms and obtain 4x² = 48. Then we divide both sides by 4 to obtain x² = 12. Finally, we take the square root of both sides, remembering to include the ± symbol, and obtain x = ±√3.

To solve (2x + 1)² = 36 using the square property, we first expand the square on the left side and obtain 4x² + 4x + 1 = 36. Then we isolate the variable terms and obtain 4x² + 4x - 35 = 0. Next, we use the quadratic formula to obtain x = (-4 ± √68)/8, which simplifies to x = -2 ± √2.

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The derivative of a function represents the rate of change of the function with respect to its variable. This rate of change is described as the slope of the tangent line to the curve of the function at a specific point. The derivative of the cosine function can be found by applying the limit definition of the derivative to the cosine function.

\(f(x) = cos(x) then f'(x) = -sin(x)\).

Let's proceed with the proof.  Definition of the Derivative: The derivative of a function f(x) at x is defined as the limit as h approaches zero of the difference quotient \(f(x + h) - f(x) / h\) if this limit exists. Using this definition, we can find the derivative of the cosine function as follows:

\(f(x) = cos(x) f(x + h) = cos(x + h)\)

Now, we can substitute these expressions into the difference quotient: \(f'(x) = lim h→0 [cos(x + h) - cos(x)] / h\)

We can then simplify the expression by using the trigonometric identity for the difference of two angles:

\(cos(a - b) = cos(a)cos(b) + sin(a)sin(b)\)

Applying this identity to the numerator of the difference quotient, we obtain:

\(f'(x) = lim h→0 [cos(x)cos(h) - sin(x)sin(h) - cos(x)] / h\)

We can then factor out a cos(x) term from the numerator:

\(f'(x) = lim h→0 [cos(x)(cos(h) - 1) - sin(x)sin(h)] / h\)

We can then apply the limit laws to separate the limit into two limits:

\(f'(x) = lim h→0 cos(x) [lim h→0 (cos(h) - 1) / h] - lim h→0 sin(x) [lim h→0 sin(h) / h]\)

The first limit can be evaluated using L'Hopital's rule:

\(lim h→0 (cos(h) - 1) / h = lim h→0 -sin(h) / 1 = 0\)

Therefore, the first limit becomes zero:

\(f'(x) = lim h→0 - sin(x) [lim h→0 sin(h) / h]\)

Applying L'Hopital's rule to the second limit, we obtain:

\(lim h→0 sin(h) / h = lim h→0 cos(h) / 1 = 1\)

Therefore, the second limit becomes 1:

\(f'(x) = -sin(x)\)

Thus, we have proved that if \(f(x) = cos(x), then f'(x) = -sin(x)\).

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Answer:41.8

Step-by-step explanation:

Answer:

3b/2 + 3

Step-by-step explanation:

The formula to calculate perimeter of rectangle is 2l + 2w

The length is half the width so length is 1/2 (b/2 +1), which when simplified is b/4 + 1/2

Using the formula to calculate perimeter you can substitute and calculate

p= 2l + 2w

p= 2(b/4 + 1/2) + 2(b/2 + 1)

p= 2b/4 +2/2 + 2b/2 +2

p= 1/2b + 1 + b + 2

p= 3/2b + 3

Simplified it's 3b/2 +3

The answer to 32z - 48 using factoring is 3/2.

Given,

32z - 48

We have to find the answer using factoring:

Factoring:

Finding things to multiply together to produce an expression is known as factoring. It is comparable to splitting an expression into numerous smaller expressions.

Here,

32z - 48 = 0

Add 48 to both sides

32z - 48 + 48 = 0 + 48

32z = 48

Divide 32 on both sides

32z/32 = 48/32

z = 48/32

Now, we can factorize 48/32

Take 2 as common factor

(48/2) / (32/2) = 24/16

Again, take 2 as common factor

(24/2) / (16/2) = 12/8

Now, take 4 as common factor

(12/4) / (8/4) = 3/2

Here, z = 3/2

That is, the answer for 32z - 48 using factoring is 3/2.

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Answer:

4/33

Step-by-step explanation:

do the normal steps to conversion

Total cups of flour to be filled= 5 cups

Capacity of measuring cup = 1/2 cup

Number of times Marc need to fill the 5 cups with his measuring cup = 5 / (1/2)

In conclusion, changing one score can have an impact on both the mean and the standard deviation of a set of data. The extent of the influence depends on the deviation of the changed score from the original mean.

Changing one score can have an impact on both the mean and the standard deviation of a set of data. The mean is the average of all the scores, so if one score changes, it can affect the overall mean. The standard deviation, on the other hand, measures the deviation of each score from the mean. If one score changes, it can also affect the standard deviation, as the deviation of that score from the mean will be different.

For example, let's say we have a set of scores: 2, 4, 6, 8, 10. The mean of these scores is 6, and the standard deviation is 2.86. If we change the score of 2 to a 12, the new set of scores will be 12, 4, 6, 8, 10. The new mean will be 8, and the new standard deviation will be 2.94. As you can see, changing one score influenced both the mean and the standard deviation.

In conclusion, changing one score can have an impact on both the mean and the standard deviation of a set of data. The extent of the influence depends on the deviation of the changed score from the original mean.

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It is requred to test the exactness of the given ODE and then find its general solution. Then, if the given ODE is not exact, an integrating factor must be used to make it exact.

This given ODE is:(2xy - 2y²e^(3x))dx + (x² - 2ye^(2x))dy = 0.To verify the exactness of the given ODE, we determine whether or not ∂Q/∂x = ∂P/∂y, where P and Q are the coefficients of dx and dy respectively, as follows: P = 2xy - 2y²e^(3x) and Q = x² - 2ye^(2x).Then, we have ∂P/∂y = 2x - 4ye^(3x) and ∂Q/∂x = 2x - 4ye^(2x).Thus, since ∂Q/∂x = ∂P/∂y, the given ODE is exact.To solve the given ODE, we have to find a function F(x,y) that satisfies the equation Mdx + Ndy = 0, where M and N are the coefficients of dx and dy respectively. This is accomplished by integrating both P and Q with respect to their respective variables. We have:∫Pdx = ∫(2xy - 2y²e^(3x))dx = x²y - y²e^(3x) + g(y), where g(y) is a function of y. We differentiate both sides of this equation with respect to y, set it equal to Q, and then solve for g(y). We have:(d/dy)(x²y - y²e^(3x) + g(y)) = x² - 2ye^(2x)Thus, g'(y) = 0 and g(y) = C, where C is a constant.Substituting the value of g(y) in the equation above, we get:x²y - y²e^(3x) + C = 0, as the general solution.The given ODE is exact, so we can solve it by finding a function that satisfies the equation Mdx + Ndy = 0. After integrating both P and Q with respect to their respective variables, we find that the general solution of the given ODE is x²y - y²e^(3x) + C = 0.

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The probability distributions whose graphs can be approximated by bell-shaped curves are commonly known as normal distributions or Gaussian distributions.

These distributions are characterized by their symmetrical shape and the majority of their data falling within a certain range around the mean. The normal distribution is widely used in statistics and is a fundamental concept in many fields of study, including psychology, economics, and engineering. The normal distribution is also known for its many practical applications, such as predicting test scores, stock prices, and medical diagnoses. In summary, the bell-shaped curve is a useful tool in probability theory that can help us understand and make predictions about a wide range of phenomena. The probability distributions whose graphs can be approximated by bell-shaped curves are called Normal Distributions or Gaussian Distributions. They have a symmetrical shape and are characterized by their mean (µ) and standard deviation (σ), which determine the central location and the spread of the distribution, respectively.

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Since the p-value (0.034) is less than the significance level of 0.05, we reject the null hypothesis. This suggests evidence against the claim that the median percent of impurities in the brand of jam is 2.5%.

To perform the sign test, we compare the observed values to the hypothesized median value and count the number of times the observed values are greater or less than the hypothesized median. Here's how we can proceed:

State the null and alternative hypotheses:

Null hypothesis (H0): The median percent of impurities in the brand of jam is 2.5%.

Alternative hypothesis (Ha): The median percent of impurities in the brand of jam is not 2.5%.

Determine the number of observations that are greater or less than the hypothesized median:

From the given data, we can observe that 5 jars have impurity percentages less than 2.5% and 11 jars have impurity percentages greater than 2.5%.

Calculate the p-value:

Since we are performing a two-tailed test, we need to consider both the number of observations greater and less than the hypothesized median. We use the binomial distribution to calculate the probability of observing the given number of successes (jars with impurity percentages greater or less than 2.5%) under the null hypothesis.

Using the binomial distribution with n = 16 and p = 0.5 (under the null hypothesis), we can calculate the probability of observing 11 or more successes (jars with impurity percentages greater than 2.5%) as well as 5 or fewer successes (jars with impurity percentages less than 2.5%). Summing up these probabilities will give us the p-value.

Compare the p-value to the significance level:

Since the significance level is 0.05, if the p-value is less than 0.05, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

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Answer:

I dont think you gave the entire question but
bridget is saying x > 3
dana is saying x < 3

Answer:

x=12.5, y=10.5

Step-by-step explanation:

(8x+34)+46=180 --> x=12.5

vertical angles are same, 46=(2x+2y), x=12.5. --> y=10.5

Answer:

Step-by-step explanation:

the sum of straight angle=180

8x+34+46=180

8x+80=180

8x=180-80

8x=100

x=100/8

x=12.5

8(12.5)+34

46=2x+2y ( vertical angles)

46=2(12.5)+2y

46-25=2y

21=2y

y=21/2

Answer:

5x + 16

Step-by-step explanation:

First you have to distribute the 2 into the parentheses

2 times x is 2x

2 times 6 is 12

so now the equation is

2x + 12 + 3x + 4

add the 2x and 3x and that is 5

so now the equation is...

5x + 12 + 4

add 12 + 4 and that is 16

so now the answer is

5x + 16

Answer:

\( \displaystyle B) {x} = \log_{6} 118\)

Step-by-step explanation:

we would like to solve the following exponential equation:

\( \displaystyle 2 \cdot {6}^{x} = 236\)

to do so divide both sides by 2 which yields:

\( \displaystyle {6}^{x} = 118\)

take log of base 6 in both sides so that we can solve the equation for x by using \(\log_ab^c=c\log_ab\) and that yields:

\( \displaystyle \log_{6} {6}^{x} = \log_{6} 118\)

use the formula:

\( \displaystyle {x} = \log_{6} 118\)

hence,

our answer is B)

Answer:

\(\boxed{\sf Option \ B }\)

Step-by-step explanation:

A equation is given to us and we need to find out the value of x . The given equation is ,

\(\sf\dashrightarrow 2 \times 6^x = 236 \)

Transpose 2 to RHS , we have ,

\(\sf\dashrightarrow 6^x = \dfrac{236}{2} \)

Simplify ,

\(\sf\dashrightarrow 6^x =118 \)

Use log both sides with base "6"

\(\sf\dashrightarrow log_6 ( 6^x) = log_6 118 \)

Using the property of log ,

\(\sf\longmapsto \bigg\lgroup \red{\bf log_p q^r = r log_p q}\bigg\rgroup\)

\(\sf\dashrightarrow x \ log_6 6 = log_6 118 \)

Again we know that ,

\(\sf\longmapsto \bigg\lgroup \red{\bf log_p p= 1}\bigg\rgroup\)

We have ,

\(\sf\dashrightarrow x \times 1 = log_6 118 \)

Therefore ,

\(\sf\dashrightarrow\boxed{\blue{\sf x = log_6 118 }} \)

Hence option B is correct .

Using probability, we can find that the probability of getting a triangle shape block when selected at random is 1/5.

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

The likelihood of an event occurring can be anything between 0 and 1, as the favourable number of outcomes can never exceed the total number of outcomes. Therefore, the percentage of successful results cannot be zero.

In the question,

Malaya has 5 different shapes of blocks.

Malaya has 10 blocks of each shape.

So, the total no. of blocks = 5 × 10 = 50.

Now, Malaya has 10 blocks of triangular shape.

probability of getting a triangular shape is:

P = 10/50

= 1/5

Therefore, the probability of getting a triangle shape block when selected at random is 1/5.

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The complete question is:

Malaya has 5different shapes of blocks: rectangle, rhombus, square, trapezoid, and triangle. She has 10 of each shape. She selects a block at random. What is the probability of getting a triangle shape block when selected at random?

Answer:

y = 51.32º

Step-by-step explanation:

z = 180 - 47 - 90

z = 43º

sin43 = opp/hyp

sin43 = 35/y

y = 35/sin43

y = 51.32º

Answer:

1/3

Step-by-step explanation:

10 to 10:30

10:30 to 11

11 to 11:30

3 periods of time

10 to 11 is 2/3 periods

3/3 - 2/3 = 1/3

The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

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

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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