find the product 5^56 × 5^22 × 5^-96

The length of time will the two marathon runners will be one - half of a mile apart is 15 minutes.

The first marathon runner is going at 10 miles per hour while the second runner is going at 8 miles per hour.

This means that in one hour, the first runner would have covered 10 miles while the second would have covered 8 miles. They would be 2 miles apart.

If they would be 2 miles apart in one hour, the time till they are half a mile apart would be:

= 0. 5 / 2 x 60 minutes in an hour

= 15 minutes

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Answer: 140

Step-by-step explanation: am big brain

The per cent of 32 out of 80 will be 40% out of 80.

To translate this per cent problem, we can establish up a ratio table and use cross-multiplication to calculate the answer.

32 is x% out of 80

Set up the ratio table:

32 x%

-- = ---

80 100%

Now, cross-multiply to solve for x:

32 × 100 = x% × 80

3200 = 80x

Now, divide both sides by 80 to calculate x:

3200 / 80 = 80x / 80

40 = x

So, the answer is 40%. Therefore, 32 out of 80 is 40% out of 80.

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Answer:

3cm.

Step-by-step explanation:

As you know, a diameter is the same as twice a radius.

AO= OC.

OC= 2.5cm.

therefore, AC= OA+OC

AC= 2.5+2.5

AC= 5cm.

AB= 4cm.

Using Pythagorean theorem.

BC= √(AC²-AB²).

BC= √(5²-4²)

BC= √(25-16)

BC= √9

BC= 3cm.

a. The mean of the sampling distribution of ô is 8%.

b. The standard deviation of the sampling distribution is 0.0115

c. The sampling distribution of p is approximately Normal

d. Probability that the random sample of 1000 adults will give a result within 2 would be -17.39 and 17.39.

e. No, finding that 10% of a sample of 1000 adults have never had a cavity does not provide convincing evidence that the American Dental Association needs to update their statistics and there is more than 8% of adults who have never had a cavity.

What is Standard deviation, Probability?

Standard deviation: Standard deviation is a measure of how evenly distributed numbers are. It is the square root of the Variance, which is the average of the squared deviations from the Mean.

Probability: Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true.

a. The mean of the sampling distribution of ô is 8%. This is the proportion of adults in the population who have never had a cavity, as stated by the American Dental Association.

b. The standard deviation of the sampling distribution of p is given by the formula:

[tex]$\sigma_{\hat{p}}\\ = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\= \sqrt{\frac{0.08(1-0.08)}{1000}} \\= 0.0115$[/tex]

The standard deviation measures how much the sample proportions are likely to vary from the true population proportion.

In this case, the standard deviation of the sampling distribution is 0.0115, which means that the sample proportions are likely to vary by approximately 0.0115 from the true population proportion.

c. The sampling distribution of p is approximately Normal because the Large Counts condition is met. The Large Counts condition states that the sample size is large enough such that the sample proportions are approximately normally distributed, even if the population is not normally distributed. In this case, with a sample size of 1000, the sample proportions are likely to be approximately normally distributed.

d. To find the probability that the random sample of 1000 adults will give a result within 2 percentage points of the true value (6%-10%), we need to find the area under the normal curve that corresponds to this interval.

First, we need to standardize the interval by using the standard deviation of the sampling distribution:

[tex]$z_1 = \frac{6 - 8}{0.0115} = -17.39$[/tex]

[tex]$z_2 = \frac{10 - 8}{0.0115} = 17.39$[/tex]

Using a standard normal table or a normal calculator, we find that the area under the normal curve to the left of -17.39 is approximately 0 and the area under the normal curve to the right of 17.39 is approximately 0. Hence, the area under the normal curve between -17.39 and 17.39 is approximately 1, which means that the probability of getting a result within 2 percentage points of the true value is 100%.

e. No, finding that 10% of a sample of 1000 adults have never had a cavity does not provide convincing evidence that the American Dental Association needs to update their statistics and there is more than 8% of adults who have never had a cavity. The result of 10% is within the range of values that can be expected based on random sampling error. It is possible that the sample proportion of 10% is due to random chance, rather than a true change in the population proportion. To determine if the true population proportion has changed, more data and statistical analysis are needed.

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The results in a two-way table are shown below.

Suppose two dimensions are there, viz X and Y. Some values of X are there as X_1, X_2, ... , X_n and some values of Y are there as Y_1, Y_2, ... , Y_n

List them in title of the rows and left to the columns. There will be n \times k table of values will be formed(excluding titles and totals), such that:

Value(ith row, jth column) = Frequency for intersection of  X_i  and Y_j  (assuming X values are going in rows, and Y values are listed in columns).

Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.

For n = 2, and k = 2, the table would look like:

[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]

where S denotes total of totals, also called total frequency.

n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.

Given;

35 of the students are in Math Club

20 of those students are also in Chess Club

38 of the students are not in Math Club or Chess Club

Now

number of students        math club        chess club       none

            85                              35                     20                38

Therefore, the table is given above.

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Step-by-step explanation:

So the first step is to find the second number. Let the first missing number next to x be m and the second missing one be n

First find n

You would do this by using the first given set of variables, (0,7), this is because everything multiply by 0 is going to be 0, so it’s easy to find what is needed to make 7.

Step 2 is to take another pair, I used (3,13), but any other one will work that’s not 0. You would plug everything in to find m.

Step 3 is to check with a third pair to make sure it works.

Answer:

The value of a is 4. This can be determined by multiplying both sides of the equation by 10, which yields 5√10 = 4√10 + 6√10. Subtracting 4√10 from both sides yields a√10 = 6√10, and dividing both sides by 6 yields a = 4.

Answer:

Step-by-step explanation:

Sorry if the dots confuse you, it's where the dots are graphed for people to see where I place them and to see if it matches. (Blue marks are 5 intervals.)

Answer:

(-3, -1/2)

Step-by-step explanation:

[tex]y=\frac{1}{2}x+1[/tex]

[tex]y=\frac{3}{2}x+4[/tex]

Move all the variables to one side and the numbers to the other

[tex]\frac{1}{2}x-y=-1[/tex]

[tex]\frac{3}{2}x-y=-4[/tex]

Multiply the first equation by -1 to solve by elimination

[tex]-\frac{1}{2}x+y=1[/tex]

[tex]\frac{3}{2}x-y=-4[/tex]

Subtract

[tex]x=-3[/tex]

Use substitution

[tex]y=\frac{(-3)}{2} +1[/tex]

[tex]y=-1.5+1[/tex]

[tex]y=-0.5=\frac{-1}{2}[/tex]

Given two sets, A ⊂ B this statement is true.

A little letter, like x, y, or z, is typically used to represent a set element. You may sum up a set by listing all of its components inside of brackets. The items that make up a set are referred to as its elements (or members), and the set is said to contain the elements when they are claimed to belong to it. A set often consists of other mathematical objects like numbers, variables, or geometric points as its elements.

Given that,

A = {1,2}

B = {1,2,3,4}

Thus, A ⊂ B, because all elements of the set A are the elements of the set B.

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The complete question is as follows:

The measure of angle 5 of the transverse lines is; C.) 105°

The line transversal theorem states that If two parallel lines are cut by a transversal, then it means that corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Now, we are given that the measure of 2 is 75°. It is clearly seen that angle 5 is a corresponding angle to angle 1 and angle 1 forms a straight line with angle 2. Sum of angles on a straight line is 180 degrees. Thus;

angle 5 = 180 - 75

angle 5 = 105°

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the expression x + (x - 5) can be used to determine how many apples Martin and Omar used in total. It helps us understand that Martin used more apples than Omar and that the number of apples in total is greater than 10.

a. Let x represent the number of apples that Martin used.

The expression is x + (x - 5).

b. We can substitute 10 for x in the expression to see if it is possible for Martin to have used 10 apples: 10 + (10 - 5). The answer is 15, which is greater than 10, so it is not possible for Martin to have used 10 apples.

Martin and Omar both used apples in their recipes, but Omar used 5 fewer apples than half as many as Martin used. To represent the number of apples that they used altogether, we can use an expression that includes a variable x, which represents the number of apples that Martin used. The expression is x + (x - 5). To check if Martin could have used 10 apples, we can substitute 10 for x in the expression: 10 + (10 - 5). The answer is 15, which is greater than 10, so it is not possible for Martin to have used 10 apples. Therefore, the expression x + (x - 5) can be used to determine how many apples Martin and Omar used in total. It helps us understand that Martin used more apples than Omar and that the number of apples in total is greater than 10.

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Answer:

80°

Step-by-step explanation:

180° - 100° = 80°

Answer:

2%

Step-by-step explanation:

3/60 = 2%

Answer:

5%

Step-by-step explanation:

[tex] \frac{3}{60} \times 100 = 5[/tex]

The price of one citron is 2.5 units and the price of one fragrant wood apple is 8 units.

Let's write "x" for the cost of citron and "y" for the cost of a fragrant wood apple.

We know that 4 citrons + 3 fragrant wood apples = 34 units => 4x + 3y = 34

And, 3 citrons + 4 fragrant wood apples = 29 units => 3x + 4y = 29

The values of x and y can be determined by solving this system of equations.

We can isolate x starting with the first equation:

4x + 3y = 34 => 4x = 34 - 3y

We can now change x in the second equation to the following expression:

3(34 - 3y) + 4y = 29

102 - 9y + 4y = 29

102 = 29 + 9y

73 = 9y

So, y = 8, and the price of a fragrant wood apple is 8 units.

And finally, substituting this value of y in the first equation:

4x + 3(8) = 34

4x + 24 = 34

4x = 10

x = 2.5, the price of citron is 2.5 units.

Therefore, the price of one citron is 2.5 units and the price of one fragrant wood apple is 8 units.

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There are 16215 ways in which the top 3 cars can finish the race.

From the question, we have the following parameters that can be used in our computation:

People = 47

Positions = 3

The number of ways to select the top 3 cars from 47 cars is can be calculated using the following combination formula

C(n, r) = n!/(r! * (n - r)!)

Substitute the known values in the above equation, so, we have the following representation

C(47, 3) = 47! / (3! * (47-3)!)

Evaluate

C(47, 3) = 16215

So there are 16215 ways in which the top 3 cars can finish the race.

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The equation does not represent a direct proportion

From the question, we have the following parameters that can be used in our computation:

2.5=q-1.6

The above equation is a linear equation

When the equation is solved, we have"

q = 2.5 + 1.6

Evaluate the like terms

q = 4.1

The equation q = 4.1 is not a direct proportion

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A. The rate of change for function A is, 3

B. The rate of change for function B is, 2

C. The function which has greater rate of change is, Function A

Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.

So formula for the rate is,

m = change in one quantity/change in another quantity = Δy/Δx

Given that,

Two functions,

A.   y = 3x - 4

B.   x     -7    -5   -3    -1    1

     y      -10  -6  -2    2   6

Rate of change in both  =?

In simple words, rate of change is known as slope of the line,

Function A is already given in standard form of line, y = mx + c

So, by comparing it

m = 3

Rate of change in function A, 3

For function B, it is required to form equation of line,

By taking two values of x & y,

(-1, 2) & (1, 6)

Two points form of equation is,

y-y₁ =  y₂-y₁/x₂-x₁(x-x₁)

By putting values we get the equation,

y - 2 = (6-2)/(1-(-1))*(x - (-1))

y-2 = 4/2(x + 1)

y   =  2x + 4

By comparing it with, y = mx+ c

m = 2

Rate of change in function B = 2

And, it clearly visible, Rate of change in A is greater than In B

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If the first equation is in format y=mx+b, (if not convert to it) the second equation would have the same m value, and any b value.

The same value indicates that they have the same slope, therefore parallel.

The function f(x) = (x² - 4)/x is increasing over it's entire domain as the derivative is always positive.

The function for this problem is defined as follows:

f(x) = (x² - 4)/x.

Applying the quotient rule, the derivative of the function is given as follows:

f'(x) = [2x(x) - (x² - 4)]/x²;

f'(x) = [2x² - x² + 4]/x²;

f'(x) = (x² + 4)/x²;

We have a quotient in which both terms are always positive(x² is always positive, and so is x² + 4), hence the derivative is always positive and the function is increasing over it's entire domain.

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3/15

1/3 of 3/5 is the same as multiplying

if it were only 1 acre it would look like 1/3 x 1 so for 3/5 of an acre, it is

(1/3) x (3/5)

remember, multiplying fractions is numerator to numerator, and denominator to denominator.

so (1/3) x (3/5) = 3/15

The cost of the soil for each seedling is $0.35.

Division is an arithmetic operation that is the reverse of multiplication. It is used to find the number of times a quantity is contained within another quantity. Division can be represented using the division symbol (÷) or a fraction bar (/) and is performed by dividing the dividend by the divisor. The result of division is the quotient, which represents the number of times the divisor fits into the dividend. For example, if you have 8 apples and you divide them into 4 equal parts, each part would contain 2 apples. The expression 8 ÷ 4 = 2 represents this division, where 8 is the dividend, 4 is the divisor, and 2 is the quotient.

First, we need to find out how many seedlings Lara can plant with the bag of soil she bought. To do this, we divide the total amount of soil by the amount of soil required for each seedling:

16.25 cups of soil ÷ 1.25 cups of soil per seedling = 13 seedlings

Next, we divide the total cost of the soil by the number of seedlings to find the cost of the soil per seedling:

$4.55 ÷ 13 seedlings = $0.35 per seedling.

Therefore, the cost of the soil for each seedling is $0.35.

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Answer:

1st table: -2/1   2nd table: 3/-4

Step-by-step explanation:

Slope=m=[tex]\frac{rise}{run}[/tex]

1st table:

rise -2

run 1

2nd table:

rise 3

run -4

A randomized experiment would be the best design for determining the relationship between cell phone use and brain cancer.

In a randomized experiment, individuals are randomly assigned to either a cell phone use group or a non-cell phone use group, and then the incidence of brain cancer is compared between the two groups.

This type of study can establish causality because it eliminates the possibility of confounding variables and ensures that any observed difference in brain cancer incidence is truly due to cell phone use and not some other factor.

Additionally, randomized experiments provide more robust results than observational studies, as they reduce the potential for selection bias and allow for control over extraneous variables.

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0.1574 is the probability that more than half of the sampled students live on the campus.

It is well known that 45% of students at a large university live on campus. A random sample of 100 students will be chosen by the head of student life. The fixed value that offers the potential of the number of successful outcomes is the sample proportion. The sample proportion is an estimate of the population proportion's actual value.

100 samples are taken.

45 percent of students reside on campus.

The normal probability distribution is used to assess the likelihood that more than half of the sampled students live on campus.

[tex]P(p^{O} > 0.5)=P(\frac{p^{o}-p }{\sqrt{\frac{p(1-p)}{n} } } > \frac{0.5-0.45 }{\sqrt{\frac{0.45(1-0.45)}{100} } })[/tex]

=P(Z>1.00)

=0.1574 (Z- score table)

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Answer:

Before the price reduction, the cost was 120 dollar.

What is the fundamental principle of multiplication?

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that shop advertises 25% off its prices in a sale a dress is 90% .

Here 90 percent is equivalent to 75%

Let X = 100%

So,X=(90×100)÷75

x =120

The price was 120 dollar.

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Answer:

108

Step-by-step explanation:

480÷30= 6 [no. of groups in 30]

18×6= 108

Answer:

288

Step-by-step explanation:

To estimate the number of 7th graders attending the dance, we need to extrapolate the sample proportion to the total population.

The sample proportion of 7th graders who are going to the dance is 18/30 = 0.6.

So, the estimated number of 7th graders who will attend the dance is:

0.6 * 480 = 288.

Answer:

9/8

Step-by-step explanation:

3/16 x 6

= 3/16 x 6/1

= 18/16

= 9/8

The solution is Option C.

The number of data points that are incorrectly marked on the scatter plot is 2 and they are G ( 5 , 5 ) , H ( 5 , 7 )

Dots are used in a scatter plot to show the values of two different numerical variables. Each dot's location on the horizontal and vertical axes represents a data point's values. To view relationships between variables, utilize scatter plots.

The closer the data points come to forming a straight line when plotted, the higher the correlation between the two variables, or the stronger the relationship. If the data points make a straight line going from near the origin out to high y-values, the variables are said to have a positive correlation.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

Given data ,

Let the equation of graph be represented as A

Now , the value of A is

Let the values of x be = { 1 , 1 , 2 , 3 , 3 , 4 , 5 , 5 , 6 }

Let the values of y be = { 2 , 3 , 4 , 4 , 5 , 5 , 5 , 7 , 8 }

So , the points on the graph will be

A ( 1 , 2 ) , B ( 1 , 3 ) , C ( 2 , 4 ) , D ( 3 , 4 ) , E ( 3 , 5 ) , F ( 4 , 5 ) , G ( 5 , 5 ) , H ( 5 , 7 ) , I ( 6 , 8 )

The points G and H are marked incorrectly as ( 5 , 4 ) and ( 5 , 6 )

Hence , the graph is plotted and there are two incorrect data points on the scatter plot

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