There are 7 1/5 groups of 2/5 in 3 do you agree with this statement show reasoning

12 hours

If it takes 6 people 8 hours to finish a job, then 24 would take 2 hours, and then 4 would take 12 hours

Answer:

5.333 hours.

Step-by-step explanation:

Put this on a chart:

6 people = 8 hours

4 people = ? hours

To find ? Use crisscross multiplication and solve:

? = (4 * 8) / 6

? = 32 / 6

? = 5.333

Therefore, if it takes 6 people 8 hours to finish a job then it will take 5.333 hours for 4 people to finish a job.

The conclusion is that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

The test statistic for this hypothesis test can be calculated as follows:

t = (μ1 - μ2) / sqrt(s1^2 / n1 + s2^2 / n2)

Plugging in the values, we get:

t = (1090 - 485) / sqrt(403^2 / 5 + 382^2 / 8) = 4.36

Next, we need to find the critical value for a two-tailed test at a significance level of 0.10 using a t-distribution table or using a t-distribution calculator.

Using a t-distribution table or calculator, we find the critical value for a two-tailed test at a significance level of 0.10 and df = 9.57 is ±1.833.

Since the calculated t-value (4.36) is greater than the critical value (1.833), we reject the null hypothesis and conclude that there is evidence to suggest that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

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Answer:

P = 72.5 * e^(0.025t)

Step-by-step explanation:

Here's a step by step solution with all the details and calculus involved.

(a) Express P as a function in the form P = Poat.

Since the population is growing continuously at a rate of 2.5% per year, we can use the formula for continuous growth:

P = Po * e^(rt)

where Po is the initial population (72.5 million), r is the continuous growth rate (0.025), and t is the time elapsed in years since 2004.

The continuous growth rate, r, is related to the annual growth rate, g, by:

r = g / 100

So, the continuous growth rate is 0.025.

Substituting the values into the formula for continuous growth, we get:

P = 72.5 * e^(0.025t)

This is the expression for the population as a function of time in the form P = Poat.

(b) Express P as an exponential function using base e.

The exponential function using base e is already in the desired form. So, we can simply write:

P = 72.5 * e^(0.025t)

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The below area rate can also be further answered as 14, since the supplied border rate can be further answered as 12. Their areas are compared 4/16.

What's meant by rate?

Areas If the scale factor of the sides of two analogous polygons is m/ n

 also the rate of the areas is (m/n)^2.

Area of analogous Polygons Theorem). Because area is a two- dimensional volume, you square the rate.

It's given that, the rate of peripheries of two analogous quadrilateral is 2 4

 now,  

to find the rate of area, we can take two quadrilaterals, say square.

Square ABCD of side 2 units and Square PQRS of side 4 units.

now rate of areas,

[tex]=\frac{area \ of\ square\ ABCD }{area \ of\ square\ PQRS }[/tex]

[tex]=\frac{2 \times 2}{4 \times 4}[/tex]

= 4/16

= 1/4

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Answer: the weight of the wheat still in the truck is 5000 pounds.

Step-by-step explanation:

Here are the steps to calculate the weight of the wheat still in the truck:

Convert the weight of the unloaded wheat to tons. To convert from pounds to tons, divide by 2,000:

1000 lbs / 2000 lbs/ton = 0.5 tons

Subtract the weight of the unloaded wheat from the original weight:

3 tons - 0.5 tons = 2.5 tons

Convert the answer back to pounds:

2.5 tons * 2000 lbs/ton = 5000 lbs

Therefore, the weight of the wheat still in the truck is 5000 pounds.

Using Euler's formula, the expressions can be rewritten as Im = sin(e^j) - sinh(1), exp(e^j) = e^(cos(1) + j*sin(1)) and e^[(1/2)√(2)e^(j(π/4+2π*n))] respectively

1.

Cos(e^j) can be expressed using Euler's formula as:

Cos(e^j) = (e^(je^j) + e^(-je^j)) / 2

= (cos(e^j) + cosh(1)) + j(sin(e^j) - sinh(1))

Re = cos(e^j) + cosh(1)

Im = sin(e^j) - sinh(1)

2.

exp(e^j) can also be expressed using Euler's formula as:

exp(e^j) = e^(cos(1) + j*sin(1))

3.

(sqrt(j))^sqrt(j) can be written as:

(sqrt(j))^sqrt(j) = e^[(1/2)√(2)e^(j(π/4+2π*n))]

where n is an integer. This is because the logarithm of a complex number has infinitely many possible values due to the periodicity of the exponential function.

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Answer:

89392i + 788

Step-by-step explanation:

The divide by 5 and the multiply by 5 cancel out, and we cannot simplify 89392i + 788 any further, since we don't know what i is. Therefore the answer is 89392i + 788.

Hope that helps!

Answer:

The height of the triangle is 14 m,

Step-by-step explanation:

Let the base be x, then the height is:

The area is half the product of base and height.

Set up equation and solve for x:

The first root is discarded as negative. The second root is the answer.

The base is 3 m, so the height is:

Answer:

The height of the triangle is 14 m.

Step-by-step explanation:

The area of a triangle can be found by using the following formula:

[tex]\boxed{A=\dfrac{1}{2}bh}[/tex]

where:

If the height of a triangle is 8 m more than twice the length of the base, then an expression for h in terms of b is:

[tex]h = 2b + 8[/tex]

Rewrite this equation to make b the subject:

[tex]\implies 2b=h-8[/tex]

[tex]\implies b=\dfrac{1}{2}h-4[/tex]

Given the area of the triangle is 21 m², substitute this value along with the found expression for b into the formula for area of a triangle:

[tex]\implies \dfrac{1}{2}\left(\dfrac{1}{2}h-4\right)h=21[/tex]

To find the height of the triangle, solve the equation for h.

[tex]\implies \dfrac{1}{4}h^2-2h=21[/tex]

[tex]\implies h^2-8h=84[/tex]

[tex]\implies h^2-8h-84=0[/tex]

[tex]\implies h^2-14h+6h-84=0[/tex]

[tex]\implies h(h-14)+6(h-14)=0[/tex]

[tex]\implies (h+6)(h-14)=0[/tex]

Apply the zero-product property:

[tex]h+6=0 \implies h=-6[/tex]

[tex]h-14=0 \implies h=14[/tex]

As length cannot be negative, the height of the triangle is 14 m.

Answer:

Step-by-step explanation:

Here's a step by step explanation for writing a function to approximate the number of annual visitors to the overlook x years after the nature center is built:

Start by defining the initial number of visitors as the baseline. We'll call this y0 and set it equal to 3,500 tourists:

y0 = 3,500

Define the rate of growth as a percentage increase. We're told that the number of visitors is expected to increase by 5% each year, so we'll call this rate "r" and set it equal to 0.05:

r = 0.05

Write the equation for exponential growth. The formula for exponential growth is given by:

y = y0 × (1 + r)^x

where x is the number of years after the nature center is built.

So, the equation for the function in this case would be:

f(x) = 3,500 × (1 + 0.05)^x

This function models the expected number of annual visitors to the overlook x years after the nature center is built. The function is exponential because the number of visitors is multiplied by a constant factor (1 + 0.05) raised to a power (x) at each time step.

Answer:

Step-by-step explanation:

The graph of the geometric sequence 640, 160, 40, 10, ... should have the following characteristics:

Decreasing: The values in the sequence decrease at a constant rate, so the graph should decrease as well.

Straight Line: Since the sequence is a geometric sequence, the graph will be a straight line when plotted on logarithmic axes.

Negative Slope: The slope of the line should be negative, since the values are decreasing.

Non-Linear: When plotted on linear axes, the graph will not be a straight line and will curve downward, since the difference between consecutive terms is decreasing.

Therefore, the graph of the geometric sequence should appear as a straight line with a negative slope when plotted on logarithmic axes, and as a non-linear curve with a downward slope when plotted on linear axes.

Answer:

  77.5°

Step-by-step explanation:

You want the measures of the angles formed when ray OX bisects the 155° angle AOB.

The angle bisector creates two equal angles, each of which is half the measure of the original angle. The measures of the angles formed are ...

  155°/2 = 77.5°

Answer:

the answer to this question is 936

To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.

We can use the formula for the average (or mean) of a series of variables to determine Laurence's next biology test score in order to achieve an average of 85:

Average = (sum of values) / (number of values)

The total of Laurence's marks on the first four biology exams can be calculated using the following formula:

Sum of scores = 87 + 80 + 75 + 85

= 327

We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.

Therefore, We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.

By deducting Laurence's first four scores from the desired total of all five scores, and dividing the result by one (the number of scores left), we can get the score that Laurence has to achieve in his next biology exam:

Next score = (sum of all five scores) - (sum of first four scores)

= (85 x 5) - 327

= 25

Therefore, To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.

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The average daily balance for Pete's credit card last month was a dollars. The finance charge was f dollars. APR algebraically is: 12f/a.

Finance charge = Monthly interest rate · Average daily balance

Monthly interest rate = APR/12

Where:

Finance charge = f

Average daily balance = a

f= Monthly interest rate · a

f = APR/12 · a

f/a  = APR/12

12.f/a = APR

Therefore APR algebraically is: 12f/a.

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One reason to compute a correlation coefficient to measure the strength of the relationship between two variables is that quantify the strength and direction of the correlation in a precise and standardized way..

When we have two variables that are related, we say that there is a correlation between them. The most common way to visually represent a correlation is by plotting the data on a scatter plot, where each point represents a pair of values for the two variables.

While a scatter plot is a useful tool to visualize the relationship between two variables, it doesn't tell us how strong or weak the correlation is. For instance, two variables might show a positive correlation, but the scatter plot might be quite dispersed, indicating that there is a lot of variability in the data. In this case, we would say that the correlation is weak. On the other hand, if the scatter plot is tightly clustered around the line, we would say that the correlation is strong.

This is where the correlation coefficient comes in. The correlation coefficient is a mathematical measure that quantifies the strength and direction of the relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfect negative correlation, a value of 0 indicates no correlation, and a value of 1 indicates a perfect positive correlation.

To compute the correlation coefficient, we first need to calculate the covariance between the two variables. Covariance is a measure of how much the two variables vary together, and it is defined as the sum of the products of the deviations of the values from their respective means. Once we have the covariance, we can divide it by the product of the standard deviations of the two variables to get the correlation coefficient.

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The probability that the hiker will reach his destination is, 1/2

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Since the hiker chooses one of the four trails with equal probability by rolling a fair 4-sided die,

the probability of taking any one trail is 1/4.

Once the hiker is on a trail, there are two sub-trails, and the hiker chooses one of them by flipping a fair coin.

The probability of taking the correct sub-trail is 1/2.

P(reaching destination) = P(trail 1) x P(correct sub-trail on trail 1) + P(trail 2) x P(correct sub-trail on trail 2) + P(trail 3) x P(correct sub-trail on trail 3) + P(trail 4) x P(correct sub-trail on trail 4)

P(reaching destination) = (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2)

P(reaching destination) = 4/8

P(reaching destination) = 1/2

Therefore, the probability that the hiker will reach his destination is 1/2, or 50%.

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Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.

What is meant by budget?

Let's assume that Hannah needs to use x gallons of soda and y gallons of fruit drink to make 168 gallons of punch.

We know that the cost of soda is $1.57 per gallon and the cost of fruit drink is $2.41 per gallon, and Hannah's budget requires that the punch cost $1.66 per gallon.

So we can set up the following system of equations:

x + y = 168 (total amount of punch)

1.57x + 2.41y = 1.66(168) (total cost of punch)

Simplifying the second equation:

1.57x + 2.41y = 278.88

Now we can use substitution or elimination method to solve for x and y.

Using substitution:

x = 168 - y

1.57(168 - y) + 2.41y = 278.88

264.36 - 1.57y + 2.41y = 278.88

0.84y = 14.52

y = 17.29

So Hannah needs 17.29 gallons of fruit drink.

Using x + y = 168, we can find that she needs 150.71 gallons of soda.

Therefore, Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.

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The predicted number of principals in attendance at the conference can be 161

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

A recent conference had 850 people in attendance.

In one exhibit room of 60 people, there were 46 teachers and 14 principals.

The predicated number of principals = ?

The ratio of teachers to principals  = 60/14

                                                          = 30/7

In the same ratio there will be total teachers and principals:

Suppose, the number of teachers = x

the number of principals = y

x + y = 850

x/y = 30/7

x = (30/7)y

(30/7)y + y = 850

37y = 850 x 7

y  = 161 (approx)

Hence, the number of principals cab be 161

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Answer:

D

Step-by-step explanation:

There were about 198 principals in attendance. EZ

Answer:

This system of equations can be solved using substitution or elimination methods.

Using substitution, we can solve for one of the variables in one of the equations and substitute that expression into the other equation.

Solving for x in the second equation:

x + 3y = 1

x = 1 - 3y

Substituting this expression for x into the first equation:

-4(1 - 3y) - 15y = -10

Expanding and solving for y:

-4 + 12y - 15y = -10

12y - 4 = -10

12y = -6

y = -1/2

Now that we know y = -1/2, we can substitute this value back into the expression for x:

x = 1 - 3(-1/2) = 1 + 3/2 = 7/2

So the solution to the system of equations is (7/2, -1/2).

Checking the solution in both equations:

-4(7/2) - 15(-1/2) = -4(7/2) + 15/

Step-by-step explanation:

If the x-values are equal for two points, then the two points are on a vertical line.

When there is a vertical line, then it will cross the x - axis at only a single point. This point will be such that all the x - values on the line would be  - values because the line stands on only one point on the x - axis.

The same applies to the y - axis for horizontal lines. This is because the horizontal line would cross the y - axis at a single point. For instance, all the points on y = 2, would have a y - value of 2.

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Answer:

1: 9 polar bears and 38 penguins

2: 47 snowglobes

3: 130 snowballs

4: 97 penguins

Step-by-step explanation:

i did the math

The value of x is 9 by using the concept of corresponding angles.

Corresponding angles are the angles formed when two parallel lines are crossed by any other line. It may also be generated in matching edges(corners) or corresponding corners with the transversal.

From the information given:

(8x + 9) is corresponding to the opposite side of the transversal with an angle of 99 degrees.

Using the sum of angles on a straight line.

Step 1: (8x + 9)° + 99 = 180°

Step 2: 8x + 108 = 180

Step 3: 8x = 72

Step 4: x = 9

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Solving the provided question, we can say that equatiοn of slope intercept will me as y -y1 = m(x-x1) => 3x - y = -1

In mathematics, the intersectiοn point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crοsses on a line or curve. Y = mx+c, where m stands fοr the slope and c for the y-intercept, is used as the equation fοr the straight line to show this.

The slope (m) οf the line and its y-intercept (b) are emphasised in the equatiοn's intercept fοrm. When an equatiοn has the intercept form (y=mx+b), the slοpe is m and the y-intercept is b. Sοme equations can also be rewritten such that they seem to be slοpe intercepts. If y=x is rewritten as y=1x+0, fοr instance, the slοpe and y-intercept are bοth changed to 1.

Here,

coordinates are

M(2,5) and P(a,-2)

equation of slope intercept will me as

y -y1 = m(x-x1)

y - 5 = 3x-4

3x - y = -1

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Liters of 10% solution = 1 liters

Liters of 70% solution = 5 liters

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x +3 = 8 is an equation.

We have,

10% solution = x

70% solution = y

Now,

A 10% antifreeze solution is to be mixed with a 70% antifreeze solution to get 6 liters of a 20% solution.

This means,

We can make two equations.

0.10x + 0.70y = 6 x 0.20

0.10x + 0.70y = 1.2 ______(1)

x + y = 6 ______(2)

Solve for x and y.

From (2),

x = 6 - y

Substituting in (1) we get,

0.10x + 0.70y = 1.2

0.10 (6 - y) + 0.70y = 1.2

0.6 - 0.10y + 0.70y = 1.2

0.6 + 0.60y = 1.2

0.60y = 1.2 - 0.6

0.60y = 0.6

y = 1

And,

x = 6 - y

x = 6 - 1

x = 5

Thus,

10% solution = 1 liter

70% solution = 5 liters

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Answer: The median is one of several measures of center that can be used to summarize a dataset. The median is the middle value in a set of data when the data is arranged in order from smallest to largest. The median divides a dataset into two equal parts, with half of the data values being smaller than the median and half being larger.

Step-by-step explanation:

The median is one of several measures of center that can be used to summarize a dataset. The median is the middle value in a set of data when the data is arranged in order from smallest to largest. The median divides a dataset into two equal parts, with half of the data values being smaller than the median and half being larger.

The reason why the median can differ relative to the data set is because it is affected by extreme values, or outliers, in the data. For example, if a dataset has a few very large or very small values, the median can be significantly different from the mean (another measure of center), which is affected by all values in the dataset. In these cases, the median provides a better measure of center because it is less sensitive to outliers.

In general, the median is considered the best measure of center when the data is skewed (not symmetrical) or has outliers. In these cases, the median provides a better representation of the "typical" value in the dataset. However, when the data is symmetrical and does not have outliers, the mean can be a good measure of center because it takes into account all values in the dataset.

In conclusion, the best measure of center depends on the shape and distribution of the data. When the data is skewed or has outliers, the median is the best measure of center, while in symmetrical and non-outlier datasets, the mean can provide a good measure of center.

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Answer:

3 inches is approximately equal to 76.2 millimeters.

Step-by-step explanation:

Answer:

3 inches = 76.2 millimeters

Step-by-step explanation:

The angle of the base and the ladder is 69. 34 degrees

Note that the six trigonometric identities are;

From the information given, we have that;

Hypotenuse = 17 meters

Adjacent = 6 meters

The identity to use is the cosine

cos θ = adjacent/hypotenuse

Substitute the  values

cos θ = 6/17

cos θ =,0. 3529

Take inverse of cos

θ = 69. 34 degrees

Hence, the value is 69. 34 degrees

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