Mary used a sample of 68 large u. S. Cities to estimate the relationship between crime (annual property crimes per 100,000 persons) and income (median annual income per capita, in dollars). Her estimated regression equation was crime = 428 + 0. 050 income. If income decreases by 1000, we would expect that crime will:.

If the equation be 3log₂x-(log₂3-log₂ (x+4)) then we get[tex]$\log _2\left(\frac{x^2(x+4)}{3}\right)[/tex].

An exponential function has an opposite called a logarithmic function. In both exponential and log functions, the basis is the same.

An exponent and a number (the base) are inputs into a logarithmic function, which yields a result (the logarithm). The base that must be raised in order to obtain a number is represented by the number's logarithm.

The features of exponential functions can be investigated and exponential equations can be solved using logarithms. In calculus, where they are used to determine the slope of specific functions and the region enclosed by specific curves, they also become incredibly useful.

Let the given equation be 3log₂x-(log₂3-log₂ (x+4))

[tex]$$& \log _a(x)-\log _a(y)=\log _a\left(\frac{x}{y}\right) \\[/tex]

[tex]$$& {alog}(x)=\log \left(x^a\right)[/tex]

3 log₂ x - (log₂3 - log₂ (x+4))

simplifying the above equation, we get

log₂(x²) - log₂(3/x+4)

[tex]$& \left.\log _2 \left(\frac{\frac{x^2}{3}}{\frac{3}{x+4}}\right)=\log _2\left(\frac{x^2(x+4)}{3}\right)[/tex]

Therefore, by simplifying the equation 3log₂x-(log₂3-log₂ (x+4)) we get[tex]$\log _2\left(\frac{x^2(x+4)}{3}\right)[/tex].

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Answer:

x=43

2x=86

x+8=51

Step-by-step explanation:

2x+x+(x+8)=180

2x+x+x+8=180

4x+8=180

4x=172

x=43

2x=86

x+8=51

43+86+51

Answer:

1/2

Step-by-step explanation:

I first turned 1 1/3 into 4/3 because it's easier to work with.

[tex]\frac{4}{3} * \frac{3}{8}[/tex]

You can cancel out the threes, so all that's left is:

[tex]\frac{4}{8}[/tex]

which can then be simplified into 1/2

Answer: Shoot sorry I thought it was 11/3 x 3/8 I'm so sorry! But its 1/2

The  [tex]\sqrt{18}[/tex] can be write in the radical form and decimal form

The given number is [tex]\sqrt{18}[/tex]

The root 18 can be written in 2 forms, radical form and decimal form

The radical form is the mathematical expression that consist of radical signs like square root, cube root etc

The decimal form that consist of a whole number and the fractional part, the whole number part and the fractional parts are separated by the decimal sign

The number = [tex]\sqrt{18}[/tex]

Prime factorization

18 = 2 × 3 × 3

= [tex]3\sqrt{2}[/tex]

This is the radical form

The decimal form is

The value of [tex]\sqrt{2}[/tex] = 1.414

Then

[tex]\sqrt{18}[/tex] =  [tex]3\sqrt{2}[/tex] = 3 × 1.414

= 4.242

Therefore, the radical form is [tex]3\sqrt{2}[/tex] and the decimal form is 4.242

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Answer:

4.5.

Step-by-step explanation:

To find the median of a set of data, we need to first arrange the data in numerical order. Once the data is arranged in order, the median is the middle value in the set. In this case, the data arranged in numerical order is: 2.5, 3.5, 4.5, 5.5, 6.5. The median is the middle value, which is 4.5.

Answer:

7 months

Step-by-step explanation:

Answer:

in a class of 80 students, 56 are boys and the rest are girls. what percentage of students are girls?

30% is the answer

The value of the function f(x) = x when the limit x approaches to 0 is equal to 0.

As given in the function,

Given function is equal to:

f(x) = x

Value for the limit x approaches to zero

When x approaches to zero means x approaches to right hand side limit to zero or left hand side limit to zero

When limit x→0+ then the function f(x) = x is equal to 0

When limit x → 0- then the function f(x) = x is equal to 0.

[tex]\lim_{x \to 0} f(x)[/tex]

= [tex]\lim_{x \to 0} ( x )[/tex]

= 0

Therefore, the value of the function f(x) when limit x approaches to zero is equal to 0.

The complete question is:

What is the limit of f(x) = x when x approaches to 0?

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Latanya has has 10 nickels and 14 dimes in total of 24 nickels and dimes altogether

Given is that Latanya has $1.90 worth of nickels and dimes. She has a total of 24 nickels and dimes altogether.

Let the number of nickels and the number of dimes that Latanya has be [a] and [b] respectively. Then, we can write the simultaneous equations as -

(a/20) + (b/10) = 1.90

a + b = 24

The equation is solved graphically. The graph is attached at the end. We get -

a = 10, b = 14

Therefore, she has 10 nickels and 14 dimes in total.

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Answer:

Step-by-step explanation:

5 x w=w^3?

(I don't know but that's how I would put it based on that...)

Answer: 10 burritos

Step-by-step explanation:

Let y be the total cost, and b is the number of burritos

So we have the equation is

y= 5.50b + 7

Now we put a total cost of $62 in the y spot

62 = 5.50b + 7

Subtract 7 from both sides

55 = 5.50b

Divide 5.50 from both sides

b = 10 burritos

Answer: 10 burritos

Step-by-step explanation:

This is a worded question. The first step would be to extract the essential information and represent it as an easily understandable equation:

b is the number of burritos

$5.50 is the cost for each burrito

$7 is additionally charged for a service fee

We have to find the number of burritos (b)

Therefore, we can write the equation like this:

(5.50 * b) + 7 = 62

We can then rearrange the equation to get b on one side. Remember to follow the BIDMAS rules backwards!

(5.50 * b) + 7 = 62

5.50*b = 62-7

5.50*b = 55

b = 55/5.50

b = 10

Finally, always write a worded answer because it is a worded equation. For example, you could write:

Marie bought 10 burritos

Hoped this helped!

In order to prove that △VWZ ~ △YXZ by SAS theorem we must have ∠VZW ≅ ∠YZX. Thus, option c is the most appropriate choice.

To prove that △VWZ ~ △YXZ by SAS theorem, we must prove that two sides of each triangle such that the angle between these sides is congruent are also congruent.

now △VWZ ~ △YXZ is to be proved, it implies that -

∠V ↔︎ ∠Y

∠W ↔︎ ∠X

∠Z ↔︎ ∠Z

thus  ∠VZW ≅ ∠YZX should be true.

hence, option c is correct and that automatically strikes out option d.

now the sides involving Z should also be congruent to prove that

△VWZ ~ △YXZ

thus, side WZ ≅ side XZ and side VZ ≅ side YZ

since we don't have such an option- options a and b are not the correct choices for this question.

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The complete question is -

In the diagram, VZ/YZ=WZ/XZ

To prove that VWZ~YXZ by the SAS similarity theorem, Which other sides or angles should be used?

a. WV and XY

b. WV and YZ

c. ∠VZW ≅ ∠YZX

d. ∠VWZ ≅ ∠YXZ

A simple random sample of tanks is selected and the sample mean capacity is found to be 8550 gallons. Therefore, The z score corresponding to a tank with a capacity of 8550 gallons is z = 0.50.

We can see that the actual capacity of the tank is normally distributed with a mean of 8544 gallons and a standard deviation of 12 gallons.

The actual capacity of the tank is normally distributed.

Let X = the actual volume of the tank

SO, X ~ Normal(μ = 8544 , σ² = (12)²)

The normal z-score probability distribution is given by:

                   Z = ~ N(0,1)

where μ = average capacity = 8544 gallons

           σ = standard deviation = 12 gallons

Z score measures how many standard deviations the measurements are from the mean To do. Once you have determined the Z-score, look at the Z-score table to find the p-value (area) associated with that Z-score. This p-value is the probability that the value of the measure is less than X. which means that Percentile of X.

Now,

The probability of a randomly selected tank having a capacity of less than 8550 gallons is given by = P(X < 8550 gallons)

   P(X < 8550 gallons) = P ( X - μ /σ < 8550 - 8544/12 )

                                     = P(Z < 0.50)

                                      = 0.6915

The above probabilities are calculated considering the value of x = 0.50 in a z-table with an area of ​​0.6915.

Therefore,  The Z value corresponding to a tank with a capacity of 8550 gallons is z=0.

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a) 0.7 % percentage of students taking the test had scores between 60 and 80.

b) 73.8% percentage of students taking the test had scores of at least 90.

c) 68% percentage of students taking the test had scores that were more than one standard deviation away from the mean.

d) The terms "probability distribution function" and "probability function" are also sometimes used to denote probability density functions. Probability Distribution Function can be used when the probability distribution is defined as a function over a general set of values. Alternatively, you can refer to the cumulative distribution function.

Let us assume that distribution is normal. As mean is 69.5

and standard deviation is 28.55,

z−score for 60 is (60-80)/ 28.55 = -0.7, and

z−score for 80 is (80-80)/28.55 = 0

Therefore, the area under the curve of the z result is −2 is 0.7. This is

z = +2 to z

  =0.7 (4 or z = 0 to z = −2).

So the percentage of values ​​between 60 and 80 is 0.7%.

b) (x > 90) = 1 - P( z < 90 - 69.5/ 28.55)

                 = 1 - (z < 0.71)

                 = 0.738

                 = 73.8%

Therefore, the percentage of students taking the test had scores of at least 90 is 73.8%.

c) The rule of thumb, or the 68-95-99.7% rule, falls within 1 standard deviation (68%), 2 standard deviations (95%), and 3 standard deviations (99.7%) of the mean Shows approximate percentage of data.

d) In probability theory, the probability density function (PDF) or continuous random variable density describes the value at a particular pattern (or point) in the pattern space (the set of possible values ​​taken by a random variable) as is a function that can be interpreted as Relative probability that the value of the random variable is close to this sample. Probability density is the probability per unit length. That is, the absolute probability that a continuous random variable will take on a particular value is 0 (because there is an infinite set of possible values ​​after all), but given the PDFs of two different samples, any random variable For a plot of , we can derive how much more likely the random variable is to be close to one sample than the other.

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The number of chairs that are in that row length is 3.

Let the chairs in 1 row be x

Let the total chairs be y.

Since Hue can form 2 rows of a given length with 8 chairs left over, this will be:

y = 2x + 8

Also, it can be 8 rows of that same length if she gets 10 more chairs. This will be:

y = 8x - 10

Combine the equations

2x + 8 = 8x - 10

Collect like terms

8x - 2x = 10 + 8

6x = 18

Divide

x = 18 / 6

x = 3

There are 3 chairs per row.

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Answer: m=-18

Step-by-step

9*-2=-18 to get m, as 4/-2 = -2

The linear  equation [tex]\frac{17}{3} - \frac{3}{4}x = \frac{1}{2}x + 5[/tex] has been solved

Value of x is [tex]\frac{8}{15}[/tex]

What is linear equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign

A one degree equation is known as linear equation.

The linear  equation is [tex]\frac{17}{3} - \frac{3}{4}x = \frac{1}{2}x + 5[/tex]

Now,

[tex]\frac{17}{3} - \frac{3}{4}x = \frac{1}{2}x + 5[/tex] [ Given]

[tex]\frac{17}{3} - \frac{3}{4}x-\frac{17}{3} = \frac{1}{2}x + 5-\frac{17}{3}[/tex] [Subtraction property of equality]

[tex]- \frac{3}{4}x = \frac{1}{2}x -\frac{2}{3}[/tex] [Simplification]

[tex]- \frac{3}{4}x - \frac{1}{2}x = \frac{1}{2}x -\frac{2}{3} - \frac{1}{2}x[/tex] [Subtraction property of equality]

[tex]-\frac{5}{4}x = -\frac{2}{3}[/tex] [Simplification]

[tex]-\frac{5}{4}x. -\frac{4}{5}= -\frac{2}{3}.-\frac{4}{5}[/tex] [Division property of equality]

[tex]x = \frac{8}{15}[/tex] [Simplification]

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Answer:

1/4 pound of cheese on each pizza.

Step-by-step explanation:

To find the amount of cheese that goes on each pizza, we first need to find the total amount of cheese the family has. They have 1/2 + 1/2 = 1 pound of cheese in total. Since they are making 4 pizzas, they will put 1 / 4 = 1/4 pound of cheese on each pizza. Therefore, they will put 1/4 pound of cheese on each pizza.

Answer:

The compound inequality that has no solution is 3(x+4) < 12 or 3x + 1 > 10. To solve this inequality, we need to first consider each inequality separately. For the first inequality, 3(x+4) < 12, we can solve for x by dividing both sides of the inequality by 3, like this:

(x+4) < 4

x < 0

This means that the solution to the first inequality is all values of x that are less than 0. For the second inequality, 3x + 1 > 10, we can solve for x by subtracting 1 from both sides of the inequality and then dividing by 3, like this:

3x > 9

x > 3

This means that the solution to the second inequality is all values of x that are greater than 3.

Now that we have the solutions to each inequality, we need to combine them to find the solution to the compound inequality. To do this, we need to consider the "or" that connects the two inequalities. This means that the solution to the compound inequality is the set of values that are either less than 0 or greater than 3. Since there are no values that are both less than 0 and greater than 3, this compound inequality has no solution. The other compound inequalities listed have solutions, so they are not the answer to the question.

Step-by-step explanation:

The garden will stretch by 2/3 miles.

What do you mean by stretch ?

Stretch is to extend or lengthen something beyond the normal length.

Given that :

Garden covers an area of 1/6 of a square mile and the garden is 1/4 mile wide.

We know that,

      The garden is a rectangle in shape

Formula for area of rectangle

    Area of rectangle = length x breath

                         Area = l x b

substitute the given values in the formula , we get

     1/6 = l x (1/4)

     4/6 = 4 l / 4   [ multiply both sides with 4 ]

     4 / 6 = l

     2 / 3 = l         [ cancel by using 2 table ]

Therefore, the length of garden stretch when the garden covers an area of 1/6 of a square mile and the garden is 1/4 mile wide is 2/3 mile.

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The flour will last for about 11 days.

What is equation ?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.

Suppose, the flour will last for x days.

She uses 15 pounds of flour each day.

So, the total amount of flour used in x days 15x pounds.

Given that, she has 157.86 pound of flour.

So, the equation will be

15 x = 157.86

x = 157.86 / 15

  = 10.524

  ≈ 11

Thus, the flour will last for about 11 days.

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A map's scale reveals that 2. 5 2. 15.1515 kilometers are represented by 52, point, 5 centimeters, while 17 symbolizes 105 kilometers. 5 17. On the map, 517, point, 5 centimeters.

The ratio between a distance on a map and its corresponding distance on the ground is referred to as the "map scale." One kilometer on the ground is equal to one centimeter on a map with a scale of 1:100,000. There are three primary scale types found on maps: fractional scales, graphic scales, and written or verbal scales.

The link between the map's landscape and the one it shows is expressed using words in a written or verbal scale, for example, one inch equals one mile. To calculate distances and regions on a map, we can utilize the scale. Calculating distance is easy compared to converting scale types. Since we must square the integers, area computations are more difficult.

If d stands for the desired distance, then the percentage...

d/(17.5 cm) = (15 km)/ (2.5 cm)

can be applied to locate it.

Add 17.5 cm to the result to get...

d = (17.5/2.5)·(15 km) = 105 km

The exact distance is 105 kilometers.

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Correct Question:

A scale on a map having a reading which is 2. 5, 2.52, point, 5 centimeters represents 15.1515 kilometers. What number of actual kilometers are represented by 17. 5, 17.517, point, 5 centimeters on the map?

The angle measure w is 1.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

tan w = 0.0175

Multiply [tex]tan^{-1}[/tex] on both sides.

w = [tex]tan^{-1}[/tex] 0.0175

w = [tex]tan^{-1}[/tex] tan 1

w = 1

Thus,

If tan w = 0.0175

The angle w is 1.

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Answer:

g(x) = -x + 1|-2

Step-by-step explanation:

Negating the x-values flips everything over the y-axis. See attached for example

The option that correctly describes the domain of d(t) is given as follows:

0 ≤ t ≤ 2.1.

The domain of a function is composed by the set that contains all possible input values of a function.

Hence, from the graph of a function, the domain is composed by the values assumed by the horizontal axis of the graph.

In this problem, the input and the output variables are defined as follows:

The values assumed by the horizontal axis of the graph are given as follows:

Between 0 and 2.1.

Hence the interval that gives the domain of d(t) is given as follows:

0 ≤ t ≤ 2.1.

As the input variable is t.

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Yes, to prove triangles to be congruent it is compulsory to have at least three congruent corresponding parts.

Explanation:

Minimum congruent corresponding parts required to prove triangles to be congruent are as follow:

Therefore, minimum three congruent corresponding parts are required to prove any two triangles to be congruent.

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The current growth rate of the island is given as follows:

-43%.

The first step in calculating the growth rate is obtained the increases and the decreases in the population, as follows:

The total change is obtained by the subtraction of the increases by the decreases, as follows:

Total change = 12,000 - 25,000 = -13,000

Then the growth rate, as a percentage, is obtained by the division of the total change of -13,000 by the initial population of 30,000 and then multiplied by 100%, as follows:

-13,000/30,000 x 100% = -43%.

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The proof of OP=1/2MN will get us 2

MNO is a right-angled triangle with right-angle MON, and P is the midpoint of MN. To demonstrate: OP=1/2MN Because midpoints will be involved, names for M and N should be multiples of 2.

Let M and N have receptive coordinates of (0,2m) and (2n,0).

Midpoint = [tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2}[/tex]

The coordinates of P are

midpoint = [tex]\frac{2n+0}{2} , \frac{2m+0}{2}[/tex]

midpoint =(n,m)

The coordinates of P are (n,m).

Distance formula:

d=√([tex]x^{2}-x_{1} ^2 +(y_{2} -y_{1} )^2\\[/tex]

Using distance formula, the distance between O(0,0) and P(n,m) is

OP=√(n-0)^2+(m-0)^2 =√n^2+m^2

Using distance formula, the distance between M(0,2m) and N(2n,0) is

MN=√(2n-0)^2+ (0-2m)^2

MN=2√(4n^2+4m^2

On further simplification we get

MN=√4(n^2+m^2)

MN=2√(n^2+m^2)

MN=2(OP)

Divide both sides by 2.

1/2MN=OP

Interchange the sides.

OP=1/2MN

Hence proved

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The probability they choose the same number is 0.1 or 1/10.

What is probability?

Mathematical descriptions of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between zero and one represents the likelihood of an event, with 0 roughly denoting impossibility and 1 denoting certainty. It is more likely that an event will occur if its probability is higher. The flip of a fair (impartial) coin serves as a straightforward illustration. Given that the coin is fair, the outcomes "heads" and "tails" are equally likely; therefore, the likelihood of "heads" equals the possibility of "tails"; since no other outcomes seem to be possible, the likelihood of either "heads" as well as "tails" is 1/2 (also known as 0.5 or 50%).

Whichever number the professor picks doesn't matter. The only thing that matters is that the student matches the predetermined number.

That probability is one-tenth(1/10) for any given number.

Hence, the probability they choose the same number is 0.1 or 1/10.

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Answer:

r ≤ 8

Step-by-step explanation:

-1-2(1+6r) ≥ -99

-1-2-12r ≥ -99

-3-12r ≥ -99

-12r ≥ -96

r ≤ 8

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