The scale on a map states that 1 centimeter corresponds to 15 kilometers Find how far apart two cities are if their corresponding points on the map are 13 centimeters apart​

The given infinite series is divergent.

Given,

[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\frac{3n^2+n+1}{2n^2-1}}[/tex]

it is in the form,

[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\ a_n[/tex]

If the series is convergent then it satisfies,

i)[tex]b_{n+1}\ \leq\ b_n\ for\ all\ n[/tex]

ii)[tex]\lim_{n \to \infty} a_n =0[/tex]

if any of the above condition dissatisfies then the series is divergent

First check the 2nd condition,

[tex]\lim_{n \to \infty}\frac{3n^2+n+1}{2n^2-1}}\\\\= \lim_{n \to \infty}\frac{n^2(3+\frac{1}{n}+\frac{1}{n^2})}{n^2(2-\frac{1}{n^2})}}\\\\=\frac{3+0+0}{2-0}\\\\=\frac{3}{2}[/tex]

Here, [tex]\lim_{n \to \infty} a_n \neq 0[/tex]

Thus, the given series is divergent.

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According to the SSS Postulate, two triangles are congruent if three of one triangle's sides are congruent with three of another triangle's sides.

A postulate is an assertion that is not backed by any evidence. Axiom is another name for a postulate. For instance, you would believe Pam if she said that all of her siblings were at least five feet one tall since you are aware of her height and that of all of her siblings, who are all taller than her.

When two figures or objects in geometry have the same shapes, sizes, or are mirror images of one another, they are said to be congruent.

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

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The value of the function  (f - g)(x) is x² + 3x + 5

A function is defined as a relation between a set of inputs having one output each.

In a simpler terms, a function relates input and output.

Therefore, let's solve the function (f - g)(x)

f(x) =  √16x⁴

g(x) = 3x² - 3x - 5

Therefore,

(f - g)(x) = f(x) - g(x)

(f - g)(x) = √16x⁴ - (3x² - 3x - 5)

(f - g)(x) = √16x⁴ - 3x² + 3x + 5

(f - g)(x) = 4x² - 3x² + 3x + 5

Therefore,

(f - g)(x) = x² + 3x + 5

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Answer:

  (b)  15, 36, 39

Step-by-step explanation:

You want to know which sets of segment lengths could form a right triangle.

For segments to form a right triangle, the lengths must satisfy the triangle inequality and the Pythagorean theorem. The latter condition can often be determined by looking at the reduced ratios of the lengths, and comparing to known Pythagorean triples.

The ratio of lengths is 3:6:7. There are no integer side lengths that will form a right triangle when one of them is double another. Not a right triangle.

The ratio lengths is 5:12:13. These numbers are a common Pythagorean triple, so will form a right triangle.

The ratio of the smaller two numbers is 3:4. In order for these to form a right triangle, they must be part of a triangle with ratios 3:4:5. That would be 15, 20, 25. The side length 29 is too long for a right triangle. Not a right triangle.

The two short sides are too short to reach the ends of the long side. These lengths will not form a triangle.

__

Additional comment

The table in the attachment computes a²+b²-c². When that value is 0, the Pythagorean theorem is satisfied, and the triangle is a right triangle. Positive numbers indicate an acute triangle; negative numbers indicate an obtuse triangle.

The Pythagorean triples that came into play in this answer are {3, 4, 5} and {5, 12, 13}. Other triples commonly seen are {7, 24, 25} and {8, 15, 17}.

The value of d in the expression, 4d/5+3 = -2-d/5, is -5.

According to the question,

We have the following expression:

4d/5+3 = -2-d/5

Now, moving the terms with the same variables on the left hand side will result in the change of the sign from minus to plus:

4d/5+d/5 -3 = -2

5d/5+3 = -2

d+3 = -2

Now, moving 3 from the left hand side to the right hand side will result in the change of the sign from plus to minus:

d = -2-3

We know that two negative integers are added but the sign before the result remains negative.

d = -5

Hence, the value of d is -5.

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Answer:

d [tex]\frac{-4}{3}[/tex]

Step-by-step explanation:

change in y over the change in x

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

Step-by-step explanation:

so, let's do the multiplications and squaring. and then compare the result with the target.

(x + a)² + b = x² + 2ax + a² + b

and the original expression is

x² - 4x + 19

x² = x² done

2ax = -4x

2a = -4

a = -2

a² + b = 19

(-2)² + b = 19

4 + b = 19

b = 15

so, the result is

(x - 2)² + 15

Answer: (x-2)^2+15

Step-by-step explanation:

Given x^2-4x+19

=here b=-4 and c=19

B=b/2=-4/2=-2

C=c-B^2=19-(-2)^2=19-4-15

so

(x-B)^2+C

(x-2)^2+15

The linear function that is graphed on the grid is g(x) = (15/2)x + 45   , the correct option is (d) .

In the question ,

a linear function graph is shown ,

we have to find that linear function .

So , From the given graph we can see that

the graph passes from the points (2 , 60) and (6 , 90)

in order to find the equation , we first need to find the slope .

slope = (90 - 60)/(6 - 2)

= 30/4

= 15/2

So , the equation of the line passing through the points (2 , 60) and slope 15/2 is

(y - 60) = 15/2(x - 2)

y - 60 = (15/2)x - 15

Adding 60 to both the sides ,

we get

y - 60 + 60 = (15/2)x - 15 + 60

y = (15/2)x - 15 + 60

y =  (15/2)x + 45

function is (15/2)x + 45

Therefore , The linear function that is graphed on the grid is g(x) = (15/2)x + 45  .

The given question is incomplete , the complete question is

Which linear function is graphed on the grid shown below ?

(a) g(x) = (2/15)x - 6

(b) g(x) = (2/15)x + 45

(c) g(x) = (15/2)x - 6

(d) g(x) = (15/2)x + 45

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By solving a linear equation, it can be calculated that

There are 4 guppies in  each family

What is a linear equation?

At first it is important to know about equation.

An equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sigh

A one degree equation is known as linear equation.

Here a linear equation needs to be solved

Let the number of guppies in each family be x

Allison has 2 aquariums.

In each aquarium she has 2 families of guppies and 3 tetras.

Total number of fishes Allison have = 2(2x + 3) = 4x + 6

Leigh has 1 aquarium with 10 tetras and 3 families of guppies.

Total number of fishes Leigh have  = 3x + 10

By the problem,

4x + 6 = 3x + 10

4x - 3x = 10 - 6

x = 4

There are 4 guppies in each family

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Step-by-step explanation:

Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the wire they need. Andy needs 24 feet of the wire. Emily needs 15 yards of the wire. How much will each of them spend for wire?​

Looking at your chart:

cost/length in inches

6/100 = $0.06 per inch

8.1/135 = $0.06 per inch

9.6/160 = $0.06 per inch

10.8/180 = $0.06 per inch

So the rate stays at a constant rate of $0.06 per inch.

Andy needs 24 feet or 288 inches at a constant rate of $0.06 per inch.

= 288 * $0.06  

= $17.28

________________________________

Emily needs 15 yards or 540 inches at a constant rate of $0.06 per inch.

= 540 * $0.06  

= $32.40

The Compound Interest is $7,290.00.

In order to calculate compound interest, multiply the principal of the original loan by the annual interest rate multiplied by the number of compound periods minus one.

Given:

P= 6250

T= 2 years

r = R/100

r = 8/100

r = 0.08 rate per year,

Then solve the equation for A

A = P[tex](1 + r/n)^{nt[/tex]

A = 6,250.00[tex](1 + 0.08/1)^{(1)(2)[/tex]

A = 6,250.00(1 + 0.08)²

A = $7,290.00

Hence, The Compound Interest is $7,290.00.

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The generalized rule of the indices to be negative fraction can be written as [tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex].

Index (indices) in Maths is the power or exponent which is raised to a number or a variable.

An algebraic expression is a quantity made up of symbols and processes + - / and multiplication Expressions utilizing indices are made simpler using the laws of indices.

Let's consider a negative fraction exponent as, [tex]a^{-m/n}[/tex]

[tex]a^{-m/n}=1/a^{m/n}[/tex]

Since,[tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex]

Therefore, the above expression converts as,

[tex]a^{-m/n} =1/(\sqrt[n]{a})^{-m}[/tex]

[tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex]

Hence "The generalized rule of the indices to be negative fraction can be written as  [tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex].".

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Answer:

19 and 21|

Step-by-step explanation:

a + (a+2) = 40

2a + 2 = 40

2a = 40 - 2

2a = 38

a = 38/2

a = 19

a+2 = 21

Check:

19 + 21 = 40

Based on the given equation and the given value of (), the value of 5() from the equation is 490

If

() = 94 + 2 + 2

The equation can be solved by substituting the value of () into 5()

Substituting is the method of inserting the known value of a variable into an equation to solve for the value of the equation.

Then,

(5)()

= 5(94 + 2 + 2)

= 5(98)

= 490

So therefore, the value of 5() is given by 490.

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Answer:

Step-by-step explanation

Answer:

6 students

Step-by-step explanation:

[tex]\frac{1}{5} = \frac{x}{30}[/tex]
[tex]30 = 5x[/tex]
[tex]6=x[/tex]

The ordered pairs of the function, h(x) = 3x², are (1,3) and (-1,3).

According to the question,

We have the following information:

h(x) = 3x²

Now, we will look at the options to know the correct option of ordered pairs.

Now, in the options, there are only two values of x (1 and -1). So, we will solve the given function using these two values and we will find the value of h(x).

h(x) = 3x²

h(1) = 3*1*1

h(1) = 3

So, the first ordered pair is (1,3).

When x = -1:

h(x) = 3x²

h(-1) = 3*-1*-1

h(-1) = 3

Now, the second ordered pair of the function is (-1,3).

Hence, the correct options are A and C.

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The null and alternative hypothesis regarding the test on whether the mean error is of zero is given by the following option:

D. H0: μ = 0 minutes, H1: μ ≠ 0 minutes.

The first step in identifying the hypothesis is to identify the claim tested, given as follows:

The mean prediction error is equals to zero.

At the null hypothesis, it is tested if there is not enough evidence to go against the claim, hence we suppose that the mean is of zero minutes, as follows:

H0: μ = 0 minutes.

At the alternative hypothesis, it is tested if there is enough evidence to reject the null hypothesis, that is, if there is enough evidence to conclude that the mean prediction error is different of zero minutes, hence it is given as follows:

H1: μ ≠ 0 minutes.

Thus option D gives the correct null and alternative hypothesis in the context of this problem.

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Answer:

the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, is equal to k, where k is the unit rate.

The proportional equation between y and x^2 is:

y = 3*x^2

We know that y is directly proportional to x^2, then we can write:

y = k*x^2

Where k is the constant of proportionality.

We also know that when x = 10, the value of y is 300, replacing that in the above equation we get:

300 = k*(10)^2

Now we can solve this for k:

300 = k*100

300/100 = k

3 = k

Then the equation is:

y = 3*x^2

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Answer:

------------------------

Correct choice is B.

Answer:

b)  -6

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given the interval is [-2, 0]:

Substitute the endpoints of the interval into the function and solve:

[tex]\begin{aligned}x=-2 \implies f(-2)&=4\left(\dfrac{1}{2}\right)^{-2}\\& = 4(4)\\&=16\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies f(0)&=4\left(\dfrac{1}{2}\right)^{0}\\& = 4(1)\\&=4\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\implies\dfrac{f(b)-f(a)}{b-a}&=\dfrac{f(0)-f(-2)}{0-(-2)}\\\\&=\dfrac{4-16}{0+2}\\\\&=\dfrac{-12}{2}\\\\&=-6\end{aligned}[/tex]

The probability that the phone calls would differ from the population proportion by more than 3% is 0

From the question, the given parameters about the distribution are

The mean is calculated as

Mean = np

So, we have

Mean = 8% * 494 = 39.52

The standard deviation is calculated as

Standard deviation = √np(1 - p)

So, we have

Standard deviation = √494 * 8% (1 - 8%) = 0.77

The z-score is calculated using the following formula

[tex]z = \frac{\bar p - p}{\sqrt{p(1 - p)}/n}[/tex]

Substitute the given parameters in the above equation

[tex]z = \frac{8\% - 3\%}{\sqrt{8\% * (1 - 8\%)}/494}[/tex]

Evaluate

z = 90.9

The probability is then calculated as:

P(x > 3%) = P(z > 90.9)

From the z table of probabilities, we have;

P(x > 3%) = 0

Hence, the probability is 0

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[tex] = ( \sin(180 + 45) )^{2} - ( \cos(180 + 90) )^{2} + ( \frac{ \sqrt{3} }{1} )^{2} \\ = ( - \sin(45) )^{2} - ( - \cos(90) )^{2} + 3 \\ = ( - \frac{1}{ \sqrt{2} } ) ^{2} - ( \frac{0}{1})^{2} + 3 \\ = \frac{1}{2} - 0 + 3 \\ = \frac{1}{2} + 3 \\ = \frac{7}{2} [/tex]

ATTACHED IS THE SOLUTION

There is not enough evidence to conclude that the mean is less than 14 hours, as the p-value of the test is greater than 0.05, using the t-distribution.

At the null hypothesis, it is tested if the mean is not less than 14 hours, hence:

[tex]H_0: \mu \geq 14[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the mean is less than 14 hours, hence:

[tex]H_1: \mu < 14[/tex]

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which the parameters are defined as follows:

In the context of this problem, the values of these parameters are:

[tex]\overline{x} = 13.5, \mu = 14, s = 3, n = 64[/tex]

Hence the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{13.5 - 14}{\frac{3}{\sqrt{64}}}[/tex]

t = -1.33.

Using a z-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with t = -1.33 and 64 - 1 = 63 df, the p-value of the test is of 0.094.

Since the p-value of the test is greater than the significance level of 0.05, there is not enough evidence to conclude that the mean is less than 14 hours.

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The system of equations has its solutions to be (0, 3)

From the question, the system of equations is represented on the graph

On the graph, we have the following representations

Say the functions are f(x) and g(x)

To determine the solution to the system of equations, we set both equations equal

i.e. f(x) = g(x)

This in other words mean that we determine the coordinates of the points where the graphs intersect

In this case, they intersect at point (0, 3)

This represents the solution

Hence, the solution to the system of equations is (0, 3)

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Answer: if you multiply you will end up with 675

Step-by-step explanation: