Find the nth term of the arithmetic sequence -1, 2, 5,.. ..

Answer: Moderate negative association

Step-by-step explanation:

The value of x is 70°. The correct option is A. 70

From the question, we are to determine the value of the measure of arc x

From one of the circle theorems, we have that

The angle subtended by an arc at the center is twice the angle subtended by it at any point on the circumference.

First, we will determine the value of the third angle in the triangle formed.

Let the angle be y

y + 15° + 20° = 180°

∴ y = 180° - 15° - 20°

y = 145°

Now, the angle supplementary to this is the angle the arc subtends at the circumference.

Thus,

The angle at the circumference = 180° - 145°

The angle at the circumference = 35°

From the above theorem, we can conclude that the angle subtended by the arc at the center of the circle is 2 × 35° = 70°

∴ The measure of the arc is 70°

This is the value of x

Hence, the value of x is 70°. The correct option is A. 70

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Step-by-step explanation:

x×1/2×1/4×3/4

x×3/32

3/32x

The correct answer is  If x + 1 is odd, then x is even.

The converses of the conditional statement:

"If q then p" provides the converse statement to the conditional expression "If p then q."

The converse of the conditional statement is  If x + 1 is odd, then x is even.

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Answer: None of these are correct

Step-by-step explanation:

I believe that the equation is showing transitive property.

The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Given the polynomial:

-2x³ - 7x² + 3x - 4

Simplifying:

= -(2x² - x + 1)(x + 4)

Hence:

-2x³ - 7x² + 3x - 4 = (-2x² + x - 1)(x + 4)

(x + 4)(ax² + bx + c) = −2x³ − 7x² + 3x − 4

The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.

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A total of 204 textbooks were sold with 153 math textbooks and 51 psychology textbooks being sold, as the number of math textbooks was three times the number of psychology textbooks.

Given that,

The combined total of math and psychology textbooks sold in a week is 204.

The number of math textbooks sold is three times the number of psychology textbooks sold.

To solve this problem,

Assign variables to represent the number of math and psychology textbooks sold.

Let's say "M" represents the number of math textbooks and "P" represents the number of psychology textbooks.

We know that the combined total of math and psychology textbooks sold is 204,

So the equation be:

M + P = 204  .....(i)

We are also given that the number of math textbooks sold was three times the number of psychology textbooks sold.

In equation form, this can be expressed as:

M = 3P

Now, we can substitute the value of M in terms of P into the equation (i):

3P + P = 204

Combining like terms, we get:

4P = 204

Dividing both sides by 4, we find:

P = 51

So, the number of psychology textbooks sold is 51.

To find the number of math textbooks sold,

Substitute this value back into the equation:

M = 3P

M = 3(51)

M = 153

Therefore, the number of math textbooks sold is 153.

Hence,

153 math textbooks and 51 psychology textbooks were sold.

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The sequence of transformation carried out on ABCD is; B: Reflection about the y-axis followed by a translation left by 2 units

As in rotation, reflection and translation the transformed image is congruent to the original figure (i.e all the points undergo same change). Thus, analyzing any one point will give the series of transformation undertaken.

Taking point A(3, 1) into consideration; Reflecting a point (x, y) over y axis, it becomes (-x, y).

Thus, reflecting A(3, 1) over y - axis gives the the new coordinates as (-3, 1)

Now, translating a point (x, y) k units left, gives a new coordinate (x - k, y).

Thus, translating point (-3, 1) 2 units left, gives the new coordinates as A'(-5, 1).

This is the coordinates for A'.

Thus, we can conclude by saying that the sequence of transformation carried out on ABCD is reflected about the y-axis followed by a translation left by 2 units.

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Answer:

  (c)  Factor

Step-by-step explanation:

The constituents of a product are its factors.

Dividing a product by one of its factors will not leave a remainder.

__

A term is a constant or product of one or more variables and a constant. For example, -4 and 24xy are both terms.

A multiple is a product with one factor being an integer. For example, 3×1.5 = 4.5 is a multiple of 1.5.

A variable is a symbol for an unknown value. Commonly, a variable is a single letter, but may also be a blank (__) or a question mark (?). Sometimes a word or phrase is used as a variable. For example, ...

  3 + x = 5

  3 + __ = 5

  3 + ? = 5

  3 + (some number) = 5

The required sales in dollars needed to achieve managements target is $607,5000.

Net income is total revenue less total cost. Total cost is the sum of fixed cost and variable cost. Fixed cost is the cost that remains constant regardless of the level of output. e.g. rent. Variable cost is the cost that varies with output e.g. wages.

Net income = sales - total cost

Net income = sales - (fixed cost + variable cost)

$67,500 = sales - ($175,500 + 0.6sales)

$67,500 = sales - $175,500 - 0.6sales

$67,500 + $175,500 = sales - 0.6sales

243,000 = 0.4sales

sales = 243,000 / 0.4

sales = $607,500

Here is the complete question:

For Pharaoh Company, variable costs are 60% of sales, the fixed costs are $175,500. Managements net income goal is $67,500.Compute the required sales in dollars needed to achieve managements target net income of $67.500.

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The number of permutations of picking 4 pens from the box is 30.

There are six different unique colored pens in a box.

We have to select four pens from the different unique colored pens.

We have to find in how many different orders the four pens can be selected.

A permutation is the number of different arrangements of a set of items in a particular definite order.

The formula used for permutation of n items for r selection is:

    [tex]^nP_r = \frac{n!}{r!}[/tex]

Where n! = n(n-1)(n-2)(n-3)..........1 and r! = r(r-1)(r-2)(r-3)........1

We have,

Number of colored pens = 6

n = 6.

Number of pens to be selected = 4

r = 4

Applying the permutation formula.

We get,

= [tex]^6P_4[/tex]

= 6! / 4!

=(6x5x4x3x2x1 ) / ( 4x3x2x1)

= 6x5

=30

Thus the number of permutations of picking  4 pens from a total of 6 unique colored pens in the box is 30.

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The inverse function of the function [tex]f(x)=-3x+3[/tex] will be [tex]x=g(y)=-\frac{y}{3}+1[/tex].

Here, the given function is [tex]f(x)=-3x+3[/tex].

Then we get:

[tex]y=-3x+3\\\Longrightarrow x=-\frac{y}{3}+1[/tex]

Thus, the inverse function of the function [tex]f(x)=-3x+3[/tex] will be [tex]g(x)=-\frac{x}{3}+1[/tex].

The graph representing this inverse function is given as follows:

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1. The formula expressing the dependence of the variable s on t is: s = 60 - 12t

2. the distance travelled at time t = 3.5 h is 18 Km

Speed is the distance travelled per unit. Mathematically, it can be expressed as:

Speed = distance / time

From the question given, bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km.

Thus, we shall determine the distance travel in time t as follow

Speed = distance / time

12 = distance / t

Cross multiply

Distance = 12 × t

Distance in time t = 12t

But the total distance travelled is 60 Km. Thus, the remaining distance (s) from the bicyclist to the station at time (t) will be given as:

s = 60 - 12t

Thus, the formula expressing the dependence of the variable s on t is: s = 60 - 12t

The distance at t = 3.5 hours can be obtained as illustrated below:

s = 60 - 12t

s = 60 - (12 × 3.5)

s = 60 - 42

s = 18 Km

Thus, the distance travelled at t = 3.5 hours is 18 km

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The measure of the central angle is 290 degrees

The measure of arc GI is given as:

mGI = 145 degrees

The measure of the central angle is calculated as:

Central angle = 2 * mGI

Substitute the known values in the above equation

Central angle = 2 * 145

Evaluate the product

Central angle = 290

Hence, the measure of the central angle is 290 degrees

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See attachment for the graph of the piecewise function h(x)

The function is given as:

h(x) = | -4,    x < 3

         | x + 5,    x >= 3

The above function is a piecewise function.

It has 2 separate functions at two domains

This means that we plot the sub-functions in the piecewise function at their respective domain

See attachment for the graph of the piecewise function h(x)

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Answer:

one of several possible solutions :

18, 75, 105

Step-by-step explanation:

prime factors of 3150 :

3150 ÷ 2 = 1575

1575 ÷ 2 no

1575 ÷ 3 = 525

525 ÷ 3 = 175

175 ÷ 3 no

175 ÷ 5 = 35

35 ÷ 5 = 7

7 ÷ 5 no

7 ÷ 7 = 1

3150 = 2¹ × 3² × 5² × 7¹

these are the product of the longest streaks of prime factors in x, y and z.

the GCF(y, z) = 15.

the prime factors of 15 are simply 3¹×5¹.

so, y and z share only the factors 3 and 5.

the GCF(x, y, z) = 3.

since x is an even number, the elimination of 5 in the GCF is not surprising.

let's try the following :

x = 2¹ × 3² = 2×9 = 18

y = 3¹ × 5² = 3×25 = 75

z = 3¹ × 5¹ × 7¹ = 3×5×7 = 105

that uses all the factors of 3150, and their LCM is as the product of the longest streaks of their prime factors is

2¹ × 3² × 5² × 7¹.

fits.

the GCF(75, 105) is the product of the prime factors they have in common : 3¹ × 5¹ = 15.

fits.

the GCF(18, 75, 105) is the product of the prime factors ask 3 numbers have in common, which is only 3¹ = 3.

fits.

18 < 75 < 105

fits.

18 is an even number greater than 10.

fits.

there are more than 1 solutions.

e.g.

z = 2¹ × 3¹ × 5¹ × 7¹ = 210

is also possible.

The number of cases after two years is 221.

As a result of the disease, the population of the village would decrease by 95% per year. The number of cases at the village is function of the rate of infection, the number of years and the beginning number of cases.

The exponential function that can be used to represent this situation is:

FV = P( 1 + r)^t

FV = 200 (1.05)^2 = 221

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From the standard normal table, the respective probabilities are; 0.908 and 0.841

Formula for calculating the standard score or z score is:

z = (x - μ)/σ

where:

z is the standard score

x is the raw score

μ is the population mean

σ is the population standard deviation

A) We are given;

x = 95

μ = 110

σ = 15

Thus;

z = (95 - 110)/15

z = 1.33

From the normal standard distribution table we can find the probability from the z-score as;

P(x > 95) = 1 - 0.091759.

P(x > 95) = 0.908

B) We are given;

x = 125

μ = 110

σ = 15

Thus;

z = (125 - 110)/15

z = 1

From the normal standard distribution table we can find the probability from the z-score as;

P(x > 95) = 1 - 0.158655.

P(x > 95) = 0.841

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Answer:

angle <B = 76

Step-by-step explanation:

The measure of an exterior angle is equal to sum of two interior angles that is not adjacent to the exterior angle.

We can write the following equation with this information to find the value of angle <B

<B + 71 = 147 subtract 71 from both sides

<B = 76

The equivalent expression for the given expression is 28p + 14q + 21r.

An expression that gives the same value as the original expression when the same value of a variable is substituted is said to be an equivalent expression.

An equivalent expression is simplified to the original expression by using the distributive property.

The distributive property is

a(b + c) = ab + ac

The given expression is 7(4p + 2q + 3r)

Applying the distributive property,

7(4p + 2q + 3r) = 7(4p) + 7(2q) + 7(3r)

⇒ 28p + 14q + 21r

Thus, the equivalent expression for the given expression is 28p + 14q + 21r.

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7(4p+2q+3r)=7(4p+2q+3r)

Apply distributive law

So

This is the required expression

Answer:

If x^2 = 1, then x = 1 is NOT true because x can also be -1.

1. The sentences translated to equations looks like:

a) 4x = 32.

b) x + 6y = 43.

c) 3x + 7 = 9x - 4.

d) 76 - 2x = 8x.

2. The equations translated to sentences looks like:

a) The sum of 16 and 9 times x is 50.

b) The sum of the square of x and 6 times y is 4 times w.

c) Three times x is 52.

d) Five-sixth is equal to the product of -10 and x.

Practice Part 1: Translate sentence to equation

a)Four times a number is thirty-two.

Assuming the number to be x, we get the equation, 4x = 32.

b)The sum of and six times  is equal to forty-three.

The sentence, when translated to an equation looks like, x + 6y = 43.

c)The sum of 7 and three times  equals the difference of 9 times  and 4.

The sentence, when translated to an equation looks like, 3x + 7 = 9x - 4.

d)Two times  less than 76 is equal to the product of 8 and

The sentence, when translated to an equation looks like, 76 - 2x = 8x.

Practice Part 2: Translate equation into sentence

a) 9x + 16 = 50.

- The sentence for the given equation is, the sum of 16 and 9 times x is 50.

b) x² + 6y = 4w.

- The sentence for the given equation is, the sum of the square of x and 6 times y is 4 times w.

c) 3x = 52.

- The sentence for the given equation is, three times x is 52.

d) 5/6 = -10x.

- The sentence for the given equation is, five-sixth is equal to the product of -10 and x.

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Using the relation between velocity, distance and time, it is found that her jogging rate was of 6 mph.

Velocity is distance divided by time, hence:

[tex]v = \frac{d}{t}[/tex]

Jogging, her velocity was of v, while the time was of t, for a distance of 12 miles, hence:

[tex]v = \frac{12}{t}[/tex]

Biking, her velocity was of v + 6, while the time was of 3 - t, for a distance of 12 miles, hence:

[tex]v + 6 = \frac{12}{3 - t}[/tex]

[tex]v = \frac{12}{3 - t} - 6[/tex]

Then:

[tex]\frac{12}{t} = \frac{12}{3 - t} - 6[/tex]

[tex]\frac{12}{3 - t} - \frac{12}{t} = 6[/tex]

[tex]\frac{12t - 36 + 12t}{t(3 - t)} = 6[/tex]

18t - 6t² = 24t - 36

6t² + 6t - 36 = 0

t² + t - 6 = 0

(t + 3)(t - 2) = 0. -> t = 2 hours.

Hence her jogging rate in mph is given as follows:

[tex]v = \frac{12}{2} = 6[/tex]

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Answer:

please how

Step-by-step explanation:

I will help ypu

Answer:

788,000 =

788 x 10^3

78.8 x 10^4

7.88 x 10^5

.788 x 10^6

and so on

Using the z-distribution, it is found that since the p-value is less than 0.02, we reject the null hypothesis.

At the null hypothesis, it is tested if the proportion is of at most 59%, that is:

[tex]H_0: p \leq 0.59[/tex]

At the alternative hypothesis, it is tested if the proportion is greater than 59%, hence:

[tex]H_1: p > 0.59[/tex]

The test statistic is given by:

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

In which:

For this problem, the parameters are:

[tex]p = 0.59, n = 900, \overline{p} = 0.63[/tex]

Hence the value of the test statistic is found as follows:

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

[tex]z = \frac{0.63 - 0.59}{\sqrt{\frac{0.59(0.41)}{900}}}[/tex]

z = 2.44.

Using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is higher than a value, with z = 2.44, the p-value is of 0.0073.

Since the p-value is less than 0.02, we reject the null hypothesis.

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On looking for a pattern in the given data set, the quadratic model best describes the data.

2nd option is correct.

A data model represents the type of relationship between the variables of a data set.

Data models are of four types, namely, Linear, Cubic, Quadratic and Exponential data models.

Given data is:

Distance Traveled                      Average Speed(miles per hour)

(miles)

1                                                                7

2                                                               6.3

3                                                              5.67

4                                                              5.103

A quadratic model is the best data model for the given data set.

The pattern observed in the given data set observes the properties of a quadratic function.

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Answer:

Exponential is the correct answer.

Step-by-step explanation:

Combining the terms into one fraction, we have

[tex]kx + b - \dfrac{x^3+1}{x^2+1} = \dfrac{(k-1)x^3 + bx^2 + kx + b - 1}{x^2+1}[/tex]

If this converges to 0 as [tex]x\to\infty[/tex], then the degree of the numerator must be smaller than the degree of the denominator.

To ensure this, take [tex]k=1[/tex] and [tex]b=0[/tex]. This eliminates the cubic and quadratic terms in the numerator, and we do have

[tex]\displaystyle \lim_{x\to\infty} \frac{x - 1}{x^2 + 1} = \lim_{x\to\infty} \frac{\frac1x - \frac1{x^2}}{1 + \frac1{x^2}} = 0[/tex]

Alternatively, we can compute the quotient and remainder of the rational expression.

[tex]\dfrac{x^3+1}{x^2+1} = x - \dfrac{x-1}{x^2+1}[/tex]

Then in the limit, we have

[tex]\displaystyle \lim_{x\to\infty} \left(kx + b - x + \frac{x-1}{x^2+1}\right) = (k-1) \lim_{x\to\infty} x + b = 0[/tex]

Both terms on the left vanish if [tex]k=1[/tex] and [tex]b=0[/tex].

Answer: 30%

Step-by-step explanation:

the first 2 bars < or = to 650 add up to ~29% roughly, cant be 25%, 68%, or 99%. Therefore the only answer available is 30%

Answer:

30%

Step-by-step explanation:

For Connexus students its 30% :)