An equestrian club orders magazine subscriptions for new members.
Last year they had 32 new members and spent $624 on subscriptions.
Use the equation 32m = 624 to find the cost of each subscription.

Answer:

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Answer:

14

Step-by-step explanation:

let the number be x

2x is larger than half of x by 21: 2x = 0.5+21

Solve:

2x = 0.5+21

1.5x = 21

x = 14

The nonreal solutions to the polynomial equation are: (2 + i√11, 2 - i√11).

By critically observing the graph given, we can logically deduce that the real solutions of the polynomial are -1 and 4. This ultimately implies that, the given polynomial expression can be evaluated as follows:

(x + 1)(x - 4) = x² - 3x - 4.

x⁴ - 7x³ + 23x² - 29x - 60 = x² - 3x - 4.

Also, the nonreal solutions can be determined by dividing the polynomial expression by the real solutions as follows:

Nonreal solutions = (x⁴ - 7x³ + 23x² - 29x - 60)/(x² - 3x - 4)

Nonreal solutions = (2 + i√11, 2 - i√11).

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The cost of buying 32 shirts according to the function given is $268.

Given that the function f(x) = 8x + 12 represents the cost of ordered a shirt.

We need to find the cost to buy 32 shirts.

To find out how much it would cost to buy 32 shirts, you can use the given function f(x) = 8x + 12, where 'x' represents the number of shirts and 'f(x)' represents the cost of ordering 'x' shirts.

Let's plug in x = 32 into the function:

f(32) = 8 × 32 + 12

f(32) = 256 + 12

f(32) = 268

So, it would cost $268 to buy 32 shirts.

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The career that requires data analysis skills is a data scientist because the skills helps in computing and analyzing large amounts of data from several sources.

Data analysis skills are known as technical skills used by a data analyst to  report insights and analyze data.

Some data analysis skills include;

A career that requires data analysis skills is a data scientists

A data scientist is one that computes and analyzes large amounts of data from different sources and makes useful interpretations from it.

The skills such career needs include statistics, calculus, probability, programming, excel, visualization, database management, and machine earning.

There is also need for a high level of accuracy when solving problems.

Thus, the career that requires data analysis skills is a data scientist because the skills helps in computing and analyzing large amounts of data from several sources.

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The t- score for a sampling distribution is 2

The t-score is the number of standard deviations from the mean in the t-distribution.

The upper and lower bounds of a confidence interval when the data are approximately normally distributed.

T-scores and confidence intervals

Confidence intervals use t-scores to calculate the upper and lower bounds of the prediction interval. The t-score used to generate the upper and lower bounds is also known as the critical t or t* value.

The t- distribution is given by

t=(x – μ) / (S / √n)

t = T – Distribution

x = sample mean

μ = population mean

S = standard deviation

n = Sample size

It is given that sampling distribution mean of 10.5, a standard deviation of 1.5, and a size of 36 drawn from a population that has a mean of 10.

We need to find the t-score for sampling distribution

t=(x – μ) / (S / √n)

Here, x= 10.5 , μ= 10, S=1.5, n=36

t = (10.5 - 10)/ (1.5 /√36)

t= 2

Hence the value of t-score is 2

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The graph is shown in the attached image.

646 gallons of water are needed to fill the waterbed

The dimensions are given as:

8 ft long, 7 ft wide, and 1.5 ft tall

The volume is calculated as:

Volume = Length * Width * Height

So, we have

V = 8 * 7 * 1.5 cubic feet

Evaluate

V = 84 cubic feet

1 gallon = 0.13 cubic feet

So, we have:

V = 84/0.13 gallon

Evaluate

V = 646 gallons

Hence, 646 gallons of water are needed to fill the waterbed

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Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

The cost function, C(x) is given by 12000 + 400x − 2.6x² + 0.004x³ while the demand function, P(x) is given by 1600 − 8x.

Next, we would differentiate the cost function, C(x) to derive the marginal cost:

C(x) = 12000 + 400x − 2.6x² + 0.004x³

C'(x) = 400 − 5.2x + 0.012x².

Also, revenue, R(x) = x × P(x)

Revenue, R(x) = x(1600 − 8x)

Revenue, R(x) = 1600x − 8x²

Next, we would differentiate the revenue function to derive the marginal revenue:

R'(x) = 1600 - 8x

At maximum profit, the marginal revenue is equal to the marginal cost:

1600 - 8x = 400 − 5.2x + 0.012x

1600 - 8x - 400 + 5.2x - 0.012x² = 0

1200 - 2.8x - 0.012x² = 0

0.012x² + 2.8x - 1200 = 0

Solving by using the quadratic equation, we have:

x = 220.40 or x = -453.73.

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

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Answer: A shift 16 units down

Step-by-step explanation:

See attached image.

The transformation of the function f(x) = x is (x, y) → (x + 16, y). This transformation is said to be the translation rule and the translation is 16 units towards the right.

The translation rule for a function f(x) is given by

(x, y) → (x + a, y + b)

Where a, and b are constant.

(x, y) → (x + a, y); translation towards right

(x, y) → (x - a, y); translation towards left

It is given that the function f(x) = x and g(x) = x - 16

So, the variation is

x - a = x - 16

⇒ - a = x - x - 16

∴ a = 16

Thus, the transformation is (x, y) → (x + 16, y)

Therefore, the transformation of the function f(x) = x is (x, y) → (x + 16, y) i.e., the translation of 16 units towards the right .

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Answer:

40 3/8

Step-by-step explanation:

You can just multiple it on calculator, which 1/8 is 0.125 so convert 40.375 to 40 3/8

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Answer:

D. 6

Step-by-step explanation:

Let's first find x :-

[tex]\sf 3 + 2x + 22 = x + 17[/tex]

Now that we found x, let's find QR :-

QR = 2x + 22

Therefore, QR = 6 !!!

The solutions of the equation 2cos(2x) = x are (0.626, 0.626), (-1.607,-1.607) and (-1.798,-1.798)

The equation is given as:

2cos(2x) = x

Split the equation as follows:

y = 2cos(2x)

y = x

Next, we plot the graph of y = 2cos(2x) and y = x (see attachment)

From the attached graph, y = 2cos(2x) and y = x intersect at the following points

(x, y) = (0.626, 0.626), (-1.607,-1.607) and (-1.798,-1.798)

Hence, the solutions of the equation 2cos(2x) = x are (0.626, 0.626), (-1.607,-1.607) and (-1.798,-1.798)

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I assume you meant [tex]f(x)=3(2)^x[/tex].

First, we need to understand that these two triangles are

similar.

we know this because their lines (the arrows) prove they are the same direction. A similar triangle does

NOT mean they are proportional,

they are just similar by ratio.

Lets call the triangle on the left ABC and the triangle on the right A'B'C'.

I will attach an image of the labels.

Because they are similar triangles, angle A is the same as angle A'. Angle B is the same as angle B', angle C is the same as angle C'.

Based on that information, we know xº is = 65º. We know that the interior angles add up to 180º. So for triangle A'B'C', we can do 180º-40º-65º which is 70º. This means angle C' is 70º.

Now the important part is getting yº. A line is 180º. That means that 180º-70º=yº which is 110º.

If you do not understand anything, please let me know and I will try to teach you.

The value of the text statistic. F  is given as : 0.742 See explanation below.

A test statistic is a numerical value determined by a statistical test.

It quantifies the distance between your observed data and the null hypothesis of no link between variables or no difference between sample groups.

Test Statistic F is given by:

= σ²₁/σ²₂

= 0.93²/1.08²

= (0.93/1.08)²

= 0.8611²

= 0.742

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The simplified expression for h(x) = f(x)/g(x) is [tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex] and the domain of the function is all real numbers except x = 2/3.

In this problem we have a rational function, the domain of rational functions is the set of all real numbers except the values such that the denominator becomes zero. First, we need to simplify the division of two rational functions:

[tex]h(x) = \frac{\frac{3\cdot x^{2} + 17\cdot x + 20}{3\cdot x^{2} + 10\cdot x - 8} }{\frac{3 \cdot x^{2} + 8\cdot x + 5}{x^{2}-3\cdot x - 4} }[/tex]

[tex]h(x) = \frac{(3\cdot x^{2}+17\cdot x + 20)\cdot (x^{2}-3\cdot x - 4)}{(3\cdot x^{2}+10\cdot x - 8)\cdot (3\cdot x^{2}+8\cdot x + 5)}[/tex]

[tex]h(x) = \frac{1}{3}\cdot \frac{\left(x^{2}+\frac{17}{3}\cdot x + \frac{20}{3} \right)\cdot (x^{2}-3\cdot x - 4)}{\left(x^{2}+\frac{10}{3}\cdot x -\frac{8}{3}\right)\cdot \left(x^{2}+\frac{8}{3}\cdot x +\frac{5}{3} \right)}[/tex]

[tex]h(x) = \frac{1}{3}\cdot \frac{\left(x + \frac{5}{3} \right)\cdot (x+4)\cdot (x - 4)\cdot (x+ 1)}{\left(x-\frac{2}{3} \right)\cdot (x + 4)\cdot (x + 1)\cdot \left(x + \frac{5}{3} \right)}[/tex]

[tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex]

The simplified expression for h(x) = f(x)/g(x) is [tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex] and the domain of the function is all real numbers except x = 2/3.

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Answer:

Step-by-step explanation:

hello :

x² +5x+3=0

delta = b²-4ac   when :  a =1  and b=5    c=3

delta =5²-4(1)(3) =13

X1 =(-b-sqrt(delta))/2a

X2 =(-b+sqrt(delta))/2a

continu.....

Answer: A

Step-by-step explanation: add 6 on each side you get 2p+3>13 then subtract 3 you get

2p> 10 divide by 2 you get p>5

Using the Empirical Rule, it is found that:

a) 68% of the widget weights lie between 35 and 57.

b) The percentage is 81.5%.

c) The percentage is 99.85%.

It states that, for a normally distributed random variable:

For this problem, we have that:

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area = 25.5 cm²

Step-by-step explanation:

i have shown in the image you have to rotate it to see how i worked the area out

i am very sorry i cant work the perimeter out since i have no idea what the length of the two sides of the triangle are . if you need help on understanding how i worked out the area please let me know .

hopefully i was able to help you in half of the question i am sorry for not helping on the perimeter :)

Answer:

Step-by-step explanation:

Perimeter=25

The margin of sampling error is obtained by multiplying the standard error with the critical value.

The margin of sampling error is a statistic that tells a researcher by how many percentage points the result gotten from the sample value would differ from that of the population. This value is obtained by multiplying the standard error with the critical value.

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The measure of the missing length from the given diagram is 25

According to the theorem, the altitude on the hypotenuse is equal to the geometric mean of line segments formed by altitude on the hypotenuse.

According to the given diagram, the expression below will be used to determine the value of x

x/60 = 60/144

Cross multiply yo have:

144x = 60 * 60

Simplify the result to have

144x = 3600

Divide both sides by 144

144x/144 = 3600/144
x = 3600/144

x = 25

Hence the measure of the missing length from the given diagram is 25

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[tex]5-3=2\\\\6-10=-4\\\\11.6-3=8.6\\\\63-4\times 5=63-20=43[/tex]

So, the first, second, and fourth equations are integers.

The first and last are positive integer and second is negative integer.

Integers come in three types:

Given:

a) 5-3 =2

b) 6-10 = -4

c) 11.6 - 3 =8.6

d) 63 - 4 x 5 =63- 20 = 43

So, among the above first and last are positive integer and second is negative integer.

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The probability that it will have an annual snowfall greater than 170 inches is 0.4.

The information is incomplete and the complete question wasn't found. An overview will be given. It should be noted that a probability means the likelihood of the occurence of an event.

Probability is calculated as:

= Number of ways of achieving success/Total number of possible outcomes

Let's assume that the total number of resort is 10 and those that have more than 170 inches are 4.

In this case, the probability will be:

= 4/10

= 0.4

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The given numbers written in standard forms are

1.0 × 10⁷

1.0 × 10⁵

1.0 × 10⁸

1.0 × 10¹²

1.0 × 10⁶

respectively

From the question, we are to write the given numbers in standard form

To write the given numbers in standard form,

Multiply each of the numbers by 1.0

Then,

10⁷ in standard form is 1.0 × 10⁷

10⁵ in standard form is 1.0 × 10⁵

10⁸ in standard form is 1.0 × 10⁸

10¹² in standard form is 1.0 × 10¹²

10⁶ in standard form is 1.0 × 10⁶

Hence, the given numbers written in standard forms are

1.0 × 10⁷

1.0 × 10⁵

1.0 × 10⁸

1.0 × 10¹²

1.0 × 10⁶

respectively

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Answer:

Answer:

Step-by-step explanation:

A right triangle with one acute angle measuring 30° is the 30°-60°-90° "special" triangle. The ratios of its side lengths are well known to be ...

  1 : √3 : 2

In the given triangle, the longest side is labeled 10, so is 5 times the measure of the longest side in the ratios given above. Multiplying those ratio values by 5, we have side lengths ...

  a : b : c = 5 : 5√3 : 10

That is ...

  a = 5

  b = 5√3

__

Additional comment

If you want to figure the side lengths using trigonometry, you have ...

  a = c·sin(30°) = 10·(1/2) = 5

  b = c·cos(30°) = 10·(√3/2) = 5√3