What is 72 decreased by 32%

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 exponential growth function is P(t) = 6.38 million x (1.0238^t).

The population of the city in 2018 is 7.35 million.

The year the population would be 9 million is 14.46 years.

The doubling time is 29.12 years.

FV = P (1 + r)^n

6.38 million x (1.0238^t)

Population in 2018 = 6.38 million x (1.0238^6) = 7.35 million

Number of years when population would be 9 million : (In FV / PV) / r

(In 9 / 6.38) / 0.0238 = 14.46 years

Doubling time = In 2 / 0.0238 = 29.12 years

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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 !!!

Answer:

17/9

Step-by-step explanation:

Plug in 1/3 as m.

2*(1/3)^2 - 4(1/3) + 3 = 17/9

Answer:

All the correct statements are,

The vertex of the graph is (5, -37).

The parabola has a minimum.

The parabola opens up.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The function g(x) = 10x² - 100x + 213 written in vertex form is,

⇒ g(x) = 10(x – 5)² – 37.

Since, General equation is,

y = a (x - h)² + k

Where, (h, k) is vertex of parabola.

Hence, We get;

The vertex of the graph is (5, -37)

Since, the coefficient of x² is positive

Hence, The parabola has a minimum

And, The parabola opens up.

Thus, All the correct statements are,

The vertex of the graph is (5, -37).

The parabola has a minimum.

The parabola opens up.

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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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Answer:

watch oreimo..

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

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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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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[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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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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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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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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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

It would cost $72,000 for 7 units of that product.

The term “discount” refers to the pricing system in which the price of a commodity (goods or services) is lower than its marked price listed price. It is simply to say, 'discount' is a percentage of the listed price. A discount is a kind of price deduction in products that is noticed in consumer transactions, where the buyers have proposed a percentage of rebates on various products in order to boost sales. This rebate offered by the seller to buyer is known as a discount.

Original cost of product = $15,000.

For the second product there is a discount of 15%, thus selling price for the second product = $15,000 x 0.85 = $12750

For the fourth product and on there is a discount of 30%, thus selling price for the fourth product and on = $15,000 x 0.70 = $10500.

Thus total price of 7 units =  $15,000 + $12750x2 + $10500x3

=   $15,000 +   $25,500 + $31500

= $72,000

Thus it would cost $72,000 for 7 units of that product.

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The solution to the equation [tex]3p^2-9p-6=0[/tex] are p = 1, p = 2

The given equation is:

[tex]3p^2-9p=6[/tex]

This can be re-written as:

[tex]3p^2-9p-6=0[/tex]

Solve for p by factorization

[tex]3p^2-3p-6p+6=0\\\\3p(p-1)-6(p-1)=0\\\\(3p-6)(p-1)=0[/tex]

Equate each of the factors to zero

3p - 6 = 0

3p = 6

p = 6/3

p = 2

p - 1 = 0

p = 1

Therefore, the solution to the equation [tex]3p^2-9p-6=0[/tex] are p = 1, p = 2

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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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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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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.

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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The equations which represents the minimum and maximum scores of the students is; x = 87 ± 1.8.

According to the task content, the

Average score of the students in the science class is; 87 points

All students are within 1.8 points of the average,

it therefore follows from the task content that the

minimum score is;

= 87 -1.8

= 85.2

maximum score is;

= 87+1.8

= 88.8 points.

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Answer:

Step-by-step explanation:

A. |x − 87| = 1.8

-hope this helps.

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.....

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:

the ans is 9000

Step-by-step explanation:

simple interest= 60000*3*5/100

Answer:

2358.1

Step-by-step explanation:

2.3581 x 10^3

= 2.3581 x 10000

=2358.1

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

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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