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2 by the power of 3 times 2= what


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The value of the variable 'x' is 10. Then the measure of angle ∠2 is 113°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

If angles ∠1 and ∠2 form a linear pair, m∠1 = (7x - 3) and m∠2 = (12x - 7). Then the equation is given as,

∠1 + ∠2 = 180

7x - 3 + 12x - 7 = 180

Simplify the equation, then we have

7x - 3 + 12x - 7 = 180

19x = 190

x = 10

Then the measure of angle ∠2 is calculated as,

∠2 = 12(10) - 7

∠2 = 120 - 7

∠2 = 113°

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Answer:

Van Dressler's total sales amount is $12,166.6666667

Step-by-step explanation:

3% = $365

365/3*100 =$12,166.6666667

The number of commercials and movies on which the songs were played are 5 and 2.respectively

From the question, we have the following parameters that can be used in our computation:

The number of commercials is x, and the number of movies is y

The above parameters when represented as an equation is as follows

40x + 120y = 440

x = y + 3

Substitute x = y + 3 in 40x + 120y = 440

40(y + 3) + 120y = 440

Expand

40y + 120 + 120y = 440

Evaluate the like terms

160y = 320

Divide by 160

y = 2

Recall that

x = y + 3

So, we have

x = 2 + 3

x = 5

Hence, the number of commercials is 5 times

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Answer:

100

Step-by-step explanation:

x^3 = 1,000,000  Find the cube root of 1,000,000

x^3 = 1.0x10^6     Using scientific notation, we can split the 1,000,000 into a 1.0 and a factor of 10*10*10*10*10*10 or 10^6

x = 1.0x10^2         The cube root of 1.0 is 1.0.  The cube root of 10^6 is found by dividing the exponent by 3:  10^2

The cube root of 1,000,000 is 1.0X10^2, or 100.

x = 100

True, with a probability sample, the researcher has some savings in cost and/or time but at the expense of using a sample that is not truly representative of the population

Probability sampling refers to the selection of a sample from a population when this selection is based on the principle of randomization, that is, random selection or chance. Probability sampling is more complex, more time-consuming, and usually more costly than non-probability sampling. However, because units from the population are randomly selected and each unit’s selection probability can be calculated, reliable estimates can be produced and statistical inferences can be made about the population.

In a probability sampling method, in order to reduce cost and/or time, researchers resort to a selection process that is inherently biased. As a result, they use a sample for research that is not truly representative of the population.

So,the answer is true, with a probability sample the researcher has some savings in cost and/or time but at the expense of using a sample that is not truly representative of the population

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We can solve this question using the concept Sets and Relations . The complement of set A is (1,3,5,7,9).

A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the objects x and y come from different sets, then the objects are said to be connected. Sets are collections of clearly defined objects, relations show connections between individuals in two sets A and B, and functions are a special kind of relation where each element in A has exactly one relationship (or no more than one) with each element in B.

So the given universal set S contains all positive  integers less than 10.

  So S={1,2,3,4,5,6,7,8,9}

  Set A={2,4,6,8}

Complement of Set A is nothing but the elements missing in the Set A.

  so complement of Set A= {1,3,5,7,9}

We can solve this question using the concept Sets and Relations . The complement of set A is (1,3,5,7,9).

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The values (-7.5)-21.04 and (-7.5)+21.04 are not the same

A decimal can be defined as a number consisting of a whole number and also a fractional part.

These numbers are separated by a dot known as the decimal point

The decimal numeral system is seen as a standard system that denotes integer and non-integer numbers.

It is important to note the following operations;

From the information given, we have;

(-7.5)-21.04

Multiply the operation

+ 157. 8

Then,

(-7.5)+21.04

Multiply the operation

- 157. 8

Hence, the values are either negative or positive.

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Adult tickets cost $8.25 and children ticket is $6.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

Let adult tickets = a

Let children tickets = c

Since Johnny bought 4 adult tickets and 8 children tickets for $81. Leslie bought 2 adult

tickets and 2 children tickets for $28.50.

This will be:

4a + 8c = 81 ....i

2a + 2c = 28.50... ii

From equation ii a + c = 14.25

a = 14.25 - c

Put this into equation I

4a + 8c = 81 .

4(14.25 - c) + 8c = 81

57 - 4c + 8c = 81

4c = 81 - 57.

c = 6

Since a = 14.25 - c

a = 14.25 - 6.

a = 8.25

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The expression  5w + 2w²   represents the area, in square feet, for each cabin size

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

Area of a rectangle = length * width = l*w

length is equal to 5 feet more than twice the width.

=> l= 5+2w

So, area = ( 5+2w  ) *w

             = 5w + 2w²  

Thus, the expression  5w + 2w²   represents the area, in square feet, for each cabin size

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Answer: 12=2

x y =3 so 2x3+2x3=12 (2x3 = 6) so 6+6=2 6+6=12 so therefore 12=2

The value of  h’(1) is = 22

How may the chain rule example be used?

Solution: Since f′(x)=ex, the exponential function with base e's derivative is simply the function itself. G′(x)=4 is the derivative of g. The chain rule states that h′(x)=f′(g(x))g′(x)=f′(4x)4=4e4x. It was crucial that we assessed f's derivative at 4x in this example.

Given that :

h(x) = 2f(x).g(x)

f(1) = 3, g(1) = 2, f’(1) = 4, g’(1) = 1

h’(x) = 2 f'(x)g(x) + g'(x)f(x) by chain rule

h’(1) = 2 f'(1)g(1) + g'(1)f(1)

= 2 * (4 * 2 + 1 * 3)

= 2* (11)

= 22

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The inequality to describe the possible side length for the third side is  5 < x ≤ 23.

What is the inequality of a triangle?

According to the triangle inequality theorem, the sum of any two sides of a triangle is greater than or equal to the third side of a triangle. This statement can symbolically be represented as; a + b > c. a + c > b.

The triangle inequality tells that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

We have given,

Two sides of a triangle have lengths 9 and 14.

The third side is represented by x.

So by triangle inequality, we have the following inequality:

x ≤ 9 + 14

x ≤ 23

Also, the difference between the lengths of any two sides of a triangle is less than the length of the third side.

14 - 9 < x

5 < x

Hence, the inequality to describe the possible side length for the third side is 5 < x ≤ 23.

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The rocket hit the ground is 6.3 sec.

The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.

A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.

To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:

h = -5*t2 + 30*t + 10

h = -5(2)2 + 30(2) + 10

h = -5(4) + 30(2) + 10

h = -20 + 60 +10

h = 50 m

The height of the rocket 2 seconds after launching it is 50 meters.

To find the x-coordinate of the vertex of a parabola, we use the formula:

t - 3 = ± √(11)

t = 3 ± √(11)

t = 3 ± 3.3

Solving for t, we get two solutions:

t = 3 - 3.3

t = -0.3 sec

and

t = 3 + 3.3

t = 6.3 sec

Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.

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The park's total water use when the new attraction is built will be 2406.8  × 10³gallons.

Logic is the manipulation of mathematical signifiers, whereas algebra is the study of those signifiers.

The PEMDAS concept stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This guideline must be adhered to in order to provide an accurate solution to the issue.

Total water consumption for a water park's pools, slides, and other features is 2.4 *10⁶ gallons. A ride that would use an additional 6.8 × 10³gallons of water is planned.

Following the completion of the new attraction, the park will have utilized a total of

⇒ 2.4 × 10⁶ + 6.8 × 10³

⇒ 2400 × 10³ + 6.8 × 10³

⇒ 2406.8 × 10³

After the new attraction is constructed, the park will have used 2406.8 × 10³ total gallons of water.

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What is true about the individual angles that are linear pairs is that; They are right angles

Linear pairs is also called supplementary angles and it means that both angles sum up to 180 degrees.

Now, we are told that Dave constructed two angles that are congruent to each other. Now, if both angles are congruent to each other, then it means that they are equal and since they are linear pairs, they still sum up to 180 degrees.

If we denote these congruent angles as x, then it means that;

x + x = 180

2x = 180

x = 180/2

x = 90°

Thus, we can say that both of the angles are right angles.

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Answer:

Step-by-step explanation

The slope intercept form is M=y2-y1 over x2-x1.

The answer for the equation is 12/3. 3 goes into 12 four times, so the answer is 4.

the area of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8 is 9, using the concept of area under the curve.

The region between a curve and the -axis is referred to as the "area under a curve." This region may be wholly above the -axis, entirely below the -axis, or somewhere in between. The area under a curve in calculus is a picture of an integral.

The region enclosed by the curve, the axis, and the boundary points is referred to as the "area under the curve." Using the coordinate axes and the integration formula, the area under the curve has been determined as a two-dimensional area. The area of the asymmetric plane form in a two-dimensional array is provided by the region beneath the curve.

The region bounded by the lines y = 5 and 2y + 4x = 8 and the curve

2y = 4√x

Now, finding the intersecting point between 2y + 4x = 8 and 2y = 4√x

so, 4√x + 4x = 8

or,  √x + x = 2

or, √x = (2 - x)

or, x = (2 - x)²

or, x = x² - 4x + 4

or, x² - 5x + 4 = 0

or, ( x - 4) ( x - 1) = 0

or, x = 4, 1

when x = 4 then y = 2√4 = 4

when x = 1 then y = 2 √1 = 2

when y = 4 and x = 4 then equation 2y + 4x = 8 is not satisfied.

Thus, only intersection point is: (1,2)

This is the type (II) region.

So, integrate the region with respect to y.

Now, area =

= [tex]\int\limits^5_2 {(y/2)^2 - ((8-2y) / 4)} \, dy[/tex]

= [tex]\int\limits^5_2 {[(y^2/4) -2 + (y/2)]} \, dy[/tex]

= [tex]\frac{1}{4} [y^3/3]^5_2 - 2 [y]^5_2 + \frac{1}{2} [y^2/2]^5_2[/tex]

= [tex]\frac{117}{12} - 6 + \frac{21}{4}[/tex]

= [tex]\frac{108}{12}[/tex]

= 9

Thus, area = 9 of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8.

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The f-distribution's curve is positively skewed. Hence, the statement is true.

We have to check whether the statement is true and false.

The given statement is "The f-distribution's curve is positively skewed."

We can compare two populations using a F statistic thanks to the F distribution. The F distribution can be used to detect whether there is a significant difference in the variance between the means of two populations for ANOVA testing. Regression analysis can also make use of the F distribution to assess how well various models fit together.

The F distribution's graph is always positive and slanted to the right, while the form might vary based on the numerator and denominator degrees of freedom.

The f-distribution's curve is positively skewed. Hence, the statement is true.

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On closely observing and solving the Probability it can be stated that  the batter will hit around 3 balls out of the next nine balls

What is Probability?

The ratio of the number of outcomes in an exhaustive collection of equally probable options that create a particular event to the entire number of conceivable outcomes.

Solution:

Average of Batter is 0.303 which means that the batter hits 303 shots of 1000 balls

So, in the next nine balls he will hit 9 * 303/1000 = 2.7 balls

Which means the batter will hit around 3 balls

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The point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.

The point estimate of P, is defined as the proportion of successes in the sample.

P' = X/N ; where X = number of successes; N = total trials.

Here, N = 1000

According to the Child outlook file, number of "yes" = 240.

Hence, P' = 240/1000

P' = 0.24

Therefore, the point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.

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Mitchell's family will take 4 1/8 hours of time to cook the meat.

Maltiplication is reffered as adding multiple times. It is a one of the fundamental Mathematical operation. The symbol '×' used to denote the Maltiplication.

We use Multiplication to simplify the addition of the same number multiple times.

Here in this problem we use multiplication to solve the problem.

Here we have

Mitchell's family is slow cooking 2 and 3-fourths pounds of meat.

=> 2 and 3-fourth = 2 3/4 = 11/4 pounds of meat

The recipe says to cook the meat for 1 and a half hours per pound

For 1 pound of meat = 1 and 1/2 hours = 3/2 hours

The time required to cook 11/4 pounds = (11/4)(3/2) hours

= [tex]\frac{11}{4} (\frac{3}{2})[/tex] = [tex]\frac{33}{8}[/tex] = 4 (1/8) hours  

Therefore,

Mitchell's family will take 4 1/8 hours of time to cook the meat.

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The function is given as g(n) = -n + 5 then the value of g(1) is 4. the correct option is B.

Function is a type of relation, or rule, that maps one input to specific single output. . Simplification usually involves making the expression simple and easy to use later.

The procedure in mathematics to utilize and analyze the function or expression to make the function or expression uncomplicated or more coherent is called simplifying and the process is called simplification.

From the given function, g(n) = -n + 5

By plugging in the value of 'x' in the bracket, we have;

g(n) = -n + 5

g(1) = -1 + 5

g(1) = 4

Therefore, the value of function is 4.

Hence, the correct option is B.

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At 5 percentage significance level, we have sufficient evidence to conduct that μ is less than 20.

After getting excellent news, people often behave more generously. After receiving negative news, do they become less giving? Adult Americans tip 20% of the whole bill on average. Give 20 diners a notice on their bill informing them that the weather is going to be poor tomorrow, and then keep track of the tip % they left. The tips are shown in Table 1 as a percentage of the total bill.

Table :  18.0 19.1 19.2 18.8 18.4 19.0 18.5 16.1 16.8 18.2 14.0 17.0 13.6 17.5 20.0 20.2 18.8 18.0 23.2 19.4

Suppose that tip percentage is Normal with ? = 2 and assume that the patrons in this study are a random sample of all patrons of this restaurant. Is there good evidence that the mean tip percentage for all patrons of this restaurant is less than 20 when they receive a message warning them of tomorrow’s bad weather? State [tex]H_{o}[/tex] and [tex]H_{a}[/tex] and carry out a significance test. Use significance level 0.05.

The given data is :

18.0, 19.1, 19.2, 18.8, 18.4, 19.0, 18.5, 16.1, 16.8, 18.2, 14.0, 17.0, 13.6, 17.5, 20.0, 20.2, 18.8, 18.0, 23.2, 19.4

Therefore, sample mean,

X = ∑x / n

X = [tex]\frac{18+19.1+19.2+19.3+....19.5}{20}[/tex]

X = 18.19

Now test : μ  < 20 with normal distance

Hypothesis test:

[tex]H_{o}[/tex] = μ ≥ 20

[tex]H_{a}[/tex] = μ ≤ 20

This is the lower tailed test.

X = 18.19

σ = 2

n = 20

Significant level, α = 0.05

Test statistics,

z = ( X-μ ) / (σ / [tex]\sqrt{n}[/tex] )

z = [tex]\frac{18.19-20}{2\sqrt{20} }[/tex]

z = -4.05

P value is in direction of alternative hypothesis or [tex]H_{a}[/tex]

Since,  [tex]H_{a}[/tex] ≤ 20 P value = P(Z<-4.05)

P value is the area to the left of the test statistics = -4.05 (from the figure)

P value = P(Z< -4.05) = 0.000 (from z table)

P value = 00000

Rejection rule : Reject  [tex]H_{o}[/tex]  if P value < α

Using excel functional normdist (   [tex]\frac{18.19-20}{2\sqrt{20} }[/tex] , 0 , 1 , TRUE ) or TI's function normaldf ( 1E-99 ,   [tex]\frac{18.19-20}{2\sqrt{20} }[/tex] )  answer is 0.0000259078

Decision : Since 0.0000 < 0.05, we reject the null hypothesis

Therefore,

At 5 percentage significance level, we have sufficient evidence to conduct that μ is less than 20.

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In order to regain the amount of water Joe losed during practice he should drink 10 cups of water.

A pound is equivalent to 453.59 mg, whereas a cup is equivalent to 236.59 ml.

You may roughly calculate that 2 cups equal 1 pound of water. The density should be 1 mg/ml if the fluid is mostly water.

The number of cups will be,

6 pounds * 453.59 (mg/pounds) * (1mg/ml) / (236.59 ml/cups)

= 10 cups .

Water is a crucial component for all living things, including people and other animals. Naturally, the water must go somewhere when it ascends the plant. Water loss will result from water evaporation (transpiration in plants)

Our breath, skin, urine, and sweat all cause water loss. A person's body will typically consume 2.5 L of water every day and expend the same amount. Your body will "inform you" you are thirsty and need to drink water if you get dehydrated (Figure 5). You have undoubtedly also noticed that when you drink less water, your pee is more concentrated.

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The equivalent exponential expression for the radical expression [tex]\sqrt{2 + 3}[/tex]

is [tex](2 +3)^{\frac{1}{2} }[/tex].

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent expression may not look the same but substituting the variables  will result to the same values.

Therefore, let's find the equivalent exponential expression for the radical expression can be found as follows:

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

Using exponential law,

[tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]

Therefore,

[tex]\sqrt{2+3} = (2 +3)^{\frac{1}{2} }[/tex]

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Answer:All I know is that it’s not < or > but It might be ≤

Step-by-step explanation: Bye the way, you can only give brainliest when there is two questions.

[tex]\leq[/tex]

Step-by-step explanation:

Function representing the sequence will be f(n) = (23 - 3n

The first five terms of an arithmetic sequence are as 20, 17, 14, 11, 8....

Let n represents the number of term and f(n) the the term in the sequence.

Then we have to find the function that represents the sequence.

As we know explicit formula of an arithmetic sequence is given by

Or the function representing the sequence will be

f(n) = a + (n-1)d

where a represents first term of the sequence a = 20

and common difference d = 17-20 = (-3).

Now the function which represents this sequence will be

f(n) = 20 + (n-1)(-3) = 20 - 3n + 3 = 23 - 3n

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Answer:

Step-by-step explanation:

Hope it helps!

If the company has made 6732.16 in³ wax , Total number of candles made is 67

According to the question,

It is given that a wax candle is in cylindrical shape

Diameter of candle = 4 in

Radius will be = 4 / 2

=> 2 in

Height of each candles = 8 in

Company has used 6732.16 in³ of wax

We have to calculate number of candles company has made

Volume of cylinder = πr²h

Where r is radius and h is height

Substituting all the values,

Volume of candle = π (2)² (8)

=> V = 3.14 × 4 × 8   (putting π = 3.14)

=> V = 100.48

Therefore , Number of candles made = Total volume /volume of one candles

=> 6732.16 / 100.48

=> 67 candles are made by company

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