\(f(x) = 16 + \sqrt[3]{x} \\ f {}^{ - 1} (x) = \)Inverse function

Answer:

? = 77°

Step-by-step explanation:

the 3 angles in a triangle sum to 180° , that is

? + 35° + 68° = 180°

? + 103° = 180° ( subtract 103° from both sides )

? = 77°

Answer:77

Step-by-step explanation:

180-103=77

The equilibrium point for James T-shirt business is (P, Q) = (7, 24).

To find the equilibrium point (P, Q) for James T-shirt business

we need to set the demand function equal to the supply function and solve for the values of P and Q.

Demand function: P = -Q + 31

Supply function: P = Q - 17

Setting them equal:

-Q + 31 = Q - 17

Adding Q to both sides and subtracting 31 from both sides:

2Q = 48

Dividing both sides by 2:

Q = 24

Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.

P = Q - 17

P = 24 - 17

P = 7

Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).

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Using proportions, it is found that the club needs to sell at least 832 tickets to make their desired profit.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The prize is of €58, with the event making a profit of €150, hence the amount of money they have to earn from tickets is given by:
A = 150 + 58 = €208.

The tickets are sold at €0.25, hence the number of tickets they have to sell is:

n = 208/0.25 = 208 x 4 = 832.

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Examining the word problem we can say that, Molly used 160 beads to make the necklace.

Let's assume the number of beads used to make the bracelet is x.

We also know that Molly used a total of 192 beads for both the necklace and the bracelet. and It takes 5 times as many beads to make a necklace as it does a bracelet, So,

x + 5x = 192

6x = 192

solve for x

x = 192 / 6

x = 32

Molly used 32 beads to make the bracelet.

number of beads used to make the necklace

Number of beads used for the necklace = 5 * 32

Number of beads used for the necklace = 160

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Answer:

8 is the correct answer

The value of p is 15

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: Davey reads 58 pages on Saturday and on rest of the days p pages per day

Therefore everyday he reads 58+p pages per day

If he reads for 10 days and he reads a total 1408 pages then we have

In a week there is one Saturday

thus

9p+58=1408

9p=1350

p=15

Thus on the other days p is equal to 15 pages per day.

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The complete question is Davey reads 58 pages on Saturday and p pages on other days and on a span of 10 days he reads 1408 pages. Find the value of p.

The union of two subspaces of V is a subspace of V if and only if one of the subspaces of v is contained in the other

Let \($V_1, V_2$\) be the two subspaces of V. Suppose \($V_1 \cup V_2$\) is a subspace of V.

Then if \($x_1 \in V_1$\) and \($x_2 \in V_2$\) then we must have \($x_1 \in V_1 \cup V_2$\) and\($x_2 \in V_1 \cup V_2$\) so that we must have \($x_1+x_2 \in V_1 \cup V_2$\).

If and only if one of the subspaces is contained in the other, the union of the two subspaces is a subspace.

But this by definition means \($x_1+x_2 \in V_1$\) or \($x_1+x_2 \in V_2$\). Either way, by the existence of additive inverses and the closure properties for the subspaces we have:

\(\left(x_1+x_2\right)+\left(-x_1\right) \in V_1\)

Or

\(\left(x_1+x_2\right)+\left(-x_2\right) \in V_2\)

By the associative/commutative properties, we have:

\(x_2 \in V_1 \text {, or, } x_2 \in V_1\)

Thus we have shown if \($x_1 \in V_1$\) and \($x_2 \in V_2$\) then \($x_1 \in V_2$\) or \($x_2 \in V_1$\). If \($x_1 \in V_2$\) for all \($x_1 \in V_1$\) then we have \($V_1 \subseteq V_2$\). If \($x_2 \in V_1$\) for all \($x_2 \in V_2$\) then \($V_2 \subseteq V_1$\). In either case, we see one subspace is a subset of the other.

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Answer:

6

Step-by-step explanation:

Given that 4 points lie in a plane so that no 3 points of them lie on a line.

Let A, B, C, and D are four points as shown in the figure.

One line to be drawn, only 2 points are needed.

As no 3 points are collinear, so the number of combination of 2 points among the total 4 points gives the number of lines can be drawn.

As the total number of combinations of \(r\) elements, taken at a time, among \(n\) elements are

.

So, the required number of lines

\(=\binom{4}{2}=\frac{4!}{2!\times(4-2)!}=\frac{4!}{2!\times2!}=\frac{4\times3\times2\times\1}{2\times1\times2\times1}=6\)

All the 6 possible lines can be verified from the figure.  

In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.

A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.

Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.

From the data given:

a.

In calculating the factor A variation, there are two degrees of freedom.

In determining the variation of factor B, there are two degrees of freedom.

b.

Finding the degree of freedom using the interaction variation, there are four degrees of freedom.

c.

In finding the random variable, there are 9(4-1) = 27 degrees of freedom.

d.

In calculating the total variable, there are 9*4-1 =35 degrees of freedom.

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Answer:

x = -5

Step-by-step explanation:

Original equation:

2(2x - 7) = -34

Use distributive property

2 · 2x = 4x

2 · (-7) = -14

Plug these values back into the equation

4x - 14 = -34

Add 14 to both sides

4x = -20

Divide both sides by 4

x = -5

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Answer:

Step-by-step explanation: 21

Answer:

C

Step-by-step explanation:

Given

x + 10 = 3(x - 1)² ← expand (x - 1)² using FOIL

x + 10 = 3(x² - 2x + 1) ← distribute

x + 10 = 3x² - 6x + 3 ← subtract x + 10 from both sides

0 = 3x² - 7x - 7 → C

Answer:

Step-by-step explanation:

The expression with a rational exponent as a radical expression is \(\sqrt[9]{3}\). Therefore, option B is the correct answer.

The given expression is \((3^{\frac{2}{3} } )^{\frac{1}{6} }\).

Rational exponents are exponents of numbers that are expressed as rational numbers, that is, in \(a^\frac{p}{q}\), a is the base and p/q is the rational exponent where q ≠ 0.

Now, the given expression can be solved as follows:

Using power law \((a^m)^n=a^{m\times n}\), we get

\((3^{\frac{2}{3} } )^{\frac{1}{6} }=3^{\frac{2}{3}\times \frac{1}{6}}\)

\(=3^{\frac{1}{9} }\)

The equivalent expression to \(=3^{\frac{1}{9} }\) is \(\sqrt[9]{3}\).

The expression with a rational exponent as a radical expression is \(\sqrt[9]{3}\). Therefore, option B is the correct answer.

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Answer:

22

Step-by-step explanation:

64+20= 84 (number of students in total)

84/2= 42 (number of students each session)

Moving 22 students to Monday will result in equal number of students.

There are many property in mathematics like Reflexive Property, Substitution Property or Addition Property. Therefore option A is correct option

According to reflexive property,  for every real number x , x=x. According to substitution property, if  x=y , then we can replace y with x in any equation or expression. According to additive property if we add zero to any number then we get the same number back. According to subtraction property if we substract zero from any number we get the same number back

JK+LM=NP+LM

According to our questions, since LM is same on both sides of equations so same thing can be cancelled out on the left and right hand side of equation so LM can be cancelled from both side

Hence we are left with

JK=NP

This property is called reflexive property. Therefore option A is correct option

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√36 indicates the principal (or positive) square root so √36=6 .

The square root of √36 is 6.

Hope this helps ! <3

Answer: 2,16

Step-by-step explanation:

The missing statement is the quadratic formula and the correct option therefore is the third option;

The quadratic formula is used to find the solution of a quadratic equation. The quadratic formula is; \(x = \frac{-b\pm\sqrt{b^2-4\cdot a\cdot c} }{2\cdot a}\)

The statements and reasons can be presented algebraically as follows;

Statements \({}\)                                          Reasons

\(x^2+\frac{b}{a}\cdot x+(\frac{b}{2\cdot a} )^2 = -\frac{4\cdot a\cdot c}{4\cdot a^2}+ \frac{b^2}{4\cdot a^2}\)        Find a common denominator on the

                                                            right side of the equation

\(x^2 + \frac{b}{a} \cdot x+(\frac{b}{2\cdot a} )^2 = \frac{b^2-4\cdot a \cdot c}{4\cdot a^2}\)                 Add the fractions together on the

                                                     \({}\)        right side of the equation

\((x +\frac{b}{2\cdot a} )^2 = \frac{b^2 - 4\cdot a \cdot c}{4\cdot a^2}\)                             Rewrite the perfect squared equation

                                                      \({}\)      to the left side of the equation as a

                                                        \({}\)    binomial squared

\(x + \frac{b}{2\cdot a} = \pm\sqrt{\frac{b^2 - 4\cdot a \cdot c}{4\cdot a^2} }\)                   Take the square root of both sides of  the

                                                    \({}\) equation

\(\underline{x = \frac{-b\pm\sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}}\)                                 Simplify the right side of the equation    

The correct option is therefore;

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Answer:

A

Step-by-step explanation:

i took the test

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The observational study is the Cross-sectional studies.

It should be noted that an observational study is simply used to answer a research question that is based on what the researcher observes.

This is a cross-sectional studies because it analyzes a population of study at a specific point in time. It should be noted that this involves narrowing previously collected data to one point in time to test the prevalence of a theory.

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Answer:

4:3

Step-by-step explanation:

ratio of H20 to Oil = (Amount of H20) / (Amount of Oil) = (2/3 cup)/(1/2 cup) =

(2/3) / (1/2) = (2/3) * (2/1) = 4/3 = 4:3

The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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Total no. of births = 2000

Births of girls = 64

Birth% of girls

\( = \frac{64}{2000} \times 100\)

\( = \frac{64}{20} \)

\( = \frac{6.4}{2} \)

\( = 3.2\%\)

Hence, the number of girls are significantly low.

9514 1404 393

Answer:

  A. parabola

Step-by-step explanation:

The curves ellipse, circle, and hyperbola are formed by a relation between the squares of the variables. Here, the y-variable is squared, but the x-variable is not. This equation describes a parabola.

_____

Additional comments

Its vertex is at (4, 4) and it is compressed horizontally by a factor of 9.

__

The hyperbola equation is the difference of squares; the circle and ellipse equations involve the sum of squares. If the variable coefficients are the same, then the sum of squares equation will describe a circle; an ellipse otherwise.

Step-by-step explanation:

20 ml is your answer

i hope it helps u

Answer:

If I'm reading it correctly the answer should be 20.

To get that answer all you do is 4x5.

Complete Question:

A small jet can carry up to 41 passengers and 3 crew members. There is a weight restriction of 9200 pounds on board. The combined weight of each passenger (or crew member) and his luggage has a mean of 197.9 pounds, with a standard deviation of 64.1 pounds. What is the probability that the weight limit will be exceeded when there are exactly 41 passengers and 3 crew members on board? Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.

Answer:

The probability that the weight limit will be exceeded when there are exactly 41 passengers and 3 crew members on board is;

0.253

Step-by-step explanation:

a) Data and Calculations:

Capacity of the small jet = 41 passengers and 3 crew members = 44

Weight restriction = 9,200 pounds

Mean of the combined weight of passengers and crew = 8,707.6 (44 * 197.9) pounds

Weight's standard deviation = 2,802.4 (44 * 64.1) pounds

Excessive weight total = 11,528 (8,707.6 + 2,802.4)

Excess weight = Excessive weight total minus Total Weight Restriction

=2,328 (11,528 - 9,200)

Probability of exceeding weight limit = Excess weight/Weight restriction

= 2,328/9,200

= 0.253

The x-coordinates where the graphs of the equations intersect are x = -1 and x = 3

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

y = 2x

y = x² - 3

The x-coordinates where the graphs of the equations intersect is when both equations are equal

So, we have

x² - 3 = 2x

Rewrite the equation as

x² - 2x - 3 = 0

When the equation is factored, we have

(x + 1)(x - 3) = 0

So, we have

x = -1 and x = 3

Hence, the x-coordinates are x = -1 and x = 3

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Question

From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.

y = 2x

y = x² - 3

well, to do this we first need to find the mean of all values.

we need to find the distance of each value from that mean (subtract the mean from each value, ignore minus signs)

Then find the mean of those distances.

so, after we do all of that with the given numbers, our final result would be 2.333333333..... (It goes on) we round it up to 2.3, and viola! the answer is C.

Answer: the answer is c

Step-by-step explanation: i took the test