Which of the following is a zero of 3x² + 5x - 2?

Answer:

1/16

Step-by-step explanation:

Rational Exponents can be rewritten as Radicals:

[tex](\frac{1}{8})^{\frac{4}{3}}=\sqrt[3]{\frac{1}{8}}^{4}[/tex]

Take the cube root of 1/8 = 1/2.

Raise (1/2) to the 4th power

Step-by-step explanation:

the numerator (top part) of a fractional exponent means "to the power of ...".

the denominator (bottom part) of a fractional exponent means "the ...th root".

so,

(1/8)^(4/3) means the cubic root of 1/8 to the power of 4.

these 2 operations can be done in any sequence.

it is the same if we first put 1/8 to the power of 4 and then get the cubic root, or if we first get the cubic root of 1/8 and then put that result to the power of 4.

to keep the numbers small, I prefer here to start with the cubic root :

cubic root (8) = 2, because 2³ = 8.

and so, cubic root (1/8) = 1/2

(1/2)⁴ = 1/16

that's it.

(1/8)^(4/3) = 1/16

The sum of the infinite geometric series 16 + 12 + 9 + ... is 64.

To find the sum of an infinite geometric series, you can use the formula:

sum =[tex]\frac a{(1 - r)}[/tex]

where "a" is the first term in the series and "r" is the common ratio between terms.

In this case, the first term is 16 and the common ratio is 3/4, so the sum is:

sum [tex]= \frac{16}{(1 - \frac{3}4)} =\frac{16}{(\frac{1}4)} = 64[/tex]

Therefore, the sum of the infinite geometric series 16 + 12 + 9 + ... is 64.

Note that this formula is only valid if the absolute value of the common ratio is less than 1. If the absolute value of the common ratio is 1 or greater, the series will either converge to a finite value or diverge to infinity, and the sum cannot be calculated using this formula.

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Answer:

Step-by-step explanation:

[tex]\displaystyle\\\frac{1}{2}z+6=\frac{3}{2}( z+6)[/tex]

[tex]\displaystyle\\Didtribute\ \frac{3}{2}:\ \frac{1}{2}z+6=\frac{3}{2}z+9[/tex]

[tex]\displaystyle\\Substract\ \frac{1}{2} z\ on\ each\ side:\ 6=z+9[/tex]

[tex]\displaystyle\\Substract\ 9\ on\ each\ side:\ -3=z\\\\[/tex]

[tex]z=-3[/tex]

The correct option B. two complex (nonreal) solutions, for the given quadratic equation.

The given quadratic equation is-

3x² + 4x = - 5

3x² + 4x + 5 = 0

So,  D = b² - 4ac

In which, b = 4, a = 3, c = 5

D = (4)² - 4(3)(5)

D = 16 - 60

D= -44

D < 0

2 complexes (nonreal) solutions are found for the given quadratic equation.

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The correct question is-

Use the discriminant to determine how many and what kind of solutions the quadratic equation 3x² + 4x = - 5 has.

A. one real solution

B. two complex (nonreal) solutions

C. no real or complex solutions

D. two real solutions

Considering the definition of parallel line, the line that contains the point (1, -1) and is parallel to y = 3x - 2 is y= 3x -4.

A linear equation o line can be expressed in the form y = mx + b

where

Parallel lines are two lines that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts.

In this case, the line is y= 3x -2

where:

Two lines are parallel if they have the same slope. So, the parallel line has a slope of 3.

The line passes through the point (1, -1). Replacing in the expression for a line:

-1= 3× 1 + b

-1= 3 + b

-1-3 = b

-4 = b

Finally, the equation of parallel line is y= 3x -4.

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The probability that exactly 7 of them are 16 to 24 years old is 0.222

In this question we have been given a recent study of minimum wage earners found that 55% of them are 16 to 24 years old.

A random sample of 12 minimum wage earners is selected. we need to find the probability that exactly 7 of them are 16 to 24 years old.

Here, n = 12

p = 0.55

1 - p = 0.45

x = 7

Using binomial distrubution the required probability would be,

P = 12C7 * (0.55)^7 * (0.45)^(12 - 7)

P = 792 * 0.01522 * (0.45)^5

P = 792 * 0.01522 * 0.01845

P = 0.2224

Therefore, the required probability is 0.222

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Answer:

Below

Step-by-step explanation:

IF b is even :   b+2      b+4      b+6    b+8    b+10    b+12

If b is ODD  :   b+1     b+3    b+5   .....  b+11

The amounts of pupils that gives each answer is given as follows:

The amounts are obtained by the multiplication of the decimal equivalent of each percentage by the total number of students, which is 40.

The percentages are given as follows:

Then the decimal equivalents of each of these percentages is given as follows:

Finally, the number of students that gave each student is given as follows:

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1. Distribute

2. Subtract 1/2z on both sides

3. Subtract 9 on each side

4. x=-3

5. CHECK

Any method of sampling in which every individual is equally likely to be selected.

What does "simple random sampling" mean?

Simple random sampling is a sort of probability sampling in which a subset of participants from a population is randomly chosen by the researcher.

                      There is an equal opportunity for selection for every person in the population. Then, data are gathered from as many of the individuals in this chosen subset as is feasible.

A simple random sampling is a method of sampling where each potential participant has an equal chance of being chosen. In other words, the likelihood that any given person will be chosen is 1/n if there are n people.

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Answer:

Step-by-step explanation:

ans will be (c) 11 cm, 7 cm, 2 cm

Step-by-step explanation:

Though the sum of any two sides of a triangle should be always greater than the third side i.e.,

11 + 7 > 2

7 + 2 = 9 < 11

so, no triangle can be formed of such sides.

The probability the researcher will make a type i error 0.10

The hypothesis testing, type I error involves rejecting true null hypothesis also referred to as 'false-positive' conclusion and type II error occurs when false null hypothesis is not rejected. It is also known as 'false negative' conclusion. And they are opposite to each other.

Here we have given that suppose a researcher plans to conduct a test of hypotheses at the 5% significance level. she designs her study to have power of 0.90 at a particular alternative value of the mean

And we need to find the probability the researcher will make a type i error

While looking into the given question,

We know that,

Significance level = 5%

alternative value of the mean = 0.90

Then the probability the researcher will make a type i error is calculated as,

mean = 1 - error

0.90 = 1 - error

=> error = 0.10

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The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).

The domain of a function is the input value for which the function exists while the range is the output value for which the function exists.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

For the graph given, the domain lie across the x-axis.

The range is possible y values. Since we can use negative x values, if we plug in x values for the function, we are going to get positive numbers, as we plug in higher negative numbers, our range is bigger.

The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).

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Answer:

answer is in explanation

Step-by-step explanation:

The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).

How to find the domain and range of a function?

The domain of a function is the input value for which the function exists while the range is the output value for which the function exists.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

For the graph given, the domain lie across the x-axis.

The range is possible y values. Since we can use negative x values, if we plug in x values for the function, we are going to get positive numbers, as we plug in higher negative numbers, our range is bigger.

The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).

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6x - 11y = - 13 is the the equation of this line in standard form that is option A from the group of choices.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign. Linear equations are classified into three types: point-slope, standard, and slope-intercept. Coefficients, variables, operators, constants, terms, expressions, and an equal to sign are all components of an equation. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other.

Here,

6x - 11y = - 13 is the the equation of this line in standard form that is option A from the set of possibilities.

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Answer:

360 inches.

Step-by-step explanation:

because 1 yard is 36 inches (3 rulers) so just multiply 36 by your number of yards.

The total number of adults who attended the play are 210.

Here, we are given that tickets for a play cost $ 7 for students and $ 10 for adults.

Total number of seats = 380

Box office revenue on opening night =  $ 3290

Let the number of adults be x

Then, the number of students will be = (380 - x)

thus, we can form the following equation-

10x + 7(380 - x) = 3290

10x + 2,660 - 7x = 3290

3x + 2,660 = 3290

3x = 3290 - 2660

3x = 630

x = 630/3

x = 210

Thus, the total number of adults who attended the play are 210.

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The total length of two line segments is 80 cm

A line segment is just part of a line. It has two endpoints,

given that

the first line segment is 30cm

the second line segment is 500mm

now we need to convert it into cm from mm

To convert mm to cm, we need to multiply the length in mm by 0.1 cm since 1 mm is equal to 0.1 cm.

500 mm × 0.1 cm = 50cm

now we need to add two line segments

30 cm + 50 cm = 80 cm

The total length of two line segments is 80 cm

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The Computation results of given combination and permutation expression,

(A) P(9, 3) = 504

(B) C(9, 3) = 84

(C) P(8,8) = 40,320

(D)P(9,9) = 1

A permutation is an arrangment of arranging objects or numbers in order.

The formula for permutations is

ⁿPᵣ = n!/(n-r)!

Combinations are the way of selecting objects or numbers from a group of objects, in such a way that the order of the objects does not matter.

The formula for combinations is,

ⁿCᵣ = n!/[r! (n-r)!]

ⁿCᵣ represents the number of combinations from “n” objects taken “r” at a time.

We have given some expressions and we shall compute these.

(A) P(9, 3) , here n = 9 and r = 3

=> P(9, 3) = 9!/(9-3)! = 9!/6! = 9×8×7×6!/6!

P(9, 3) = 9×8×7 = 504

(B) C(9, 3) = 9!/3!(9-3)! = 9!/6!×3!

= 9×8×7×6!/6!(3×2×1) = 9×8×7/6 = 84

(C) P(8, 8) = 8!/(8-8)!

= 8!/0! = 8! = 8×7×6×5×4×3×2×1 = 40,320

(D) C (9, 9) = 9!/9!(9-9)!

= 9!/9! 0! = 1

Hence ,we get all the values of given expression.

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The probability of getting a full house is 0.001441 or 0.14%.

When you dealt five cards from a thoroughly shuffled standard check of cards then for the probability of getting a full house we need to know the total number of full house combinations and possible cards hands.

This is calculated by taking the number of possible full house combinations (3,744) and dividing it by the total number of possible 5-card hands (2,598,960). This can be written as :

Mathematically, this can be expressed as:

P(Full House) = 3,744 / 2,598,960 = 0.001441 or 0.14%

Therefore the probability of getting a full house is 0.001441 or 0.14%

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By using the concept of percentage, it can be calculated that

65% people are completely satisfied with the car

What is percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 2% means [tex]\frac{2}{100}[/tex]. Here, 2 is expressed as a fraction of 100.

This is a word problem on percentage

Number of people who are completely satisfied with the car = 1495

Total number of people surveyed = 1495 + 210 + 595 = 2300

Percentage of people who are completely satisfied with the car = [tex]\frac{1495}{2300}\times 100[/tex]

  = 65%

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The value of the numerical expression -(5⁻⁴)(5²) will be - 1/25. Then the correct option is C.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ -(5⁻⁴)(5²)

Simplify the expression, then we have

⇒ -(5⁻⁴)(5²)

⇒ -(1/5⁴)(5²)

⇒ -(5² / 5⁴)

⇒ - 25 / 625

⇒ - 1/25

The value of the numerical expression -(5⁻⁴)(5²) will be - 1/25. Then the correct option is C.

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If you have two main effects, and one main effect is significant, this means that d. The other main effect and the interaction effect may or may not be significant

A statistically significant result indicates that it is unlikely to be explained solely by chance or random factors. In other words, if there is no true effect in a research study, a statistically significant result has a very low chance of occurring.

The significance level is the threshold at which one can accept whether an event is statistically significant. Researchers use the p-value to determine statistical significance: if the p-value is less than the significance level, the result is statistically significant.

If you have two main effects and one of them is significant, the other one and the interaction effect may or may not be significant.

In conclusion, based on the information illustrated, the correct option is D.

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Answer: x=-3/28

Step-by-step explanation:

isolate x alone and move all other numbers to the right

-2/3x+3/7-(3/7)=1/2-3/7

-2/3x= 1/14

-2/3(-3/2)+x=1/14*-3/2

x=-3/28

Answer:

-25.77200

Step-by-step explanation:

The type II error in this hypothesis test will occur when there is lack of enough evidence to conclude that less than 87% of the graduates of the academic program find full-time employment.

It is given to us that -

A certain academic program boasts that 87% of their graduates find full-time employment in their field within the first year of graduation.

The academic director wants to perform a hypothesis test to see if her concern is warranted.

We have to explain the meaning of a type II error for this type of hypothetic test.

In Hypothesis test, type II error occurs when the null hypothesis is not rejected even if it is actually false.

When performing hypothesis test, there are two factors that play an important role -

(a) The significance level of the hypothesis test

(b) The p-value obtained

In the given situation,

Null hypothesis, [tex]H_{0}[/tex]: p = the proportion is equal to 87%, i.e., 0.87

Alternative hypothesis, [tex]H_{A}[/tex]: p = the proportion has reduced than 0.87

The type II error may occur when -

the p-value is greater than the significance level

This condition will arise when there is lack of enough evidence to conclude that less than 87% of the graduates of the academic program find full-time employment.

In such situation, we cannot reject the null hypothesis because the p-value must be greater than the significance level.

Thus, the type II error in this hypothesis test will occur when there is lack of enough evidence to conclude that less than 87% of the graduates of the academic program find full-time employment.

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The type II error in this hypothesis test will occur when there is lack of enough evidence to conclude that less than 87% of the graduates of the academic program find full-time employment.

What is type II error ?

In Hypothesis test, type II error occurs when the null hypothesis is not rejected even if it is actually false.

When performing hypothesis test, there are two factors that play an important role -

(a) The significance level of the hypothesis test

(b) The p-value obtained

In the given situation,

Null hypothesis, : p = the proportion is equal to 87%, i.e., 0.87

Alternative hypothesis, : p = the proportion has reduced than 0.87

The type II error may occur when -

the p-value is greater than the significance level

This condition will arise when there is lack of enough evidence to conclude that less than 87% of the graduates of the academic program find full-time employment.

In such situation, we cannot reject the null hypothesis because the p-value must be greater than the significance level.

Thus, the type II error in this hypothesis test will occur when there is lack of enough evidence to conclude that less than 87% of the graduates of the academic program find full-time employment.

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Answer:

I couldn't read the full problem but I could read the first problem.

Step-by-step explanation:

The hourly rate is 8 dollars because $52-$44 is $8. $44-$36 is also $8. So $36- (the amount for 2 hours) $28 is $8. so in one hour the cost to rent a bicycle is $8.

Answer:

0.53

Step-by-step explanation:

0.6 because you divide 9 and 17

Test c had 60 items

It is the most accurate statement that can be made about the reliability of these tests.

The reason that objective tests include so many items is to increase the reliability of the test.

Reliability Test

It is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that might be embedded in the scores. Scores that are highly reliable are precise, reproducible, and consistent from one testing occasion to another.

Probability

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

A measure of reliability between two variants of the same test is known as alternate forms reliability. The results of two identical (but distinct) tests are correlated, and a reliability coefficient is computed. If variations in one test's observed results correspond to variations in the scores of an equivalent test, the test is said to be dependable. A psychological test's practise effect which is typical of test-retest reliability, can be mitigated by a survey instrument's alternate-form reliability. The goal is to reword the survey questions in a way that makes them functionally identical, or just rearrange the questions in the first and second surveys of the same respondents.

Test c had 60 items

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Answer:

Step-by-step explanation:

The fourth image because when looking for liner equations if you draw a line through them and it only touches once its linear equation!

sorry if im wrong...  

Answer:

$3.90

Step-by-step explanation:

3.65 / 3 = 1.22

1.22 x 3.2 = 3.90