Select the graph that represents the solution of the compound inequality –6 ≤ 4x + 6 < 14. A number line from negative 5 to 5 in increments of 1. A point is at 0 and a bold line is drawn to the right stopping at the open circle at 2. A number line from negative 5 to 5 in increments of 1. A point is at negative 5 and a bold line is drawn to the right stopping at the open circle at 3. A number line from negative 5 to 5 in increments of 1. A point is at negative 3 and a bold line is drawn to the right stopping at the open circle at 5. A number line from negative 5 to 5 in increments of 1. A point is at negative 3 and a bold line is drawn to the right stopping at the open circle at 2.

The bookstore sold a total of 150 chemistry textbooks and 225 sociology textbooks.

What is a linear equation in two variables?

An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Let C be the number of chemistry textbooks sold and S be the number of sociology textbooks sold. We can write the following system of equations to represent the given information:

C + S = 375

C = 2S

To solve this system of equations, we can substitute the second equation into the first equation to get C + 2S = 375. Then we can solve for S by subtracting C from both sides to get 3S = 375 - C. Dividing both sides by 3 gives us S = (375 - C) / 3.

Substituting this expression for S back into the second equation, we get C = 2((375 - C) / 3). Multiplying both sides by 3 and simplifying gives us 3C = 750 - 2C, or C = 750 / 5 = 150.

Substituting this value for C back into the first equation, we get 150 + S = 375, so S = 375 - 150 = 225.

Hence, the bookstore sold a total of 150 chemistry textbooks and 225 sociology textbooks.

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By using ratio, it can be calculated that-

Ratio of earnings to the stock’s price = 20 : 1

What is ratio?

Ratio between two quantities tells us how many one quantity is bigger than the other and the comparison is to be made between quantities with same unit. The first part of the ratio is called antecedant and the second part of the ratio is called consequent.

The price of a certain stock is $55.00 per share

Earnings are $2.75 per share

Ratio of earnings to the stock’s price = 55 : 2.75

                                                              = 5500 : 275

                                                              = 20 : 1

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Answer:

c

Step-by-step explanation:

all triangles equal 180°

The alternative hypothesis in this case would be that at least one of the four treatments has a different effect on the mean time kept awake compared to the others.

If the one-way ANOVA test rejects the null hypothesis, it means that there is a significant difference in the mean time kept awake among the four treatments. This means that at least one of the treatments is more effective in keeping you awake than the others. It is important to note that the alternative hypothesis does not specify which of the treatments is more effective, only that at least one is different from the others. To determine which treatment is more effective, you would need to conduct additional tests, such as post-hoc tests.

The alternative hypothesis in this case would be that at least one of the four treatments has a different effect on the mean time kept awake compared to the others.

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Using the Poisson distribution, the probability of an earthquake in the 0.8-0.9 magnitude range sometime in the next 30 years is

1 - 1.9287 x 10⁻²².

It is given that mean recurrence of an earthquake is the 8.0-9.0 magnitude is approximately 1500 years.

We have to find the probability of an earthquake in this magnitude range sometime in the next 30 years.

Since, an occurrence of an earthquake is a rare event, we can use Poisson distribution here.

Poisson distribution gives the probability of occurrence of any event in a given time interval.

Let the average number of event per year in 30 years of period is λ.

[tex]\lambda = \frac{1500}{30}[/tex]

λ = 50

Let, the occurrence of an earthquake is a random variable x.

Then the probability that at least an earthquake occur in next 30 years is calculated as:

P(x ≥ 1) = 1 - P(x<1)

P(x ≥ 1) = 1- P(x=0)   -----(1)

PDF of Poisson distribution with parameter λ is given as:

[tex]P(X = x) = \dfrac{e^{-\lambda}{\lambda}^x}{x!}[/tex]

So, in this case

[tex]P(x=0)= \dfrac{e^{-50}{(50)}^0}{0!}[/tex]

[tex]P(x=0)= \dfrac{1.9287 \times 10^{-22}}{1}[/tex]

[tex]P(x=0)={1.9287 \times 10^{-22}[/tex]

Substitute this value in equation (1)

P(x ≥ 1) = 1 - 1.9287 x 10⁻²²

Hence, the probability of an earthquake in next 30 years is

1 - 1.9287 x 10⁻²².

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If an original conditional statement is true, the option that will always be true as

well is B. Contrapositive.

A conditional statement is one that has the syntax "If P then Q," with P and Q denoting sentences. P is referred to as the hypothesis and Q is referred to as the conclusion for this conditional statement. If P then Q logically implies that Q must be true whenever P is true.

A conditional statement is present. In the event of rain, we will not play. Let's say A: It's raining and B: We're not going to play. If A is true—that is, if it is raining—and B is false—that is, if we played—then A implies that B is untrue.

Therefore, based on the information, the correct option is B.

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Answer:

16p + 4

Step-by-step explanation:

the first thing you should do when you simplify an equation is to distribute the parenthesis

4p * 4 + 1 * 4

16p + 4

you cannot simplify any further so that is your answer

Output for the givin input for function f(x)=-5x+1, f (3) is -14.

What is  function ?

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

f(x)=-5x+1

Then, f(3)=-5*3+1

f(3)= -15+1

f(3)=-14

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The type of linear relationship is positive.

Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect. The correlation coefficient is a statistical measure of the strength of a linear relationship between two variables. Its values can range from -1 to 1. A coefficient of 1 shows a perfect positive correlation, or a direct relationship. A correlation coefficient of 0 means there is no linear relationship.

The type of linear relationship is positive.

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Step-by-step explanation:

SWT + TWU =180º therefore SWU must be a line. Aka SWU is linear. So SWT and TWU must be a linear pair.

SWT + SWT = 180º therefore 2SWT=180º deviding both sies by 2 we get SWT = 90º Therefore SWT is replacing TWU. SWT is substituted into TWU. So substitution.

SU | TV basically means the line that passes through both points S and U is perpendicular to the line that passes through both points T and V. Therefore it is the Defenition of perpendicular lines.

If this helped please rate the answer.

Percent decrease from 100 to 82 is 18% decrease.

Calculating the % decrease from 100 to 82,

[tex]\frac{82-100}{100}[/tex]×100%

[tex]\frac{-18}{100}[/tex]×100%

on simplifying we get,

-18%

here, negative sign indicates that there is a decrease of percentage.

Hence, we get 18% decrease from 100 to 82.

How to calculate Percent decrease?

Do the % growth and reduction calculations. By dividing the new number by the initial value, the percentage is computed.

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Dividing the ones and then put the decimal point and divide the tenths and so on.

what is a meant by decimal point?

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Answer:

4.) a.) 2.01 b.) 404.01

6.) a.) 152.17 b.) 18412.17 c.) 153.14 d.) 18565.60

Step-by-step explanation:

To solve, use the exponential growth formula [tex]A_t=A_0(1+\frac{r}{p})^t[/tex] where

[tex]A_t[/tex] = Amount as a function of time

[tex]A_0[/tex] = Original amount

[tex]r[/tex] = rate

[tex]p[/tex] = period

[tex]t[/tex] = time

For question 4, let

[tex]A_0=400\\r=0.06\\p=12\\t=2[/tex]

So,

[tex]A_t=400(1+\frac{0.06}{12})^2\\A_t=400(\frac{201}{200})^2\\A_t=400(1.01)\\A_t=404.01[/tex]

So, the second-period interest would be 404.01-402=2.01

Question 6 can be solved using the same formula, but let

[tex]A_0=18260\\r=0.025\\p=\frac{12}{4}=3\\t_1=1\\t_2=2[/tex]

So,

[tex]A_t=18260(1+\frac{0.025}{3})^1\\A_t=18260(\frac{121}{120})^1\\A_t=18412.17[/tex]

The first-period interest would be 18412.17-18260=152.17

For the second-period, use [tex]t_2[/tex]:

[tex]A_t=18260(1+\frac{0.025}{3})^2\\A_t=18260(\frac{121}{120})^2\\A_t=18260(1.02)\\A_t=18565.60[/tex]

The second-period interest would be 18565.60-18412.17=153.43

Triangle ABC is similar to triangle A prime B prime C prime, because Triangle A prime B prime C prime is obtained by dilating Triangle ABC. By a scale factor of 1 over 4 and then rotating it about the origin by 180 degrees. The correct answer is B.

Dilation is a transformation that is used while resizing an object. The structures can be made longer or shorter via dilation. This transformation produces a picture that retains the original shape. There is, however, a significant fluctuation in the form. During a dilatation, the starting shape should be elongated or compressed.

All the coordinates of A'B'C' are -1/4 times those of ABC.

The dilation factor is 1/4, and rotation by 180° is indicated.

A'(-1, -1) = (-1/4) × A(4, -4)

            = A(4x-1/4, -4x-1/4)

            =  (-1, -1)

B'(-3, 1) = (-1/4) × B(12, -4)

            = B(12x-1/4, -4x-1/4)

            = (-3, 1)

C'(-2, 3) = (-1/4) × C(8, -12)

             =  C(8x-1/4, -12x-1/4)

             =  (-2, 3)

Both coordinates are invalidated by a 180° rotation. In either sequence, it is the same as reflection across the x-axis and reflection across the y-axis.

Therefore, triangle A′B′C′ is obtained by dilating Triangle ABC by a scale factor of 1 over 4 and then rotating it about the origin by 180°.

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The complete question is:

Triangle ABC is transformed to obtain triangle A′B′C′:

A coordinate grid is labeled from negative 12 to 0 to 12 on both x- and y-axes at increments of 1. Triangle ABC has A at ordered pair 4, negative 4, B at 12,negative 4, C at 8, negative 12. Triangle A prime B prime C prime has A prime at ordered pair negative1, 1, B prime at negative 3, 1 C prime at negative 2, 3.

Which statement is correct for Triangle ABC. and Triangle A prime B prime C prime.?

Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 6. and then rotating it about the origin by 90 degrees

Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 4. and then rotating it about the origin by 180 degrees

Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 180 degrees

Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 90 degrees

Answer:

12 visits.

Step-by-step explanation:

Jocelyn receives a flat 25 reward point, and 12.5 points for each visit. She wants to redeem a free movie ticket that costs 170 points.

Set the equation. Let "each visit" be denoted by the variable, x:

12.5 per visit + a flat 25 reward point ≥ Free movie ticket that costs 170 points.

12.5x + 25 ≥ 170

Isolate the variable, x. Note that what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, subtract 25 from both sides of the equation:

12.5x + 25 ≥ 170

12.5x + 25 (-25) ≥ 170 (-25)

12.5x ≥ 170 - 25

12.5x ≥ 145

Next, divide 12.5 from both sides of the equation:

(12.5x)/12.5 ≥ (145)/12.5

x ≥ 145/12.5

x ≥ 11.6

x ≥ 11.6 is your answer. Therefore, Jocelyn would have to make 12 trips to earn her first free movie ticket.

~

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The first option is true since the item achieved its maximum height of 73.5 feet.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem. The answer could be simple or complicated.

This quadratic equation, which has the form y=a(x-h)2 + k, is referred to as being in vertex form. It is so named because the vertex point (peak point) lies on the graph of this equation (h,k)

We may deduce from the facts above that

-4.9 t2 + 19.6 t + 58.8 = 0

The equation will logically fit into the square upon completion.

y = a(x-h)^2 + k

where h will be the time it takes to get to a height of k.

-[tex]4.9t^{2}[/tex] + 19.6t + 58.8 = 0

-[tex]4.9t^{2}[/tex] + 19.6t = - 58.8

-4.9( [tex]t^{2}[/tex] - 4t ) = -58.8

Now take half the linear term, square it, and add it to both sides.

-4.9( [tex]t^{2}[/tex] - 4t ) = -58.8

-4.9( [tex]t^{2}[/tex] - 4t + 4 ) = -58.8 + 19.6

-4.9 [tex](t-2)^{2}[/tex] = - 78.8

s(t) = -4.9 [tex](t-2)^{2}[/tex] + 78.8

now we have t = 3sec

s(t) = 73.5ft

The object reached its maximum height of 73.5 ft, the first choice is correct.

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Given that the second student chosen is a girl, the probability that both students are female is 0.175.

The occurrence of likely events is referred to as probability. It is the branch of mathematics concerned with numerical estimates of the likelihood of an event occurring or a statement being true.

Probability is nothing but likelihood of something is to occur. When we are unsure about the outcome of an event, we can discuss the probabilities of certain outcomes—how likely they are.

The probability of selecting a girl from the class is

[tex]= \frac{Number\ of\ girls}{ Total\ number\ of\ students}= \frac{14}{26}\\\\= \frac{7}{13}[/tex]

It is known that the one of the chosen student from 2 students is girl, the probability of having both girls will be:

[tex]= \frac{7}{16} * \frac{6}{15}\\\\= 0.175[/tex]

Hence, the probability is 0.175.

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Your question is incomplete, here is the complete question.

Your statistics class has 26 students in it - 14 girls and 12 boys.Your teacher uses a calculator to select two students at random to solve a problem on the board. Given that the second student chosen is a girl, what is the probability that the first student was also a girl?

Answer:

–2.4 + 3.2t

Step-by-step explanation:

= –3.6 – 1.9t + 1.2 + 5.1t

= –3.6 + 1.2 – 1.9t + 5.1t

= –2.4 + 3.2t

i hope this helped

Errors student make is the % values in the equation were wrongly written and Instead of writing x - 1 for the amount of the 7% solution, write 1 - x.

There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value of a given data set are called equation.

Given

A student has a 2% salt water solution and a 7% salt water solution. To best imitate salt water at a local beach, he needs 1 liter of a 3.5% salt water solution. He defines x as the amount of 2% solution and writes this equation:

0.2x + 0.7(x – 1) = 0.35(1)

He requires 1 litre of a 3.5% salt water solution to accurately mimic the salt water at a nearby beach.

He constructs the following equation, where x is the volume of the 2% solution:

0.2x + 0.7(x - 1) = 0.35(1)

After resolving the equation, he ascertains that x is around 1.17 litres.

Errors student make:

A) The % values in the equation were wrongly written.

B) Instead of writing x - 1 for the amount of the 7% solution, write 1 - x.

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">" makes each inequality statement true. since -19 > -20

Mathematical number comparison is the process or method of comparing two numbers to determine whether one is less, bigger, or equal to the other. The comparison symbols for numbers are "=", which stands for "equal to," "=", which stands for "greater than," and " ", which stands for "less than."

Given three inequalities symbols>, <, and = and we need to compare -19 and -20 as per the problem. Hence -19 > -20

Therefore, Each inequality assertion is true when ">" is used. since -19 > -20

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Correct option: (A) The point IS a solution to the system. Only one of the equations resulted in an identity.

An equality that is true regardless of the values selected for its variables is called an identity. They are used to rearrange or simplify algebraic formulas. The two halves of an identity are, by definition, interchangeable, and we are always free to switch one for the other.

An identity is an equation that, regardless of the values used, is always true. Since 2x + 3x will always equal 5, regardless of the value of, this statement is an identity. The example might be written as 2x+ 3x = 5x since identities can be represented with the symbol "≡"

2x + y = 4

now, putting the values in the equation (6,-8)

2(6) + (-8) = 4

or, 12 - 8 = 4

or, 4 ≡ 4

This equation, point IS a solution to the system.

x + 3y = - 20

or, 6 + 3(-8) = -20

or, 6 - 24 = -20

or, - 18 ≠ - 20

So, for this equation the result is not identity.

Thus, option A is the correct answer.

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The angle that the line 3y = 2x + 6 makes with the [x] axis is (θ) = 33°69'.

Given is the equation -

3y = 2x + 6

The given equation is -

3y = 2x + 6

y = (2/3)x + (6/3)

y = (2/3)x + 2

Slope of the line -

m = 2/3.

We know slope is also given by -

m = tan(θ)

So -

tan(θ) = 2/3

(θ) = tan⁻¹(2/3)

(θ) = 33°69'

Therefore, the angle that the line makes with the [x] axis is (θ) = 33°69'.

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Brian started cleaning at 3:33 PM and finished at 4:21 PM. The correct answer is 48 minutes

First, we are figuring out what is given we are counting numbers or we can add to get to 4:21 PM.

Counting numbers:

[tex]\boxed{3:33=3:34=3:35=3:36=3:37=3:38=3:39=3:40 }[/tex]

Add the numbers:

[tex]\boxed{3:33+7=3:40+10=3:50+10=4:00+21=4:21}[/tex]

If we add the numbers it would be faster.

Therefore, when we add we get are answer.

Therefore, Brian started cleaning at 3:33 PM and finished at 4:21 PM. The correct answer is 48 minutes

Answer:

48

Step-by-step explanation:

The value of the test statistic is 3.371

What is Hypothesis?

A hypothesis is a notion that is consistent with available data but has not been proven true or wrong.

A hypothesis (also known as a statistical hypothesis) is a statement on which hypothesis testing will be based in statistics. The null hypothesis and alternative hypothesis are two of the most important statistical hypotheses.

Given that,

s1 = 8      ,   n1 = 330

s2 =7      ,   n2 = 310

Means

x1 = 33

x2 = 31

standard error is

S ∈ = √S₁²/n₁ + S₂²/n²

S = √8²/330 +7²/310

S = 0.593

Test statistic is Ts = x1-x2/S∈

= 33-31/0.593

Ts = 3.371

The test statistic has a value of 3.371.

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It is true that the objective function and the restrictions in a linear programming problem must be linear functions of the choice variables.

The method of choosing the best result from a linear function is known as linear programming. Making a few straightforward assumptions is the easiest way to accomplish linear optimization. As the goal function, the linear function is referred to. Real-life relationships can be quite challenging. However, such interactions can be represented using linear programming, which facilitates analysis of such relationships.

When the need of a mathematical model are represented by linear relationships as, the optimal result can also be obtained using a technique known as the linear programming (LP), sometimes known as linear optimization. A particular type of mathematical programming is linear programming.

Formally speaking, linear programming is the method for optimizing a linear objective function under the restrictions of the linear equality and linear inequality. Convex polytopes, a set defined as the total intersection of a finite number of half spaces, each of which is determined by the linear inequality, make up viable region.

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Answer:

7. x=11/3

8. no solutions

Step-by-step explanation:

7.

[tex]2*\sqrt{3x-2} =6[/tex]

Divide both sides by two

[tex]\sqrt{3x-2}=3[/tex]

Square both sides

[tex]3x-2=9[/tex]

Simplify

[tex]x=\frac{11}{3}[/tex]

8.

[tex]\sqrt{43-x}+10=1[/tex]

Subtract 10 both sides

[tex]\sqrt{43-x}=-9[/tex]

Impossible to have a negative answer when square rooting, no solutions