Use the bar diagram to write an equation. Then solve. Drag numbers to complete the equations.

Option B is the correct answer, the interval in which the graph of the function is positive is -∞ < x < -1.

What do mean by interval?

In mathematics, a (real) interval is a collection of real numbers that includes all real numbers that fall inside any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1. The set of all real numbers, the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton are additional examples of intervals.

As we can see in the graph provided in the question, the graph of function reach the positive side of the y-axis at x = -1, it means one of the two end point of the interval is going to be -1. And, the graph is constantly and slowing increasing it's value as increase in the x-axis therefore, the other endpoint of the interval cab be considered as negative infinity.

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The length of the table is 1.51 meters.

Allan is measuring his dining room table to make a tablecloth. The table is 0.45 meter longer than it is wide. The width of the table is 1.06 meter. We need to find out the length of the table.

Let the length of the table be represented by the variable "L". In the context of a mathematical problem or experiment, a variable is a quantity that may vary. The length of the table is the sum of the width of the table and the difference between the two quantities.

L = 1.06 + 0.45

L = 1.51

Hence, the length of the table is 1.51 meters.

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The value of the expression when a=2 and b=7 is 41.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information, the expression given is 3a + 5b and we want to find the value of the expression when a=2 and b=7.

This will be illustrated thus:

= 3a + 5b

= 3(2) + 5(7)

= 6 + 35

= 41

The value is 41.

The complete question is given below.

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Complete question

The expression given is 3a + 5b. Find the value of the expression when a=2 and b=7

A parabola is a bowl-shaped figure. Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].

And the x-intercept is [tex](1,(\frac{-2}{3}))[/tex].

Since the additional point is [tex](3,22)[/tex]

What is a parabola?

A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface: a curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed-line. : something that is bowl-shaped.

Here the given quadratic equation is

[tex]y=3x^{2}-x-2[/tex]

The standard form of the quadratic equation is

[tex]y=ax^{2}+bx+c[/tex]

where [tex]a=3,b=-1,c=-2[/tex]

The axis of symmetry is the x-axis  of the vertex

[tex]x=\frac{-b}{2a}\\x=\frac{1}{2(3)}\\x=\frac{1}{6}[/tex]

The y-value of the vertex is determined by substituting [tex]\frac{1}{6}[/tex] for [tex]x[/tex] into the equation and solving it for [tex]y[/tex].

[tex]y=3(\frac{1}{6})^{2}-\frac{1}{6}-2\\y=3(\frac{1}{36})-\frac{1}{6}-2\\y=\frac{3-6-72}{36}\\y=\frac{3-78}{36}\\y=\frac{-75}{36}[/tex]

Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].

Since [tex]a < 0[/tex] the vertex is the maximum point and the parabola opens downward.

X-intercept values of [tex]x[/tex] when [tex]y=0[/tex]

Substituting [tex]0[/tex] for [tex]y[/tex] and solving for [tex]x[/tex] using the quadratic formula

[tex]0=3x^{2}-x-2\\x=\frac{-b+-\sqrt{b^{2}}-{4ac}}{2a}\\x=\frac{1+-\sqrt{1}-{4(3)(-2)}}{2(3)}\\\\x=\frac{1+-\sqrt({1}+{24})}{6}\\\\\\x=\frac{1+-\sqrt(25)}{6}\\\\\\\\x=\frac{1+-5}{6}\\\\\\x=\frac{1+5}{6} , x=\frac{1-5}{6}\\\x=\frac{1+5}{6},x=\frac{1-5}{6}\\\\\x=1,x=\frac{-2}{3}[/tex]

Y-intercept values of [tex]y[/tex] when [tex]x=0[/tex]

Substituting [tex]0[/tex] for [tex]x[/tex] and solving for [tex]y[/tex] using the quadratic formula

[tex]y=3(0)^{6}-0-2\\y=-2[/tex]

Y-intercept [tex](0,1)[/tex]

Now substitute [tex]3[/tex] for [tex]x[/tex] and solve for [tex]y[/tex]

[tex]y=3(3)^{2}-3-2\\y=3(9)-5\\y=27-5\\y=22[/tex]

So the point is [tex](3,22)[/tex].

Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].

And the x-intercept is [tex](1,(\frac{-2}{3}))[/tex].

Since the additional point is [tex](3,22)[/tex]

The parabola is of the form

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Answer: a) = 4

b) = 30

Step-by-step explanation:

a) They are asking for the range of the marks so you do 10-6 as 10 is the highest mark and 6 is the lowest

b) You find this out by adding the frequency up 10+4+7+4+5 = 30

For the given normal distribution, 95% of the values lie between 40 and 60.

Let the said distribution be X

Here it is given that X follows a normal distribution and it has a mean of 50 and a standard deviation of 5.

Therefore we can write X~ N(50, 25)

Now we need to find P(40< X< 60)

= P(40< X< 60) = P(X < 60) - P(X<40)

To find this we need to convert it into the form of a standard normal and then look up the p-values from the Z-table.

To do this we need to use the formula

P(X < x) = Φ[(x - μ) / σ]

where,

μ is the mean

σ is the standard deviation

Therefore we get

P(X < 60) - P(X<40) = Φ[(60 - 50) / 5] - Φ[(40 - 50) / 5]

= Φ[2] - Φ[-2]

Φ(-x) = 1 - Φ(x)

Therefore,

Φ[2] - Φ[-2]

= 2Φ(2) - 1

We get the p-value

2 X .97725 - 1

= 1.9545 - 1

= 0.9545

= 95% (approx)

Hence 95% of the values are between 40 to 60.

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If all other values remain constant, an increase in sample size will result in a broader confidence interval when constructing one.

The definition of the MoE, or margin of error, is

MoE = sigma ÷ sqrt(n)

The population standard deviation is represented by sigma. If you don't know sigma, utilize s to get a rough idea of it. The sample standard deviation is denoted by the variable s.

The MoE increases along with the sigma. The width or narrowness of the confidence interval is directly determined by the MoE. A smaller MoE indicates greater confidence with less error, whereas a larger MoE indicates greater net casting but increased error.

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Answer:

both a and b

Step-by-step explanation:

It is because in the elimination method it does not matter whether you eliminate x or y so if you use option a which multiplies -2 by 1st equation so it will become:

-4x+6y=40

4x+6y=8

so the -4x and 4x cancels and a is a valid option.

If you use the b which multiplies the second with 3 it becomes:

2x-3y=-10

4x+3y=24

so -3y and 3y cancel which also makes this a valid option.

Answer: both a and b

There is no graph in your question

Answer:

4 students for newspapers & 3 students for magazines are needed for the deliveries to be made in a day.

Step-by-step explanation:

According to the question,

So, In 8 hours each student can deliver:

35 × 8 = 280 newspapers

50 × 8 = 400 magazines

To find out minimum number of students needed to work we need to divide work done by each student in 8 hours by total deliveries to be made.

[tex] \therefore[/tex]

For Newspapers:

875/280 = 3.125

So, by rounding of the figure we will need 4 students to deliver newspapers as each student can work only for 8 hours.

For magazines:

1200/400 = 3

3 students are needed to deliver magazines.

There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.

Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes. Probability is the likelihood that something will occur or the probability that something will happen. Probability is the measure of how likely it is that a coin will land heads up after being tossed into the air.

Given,

On a particular busy section of the garden state parkway in new jersey, police use radar guns to detect speeding drivers. assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes.

Either the wait is over 25 minutes or it is less than 25 minutes. Decimal 1 represents the total of these events' probabilities. So,

P( X ≤ 25) + P(X > 25) = 1

For P(X > 25):

1 -P(X ≤ 25)

1 - e ⁻⁰⁶⁶⁶⁽²⁵⁾

0.1892

There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.

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The solution for u in the expression given as 7/u = 3/11 is u = 25.7

From the question, the algebraic expression is given as

7/u = 3/11

There is no constant to add to or subtract from the expression

So, the equation remains the same

7/u = 3/11

Multiply both sides of the equation by u

This gives

u * 7/u = 3/11  * u

Evaluate the products

So, we have the following equation

7 = 3/11u

Multiply both sides of the equation by 11/3

This gives

11/3 * 7 = 3/11u * 11/3

Evaluate the products in the above expression

77/3 = u

So, we have

25.6667 = u

Approximate

25.7 = u

Rewrite as

u = 25.7

Hence, the solution is u = 25.7

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The car use 6.67 liters of petrol to travel 160 miles of distance.

Given, the car use the same amount of petrol for each mile it travels.

A car use 55 liters of petrol to travel 495 miles.

we have to find the petrol used to travel 160 miles.

As, 55 liters = 495 miles

495 miles = 55 liters

1 mile = 55/495 liters

Now, 160 miles = 55/495×160 liters

160 miles = 6.67 liters

So, the car use 6.67 liters of petrol to travel 160 miles of distance.

Hence, the car use 6.67 liters of petrol to travel 160 miles of distance.

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Answer:

no because 60+48+36 is 144

Step-by-step explanation:

please mark brainliest

The total number of people is 144. The data is not consistent.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that at a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three.

The total number of the people in the party,

60+48+36 is 144

But it is given in the question that there are 100 in the party.

Therefore, the total number of people is 144. The data is not consistent.

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The rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.

The distance covered in a unit of time is known as speed.

Given that, the airplane travels 7680 km in 8 hours flying against the wind, and 12420 km in 9 hours.

Therefore, the rate of the airplane against the wind is:

7680/8

= 960 km / hr

The rate of the airplane with the wind is:

12420/9

=1380 km / hr

Let the rate of the airplane in still air be a and the rate of the wind be w.

The net rate while flying against the air is:

a - w = 960       (1)

The net rate while flying with the wind is:

a + w = 1380      (2)

Add equations (1) and (2):

2a = 2340

a = 1170 km/hr

Substitute a = 1170 into equation (1):

1170 - w = 960

1170 - 960 = w

210 = w

Hence, the rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.

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number 9 is 36  12x3 is 36

The solution set for the given quadratic equation is (-0.62, -5.38).

The given equation is 3x(x+6)=-10.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, 3x(x+6)=-10

⇒ 3x²+18x=-10

⇒ 3x²+18x+10=0

By comparing 3x²+18x+10=0 with ax²+bx+c=0, we get

a=3, b=18 and c=10

Using quadratic formula x = [-b ± √(b² - 4ac)]/2a

= [-18 ± √(18² - 4×3×10)]/2×3

= [-18 ± √(324 - 120)]/6

= [-18 ± √(204)]/6

= [-18 ± √(204)]/6

= [-18 ± 14.28]/6

= [-18 + 14.28]/6 and [-18 - 14.28]/6

= -0.62 and -5.38

Hence, the solution set for the given quadratic equation is (-0.62, -5.38).

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Answer:

216

Step-by-step explanation:

x^3

6^3

6x6x6

36x6

216

Hopes this helps pleas mark brainliest

The total amount of the money earned by Paige will be $1591.92.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Paige works at a department store and has a commission rate of 3 per cent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter.

The total amount of earnings will be,

TA = ( 50 x 30 ) + ( 0.02 x 4596)

TA = 1500 + 91.92

TA = $1591.92

Therefore, the total amount of the money earned by Paige will be $1591.92.

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We have coordinates (-2, -3) and (1, 1)

To find: Slope of a line that passes through these two coordinates

Let (-2, -3) be (x₁ , y₁) and (1, 1) be (x₂, y₂)

We will use the formula of Slope :

m = y₂ - y₁ / x₂ - x₁

Where 'm' stands for slope

m = 1 - (-3) / 1 - (-2)

m = 1 + 3 /  1 + 2

m = 4 / 3

The slope of the line is  4/3

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On that specific day, the US dollar was worth more than the Canadian dollar and less than the Australian dollar.

The equation u = 0. 99c depicts the value of the US dollar in relation to the Canadian dollar on a specific day.

From the equation,

For  Australian dollar; (from table)

u = 0.95 c   -->

a = 1/0.95 u

a = 20/19 u

(20/19u - u)/ u = 1/19   ....1

For Canadian dollar:

u = 0. 99c

c = 1/0.99 u --> c = 100/99 u

Thus,

(100 u / 99 - u)/ u = 1/99  .....2

From 1 and 2]

1/19 > 1/99

Thus, on that specific day, the US dollar was worth more than the Canadian dollar and less than the Australian dollar.

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The cluster sample represents the the characteristic of group of same types objects.

What is the cluster sampling?

A population is divided into clusters, such as districts or schools, and some of these clusters are randomly chosen as your sample via the probability sampling technique known as cluster sampling. In a perfect world, each cluster would be a tiny reflection of the entire population.

A researcher intends to carry out a study to evaluate sophomores' abilities in business education across the United States. There is no way to carry out a research study with participants from every university. Instead, the researcher can group the universities from each city into a single cluster by utilizing cluster sampling. The sophomore student population in the United States is then comprised of these clusters. Next, select clusters at random for the research project using either simple random sampling or systematic random sampling. The sophomores from each of these determined groups can then be picked on whom to perform the research study utilizing simple or systematic sampling.

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Answer:

x=-10

Step-by-step explanation:

2(x+3) = 2x+6

2x+6=x-4

2x+6-6=x-4-6

2x=x-10

2x-x=x-10-x

x=-10

We can use both regular and strong induction.

The Fundamentals of Inductive Mathematics (i.e., Regular Induction). If any of the following statements involving a positive number, n, are accurate: The claim is true if and only if n is 1. If the assertion is true for n=k, then it must also be true for n=k+1(x).

In a variation of induction known as strong induction, we make the assumption that the assertion is true for all values before k. This provides us with more information with which to work.

Regular Induction form

N>6 = n=7 in basic case

3n = 37 = 2187

N! = 7! = 5040

For n= 7 3n<n! is true

Induction hypothesis

Let for n= k and k>6

Assume 3k<k! is true

We prove that for k = k+1 the assumption holds true then the assumption must be true for k

K = k+1

3k+1 < (k+1)!

3k. 3 < (k+1) k!

3k < (k+1)/3.k!

For k>6

(k+1)/3 >1 and let (k+1)/3 = p

3k < P.k!

But we assumed that 3k < k! for k > 6 then 3k must be less than p.k1 since P>1

Therefore 3k<k! for k>6

3n < n! for all integers n greater than 6.

Therefore we can use both regular and strong induction

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Answer:

50 mins: 1 and a 1/2 hours

Answer:

9:5

Step-by-step explanation:

1.5 hours is equivalent to 90 minutes (60 x 1.5)

so it's a ratio of 90:50

this can be simplified to a ratio of 9:5 by dividing both sides by their shared factor of 10

Measurement of ∠ ABC is 90°

A linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

Given that ∠ CBD and ∠ ABC are linear pairs,

Therefore, m∠ CBD + m∠ ABC = 180°

m∠ ABC = 180° - 90° = 90°

Hence, Measurement of ∠ ABC is 90°

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Answer:

∠

A

=

x

=

32

∘

∠

B

=

3

x

=

3

⋅

32

=

96

∘

∠

C

=

x

+

20

=

32

+

20

=

52

∘

Step-by-step explanation: Every triangle adds up to 180.