This graph shows fuel consumption for a car during a test run. Three of the statements are true. Which is NOT?

Line graph. X axis labeled miles; y axis labeled gallons. Line with upward arrow extends from point where X and Y axes connect (0, 0) with one marked coordinate (73.5, 3.5).


The car used 312 gallons of gas to go nearly 75 miles.


The car used 70 gallons of gas to go 3 miles.


The car used gas at a unit rate of 21 miles per gallon.


At this rate, it would take 4 gallons of gas to travel 84 miles.

It is true that qualitative variable categories must be mutually exclusive and exhaustive as a whole.

It has been observed that when two occurrences are mutually exclusive, they cannot take place simultaneously. However, it need not entail that one of the two occurrences must take place. As a result, when two events are exhaustive of one another, one of them is said to occur.

It signifies that two occurrences cannot happen at the same moment if they are mutually exclusive. However, it doesn't entail that one of the two events must take place. If two occurrences are mutually exclusive, then one of them must take place.

The categories (answer possibilities) must, in the first place, be mutually exclusive, which means they cannot overlap. In order to give all alternatives that might make up a response list, survey answer options must be collectively thorough.

For instance, the act of flipping a coin is said to be both mutually exclusive and collectively exhaustive. Either heads or tails must result in this situation. These are variables, then.

Therefore,

It is true that qualitative variable categories must be mutually exclusive and exhaustive as a whole.  

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The conditional probability that a randomly-generated 4-bit string contains two consecutive 1s is 3 / 8 .

total length of four-bit strings = 16

Let S represent the collection of all four-bit bit strings.

Let A represent the occurrence of a randomly generated string beginning with 1.

Let B represent the scenario where a string created at random contains two consecutive 0s.

S has 8 strings that begin with the letter "1."

P( A ) = 8 / 16 = 1 / 2

Strings in S starting with 1 and having two consecutive zeros are 1000 , 1001 , 1100

P(A ∩ B)  = 3 / 16

Conditional probability that at least two consecutive 0s will appear in a randomly generated bit string of length four is ,

3/16 / 1/2

= 3 / 8

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The answer of the function  f(x)=7(3-x)+5 is -7x + 26.

A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.

Given the function;

f(x)=7(3-x)+5

To simplify the function:

First, solve parenthesis,

f(x)=21 - 7x +5

Taking, constant with constant term,

f(x) = -7x + 26

Therefore, the answer is  -7x + 26.

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Answer:

5

Step-by-step explanation:

The logarithm function, denoted as "log," is the inverse of the exponentiation function. This means that if we have the expression "log(x) = y," then "x" is the base "b" raised to the power "y." In other words, "x" is equal to "b^y."

Using this definition, we can simplify the expression "10^log5" as follows:

10^log5 = 10^y

Where "y" is the exponent to which the base "10" must be raised to produce the result "5."

To find the value of "y," we can use the property of logarithms that states "log(b^y) = y." Applying this property to our expression, we have:

log(10^y) = y

Since "10^y" is equal to "5," we can substitute "5" for "10^y" in the above equation:

log(5) = y

Solving for "y," we find that "y = log(5)."

Therefore, the expression "10^log5" can be simplified to:

10^log(5) = 10^(log(5)) = 5

So the simplified result is 5.

The house that they will first meet if a group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house is the 24th house.

The smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple, or smallest common multiple of two integers, or lcm(a, b), in mathematics and number theory. Since the result of dividing an integer by zero is undefinable, this definition only applies if both a and b are not equal to zero.

Before fractions can be added, subtracted, or compared, the "lowest common denominator" can be employed.

From the information, a group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house.

It should be noted that this will be illustrated through tye lowest common multiple.

Multiples of 6 = 6, 12, 18, 24

Multiples of 8 = 8, 16, 24

Therefore, they'll meet at the 24th house.

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Slope of the line is .[tex]\frac{-4}{3}[/tex]

Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. As opposed to the net change in the x coordinate, the net change in the y coordinate is y.

y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

A line's slope is a measurement of how steep it is or the direction it is going in relation to a coordinate system.

where m is the slope and m = y/x

Take notice that tanФ = y/x.

This tanФ is often referred to as the line's slope.

The given equation is of the form [tex]ax+by=c[/tex]

On comparing we can say that a is -8 and b is -6

So using the slope formula [tex]\frac{-A}{B}[/tex] we get slope as [tex]\frac{4}{-3}[/tex]

The perpendicular line slope can be found out by equation [tex]m1.m2=-1[/tex]

Therefore substituting slope from the above as m1 we get m2 = [tex]\frac{3}{4}[/tex]

Slope of the line is .[tex]\frac{-4}{3}[/tex]

Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]

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Answer:4

Step-by-step explanation:

The value of x and z are [tex]4^\circ, 96^\circ[/tex].

Now from the picture I can say that, [tex]\angleAOB[/tex][tex]\angle AOB[/tex] and [tex]\angleCOD[/tex][tex]\angle COD[/tex] are opposite angles.

We know the measure of the triangle are equal in Pair.

So we have got the equation as -

[tex]10x+44=13x+32[/tex]

⇒[tex]13x-10x=44-32[/tex]

⇒3x=12

⇒x=4.

We have got that the measure of [tex]\angle AOB, \angle COD[/tex] are both [tex]84^\circ[/tex].

Now angles around a point add to [tex]360^\circ[/tex].

So, [tex]\angle AOD[/tex] and [tex]\angle BOC[/tex] are equal since they are pairwaite wisw.

Now, [tex]z+z= 360^\circ - (84^\circ+84^\circ)[/tex]

⇒[tex]2z=192^\circ[/tex]

⇒ [tex]z=96^\circ[/tex],

Hence we have got the value of x and z i.e. 4 and 96.

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The proof that AB = CD in the concentric circles is shown below

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

The concentric circles

This means that the circles have the same center

From the circles, we have the following congruent lines

AC = BD

Subtract BC from both sides of the equation

So, we have the following representation

AC - BC = BD - BC

Evaluate the difference

This gives

AB = CD

Hence, it is true that AB = CD

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Answer:

Hope it will help you...

Answer:

SSS, SAS, ASA, AAS

Step-by-step explanation:

s = sides

a = angle

Answer:

Here is answer

Step-by-step explanation:

To find the least common multiple (LCM) of three polynomials, we need to find the smallest polynomial that is divisible by all three of them.

Let's start by factoring each of the given polynomials:

ax² - (a² + ab)x+ a²b = a(x - b)x

bx² - (b² + bc)x+ b²c = b(x - c)x

cx² - (c² + ac)x + c²a = c(x - a)x

The LCM of these three polynomials is the smallest polynomial that is divisible by all three of them. In this case, the smallest such polynomial is (x - a)(x - b)(x - c)x. This is because it is divisible by each of the given polynomials and no smaller polynomial is divisible by all three of them.

Therefore, the LCM of the given polynomials is (x - a)(x - b)(x - c)x.

The number of pounds of clay used to make 21 small vases is 10 and one half pounds.

Sandy uses three and one half pounds of clay to make 7 small vases. Using proportion, the number of pounds of clay that she can use to make 21 small vases can be calculated as follows;

Therefore,

7 small vases = 3 1 / 2 pounds of clay(7 / 2)

21 small vases = ?

cross multiply

pounds of clay used to make 21 small vases = 7 / 2 × 21 ÷ 7

pounds of clay used to make 21 small vases = 147 / 2 ÷ 7

pounds of clay used to make 21 small vases =  147 / 2 × 1 / 7

pounds of clay used to make 21 small vases = 21 / 2

Therefore,

pounds of clay used to make 21 small vases = 10 1 / 2

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The original price is $171.59 and the price during sales is $148.37 then the percent markdown will be 13.53%.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Original selling price = $171.59

Price during sales = $148.37

Then, the percentage markdown will be,

% markdown = (171.59 - 148.37)/171.59 × 100

= 23.22/171.59 × 100

% markdown = 13.53%

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Total number of ways four people line up in the straight line with the given condition is equal to 18 ways.

As given in the question,

Total number of people = 4

Given condition :

First position can not occupied by youngest person:

First position occupied in 3 ways

Second position occupied in 3 ways

Third position occupied in 2 ways

fourth position occupied in 1 ways

Total number of ways = 3 × 3 × 2 × 1

                                  = 18 ways

Therefore, the number of ways four people stand in straight line is equal to 18 ways.

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Answer:

The answer is 71

What is chemist?

A chemist is a person who specializes in the science of chemistry, which is the study of matter and its properties, structure, composition, behavior, and the changes it undergoes. Chemists are trained in the scientific discipline of chemistry and use their knowledge to study and manipulate matter. This can include anything from the analysis of materials for their chemical makeup, to the development of new products and processes. Chemists can work in a variety of fields, including pharmaceuticals, materials science, biochemistry, research and development, and more. They must be well-versed in the principles and theories of chemistry, as well as in the practical aspects of their work. Through their work, chemists contribute to the advancement and application of science.

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Answer: the answer is 15

Step-by-step explanation:

The final answer is that the probability of rolling a six sided die six times and having all numbers from 1 through 6 appear once in any order is 1.54.

This is calculated by probability of independent events.

We know that any die can get any of the six sides and all the throws are independent, so their intersection is given by the product.

So, P(A and B occurring together )= P(A)P(B) if A and B are independent.

And the probability of the throws i.e. the no. of ways every throw gets a unique number is (6/6) x (5/6) x (4/6) x (3/6) x (2/6) x (1/6)

This is because, being the probability of independent events , they are multiplied.

so, the total probability is 6.5.4.3.2.1/6^6 = 1.54

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Answer:

5/13

Step-by-step explanation:

[tex]CE=\sqrt{10^2 + 24^2}=26 \\ \\ \cos E=\frac{10}{26}=\frac{5}{13}[/tex]

Retain the null because 1.74 is greater than 1.645.

What is z - test statistic?

Any statistical test for which the test statistic's distribution under the null hypothesis can be roughly represented by a normal distribution is known as a Z-test.

Z-tests examine a distribution's mean.

Let X be the average time that prescholars spend on tablets.

X ~ N(μ, α^2)

To test H0: μ = 3 hours Vs H1: μ ≠ 3 hours.

The z - test statistic is obtained as 1.74.

Taking level of significance α = 0.05

Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex]

Since the observed z - statistic is 1.74 which is less than Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex],

so we retain the null hypothesis.

Hence, retain the null because 1.74 is greater than 1.645.

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Complete question:

Complete question is attached below.

For a system with equations y = f(x) and y = g(x), the graph of the system will be just a coordinate plane with the two functions graphed on it.

What is functions graphed?

What Does Graphing Functions Mean? Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) represents the function. As an illustration, the graph below depicts the linear function f(x) = -x+ 2.

From this, we can see that the correct option is the first one:

"On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0)."

Also a graph of the system can be seen at the end of this answer.

Here our system is:

y = 3

x + y = 4

The first one is a horizontal line at y = 3.

The second can be rewritten as:

y =  -x + 4

So this is a line with a negative slope, that passes through the points (0, 4) (when you evaluate in x = 0, you get y = 4) and (4, 0) (when you evaluate in x = 4, you get y = 0)

Then the correct option is the first one:

"On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0)."

The graph can be seen below

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The equation that gives the relationship between cost (c) and area (a) is c = 2a

A variation is a relation between a set of values of one variable and a set of values of other variables

Given that: the cost (c) to paint a building varies directly with the area of the surface being painted (a) in square feet

We can write:

c α a

c = ka

where k is the constant of proportionality

since c = $3,000 and a = 1500

c = ka

3000 = 1500k

k = 3000/1500

k = 2

Thus, the equation of the relationship is c = 2a

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Answer: 19 feet

Step-by-step explanation:

The area, 266, divided by the width, 14, equals to 19 feet.

Answer:

Step-by-step explanation:

409/5 is 1/8. then 81.8 and then check by multiplying 81.8 by 5 and that equals 409.

Answer:

1. 4

2. rise = 2; run = 1; slope = 2

3. y = 2x + 4

Step-by-step explanation:

1. Look at the graph. On the y-axis, the line passes through 4. The line crosses the y-axis at 4, so 4 is the y-intercept, and b = 4 in the equation y = mx + b.

2. Choose any two points on the line. I choose the y-intercept, (0, 4) and point (-1, 2).

slope = rise/run

We need to go from point (-1, 2) to point (0, 4) by only moving vertically and horizontally. Start at (-1, 2). Go up 2 units. That is a ris of 2. Now go right 1 unit to arrive at point (0, 4). that is a run of 1.

slope = rise/run = 2

3. We have b = 4, and m = 2.

y = mx + b

y = 2x + 4

Answer: B

Step-by-step explanation:

A - Nope.

B - Possibility.

C. Nope. (2.23606797)

D. Nope.

When facing questions like this, it can be easier to use the process of elimination.

Answer: $23.40

Step-by-step explanation:

To find out how much Olivia spent on the bracelet, we need to subtract the cost of the sunglasses from the total amount spent. In this case, that would be $39.75 - $16.35 = $<<39.75-16.35=23.40>>23.40. Therefore, Olivia spent $23.40 on the bracelet.

453 cubic units of food is poured to the cylindrical dog feeder of 18 inches tall and has a diameter of 8 inches.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that the cylindrical dog feeder is 18 inches tall and  has a diameter of 8 inches

height is 18 inches

Diameter=8 inches

Radius =4 inches

The feeder is currently half full, how much more food can be poured into the feeder.

We know that volume of a cylinder is V=πr²h

Substitute the values of r and h in the given formula.

V=22/7(4)²×18

=22×16×18/7

=6336/7

=905.142.

As the feeder is currently half full, so let divide the volume by 2.

905.142/2

=452.5

=453

Hence, 453 cubic units more food is need or poured into the feeder.

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The probability of experiencing only nausea is 0.06.

Using Venn Probabilities, it is found that there is a 0.45 = 45% probability of experiencing neither of the side effects.

What is a Venn probability?

In a Venn probability, two non-independent events are related with each other, as are their probabilities.

The "or probability" is given by:

P(N∪D) = P(N) + P(D) - P(N∩D)

In this problem, the probabilities given are:

P(N)= 0.2 , P(D)= 0.45 , P(N∩D) = 0.14

The "at least one" probability is:

P(N∪D) = 0.20 + 0.45 - 0.14 = 0.51

Hence, the "neither" probability is:

1 - P(N∩D) = 1 - 0.51 = 0.49

The probability of experiencing only nausea = P(nausea) - P(both side effects)

                                                                           =0.20 - 0.14

                                                                            =0.06

0.49 = 49% probability of experiencing neither of the side effects.

The probability of experiencing only nausea is 0.06.

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Answer:

52

Step-by-step explanation:

Order of Operations says to do Parenthesis first, then exponents.

8 x 3²- (14+ 6)

= 8 x 3²- (20)

= 8 × 9 - 20

Then multiply before subtracting in this question.

= 72 - 20

= 52

The volume of a box in the shape of a rectangular prism is y³ +7y² +10y cm³.

What is a rectangular Prism ?

A polyhedron with two congruent and parallel bases is known as a rectangular prism. It's also known as a cuboid.

A rectangular prism has six faces, each of which is in the shape of a rectangle and has twelve edges. It's called a prism because of its cross-section along its length.

It is given that length of the rectangular prism has length of 2 cm more than  the width and 3 cm less than the depth

Let the depth be x cm

and width be y cm

Then the length will be y+2 cm and x-3 cm

y+2 = x- 3

x = y+5

A rectangular prism is a cuboid with six faces

Volume of a rectangular prism can be written as

length * width * depth

= (y+2) *x*y

= (y+2)* (y+5)*y

= (y²+2y)(y+5)

= y³ +5y²+2y²+10y

= y³ +7y² +10y cm³

Therefore the volume of a box in the shape of a rectangular prism is y³ +7y² +10y cm³.

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