Lois made a dish with 5 1/3 cups of pasta. One serving of the pasta is 0.4 cups. How many servings of pasta were in the dish Lois made?

The true statement is that the counterexample must satisfy the conclusion of the conditional statement.

A counterexample is a situation in which the hypothesis and conclusion are both accurate. We employ a counter example to show that a conditional assertion is untrue.

The true statement regarding the counterexample can be written as a conditional assertion.

This is shown to be untrue by a counterexample,

Therefore, only one counter-example is enough to demonstrate the falsity of a proposition. In this case where a counterexample is used to refute a conditional statement.

The counter-example should be supported the conditional statement's hypothesis.

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The graph that represents the given table is graph 2

The table is given,

At x = 0

The value of y = -2

The y intercept of the line is -2

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line

The two points are (0, -2) and (1, -3.5)

The slope of the line m = [tex](\frac{y_2-y_1}{x_2-x_1} )[/tex]

Substitute the values in the equation

The slope of the line = -3.5 - (-2) / 1 - 0

= -1.5 /1

= -1.5

The slope of the line is negative and the y intercept of the line is negative, the correct graph is graph 2

Hence, the graph that represents the given table is graph 2

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In order to find the standard error of two samples, the following are needed:

1: Find the mean. .

2: Find each score's deviation from the mean. ...

3: Square each deviation from the mean.

4: Find the sum of squares.

5: Find the variance.

6: Find the square root of the variance.

The standard error is a statistical term that refers to the degree to which a sample distribution accurately represents a population using standard deviation.

A statistic's standard error is the standard deviation of its sampling distribution or an estimate of that standard deviation. The standard error of the mean is used when the statistic is the sample mean.

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To determine the standard error of two samples the following procedure are followed

First, determine the mean.

second: Calculate the variation between each score and the mean

third: Square each variation from the mean

4th: Determine the sum of the variance

5th: Determine the variance by dividing the sum in 3 by 1 less the number of sample

6th: Calculate the standard deviation by variance's square root

7th: find the square toot of the number of samples

lastly: divide the standard deviation by result of step 7

The population mean's likelihood to differ from a sample mean is indicated by the standard error of the mean, or simply standard error.

It reveals how much the sample mean would change if you conducted the same study again with fresh samples drawn from a single population.

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The differentiation or rate of change of the given function y = ln x² will be  2/x.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

For example the speed 3meter/second.

As per the given,

y = ln x²

By log property

y = 2ln x

Take the first derivative,

dy/dx = 2/x

Hence "The differentiation or rate of change of the given function y = ln x² will be  2/x".

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The rearranged formula with the x as subject is x = 2y - 10

Formula

Formula refers a fact or a rule written with mathematical symbols. It usually connects two or more quantities with an equal sign.

Given,

Here we have the formula y = 1/2x + 5

Now, we have to rearrange the given formula in order to make x as the subject.

Here we we need to find the formula, as x the subject,

So, the given formula,

y = 1/2 x+ 5

We have to move the number 5 to the left hand side, then the sign of the number changes into negative,

So, it can be written as,

=> y - 5 = 1/2x

Here we need the value of x alone, so move the number that is in division to the LHS, then it will be changed as multiplication, then we get,

=> 2 (y - 5)  =x

When we expand it, then we get,

=> 2y - 10 = x

Therefore, the formula that has x as subject is 2y - 10.

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The maximum value of the quadratic function F(x) = -3x² + 18x + 3 is 30 when x = 3

The quadratic equation is given as

F(x) = -3x² + 18x + 3

The above function is a quadratic function

As a general rule, a quadratic function has the following representation:

F(x) = ax² + bx + 3

This means that: a = -3

The value of a for a quadratic function must be less than 0 for the function to have a maximum

This means that the function has a maximum value because -3 is less than 0

Solving further, we have

F(x) = -3x² + 18x + 3

Differentiate and set to 0

-6x + 18 = 0

So, we have

x = 3

Substitute x = 3 in F(x)

F(3) = -3(3)² + 18(3) + 3

Evaluate

F(3) = 30

This represents the maximum value

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The amount you need to sell the job if you want to make 15% net margin, based on the costs, is $7, 857.26

First, find the total cost for the project:
= Equipment + cost of labor + overhead

Cost of labor and equipment:

= 4, 200 + ( 16 x 32 per man- hour)

= $ 4, 712

The total cost is then:
= 4, 712 x ( 1 + 45%)

= $6, 832.40

The amount to sell for is:
= Total cost x ( 1 + net margin)

= 6, 832.40 x ( 1 + 15%)

= $7, 857.26

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Using the angle sum property and the definition of congruency, the measure of angle G is determined to be 118°.

Therefore,

ΔCAT ≅ ΔDOG

m∠C = 25°

m∠O = 37°

The following formula is used to determine angle ∠G:

According to the definition of congruency, the arrangement of the letters in the congruency statement shows that angle ∠C is congruent to angle ∠D, angle ∠A is congruent to angle ∠O, and angle T is congruent to angle ∠G, indicating that we have;

m∠C = m∠D = 25°

m∠A = m∠O = 37°

m∠T = m∠G

The measure of angle ∠G and angle ∠T can therefore, be found from the angle sum property of the interior angles of a triangle.

m∠C + m∠A + m∠T= 180° (angle sum property of a triangle)

m∠D + m∠O + m∠G= 180° (angle sum property of a triangle)

m∠G = 180° - (m∠D + m∠O) (subtraction property of equality)

m∠G = 180° - (25° + 37°) = 118°

The measure of angle ∠G, m∠G is 118°

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1. ≈ 33759 bees

The parent function for exponential functions is y = a(b^x), where "a" is the initial value and "b" is the growth rate. In this case, "x" is the number of days, and "y" is the number of bees after "x" days. We already know that the initial value is 20, so we can set "a = 20". Next, we know that after 5 days, there are 29 bees, which we can also plug into our equation: "x = 5" and "y = 29". Then, we end up with the equation 29=20(b^5) and solve for the growth rate, "b". To solve for "b", first divide both sides by 20, and then take the 5th root of both sides:

29 = 20(b^5)

29/20 = b^5

^5√(29/20) = ^5√(b^5)

^5√(29/20) = b

Now, we know the equation to this problem is y = 20((^5√(29/20))^x). We can plug in "x = 100" to find the number of bees after 100 days.

y = 20((^5√(29/20))^100)

y ≈ 33759 bees

2. No, you can't find the inverse of the function y=4x^2 + 12x + 9, because, for an inverse to be possible, it must pass the horizontal line test, which this function does not pass. The domain restriction necessary would have to make it so the function passes the horizontal line test, which would mean restricting half of the function from its vertex in this case. The x-value of the vertex (refer to the vertex formula) of this function is -12/8, so we can restrict the domain by only letting the domain be [-12/8, +infinity). Finding the inverse (switch "x" and "y", and solve for "y"):

x = 4y^2 + 12y + 9                                x:  [-12/8, +infinity)

x - 9 = 4y^2 + 12y

x - 9 = 4y^2 + 12y

(x - 9)/4 = y^2 + 3y

(x - 9)/4 + 2.25 = y^2 + 3y + 2.25

(x - 9)/4 + 2.25 = (y + 1.5)^2

√((x - 9)/4 + 2.25) = y + 1.5

√((x - 9 + 9)/4) = y + 1.5

(√(x) / 2) - 1.5 = y

(-3 + √(x))/2 = y

3a. To solve this problem, we have to find a way to use "log base5 of 3" and "log base5 of 8" to get "log base5 of 2".

First, we can exclude the logbase5 so the problem is easier to look at. We need to find a way to get "2" using "3" and/or "8" (cannot use subtraction/addition in this step, and using "3" and/or "8" is required with multiplication/division). Keep in mind the rules of logs with the same base.

8^1/3 = 2

Now, we put the logbase5 back in:

logbase5 of (8^1/3) = logbase5 of 2

From log rules, we can move the exponent "1/3" down:

1/3 * logbase5 of 8

We know that logbase5 of 8 = 1.2920

1/3 * 1.2920

approximately 0.4307

3b. As previously explained, we need to use "3" and "8" to get to "75/8" while keeping in mind the rules of logs.

First, we can simplify "logbase5 of (75/8)":

logbase5 of (75/8) = (logbase5 of 75) - (logbase5 of 8)

Now, ignore the "logbase5" and use provided values of "3" and "8" to get to 75. Note that we can use the number 5: logbasex of x= 1 [x^1 = x]

(5^2) * 3 = 75

Next, place the "logbase5" back in, and simplify

logbase5 of ((5^2) * 3) - logbase5 of 8

logbase5 of (5^2) + logbase5 of 3 - logbase5 of 8

2logbase5 of 5 + logbase5 of 3 - logbase5 of 8

2(1) + 0.6826 - 1.2920

approximately 1.3906

The value of 4x - 16y is -11.

4x - 16y = -11.

Given, two equations

−5x + 10y = 1 and −x − 6y = −10

Now, On subtracting both the equations, we get

−5x + 10y + x + 6y = 1 + 10

- 4x + 16y = 11

On multiplying both the sides by -1, we get

4x - 16y = -11

Hence, the value of 4x - 16y is -11

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A. 136 in.
When spinning 180, you face backwards. When the initial spins, you can just think of it as moving the horn from the left hand to the right. That happens a second time. Two arms is equal to 68 in., so double of that is 136 in.

I don’t believe I can solve the 2nd question

Answer:

y = 8/9 x - 4

Step-by-step explanation:

y-4 = 8/9(x-9)

y-4 = 8/9 x -8

y = 8/9 x +4 -8

y = 8/9 x -4

Answer:

y=8/9x-4

Step-by-step explanation:

4=8/9(9)+2

4=72/9+2

4=8+2

4=10

10-4=6

2-6=-4

4=8/9(9)-4

4=8-4

4=4

Hopes this helps please mark brainliest

Answer:

O Liquid water warms and changes to water vapor.​

Step-by-step explanation:

Formula a = 2b + c in subject to b is b = a-c / 2

Changing the subject of formula is a way of rearranging formula to determine missing variable in terms of other variable

Changing the subject of formula is also known as rearranging formula or changing the subject of an equation.

Given ,

Formula : a = 2b + c

Subtracting by c on both sides,

=> a - c = 2b + c - c

=> a - c = 2b

Dividing by 2 on both sides,

=> [tex]\frac{a-c}{2} = b[/tex]

Formula in subject to b is

b = a-c / 2

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The difference between a positive mixed number and negative mixed number is never positive is false.

Depending on how the phrases might be ordered

Hence the given statement, the difference between a positive mixed number and negative mixed number is never positive is false.

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Answer:

35%

Step-by-step explanation:

35 divided by 100 = 0.35 = 35%

The equations that are true include the following:

(8 × 7)/2 - 12 = 22 - (2 × 3)

48 ÷ 8 + 2³ = 5 + 3²

In order to determine the equations that have a true and valid solution, we would simplify and evaluate each of the equations as follows:

(8 × 7)/2 - 12 = 22 - (2 × 3)

Opening the bracket on both sides of the equation, we have:

56/2 - 12 = 22 - 6

28 - 12 = 16

16 = 16 (True).

48 ÷ 8 + 2³ = 5 + 3²

Evaluating the exponents, we have:

48 ÷ 8 + 8 = 5 + 9

6 + 8 = 14

14 = 14 (True).

150/5² = 30 - 4² - 12

Evaluating the exponents, we have:

150/25 = 30 - 16 - 12

6 = 2 (False and incorrect).

9² - 7² = 20 ÷ (7 - 2)

Opening the bracket, we have:

9² - 7² = 20 ÷ 5

Evaluating the exponents, we have:

81 - 49 = 4

32 = 4 (False and incorrect).

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The probability that a brand new battery lasts for atleast 2 years is 0.801

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

Mean, λ = 3 years

The probability of a Poisson distribution is represented as

P(x) = λˣe⁻λ/x!

In this case,

x = At least 2

This means that

x = 2, 3....

So, we have

P(x ≥ 2) = 1 - P(0) - P(1)

This gives

P(x ≥ 2) = 1 - 3⁰ * e⁻³/0! - 3¹ * e⁻³/1!

Evaluate

P(x ≥ 2) = 1 - 0.0497 - 0.1494

Evaluate the difference

P(x ≥ 2) = 0.801

Hence, the probability is 0.801

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The answer of the problem by the SAS similarity theorem sides is [tex]\frac{AC}{GI} = \frac{HI}{BC}[/tex].

What is the SAS similarity theorem of triangle?

According to the SAS similarity theorem, two triangles are considered similar if their included angles are congruent and their two sides are proportionate to one other.

It is also known as Side-Angle-Side similarity of two triangles.

There is a common ratio of sides in the given problem figure, which is,

                                   [tex]\frac{AC}{GI} = \frac{HI}{BC}[/tex]

Additionally, these similar sides produce equal relative angles,

                              ∠[tex]ACB =[/tex] ∠[tex]GIH[/tex]

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The Y coordinate of the new point is -1.28 y.

So, the new Y coordinate is:

The rule of dilation for the quadrilateral D is:

The new coordinate plan is:

Then, calculate the Y coordinate as follows:

Therefore, the Y coordinate of the new point is -1.28 y.

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In the national park, the probability that a single doe captured (weighed and released) at random in December is undernourished is 25.5%

Data is symmetrically distributed and skew-free in a normal distribution. When the data is shown on a graph, it has the shape of a bell, with the majority of values congregating in the center and diminishing as they move outward.

Due to their structure, normal distributions are sometimes known as bell curves or Gaussian distributions.

Assuming normal distribution we calculate the probability as follows

Definition of variables

mean adult female deer, μ = 67.0 kg

Standard deviation, σ = 7.9 kg

sample, X = 58

Z score, z is given by the formula

= (X - μ) / σ

= (58 - 67) / 7.9

= -1.139 has a p value of 0.2546

P = 25.5%

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Answer:

5 and 11

Step-by-step explanation:

x =2

fx=3x-1

3(2)-1

6-1

= 5

when x= 4

fx=3x-1

3(4)-1

12-1

11

f(x) =5 and 11

Answer:

5 and 11

Step-by-step explanation:

Input the values of x in the function and solve using basic mathematical operations.

[tex]f(2)=3(2)-1=6-1=5\\\\\\f(4)=3(4)-1=12-1=11[/tex]

Answer:

9i

Step-by-step explanation:

         i² = -1

      [tex]\sqrt{-81}=\sqrt{81i^2}\\[/tex]

                [tex]\sf \bf = \sqrt{9*9*i * i}\\\\ = 9i[/tex]

Y=21,000(1.20)*. D=anan1 d = a n a n 1 is the formula for figuring out the common difference of an arithmetic series, where d is the common difference and an a n is the nth term. A common difference in an arithmetic series is one between any term and its predecessor, and it is typically denoted by the letter "d".

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Answer:

Step-by-step explanation:

10$ for cheese pizza
15$ for peproni pizza

he sold 64 pizza in which 3 of them are of cheese
so therefore,

64-3=61
61*10 = 610
3*15  =  45

           ---------

           $655

The percentage of $0.95 to $3.80: 25%

What is Percentage?

A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

The terms "out of 100" and "for every 100" can also be used to refer to percentages. For instance, you may say "it snowed 20% of the time" or "it snowed 20 days out of every 100 days."

A decimal can also be used to represent a percentage. For instance, 24 percent, 0.24, 24/100, or 24 hundredths could also be used to represent the percentage. By dividing the percentage by 10, you can obtain the percent in decimal form.

Given,

The material cost for one headband = $0.95

The cost of one headband sold = $3.80

Now to take the percentage of the cost of material of the headband to the selling price of the headband will be:

= (0.95/3.80) x 100

it can be also written as

= (0.95 x 100)/3.80

= 95 / 3.80

= 25%

Hence, The percentage of $0.95 to $3.80 is 25%

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The length longer of the green caterpillar than the orange caterpillar is 2 1/2 inches.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the green caterpillar was 4 inches long and the orange caterpillar was 1 1/12 inches long.

The difference in length will be:

= 4 - 1 1/2

= 2 1/2 inches.

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Step-by-step explanation:

A quadratic equation is in the form of

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

C is the y intercept a.k.a the value of c is when x=0,

when x is 0, c is -7 so

c=-7

[tex] {ax}^{2} + bx - 7 [/tex]

Next we know when x is 2, y is 1 so

[tex]a(2) {}^{2} + 2b - 7 = 1[/tex]

[tex]4a + 2b = 8[/tex]

When x is 5, y is -2

[tex]a(5) {}^{2} + b(5) - 7 = - 2[/tex]

[tex]25a + 5b = 5[/tex]

So we have a system of equations, using elimination.

[tex]5a + b = 1[/tex]

[tex] - 6a = 6[/tex]

[tex]a = - 1[/tex]

So

[tex]5( - 1) + b = 1[/tex]

[tex]b = 6[/tex]

Our quadratic is

[tex] - {x}^{2} + 6x - 7[/tex]