is 20 bigger than -20

Answer:

Step-by-step explanation:

Add together:  2 2/3 hrs and 2 3/4 hrs:

First determine the LCD of these two fractions.  The LCD here is 3*4 = 12.

Rewrite the given times using this LCD:

2 8/12 + 2 9/12

Adding 2 and 2 results in 4; adding 8/12 and 9/12 results in 17/12, or 1 5/12.

The final result is 4 + 1 5/12, or 5 5/12.

The movie and dinner together lasted 5 5/12 hrs.

If movie and dinner started at 3:00, dinner would have finished at

3:00 + 5:5/12, or

8:25 p.m. (since 5:5/12 is the same as 5:25).

Finished eating at 8:25 p.m.

Answer:

Finished eating at 8:25 and both lasted 5:25 hours in total

Step-by-step explanation:

Answer: The tip is $14.00

Step-by-step explanation: 20% of 70 is 14.

The nutritionist should perform hypothesis testing followed by Independent T-test to see if coffee and tea differ in mean caffeine content .

We need to Know about Hypothesis testing and independent t test to answer this-

Hypothesis testing is a type of statistical test that is used to comapare data and drawing conclusion from them.

An independent t-test is a statistical test that determines whether the means of two unrelated groups are significantly different from each other.

We can find the difference caffeine content following these steps -

1)H0=Null hypothesis=tea and coffee has same caffeine level

HA=tea and coffee has different caffeine level

2)The independent samples t-test is utilized to determine whether two different sample means come from the same population or whether they come from two distinct populations with different mean values. Two populations can be considered independent when the data in one group is not connected to the data in the other group.

The t value obtained should be then performed under hypothesis testing.

3)And the calculated T value should be comaperd with the desired significance level (generally =0.05) and if the t value comes in between the critical values the nutritionist can assume that both tea and coffee has same caffeine level in this null hypothesis will be accepted.

Whereas if the calculated t value doesn't falls in between the critical value then the nutritionist can assume that tea and coffee has different caffeine level.

Hence null hypothesis will be rejected.

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Answer:

I hope this Will help you

Answer:

yes your answer is

The z-score of apple price of $7.99/lb is 0.66

Probability is a measure of the possibility of an event occurring.

The likelihood could range from 0 to 1, where 0 indicates an impossibility and 1 indicates a certainty.

Every event in a sample space has an overall probability of one.

The probability that the apple price is less than or equal to $7.99 / lb can be calculated using the normal distribution method

                                   P(x ≤ 5.99)

The standard form of the given random sample can be found using the formula,

                               Z = (X - μ) / σ

where Z is the standard score

          X is the random sample

          μ is the mean

          σ is the standard deviation.

For x =7.99,

                  Z = (7.99 - 5.99) / 2.99

                      = 2 / 2.99

                  Z  = 0.66

Therefore, by standardizing the random sample, we get

              P(x ≤ 5.99) = P( z ≤ 0.66)

By using the z-table, we get the value of z

            P(z ≤ 0.66) = 0.7454

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The scale factor of the dilation transformation of the pre-image triangle ΔDEF to the image ΔD'E'F', with the origin as the center of dilation is 3.

A dilation transformation is one in which the lengths of the sides of the pre-image are scaled up by a common factor to get the lengths of the sides of the image.

The coordinates of the vertices of the triangle ΔDEF are;

D(1, 5), E(1, 2), F(3, 2)

The length of the sides of triangle ΔDEF, making use of the difference between the non equal coordinate points, are;

DE = 5 - 2 = 3

EF = 3 - 1 = 2

The length of the side DF can be found using the formula for the distance between two points on the coordinate plane (a form of the Pythagorean Theorem), which is presented as follows;

DF = √((3 - 1)² + (2 - 5)²) = √(2² + (-3)²) = √(13)

The coordinates of the vertices of triangle ΔD'E'F' are; D'(3, 15), E'(3, 6), F'(9, 6)

Therefore; D'E' = 15 - 6 = 9

E'F' = 9 - 3 = 6

D'F' = √((9 - 3)² + (6 - 15)²) = √(6² + (-9)²) = √(9 × 13) = 3·√(13)

The scale factor, s.f. = The ratio of the corresponding sides of the triangles which is found as follows;

D'E'/DE = 9/3 = 3

E'F'/EF = 6/2 = 3

D'F'/DF = 3·√(13)/√(13) = 3

s.f. = D'E'/DE = E'F'/EF = D'F'/DF = 3

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Answer:

\(\large \boxed{\mathrm{seven }}\)

Step-by-step explanation:

\(7^2\)

A number squared also means that the number is multiplied by itself twice.

\(7^2 =7 \times 7\)

The value of "i" squared or 1 i by 1 i results in:

(-1)

Among the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.

Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.

In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:

√(-1) x √(-1) = i²

[√(-1)]² = i²

(-1) = i²

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Answer:

C

Step-by-step explanation:

The given equation is : \(\[ \frac{11}{2} y+\frac{1}{3}=\frac{7}{4} y \]\)Step-by-step explanation to solve the given rational equation :To solve the given equation, we need to follow some steps:Step 1 : We need to get all the fractions on one side of the equation and the integers on the other side of the equation.

Here, we move the \(\[\frac{11}{2} y\]\) to the right side of the equation by subtracting it from both sides of the equation.\(\[ \frac{11}{2} y=\frac{7}{4} y-\frac{1}{3} \]\)

Step 2 : We need to simplify both sides of the equation by finding a common denominator and combining like terms.Here, we can see that the common denominator is \[12\] . Multiplying all terms in the equation by

\(\[12\]\) gives, \(\[ 6\cdot11y + 4\cdot1=3\cdot7y\] \[ 66y + 4 = 21y\]\)

Step 3 : We can now solve for \(\[y\]\).

We get, \(\[ 66y - 21y = -4 \] \[ 45y = -4 \] \[y=\frac{-4}{45}\]\)

Therefore, the solution to the rational equation

\(\[\frac{11}{2} y+\frac{1}{3}=\frac{7}{4} y\]\) is \(\[ \left\{-\frac{4}{45}\right\}\]\)

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Answer:

y - 3 = - 5(x - 6)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 5 and (a, b) = (6, 3) , then

y - 3 = - 5(x - 6)

Given :-

To Find :-

Solution :-

As we know that the point slope form of the line is ,

→ y - y1 = m ( x - x1 )

→ y - 3 = -5( x - 6)

Hence the required answer is y - 3 = -5( x - 6 ) .

Answer:

x = 121°

Step-by-step explanation:

The lower left interior angle of the triangle is adjacent to 115° and are supplementary, thus

interior angle = 180° - 115° = 65°

The angle round a point is 360°

The vertex interior angle = 360° - 304° = 56°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle, thus

x = 65° + 56° = 121°

Answer:i think its 115 degres

Step-by-step explanation:

Step-by-step explanation:

Share 20pounds in the ratio 2:3

Total ratio=2+3=5

2/5×20=8

20-8=12

Sharing 20pounds in that ratio gives 8pounds:12pounds

Share 15cm in the ratio 1:3

Total ratio=1+4=4

¼×15=3.75

15-3.75=11.25

Sharing 15cm in that ratio gives 3.75:11.25

The position of -1 and > -1 it would be located on the right side of -1 on the number line

In the above question,

We need to indicate > -1 about the positions of and −1 on the number line

The horizontal straight lines in mathematics known as number line are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. This line continues forever at both ends.

So, if we look at the position of -1 and > -1 it would be located on the right side of -1 on the number line

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The solution of the given equation is x = 4i-3.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given equation is  x² + 6x + 13 = 0. The solution of the equation will be done as,

x² + 6x + 13 = 0

( x + 3 )² - 3² + 13 = 0

( x + 3 )² - 9 + 13 = 0

( x + 3 )² = -4

( x + 3 ) = √-4

( x + 3 )²  = 4i

x = 4i - 3

Therefore, the solution of the given equation is x = 4i-3.

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The probability that the cook adds the right ingredients and cooks well is 0.75

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

Right ingredients = 9 times

Errors = 3 times

using the above as a guide, we have the following:

Total = 9 + 3

Evaluate the sum

Total = 12

The probability that the cook adds the right ingredients and cooks well is

P = Right ingredients/Total

So, we have

P = 9/12

Evaluate

P = 0.75

Hence, the probability is 0.75

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Answer:

The volume of existing cage = length x widht x height = 3 x 2 x 3 = 18 cubic ft

Now she wants cage with volume four times of this cage

New Volume = V1 = 18 x 4 = 72 cubic ft

Keeping length same = 3 ft

Length x width x height = V1

3 x Width x height = 72

Width x height = 72 /3

Width x height = 24

Now multiple of 24 must be the width and height.

Taking width = 6 ft and height = 4 ft, we will get our answer

Proof:

Length x width x height = V1

3 x 6 x 4 = 72

You poured approximately 0.267 liters of cooking oil from the entire large bottle into the smaller bottle.

To find out how much of the entire large bottle of cooking oil was poured into the smaller bottle, we need to multiply the fraction of the large bottle that was poured into the smaller bottle by the total amount of cooking oil in the large bottle.

Given that you have \(\frac{4}{9}\) of the large bottle of cooking oil, the fraction of the large bottle that you poured into the smaller bottle is \(\frac{3}{5}\) of \(\frac{4}{9}\). We can find this fraction by multiplying \(\frac{3}{5}\) by \(\frac{4}{9}\):

\(\frac{3}{5} * \frac{4}{9} = \frac{12}{45}\)

Simplifying this fraction by dividing both numerator and denominator by 3, we get:

\(\frac{12}{45}= \frac{4}{15}\)

Therefore, you poured \(\frac{4}{15}\) of the entire large bottle of cooking oil into the smaller bottle. To find the actual amount, you can multiply this fraction by the total amount of cooking oil in the large bottle. For example, if the large bottle contains 1 liter of cooking oil, then you poured:

\(\frac{4}{15} * 1 = 0.267\) liters.

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Answer:

c

Step-by-step explanation:

that's the answer dudnjdkdkd

The limiting value of the slope is 2. The equation of the tangent line to the curve at point P(2, -12) is y = 2x - 16.

To find the slope of the curve \(y = x^3 - 10x\) at the point P(2, -12), we can find the limiting value of the slope of the secants through P.

The slope of the secant through point P with another point (x, y) on the curve is given by the formula:

m = (y - (-12)) / (x - 2)

= (y + 12) / (x - 2)

To find the limiting value as the point (x, y) approaches P, we can take the limit as x approaches 2:

lim(x→2) [(y + 12) / (x - 2)]

Now, let's find the derivative of the function y = x^3 - 10x to determine the slope of the tangent line at point P. Taking the derivative with respect to x, we have:

\(y' = 3x^2 - 10\)

Now we can substitute x = 2 into the derivative to find the slope of the tangent line at point P:

\(m = 3(2)^2 - 10\)

= 12 - 10

= 2

Therefore, the slope of the curve \(y = x^3 - 10x\) at the point P(2, -12) is 2.

To find the equation of the tangent line at point P, we can use the point-slope form of a line and substitute the coordinates of P and the slope we found:

y - (-12) = 2(x - 2)

y + 12 = 2x - 4

y = 2x - 16

Therefore, the equation of the tangent line to the curve at point P(2, -12) is y = 2x - 16.

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Answer:

I think g would be correct

According one-way ANOVA, the test is false.

We learn about one-way ANOVA

"One-Way ANOVA, also known as "analysis of variance," examines the refers to two or more independent groups to see if there is statistical support for the notion that the related population means are statistically substantially different."

According to the given information, it is inappropriate to compare two means at a time using multiple independent two sample​ t-tests. It will create multiple testing problem and error.

So using one way ANOVA test when comparing three or more populations refers to within a set of quantitative data that is categorized according to one​ factor/treatment and compare two means at a time using multiple independent two sample​ t-tests is false.

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There are 10 people running for the 7 seats in the school's student council. The number of different student council combinations is 120.

To calculate the number of different student council combinations, we can use the concept of combinations, specifically the formula for selecting r objects from a set of n objects without replacement. In this case, we have 10 people running for 7 seats, which means we need to select 7 people from the group of 10.

The formula for combinations is given by:

C(n, r) = n! / (r!(n - r)!)

Plugging in the values, we have:

C(10, 7) = 10! / (7!(10 - 7)!)

= 10! / (7!3!)

Using factorials, we can simplify this calculation:

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040

3! = 3 x 2 x 1 = 6

Substituting these values back into the formula:

C(10, 7) = 3,628,800 / (5,040 x 6) = 120

There are 120 different student council combinations possible when 10 people are running for the 7 available seats. This means that out of the 10 candidates, any group of 7 can be chosen to form the student council in a total of 120 different ways.

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The two column proof to justify the complementary angles are;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

Complementary angles are defined as angles that sum up to 90 degrees.

Now, from the question, we are given that;

∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

From the image attached, we can get a two column proof based on the given questions as;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

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Complete Question is;

Identify the correct justification for each step, given that ∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

2. m∠1 + m∠2 = 90°

3. m∠2 + m∠3 = 90°

4. m∠1 + m∠2 = m∠2 + m∠3

5. m∠1 = m∠3