When solving an inequality, if you the coefficient is negative, as in-3x > 9, the inequality
True
False

Answer:

To find the coefficient of variation (CV) of a sample, we divide the standard deviation by the mean and multiply by 100 to get the percentage.

1. For the systolic sample:

•Find the mean:

mean = (116 + 130 + 157 + 94 + 155 + 122 + 115 + 138 + 124 + 122) / 10 = 130

•Find the standard deviation:

sum = (116 - 130)^2 + (130 - 130)^2 + (157 - 130)^2 + (94 - 130)^2 + (155 - 130)^2 + (122 - 130)^2 + (115 - 130)^2 + (138 - 130)^2 + (124 - 130)^2 + (122 - 130)^2

sum = 165.4

std = sqrt(sum/9) = 7.3

•Calculate the coefficient of variation:

CV = (std / mean) × 100 = (7.3 / 130) × 100 = 5.62%

2. For the diastolic sample:

•Find the mean:

mean = (82 + 78 + 74 + 51 + 89 + 88 + 56 + 63 + 72 + 83) / 10 = 72.5

•Find the standard deviation:

sum = (82 - 72.5)^2 + (78 - 72.5)^2 + (74 - 72.5)^2 + (51 - 72.5)^2 + (89 - 72.5)^2 + (88 - 72.5)^2 + (56 - 72.5)^2 + (63 - 72.5)^2 + (72 - 72.5)^2 + (83 - 72.5)^2

sum = 624.75

std = sqrt(sum/9) = 12.24

•Calculate the coefficient of variation:

CV = (std / mean) × 100 = (12.24 / 72.5) × 100 = 16.82%

So the CV for systolic is 5.62% and the CV for diastolic is 16.82%. We can see that the diastolic measurement has higher variation than the systolic measurement.

The values are a = 16.69, c=16.68 ad m∠C = 22.07°.

What are trigonometric ratios?

Trigonometric ratios are mathematical functions that describe the relationship between the angles and sides of a right triangle. The three main trigonometric ratios are the sine, cosine, and tangent.

In the given figure, by using trigonometric ratios, we can find

sin68° = a/18

18 sin 68° = a

Using a calculator, we can find that sin 68° is approximately 0.9272. Multiplying 18 by 0.9272 gives us:

a ≈ 16.69

Therefore, a is approximately 16.69.

cos68° = c/18

18 cos 68° = c

Using a calculator, we can find that cos 68° is approximately 0.3714. Multiplying 18 by 0.3714 gives us:

c ≈ 6.68

Now

sinC = c/18

[tex]C = sin^{-1}(\frac{6.68}{18})\\\\C = sin^{-1}(0.3714)\\\\C = 22.07\degree[/tex]

Hence, the values are a = 16.69, c=16.68 ad m∠C = 22.07°.

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The function g(x) = (x - 3)³ is shown in the graph. The solution has been obtained by using the concept of transformation.

What is transformation?

Any action that moves a polygon or other two-dimensional object on a plane or coordinate system is referred to as a transformation.

Translation, rotation, reflection, and dilation are all methods of transformation.

We are given a graph, from which we can say that when x = 3, then y = 0

The function must satisfy these values.

The functions g(x) = (x + 3)³ , g(x) = x³ + 3 and g(x) = x³ − 3 does not satisfy the point (3,0).

Also, the translation is 3 units to the right.

So the function shown in the graph is g(x) = (x - 3)³.

Hence, the transformed function is g(x) = (x - 3)³.

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Question: If the parent function is f(x) = x³, which transformed function is show in the graph?

g(x) = (x − 3)³ , g(x) = (x + 3)³ , g(x) = x³ + 3 , g(x) = x³ − 3

If John has 3 of 4 slices of pie, and Tom has 2 of 6 slices of pie, how many do they have all together?

I believe that is what type of story you needed, if wrong let me know.

Answer: Suppose Rita is trying to find the area of the carpet of 3/4 and 2/6 for a room of 4/4 sq to 6/6 sq with balcony of 1/4 and 4/6

Explanation: In the given rectangle fig. length is given 3/4 and breadth is given 2/6 for the whole rectangle is 4/4 to 6/6.

for each block length is given 1/4 and breadth is given 1/6. The darker shaded area represents the carpet of the above story.

The answer after multiplying it is 6/24 or 1/4.  

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Answer:

-

Step-by-step explanation:

the question isn't clear enough to answer it

The distance at which Allison should stand to catch the ball will be 8.32 m.

What is speed?

Speed of an object is defined as the ratio of distance covered by the object to the time taken by the object to cover that distance. In other words its tell how much times an object takes to cover a particular distance.

Now for the given question:

Emily throw the ball at 30° below the horizontal towards Allison at a speed of 12m/s. So here we will calculate the Horizontal and Vertical components of the speed.

[tex]v_{x}[/tex]=12cos30°=10.4 m/s

[tex]v_{y}[/tex]=12sin30°=6 m/s

Vertical distance between Alice and Emily according the question is 8 m.

s= 8 m.

Now by applying Second equation of motion to calculate time take by ball to move from Emily to Allison.

s=[tex]v_{y}[/tex]×t+[tex]\frac{1}{2}[/tex]×a×[tex]t^{2}[/tex]

4= 6×t+[tex]\frac{1}{2}[/tex]×9.8×[tex]t^{2}[/tex]           (a=9.8 m/[tex]s^{2}[/tex] acc. due to gravity a constant)

By solving above quadratic equation we get

t= 0.8 s

To find horizontal distance

d= [tex]v_{x}[/tex]×t

d=10.4×0.8

d= 8.32 m

Hence Allison should stand at a distance of 8.32 m to catch the ball.

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Answer:

To solve this problem, we can use the formula for exponential growth:

V(t) = V0 * (1 + r)^t

where:

V(t) is the value of the equipment at time t

V0 is the initial value of the equipment ($15,000)

r is the annual growth rate (15.9% or 0.159)

t is the time in years

We want to find the time t when the value of the equipment will be less than $7500. So we can set up the following inequality:

V(t) < 7500

Substituting the formula for V(t), we get:

V0 * (1 + r)^t < 7500

Substituting the given values, we get:

15000 * (1 + 0.159)^t < 7500

Simplifying and solving for t,

we get:(1 + 0.159)^t < 0.5

t * log(1 + 0.159) < log(0.5)

t > log(0.5) / log(1 + 0.159)

Using a calculator, we get:

t > 2.64

So the company's new equipment will be worth less than $7500 after about 2.64 years.

Step-by-step explanation:

The two possible locations of the fourth vertex are (4, -1) and (-6, 9). The solution has been obtained by using the properties of parallelogram.

What is a parallelogram?

A parallelogram has two sets of parallel sides, making it a quadrilateral. A parallelogram's opposing sides and angles are both the same length.

Finding the vector that depicts the shift from one of the given vertices to another is necessary in order to determine the fourth vertex of a parallelogram.

The third given vertex must then be added to the vector.

We know that the opposite sides of a parallelogram are parallel and equal in length, we may determine the coordinates of the other two vertices by adding the same displacement vector to two of the given vertices.

The difference between the first and second provided vertices i.e.

(1 - (-4), -2 - 3), is one potential displacement vector which is (5, -5).

On adding this vector to the third vertex, we get the fourth vertex as (4,-1).

Similarly, the difference between the second and third vertices i.e.

(-1 - 1, 4 - (-2))  is another potential displacement vector which is (-2, 6).

On adding this vector to the third vertex, we get the fourth vertex as

(-6, 9).

Hence, the two possible locations of the fourth vertex are (4, -1) and

(-6, 9).

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The Pythagorean inequality is given below.

Statement of Pythagoras theorem:

“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.

                                        [tex]AC^{2}=AB^{2} +BC^{2}[/tex]

Let ABC be a triangle with the longest side opposite B

We can also write as follows:

If [tex]AC^{2} > AB^{2} +BC^{2} \\[/tex], then B is an obtuse angle.

If [tex]AC^{2} < AB^{2} +BC^{2} \\[/tex], then B is an acute angle.

If [tex]AC^{2}=AB^{2} +BC^{2}[/tex], then B is a right angle.

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Answer:

  1625

Step-by-step explanation:

You want the sum of the first 25 terms of the series 5 +10 +15 +....

The first term is 5, the common difference is 5, so the general term is ...

  an = a1 +d(n -1)

  an = 5 +5(n -1)

The last term of the sum is ...

  a25 = 5 +5(25 -1) = 125

The sum of the series is the average of the first and last terms, multiplied by the number of terms:

  S25 = (a1 +a25)/2 · 25 = (5 +125)/2 · 25 = 65·25 = 1625

The sum of 25 terms of the series is 1625.

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Answer:

Step-by-step explanation:

All it's saying is that the 12% of the people are 35 and the 82% of people who did not submitted data is 175 people

The calculated test statistic (2.08) is greater than the critical value (1.96), we reject the null hypothesis and conclude that there is evidence to suggest that the contest has increased participation in the box tops for education program.

To determine if the contest has increased participation in the box tops for the education program, we need to conduct a hypothesis test.

We will use a significance level of 0.05, which means we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is actually true).

Null Hypothesis: The proportion of students submitting box tops for education is still 12% (or has decreased) after the contest.

Alternative Hypothesis: The proportion of students submitting box tops for education has increased after the contest.

To test this hypothesis, we will use a one-sample proportion test. We will use the sample proportion, p' = 35/210 = 0.1667, as an estimate of the population proportion, p. The test statistic is calculated as:

z = (p' - p) / √(p x (1-p)/n)

where n is the sample size.

Under the null hypothesis, the expected value of the test statistic is 0, and the standard deviation of the test statistic is sqrt(p*(1-p)/n).

Using p = 0.12 and n = 210, we have:

z = (0.1667 - 0.12) / √(0.12 x 0.88/210) ≈ 2.08

The critical value for a significance level of 0.05 and a two-tailed test is ±1.96.

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Answer:

The equation that matches the number of zombies after 2 hours would be:

23 × 4^2 = 23 × 16 = 368

So after 2 hours, there would be 368 aggressive zombies.

Answer

[tex] - 95.783[/tex]

For given linear inequalities in step 3 and 7 properties shown are Commutative property and addition property of inequality.

What exactly is a linear inequality?

In mathematics, inequality denotes a mathematical statement with no equal sides. An inequality happens in mathematics when a connection results in a non-equal comparison of two expressions or two numbers. Any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), replace the equal sign "=" in the sentence. In mathematics, inequalities are classified into three types: polynomial inequalities, rational inequalities, and absolute value inequalities.

The characters "< and >" denote severe inequalities, whereas ‘≤’ and ‘≥’  denote slack inequalities. A linear inequality looks to be a linear equation, however the formula is different.

Now,

As stated in Commutative property the order in addition does not matter and in addition property the value added on both sides does not affect the result.

In step 3 we can write this as 5x-x-5<11x+x-21

which will not change result and

in step 7, 21 is added both sides which will not change result.

Hence,

           For given linear inequalities in step 3 and 7 properties shown are Commutative property and addition property of inequality.

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Answer:

EF this is the correct answer

The probability that in a given week in September, it will rain on at most two days is 0.12.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The probability that it rains on any given day in September = 0.3.

P ( rains ) = 0.3

And,

The probability that it will not rain on any given day in September.

P (no rain) = 1 - 0.3

P(no rain) = 0.7

Now,

The probability is that in a given week in September, it will rain on at most two days.

= P (x ≤ 2)

= P(no rain) + P(rain) + P(rain)

= 0.7 + 0.3 + 0.3

= 0.12

Thus,

The probability that in a given week in September, it will rain on at most two days is 0.12.

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Answer:

Angle P= Angle W=2(2x-6)

=4x-12

Sure! To reduce the fraction 5 to its lowest terms, we need to find the greatest common factor of 5 and divide both the numerator and denominator by it.

The greatest common factor of 5 and 5 is 5, so we divide both the numerator and denominator by 5 to get:

5 / 5 = 1

So, 5 reduced to its lowest terms is 1.

To make it kid-friendly, you could explain it like this: "We can simplify the fraction 5 by dividing the top and bottom by the biggest number that they both share. In this case, 5 is the biggest number that 5 and 5 share, so we divide both 5 and 5 by 5 to get 1."

68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.

What is a circle graph?

A pie chart, often known as a circle chart, is a visual representation of the various values of a specific variable or a means to summarise a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments.

Let's say the total number of students = X.

From the circle graph, we can say that 15% of students chose cinnamon twists and their count is 12.

Which means that

[tex]X*\frac{15}{100}=12\\ X=80[/tex]

Therefore the total number of students is 80.

Among the 80 students except for 12 students, the remaining students asked for jumbo chocolate chip cookies.

Which is equal to 80-12=68.

Therefore 68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.

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Weighed averages show that the student has a grade point average of 2.33.

The grade point average (GPA) is calculated by multiplying the unit value for each course in which a student receives one of the aforementioned grades by the grade point total for that grade. Divide the total of these products by the total number of units. By dividing the total grade points by the total number of units, the cumulative GPA is determined.

A. The student's weighted mean grade point score is (3 classes) × (3 credits per class) × (3 points for a B) ÷ (9 total credits) = 3.00.

B. The student's weighted mean grade point score is (1 class) × (3 credits) × (1 point for a D) ÷ (3 total credits) = 1.00.

C. The student's weighted mean grade point score is (1 class) × (4 credits) × (2 points for a C) ÷ (4 total credits) = 2.00.

D. The student's weighted mean grade point score is (1 class) × (2 credits) × (2 points for a C) ÷ (2 total credits) = 2.00.

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x^2 - 2x + 1 is the required quadratic equation using the completing the square

Given the quadratic expression below

x^2 - 2x

We need to determine the constant that will make the expression a perfect square.

The constant will be the half of the square of coefficient of 'x'

Coefficient of 'x' = -2

Half of the coefficient of 'x' = -2/2 = -1

Square of the coefficient = (-2/2)^2

Square of the coefficient = 1

Hence the complete quadratic expression using the completing the square is x^2 - 2x + 1

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8. The center and radius of the circle given the following equation:

(x + 4)^2 + (y - 2) ^ 2 = 5 is

9. The  equation for the circle is

10. The length of arc AB is

Information given in the question

a circle whose equation is (x + 4)^2 + (y - 2) ^ 2 = 5

Equation of a circle is given as:

(x - h)² + (y - k)² = r²

Where

r = radius

h and k are coordinates of the center

x and y is the coordinate of point on the circumference

The equation of the circle is compared with the given equation and this shows that

Using the graph the centers are (-5, -2) and the radius is 3, this will give equation  (x + 5)² + (y + 2)² = 3²

If angle ACB = 60 deg and the radius is 12 cm,  length of arc

= 60 / 360 * 2 * π * 12

= 4π

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Answer:

The slope between the two points would be 5.

Answer: The slope would be 5

Step-by-step explanation:

Answer:

To make x the subject of the formula, we can isolate x by subtracting 1 from both sides of the equation:

x + 1 = 4y

x + 1 - 1 = 4y - 1

x = 4y - 1

So x is equal to 4y minus 1.

Answer:

[tex]x = 4y - 1[/tex]

Step-by-step explanation:

Currently x is on the left side of the equal sign and is being added to 1. x has to be isolated and be by itself on one side of the equal sign in order to be made the subject of the formula. Therefore the 1 needs to be moved to the other side of the equal sign:

             [tex]x = 4y - 1[/tex]

The first order derivative of the given function is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

The given function is [tex]f(x)=\sqrt{x+\sqrt{x+\sqrt{x} } }[/tex].

The derivative using the chain and power rules is

f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex]

Therefore, the first order derivative is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].

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Answer:

96 stamps

Step-by-step explanation:

We know

Connor collected 80 stamps last year. This year he increased his collection by 20%.

80 stamps = 100%

100% + 20% = 120%

So, this year he collected 120% of the number of stamps from last year.

120% = 1.2

How many stamps are in his collection?

We take

80 times 1.2 = 96 stamps

So, there are 96 stamps in his collection.

By using the substitution method, the value of x is equal to -1.94 and the value of y is 2.71.

In order to solve the given system of linear equations, we would apply the substitution method. From the information provided in the question above, we have the following system of linear equations:

y = 5x - 7      .......equation 1.

3y - 2x = -12          .......equation 2.

By using the substitution method to substitute equation 1 into equation 2, we have the following:

-3(5x - 7) - 2x = -12

-15x + 21 - 2x = -12

-17x = -12 - 21

17x = -33

x = -33/17 or -1.94

For the value of y, we have:

y = 5(-33/17) - 7

y = -165/17 - 7

y = 2.71

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