If 1 and -1 are the zeroes of the polynomial p(x) = ax 3 + x 2 − 2x + b, find the values of a and b

Answer:

The measure of central tendency, mean and median are approximately equal for the boys indicating that the data of the boys is more evenly spread while standard deviation of the girls data is less than those of the boys indicating that the data for the girls is less widely spread.

Step-by-step explanation:

The given data are;

,             1       2       3      4     5      6       7    8      9      10

Girls,    50    32     15    56   81    50     18    81    22    55

Boys,   75     41     25    22    7     0      43    12    45    70

Sorting the data gives;

Girls,     15,   18,     22,   32,  50,   50,   55,  56,    81,  81

Boys,     0,     7,     12,     22, 25,    41,    43, 45,     70, 75

For the even numbered sample data size, the first quartile, Q₁ is found by sharing the data into two and finding the median of the left half which  gives;

10/2 = 5 on each half

The first quartile, Q₁, is the median of the left 5 data points which is the 3rd data point = 22 for girls and 12 for boys

The third quartile, Q₃, is found in similar method to be the 8th data point which is 56 for girls and 45 for boys

The median = 50 for girls and 33 for boys

Therefore, the interquartile ranges are;

IQR = 56 - 22 = 34 for girls, 45 - 12 = 33 for boys

We check for outliers.

Q₁ - 1.5×IQR = 22 - 1.5*34 = -29

Q₃ + 1.5×IQR = 56 + 1.5*34 = 107

We check the mean of both data samples as follows;

Average for the girls = 46

Average for the boys = 34

Standard deviation for girls = 23.99

Standard deviation for girls = 25.43

Therefore, the measure of central tendency is more accurate for the boys indicating that the data of the boys is more evenly spread while the data for the girls is less widely spread.

Answer:

h = 112.5 feets

Step-by-step explanation:

The equation for horizontal distance "h" in feet of a projectile with initial velocity v₀ and initial angle theta is given by :

[tex]h=\dfrac{v_o^2}{16}\sin\theta\cos\theta[/tex]

We know that, [tex]2\sin\theta\cos\theta=\sin2\theta[/tex]

So,

[tex]h=\dfrac{v_o^2}{32}\sin2\theta[/tex]

Now we need to find the maximum horizontal distance possible and at what angle does this occur.

For maximum distance angle should be 45 degrees. Som,

[tex]h=\dfrac{60^2}{32}\sin2(45)\\\\h=112.5\ \text{feet}[/tex]

So, 112.5 feets is the maximum possible distance.

Answer:

We know that our triangle has one side along the line:

y = (1/4)*x

And other side along the line:

y = -(1/4)*x.

Now, we want to find the vertex.

And we know that the vertex is the point where the two sides conect, so the vertex must be a common point of both lines.

Then we have:

y = (1/4)*x = -(1/4)*x

x = -x

The only solution to that equation is x = 0.

now we evaluate our lines in x = 0 and get:

y = (1/4)*0 = 0

y = -(1/4)*0 = 0

Then the lines intersect in the point (0, 0)

Then the vertex must be in the point (0, 0)

Step-by-step explanation:

1. c

2. a

3. c

4. c

5. d

6. b

7. a

8. b

9. c

Answer:

49 square meters represent area of the square garden

Step-by-step explanation:

Each side length=7 meters

He multiplied 7 × 7 times to find the amount of space

=49 square meters

Jack is trying to measure the area of his square garden

Area of the square garden = length^2

=Length × length

Recall,

Length=7 meters

Area of the square garden= 7 meters × 7 meters

=49 square meters

3*sqrt(7)

3 times the square root of 7

====================================================

Explanation:

I'm assuming the V stands for square root. You can write sqrt(63).

[tex]\sqrt{63} = \sqrt{9*7}\\\\\sqrt{63} = \sqrt{9}*\sqrt{7}\\\\\sqrt{63} = 3\sqrt{7}[/tex]

The idea is to factor 63 in such a way that one factor is the largest perfect square possible, that way we can pull the root apart to simplify as shown above. The rule I used for the second step is [tex]\sqrt{x*y} = \sqrt{x}*\sqrt{y}[/tex]

Answer:

216.

Step-by-step explanation:

These numbers are perfect cubes starting with 2^3.

2^3, 3^3,  4^3,  5^3 so the next one is 6^3, which is 216.

Answer:

-17.3

Step-by-step explanation:

To solve for x, we can divide both sides by -3:

x = -52 / 3 which = -17.3

Answer:

Step-by-step explanation:

[tex] \sf{ - 3x = 52}[/tex]

Divide both sides of the equation by -3

⇒[tex] \sf{ \frac{ - 3x}{ - 3} = \frac{52}{ - 3} }[/tex]

Calculate

⇒[tex] \sf{x = - 17.33}[/tex]

Hope I helped!

Best regards!!

Answer:

[tex]19.79 - 2.8 = 16.99gallons[/tex]

Answer: is attatched to the photo I sent

Step-by-step explanation:

I admit, this is tricky, just remember to think about it as where the shapes are the most similar. I'm not exactly sure how to explain it, but where it reflects like a mirror is the "copy"

The example I'm thinking of attached too, but these over lap so its diffucult

Answer:

0.5% error

Step-by-step explanation:

We can use the percentage error formula, which is

[tex]\frac{|approx-exact|}{exact}\cdot100[/tex].

We know that the approximated value was 8.04, however it is actually 8cm, so we can substitute inside the equation.

[tex]\frac{|8.04 - 8|}{8}\cdot100 \\\\\frac{0.04}{8}\cdot100 \\\\0.005\cdot100 \\\\0.5[/tex]

Hope this helped!

Answer:

a = 53.13

b = 42.76

c= 0

Step-by-step explanation:

as the question said i was supposed to use a calculator which i did

Answer:

[tex]\boxed{4w+40}[/tex]

Step-by-step explanation:

Use the distributive property to evaluate the equation.

-4(-w - 10)

4w + 40

-4 * -w = 4w because two negatives cancel to make a positive value.

-4 * -10 = 40 for the same reason.

Answer:

B. The line of best fits shows a negative correlation between the number of months and the number of minutes

Step-by-step explanation:

In a scatter plot, when the data points are clustered along the line of best fit, it shows a trend, and it implies there's a correlation between the x-variable and the y-varisble.

Also, when the line of best fit slopes upward, from your left to your far right, it shows a positive correlation between the variables on the x-axis and y-axis.

On the other hand, if the line of best fit slopes downwards, from your left down to your right, this shows a negative correlation.

Thus, considering the line of best fit in the question, the line of best fit shows a negative correlation between the number of months and the number of minutes. The line of best fit slopes downwards, from your left to your right.

This shows that, as month number increases, number of minutes decreases.

Answer:

9x + 4y +(-5)

Step-by-step explanation:

Given

9x + 4y - 5

Required

Interpret

Write as a sum

The parts of an expression can be interpreted in the following ways; Terms, Variables, Constant, Coefficient, etc.

The terms are the expression being added together and they are 9x, 4y and -5

The variables are the represented with alphabets they change in values; the two variables in the given question are x and y

Constant are numbers standing alone; This is 5

Coefficient are numbers in front of variables; In this case, the coefficient are 9 and 4

Writing 9x + 4y - 5 as a sum

The -5 can be written as +(-5); So, we have

9x + 4y +(-5)

Answer:

Hey there!

That would result in 0.00735.

Let me know if this helps :)

Hence, the significant figures are [tex]0.00735.[/tex]

What is the approximation?

An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding. A calculation can be approximated by rounding the values within it before performing the operations.

Here given that,

Approximate [tex]0.007349[/tex] to  significant figures​

So, the significant figures are [tex]0.00735.[/tex]

Hence, the significant figures are [tex]0.00735.[/tex]

To know more about the approximation

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Answer:

Cost of sandbox = $9,375

Step-by-step explanation:

Given:

Height of sandbox = 5 m

Length of sandbox = 50 m

Width of sandbox = 25 m

Cost of 1 cubic meter = $1.50

Find:

Cost of sandbox

Computation:

Volume of sandbox = (50)(25)(5)

Volume of sandbox = 6,250 m³

Cost of sandbox = 6,250 × $1.50

Cost of sandbox = $9,375

Answer:

10a -7b

Step-by-step explanation:

9a-6b+a-b​

Combine like terms

9a+a   -6b-b

10a -7b

Answer:

10a-7b

Step-by-step explanation:

[tex]9a - 6b + a - b \\ 9a + a - 6b - b \\ 10a - 7b[/tex]

The first mistake is that she didn't use parenthesis to indicate we're dividing all of one thing (numerator) over all of another expression (denominator)

slope = rise/run = numerator/denominator

So she should write (17-4)/(1-8) to indicate all of "17-4" is divided over all of "1-8"

However, there's another error that your teacher is probably more focused on. Note how 17-4 represents subtracting the y coordinates from left to right. We start with the left point y coordinate 17 and subtract off the right point y coordinate 4

left y - right y = 17 - 4

But then the student swaps the order when they wrote 1-8. Instead it should be 8-1

-----------------

Here's what they should have written (17-4)/(8-1)

This is the same as (4-17)/(1-8)

We can subtract in any order as long as it stays consistent between the numerator and denominator

D) in the question

1002, 3001

Answer:

a) 503 b) 307 c) 56789 D) 1002

Step-by-step explanation:

Numbering starts from the left hand side and are arranged in ascending order.

A) (530, 503)

503 < 530

503 is lesser than 530 and as such it is encountered first when numbers are written, hence 503 will appear on the left side of the number line when both are written.

B.) (370, 307)

370 > 307

307 comes before 370, therefore it will appear on the left side of 370 when illustrated on a number line.

C.) (98765, 56789)

98765 > 56789

56789 will appear on the leftside of 98765 when both number are illustrated on a number line.

D.) 1002 < 3001

1002 will appear on the leftside of 98765 when both number are illustrated on a number line.

Answer:

yes

The statement 'C' explains the difference between a plane and a ray.

i.e. A plane does not have a formal definition, and a ray is described through undefined terms.

Step-by-step explanation:

A plane does not have a formal definition, and a ray is described through undefined terms. The statement is true because

A plane is basically an undefined term as it could be named using three non-straight points - also called noncollinear points. A plane is basically a flat two-dimensional object having no thickness.

In Geometry, we have a variety of undefined terms, including point, line and plane. All other terms in Mathematics (Geometry) could be defined from the mentioned three undefined terms.

Therefore, the statement 'C' explains the difference between a plane and a ray.

i.e. A plane does not have a formal definition, and a ray is described through undefined terms.

Keywords: plane, point, line, ray

Learn more about plane and ray form brainly.com/question/14471549

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Answer:

No

Step-by-step explanation:

405 repeating is

405/999

not 405/99

405/99=4.090909090909....

4.05 repeating is not equivalent to 405/99.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities.

The division is to divide two numbers by each other example 2/4.

The division is a very common phenomenon in mathematics so we need to divide two numbers or expressions.

Subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.

The most common mathematical operation is multiplication, which involves adding two or more integers to get a new multiplied number.

Given,

405/99

If we divide 405 by 99 then it will go 4 times and leave the remainder as 9.

Further, we make a decimal and again divide it will go 090909091 so it means it is repeating 09 four times.

Hence, 4.05 repeating is not equivalent to 405/99.

To learn more about the arithmetic operator

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Answer:

Step-by-step explanation:

[tex]a^{m}*a^{n} =a^{m+n}\\\\\\2^{3}*2^{5} = 2^{3+5} =2^{8}\\\\\\3^{2}*3^{4}=3^{2+4} = 3^{6}\\\\\\a^{2}*a^{5}=a^{2+5}=a^{7}[/tex]

Answer:

Cos A =1.4

Step-by-step explanation:

3sinA=5-4cosA; square both sides: 9sin^2(A)=25-40cosA+16cos^2(A);

9-9cos^2(A)=25-40cosA+16cos^2(A); 25cos^2(A)-40cosA+16=0=(5cosA-4)^2.

cosA=4/5 so sinA=3/5 (√(1-16/25) and sinA+cosA=7/5=1.4.

Answer:

i think 60 parts of blue paint are in the can.

Step-by-step explanation:

ratio should be equal in both cases

therefore,let blue part in second case be x(suppose)

5÷4=75÷x

by equating this we will be able to identify the value of x

and the value of x comes 60 which is the required answer....

hope this will help you..

i try my best to give correct answer..

if i am mistake, i am sorry for that...

THIS IS THE COMPLETE QUESTION BELOW;

Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee?

Answers:

(–3, –0.90)

(–2.5, –0.75)

(4.5, 1.35)

(8, 2.40)

Answer

(8, 2.40)

Step by step Explanation

✓We can denote the number of days library book is late = X,

✓We can denote the the total fee = Y.

We were told $0.30 fee is charged at midnight.

Then for lateness for just 1day,the charged fees= 1day ×

$0.30

For X number of days the charged fees= Xday ×$0.30

Therefore, total charge for lateness for X number of days late = Y.

Then can be expressed as

Y= 0.30 * X...............eqn(1)

We can now test the option one after the other

FIRST OPTION (-3, -0.9)

Here we should know the number of days cannot be negative so there is no need of testing in the equation (1)

SECOND OPTION (-2.5, -0.75)

Here we should know the number of days cannot be negative so there is no need of testing in the equation (1)

THIRD OPTION(4.5, 1.35)

here the number of days will definitely be a whole number not 4.5, it's either

charge for 4 days or 5 days.

FORTH OPTION (8, 2.40)

this should be correct because the number of days is whole number and not negative, then if we test it from our equation it satisfy the equation too

Y= 0.30 * X...............eqn(1)

Y= 0.30 * X

2.40= 0.30 * 8

2.40 = 2.40.

Therefore, (8, 2.40) is the answer

Answer:

[tex]\Large \boxed{{c<6}}[/tex]

Step-by-step explanation:

2>c/3

Multiply both sides of the inequality by 3.

2(3)>c/3(3)

6>c

Switch sides.

c<6

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Hi my lil bunny!

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Let's solve your inequality step-by-step.

[tex]2 > \frac{c}{3}[/tex]

Step 1: Simplify both sides of the inequality.

[tex]2 > \frac{1}{3}c[/tex]

Step 2: Flip the equation.

[tex]\frac{1}{3}c < 2[/tex]

Step 3: Multiply both sides by 3.

[tex]3 * (\frac{1}{3} c) < ( 3) * (2)\\c < 6[/tex]

Answer : [tex]\boxed {c < 6}[/tex]

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Have a great day/night!

❀*May*❀

Answer:

625

Step-by-step explanation:

5⁴ = 5x5x5x5 = 625

Answer:

Actually it's A.

Step-by-step explanation: