Determine which·of the following are subspaces of P3.
(a) All polynomials a0 + a1x + a2x2 + a3x3 for which a0 = 0.
(b) All polynomials a0 + a1x + a2x2 + a3x3 for which a0 + a1 + a2 + a3 = 0.
(c) All polynomials of the form a0 + a1x + a2x2 + a3x3 in which a0, a1, a2, and a3 are rational numbers.
(d) All polynomials of the form a0 + a1x, where a0 and a1 are real numbers.

The experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is approximately 0.263

The experimental probability is found by dividing the number of times the desired outcome occurred by the total number of trials. In this case, the desired outcome is selling a slice of pepperoni pizza as the first slice tomorrow.

Since we only know the number of slices sold today, we don't have any specific information about the number of slices that will be sold tomorrow. However, we can assume that the same types of pizzas will be sold tomorrow, and the probability of selling a slice of pepperoni pizza tomorrow will be the same as the proportion of pepperoni slices sold today.

So, the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is

Experimental probability = Number of pepperoni slices sold today / Total number of slices sold today

Experimental probability = 20 / 76

Experimental probability = 0.263

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Answer:

27.5

Step-by-step explanation:

17,21,24,24,26,29,29,29,32,33

26+29

55/2

27.5

The possible change in volume (in mm3) resulting from the error in measuring the radius is 32. 06 mm³

Given,

A spherical golf ball is measured to have a radius of $$5 mm, with a possible measurement error of $$0.1 mm

How to determine the volume

The formula for volume of a sphere is expressed by;

Volume = 4/3 πr³

Where;

r is the radius of the sphere

pi takes the value 3.14

From the information given, we have that the measured radius is 5 mm, with a possible measurement error of 0.1 mm

Then, radius  a = 5mm

Radius b = 5 + 0. 1 = 5. 01mm

Now, substitute the values into the formula

Volume, v = 4/ 3 (3.14)(5)³

v = 4/ 3 (392.5)

v = 523. 3 mm³

For radius of 5.01mm

Volume =  4/ 3 (3.14)(5.1)³

expand the bracket

Volume = 4/3 (416.52)

Volume = 555. 4 mm³

The change in volume = 555. 4 - 523. 3 = 32. 06 mm³

Hence, the change in volume is 32. 06 mm³

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Answer:

B. y-25=5(x-20)

Answer:

20 + (-45) = -25

Here ya go.

Answer in picture

Answer:

7.2%

Step-by-step explanation:

Last yaer's insurance cost: £250

This year's insurance cost: £268

Increase = £18

Percentage increase = (increase ÷ original value) × 100 = 18/250 × 100 = 7.2%

We need to know completing square method to solve the method. The solution of the given equation is \(\sqrt{11}\)±1/2.

Completing the square method is used to solve a quadratic equation. Quadratic equation is an equation that has the maximum degree of a variable as two. For a completing square method we rearrange the variables and constants on both sides of the equation so that we get two whole squares on both sides of the equation and then square root them to find the solution of the equation.

\(2y^{2} -2y=5\\y^{2} -y=5/2\\\)

\(y^{2} -y+1/4=5/2+1/4\)

\((y-1/2)^{2}\)=11/4

y-1/2=\(\sqrt{11}\)/2

y=\(\sqrt{11}\)±1/2

Therefore the solution of the quadratic equation using completing square method is \(\sqrt{11}\)±1/2.

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Hey there!

5 (-3 + k) = 20

-15 + 5k = 20

5k = 20 + 15

5k = 35

k = 35 ÷ 5

k = 7

Hope it helps ya!

\(\boxed{\underline{\bf \: ANSWER}}\)

\( \tt \: 5( - 3 + k) = 20 \\ \tt = (5 \times - 3 )+( 5 \times k) \\ = \underline{ \bf{ - 15 + 5k}}\)

Hope it helps!

RainbowSalt2222

First, calculate the average of the data set. Then, calculate the deviations of each data point from the mean and square the result of each. Next, calculate the mean of those values, which gives us the variance of the data set. Finally, take the square root of the variance, which gives us the standard deviation.

The average of the data set, is:

The squares of the deviations of each data point, are:

The variance of the data set is:

The standard deviation of the data set, is:

To the nearest hundredth, the standard deviation is 6.18.

Therefore, the answer is:

Step-by-step explanation:

\( \sqrt 2, \: \sqrt 2. 6 \: \& \: \sqrt 2 + 6\) are irrational and 6 is the only rational number.

The value of the series, to within an error of at most 10^(-3), is approximately -1.

To approximate the value of the series ∑n=1 to infinity (-1)^n / (n^2)(n^6) within an error of at most 10^(-3), we can use the Alternating Series Estimation Theorem.

The Alternating Series Estimation Theorem states that for an alternating series ∑(-1)^n b_n, where b_n is a positive sequence that approaches zero as n approaches infinity, the error when approximating the sum of the series with the nth partial sum is less than or equal to the absolute value of the (n+1)th term.

In this case, b_n = 1 / (n^2)(n^6), which is a positive sequence that approaches zero as n approaches infinity. Therefore, we can use the theorem to find an appropriate value of n that ensures the error is within the desired tolerance.

Let's set the (n+1)th term to be less than or equal to 10^(-3):

\(1 / ((n+1)^2)((n+1)^6) < = 10^-3\)

Simplifying the inequality:

\(1 / ((n+1)^8) < = 10^-3\)

Taking the reciprocal of both sides:

\((n+1)^8 > = 10^3\)

Taking the eighth root of both sides:

\(n+1 > = (10^3)^1/8\)

\(n+1 > = 10^(3/8)\)

\(n > = 10^(3/8) - 1\)

Using a calculator, we can approximate the right-hand side:

n >= 1.568 - 1

n >= 0.568

Since n must be a positive integer, the smallest value of n that satisfies the inequality is n = 1.

Therefore, using the first term of the series, the approximation of the series within an error of at most \(10^-3\) is:

\((-1)^1 / (1^2)(1^6) = -1\)

So the value of the series, to within an error of at most \(10^-3\), is approximately -1.

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Eval is a function that evaluates an expression and puts the resulting value into a new or existing field.

To calculate the value of an expression using Eval, you must use the correct syntax. The syntax for Eval is Eval(expression, optional_parameter). The expression can take the form of a mathematical equation or a logical expression. For example, if you wanted to calculate the sum of two numbers, you would use the following expression: Eval(A + B). The optional parameter allows you to specify a range of values to evaluate the expression against.

For example, if you wanted to calculate the sum of two numbers within a given range, you would use the following expression: Eval(A + B, range). The range parameter can be used to specify the starting and ending values that the expression should be evaluated against.

Using Eval to calculate an expression is a useful tool for quickly getting the desired value. It is also useful for quickly testing the accuracy of a complex expression before implementing it in your code.

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The equation of the plane passing P (1,2,1) and orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is -3x-2y-z+8=0.

Equation of plane passing through (x1,y1,z1) is given by

A(x-x1)+B(y-y1)+C(z-z1)=0

where, A, B, and C are direction ratios

In the question, it is given that the plane passes through (1,2,1)

So, the equation of the plane will be in the form,

A(x-1)+B(y-2)+C(z-1)=0

It is also given that the plane is perpendicular to give 2 planes.

So, their normal to the plane would be perpendicular to the normal of both planes.

So, the required normal is a cross-product of the normals of planes

x-y-z-10=0 and x-2y+z-2=0

i.e,

-3i-2j-k=0

so, the direction ratios,

A=-3, B=-2, C=-1

putting the direction ratios in the previous equation of the plane,

-3(x-1)-2(y-2)-1(z-1)=0

-3x+3-2y+4-z+1=0

-3x-2y-z+8=0

is the required equation of the plane

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Answer:

Around 9.72

Step-by-step explanation:

15 percenet of $8.40= 1.2675

add 1.2675 to 8.40= 9.72

The cost of the meal will be $56.00.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

In a restaurant,

Jorge left a tip of $8.40.

This tip was 15% of the cost of the meal.

Now,

Let cost of the meal in a restaurant = $x

Since, Jorge left a tip of $8.40.

And, This tip was 15% of the cost of the meal.

So, We can formulate;

15% of x = $8.40

Solve for x as;

15% × x = $8.40

15/100 × x = $8.40

Multiply by 100, we get;

15x = 8.40 × 100

15x = 840

Divide by 15, we get;

x = 840 / 15

x = 56

Thus, Cost the meal in a restaurant = x = $56.

Therefore, The cost of the meal will be $56.00.

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Answer:

x = 1 .  Hopefully im reading this correct

Step-by-step explanation:

8x - 5 = 3

8x = 5 + 3

8x = 8

x = 8/8

x = 1

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

x is 1

Step-by-step explanation:

AC =PR

AB =PQ

8x - 5 =3

8x =3+5

8x =8

x=8/8

x=1

Answer:

19v

Step-by-step explanation:

The correct answer is 19v

Answer:

19v

Step-by-step explanation:

You only add the numbers that have the same variable (The letter next to the number) Since all the numbers have the same variable it's 19v

if you need a example where there is different variables I will gladly help :)

Answer:

x = 36

y = 22

Step-by-step explanation:

Let's solve for x

<EOG is a right angle due to the marking. Since that's the case, m<EOG = 90.

<EOF + <FOG = <EOG

Now let's substitute the values in.

54 + x = 90

x = 36

Let's solve for y

<AOB is 180 because it's a line.

<BOD + <COB = 180 because of supplementary angles

<BOD + 156 = 180

<BOD = 24

Let's create the equation now.

<AOE + <EOF + <FOG + <GOD + <BOD = <AOB

Now let's substitute the values in.

y + 54 + x + 2y + 24 = 180

3y + x + 78 = 180

Now let's substitute 36 for x.

4y + 36 + 78 = 180

3y + 114 = 180

3y = 66

y = 22

Hope this helped! If not, please let me know! <3

The shapes of a cross section of the cone are circle and triangle

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

The cone

In the cone, we have the following shapes in the cross-sections

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

the shapes of a cross section of the cone are circle and triangle

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Answer:

13. 3x+10=5x-10

14. (I'm not sure how to set this one up, sowwy ;^;)

15. 5x+15=6x

16. x+10=4x-20

I'm pretty sure this is how to set it up

On solving the provided question, we can say that by using N= 2X + 1 or  N = 2X-1  will do the job for composite numbers.

By multiplying two small positive integers, you can create a composite number, which is a positive integer. Likewise, any positive integer that has at least one divisor besides itself and 1. Positive whole numbers make up composite numbers. It lacks prime (that is, it has divisors other than 1 and itself). The first several composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, and are frequently referred to simply as "composites." In other words, composite odd numbers encompass all non-prime odd numbers. for illustration: 9, 15, 21, etc. No. As a result, 2 only possesses the divisors 1 and 2. To put it another way, since 2 only has two divisors, it is not a composite number.

by using N= 2X + 1

or

N = 2X-1

will do the job for composite numbers.

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Answer:

Jenn:   12/30 incorrect  18/30 correct

Mara.    8/24 incorrect   16/24 correct

Step-by-step explanation:

Could you ask the question???? This isn’t a questions it more like a statement so I tried to do my best and I just made them into fractions

The number of T-shirts bought by the Brandywine Dance Team is 24.

The number of the T-shirts that the Brandywine Dance Team purchased is determined using basic mathematical operations of division, subtraction, addition, and multiplication.

First, the cost of the equipment is subtracted from the total cost spent by the team.  The remainder refers to the cost of the T-shirts.  Since one T-shirt costs $12, the total quantity of T-shirts bought is 24.

The total amount spent = $644

The cost of the equipment = $356

The remainder after the equipment = $288 ($644 - $356)

Unit cost of T-shirts = $12

The number of T-shirts bought = 24 ($288/$12)

Thus, the Brandywine Dance Team bought 24 T-shirts.

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How many T-shirts were purchased by the Team?

Answer:

x = -2.1

Step-by-step explanation:

1x + 3.7 = 1.6

x + 3.7 = 1.6

subtract 3.7 from each side of the equation

then simplify

Answer:

x = -2,1

Step-by-step explanation:

1x + 3.7 = 1.6

x + 3.7 = 1.6

x = 1.6 - 3.7

x = -2,1

Lane needs to eat 2/10 of the brownie to eat the same amount as Alex.

Alex cut his brownie into tenths and ate 2/10 of it.

Lane cut his brownie into fifths.

What fraction of the brownie does Lane need to eat to eat the same amount as Alex.:

In this problem, we can compare the fraction of brownie that Alex ate with the fraction of brownie that Lane needs to eat to eat the same amount as Alex.

Let’s first simplify the fraction of brownie that Alex ate.2/10 can be simplified by dividing both the numerator and the denominator by the greatest common factor, which is 2.2/10 = 1/5

Now, we need to find the fraction of brownie that Lane needs to eat to eat the same amount as Alex.

To do this, we need to find a common denominator.

The least common multiple of 5 and 10 is 10.

This means we can convert 1/5 into a fraction with a denominator of 10 by multiplying both the numerator and denominator by 2.1/5 = 2/10.

Now, we can see that to eat the same amount as Alex, Lane needs to eat 2/10 of the brownie.

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on solving the provided question we can say that A larder equity multiplier indicates a greater reliance on debt financing.

Along with addition, subtraction, and division, multiplication is one of the four arithmetic operations. Multiplication in math refers to regularly adding groups of the same size. The formula for multiplication is multiplicand multiplier Equals product. Specifically, multiplicand: First number (factor). divider:

A financial ratio called the equity multiplier gauges how much debt is being used to fund a company's assets in comparison to its owners' equity. It is determined by dividing the total assets by the entire equity of the organization.

Total Assets / Total Equity is the equity multiplier.

A larder equity multiplier indicates a greater reliance on debt financing. The equity multiplier measures the proportion of a company's assets that are funded by debt. Analysts and investors frequently use it to assess a company's financial leverage and risk profile since businesses with higher debt levels may be more susceptible to changes in interest rates, the state of the economy, or other external variables.

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Answer:

Let's define the variables:

x = yards of Organza ribbon that you buy.

y = yards of Satin ribbon that you buy.

We know that the price per yard of Organza ribbon is $0.07, this means tat if you buy x yards, the cost will be:

C = x*$0.07

And the cost of the Satin ribbon is $0.04, so if you buy y yards of that ribbon, the cost will be:

C = y*$0.04

Adding that together, the total cost is:

C = x*$0.07 + y*$0.04

Now we know that you pay $5, this means that the total cost is exactly $5, then we have the equation:

$5 = x*$0.07 + y*$0.04

Now we can isolate the variable y to get:

y = ($5/$0.04) - x*($0.07/$0.04)

y = 125 - x*1.75

Now we can just input different values of x to find the correspondent value of y.

This means that:

if x = 0 (0 yards of the Organza ribbon)

then:

y = 125 - 0*1.75 = 0

This combination is:

0 yards of organza, and 125 yards of satin.

Now, if x = 20, then:

y = 125 - 20*1.75  = 90

This combination is:

20 yards of organza, and 90 yards of satin.

if x = 40, then:

y = 125 - 40*1.75 = 55

This combination is:

40 yards of organza, and 55 yards of satin.

The 3 combinations that we found cost exactly $5.

Answer:

1:5

Step-by-step explanation:

Since 60 is divisible by 12, the answer of 5 would be used in ratio form too.

Answer:

6/21, 12/42

Step-by-step explanation:

Mary spends no more than 21 hours a week doing homework. If she spends 2/7 of the time doing her math homework.

The number of hours she spends doing her maths homework is calculated as:

= 2/7 × 21

= 6 hours

The other fractions that could represent the amount of time Mary spends doing her math homework is given as:

6 hours/21 hours = 6/21

Also , that could be represented as:

12/42

Therefore, the other fractions that could represent the amount of time Mary spends doing her math homework is : 6/21 , 12/42

Answer:

The rate of change is y with respect to x is \(\frac{25}{4}\)

Step-by-step explanation:

Given

\(25x - 4y = 50\)

Required

Determine the rate of change of y w.r.t x

\(25x - 4y = 50\)

First, make y subject of formula

\(4y = 25x- 50\)

Divide through by 4

\(y = \frac{25x}{4} - \frac{50}{4}\)

\(y = \frac{25x}{4} - 12.5\)

Next, we differentiate the above w.r.t to x

The result of the differentiation is the solution to the question

\(y' = 1 * \frac{25x^{1-1}}{4} -0\)

\(y' = 1 * \frac{25x^0}{4}\)

\(y' = 1 * \frac{25*1}{4}\)

\(y' = \frac{25}{4}\)

Hence, the rate of change is y with respect to x is \(\frac{25}{4}\)

By calculating derivative of y with respect to x we got rate of change of y with respect to x for 25x-4y=0 is 25/4

Rate of change of a function with respect to a variable is called derivative of that function with respect to that variable .

Here given relation is 25x-4y=0

\(\Rightarrow 4y=25x\\\\\Rightarrow y=\frac{25x}{4}\)

We have to calculate rate of change of y with respect to x so we will calculate derivative of y with respect to x.

we can calculate derivative of y with respect to x as

\(\frac{dy}{dx}= \frac{d}{dx} (\frac{25x}{4})\\\\\)

As 25/4 is constant we can take it out from derivative function as it is

\(\frac{dy}{dx}= (\frac{25}{4})\frac{dx}{dx}\\\\\)

And we know derivative of a variable with respect to itself is 1

so

\(\frac{dy}{dx}= (\frac{25}{4})\times 1\\\\ \frac{dy}{dx}= \frac{25}{4}\)

By calculating derivative of y with respect to x we got rate of change of y with respect to x for 25x-4y=0 is 25/4

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