Evaluate the expression
5−2−2+10
= -2

-6
14
2
22

Answer: b = 5

Step-by-step explanation:

        The standard form of a quadradic equation is 0 = ax² + bx + c. To do this, we will move all values to one side of the equation.

        Given:

8x + 4 = -2x² + 3x + 1

        Subtract (8x + 4) from both sides of the equation:

0 = -2x² - 5x - 3

        Lastly, we are given that a = 2, so we will divide both sides of the equation by -1.

0 = -2x² - 5x - 3

0 = 2x² + 5x + 3

        We are asked to find the value of b.

0 = ax² + bx + c

0 = 2x² + 5x + 3   ➜   b = 5

Answer:

5x, -2x, x

Step-by-step explanation:

Like terms have the same variable parts.

The variable part of 3x is x.

Any term that has only x as its variable part is a like term to 3x.

Answer: 5x, -2x, x

Answer:

9/17 or 52.9% or likely

Step-by-step explanation:

Answer:

Volume, V = 75.41 cubic inches.

Step-by-step explanation:

Given the following data;

Radius, r = 3 inches

Height = 8

To find the volume of the right circular cylinder;

Mathematically, the volume of a right circular cylinder is given by the formula;

V = πr²h

Where;

Substituting into the formula, we have;

Volume, V = 3.142 * 3 * 8

Volume, V = 3.142 * 24

Volume, V = 75.41 cubic inches.

The value of area of mat is,

A =  222 in²

Since, We get;

the area of the mat = total area added - the original area of the water color painting.

Here, We have;

length of the mat is,

L = 22 in + 3 in + 3 in because 1 in  is added to each side

L = 28 in

And, width of the mat is:

w = 9 in + 3 in + 3in

w = 15 in

Area of mat is,

= (28 in x 15 in) - ( 22 in x 9 in)

= 420 - 198

= 222 in²

Thus, The value of area of mat is,

A =  222 in²

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Answer:

Let's use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we are given that one leg (let's call it the shorter leg) is twice the length of the other leg. So, if we let x represent the length of the shorter leg, then the longer leg has a length of 2x.

We are also given that the length of the hypotenuse is √45 centimeters. We can simplify this by noticing that √45 = √(9 × 5) = √9 × √5 = 3√5. So the length of the hypotenuse is 3√5 centimeters.

Now we can write the Pythagorean Theorem equation:

x^2 + (2x)^2 = (3√5)^2

Simplifying, we get:

x^2 + 4x^2 = 45

5x^2 = 45

x^2 = 9

x = 3

So the shorter leg has a length of 3 centimeters, and the longer leg has a length of 2x = 2(3) = 6 centimeters.

Answer:

-8

Step-by-step explanation:

The rate of change is found by

f(x2) - f(x1)

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

x2 -x1

We know that f(x2) = -26 when x2 =5

And f(x1) = -10 when x1 = 3

-26 - (-10)

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

5 - 3

-26+10

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

2

-16/2

-8

Answer:

I don't know

Step-by-step explanation:

Answer: 32/139

Step-by-step explanation:

42+45+20+32=139

32/139

The equation is an identity. We can see that both the LHS and RHS have reached a common equivalent expression

To simplify each side of the equation independently and reach a common equivalent expression, we can use trigonometric identities.

Starting with the left-hand side:

1 + tan(x)

We can use the identity:

\(1 + tan^2(x) = sec^2(x)\)
To get:

1 + tan(x) = sec^2(x) - 1

Now, for the right-hand side:

cos(y) sin(x) + 1 + tan(x) cos(x) sin(x) - sin(x) tan(x)

We can factor out sin(x) and use the identity:

sin^2(x) + cos^2(x) = 1

To get:

sin(x) [cos(y) + cos(x) tan(x)] + 1 - sin(x) tan(x)

Next, we can use the identity:

1 + tan^2(x) = sec^2(x)

To substitute for tan(x) and simplify:

sin(x) [cos(y) + cos(x)/cos(x)] + 1 - sin(x)/cos(x)

sin(x) [cos(y) + 1] + cos(x)/cos(x) - sin(x)/cos(x)

sin(x) cos(y) + sin(x) + 1/cos(x) - sin(x)/cos(x)

sin(x) cos(y) + (1 - sin^2(x))/cos(x)

cos(x) sin(y) + cos(x)/cos(x)

cos(x) [sin(y) + 1]

Therefore, we have simplified both sides of the equation to:

sec^2(x) - 1 = cos(x) [sin(y) + 1]

To verify that this is an identity, we can manipulate the right-hand side:

cos(x) [sin(y) + 1]

= cos(x) sin(y) + cos(x)

= sin(x) cos(y) + 1

Now, we can substitute for sin^2(x) using the identity:

sin^2(x) = 1 - cos^2(x)

To get:

sin(a) cos(a) + cos(a) = sec(a) - sin(a)

Which is the desired result.
To show that the given equation is an identity, we need to simplify each side independently and reach a common equivalent expression.

Given equation: 1 + tan(x) = (sin(x)cos(x) + cos(x))/(cos(x) - sin(x)tan(x))

Left-hand side (LHS): 1 + tan(x)
We know that tan(x) = sin(x)/cos(x)
So, LHS becomes 1 + sin(x)/cos(x)

Right-hand side (RHS): (sin(x)cos(x) + cos(x))/(cos(x) - sin(x)tan(x))

Factor out cos(x) from the numerator:
RHS = (cos(x)(sin(x) + 1))/(cos(x) - sin(x)tan(x))

Now, divide both the numerator and the denominator by cos(x):
RHS = (sin(x) + 1)/((1 - sin(x))(sin(x)/cos(x)))

Recall that tan(x) = sin(x)/cos(x), so we can replace sin(x)/cos(x) in the denominator with tan(x):
RHS = (sin(x) + 1)/(1 - sin(x)tan(x))

At this point, we can see that both the LHS and RHS have reached a common equivalent expression:

1 + sin(x)/cos(x) = (sin(x) + 1)/(1 - sin(x)tan(x))

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Answer:

Q) (-2, 2)

V) (2, 2)

Step-by-step explanation:

There are a total of 900 million ( 900,000,000) 9-digit numbers where 100,000,000 is the smallest and 999,999,999 is the greatest 9-digit number. If repetition of digits is prohibited then there are a total of  3,265,920  9-digit numbers.

Digits that are used to form 9-digit numbers are 0,1,2,3,4,5,6,7,8,9

To form a 9-digit number the highest place value that is the first digit cannot be zero.

So the available choices for the first digit are 1,2,3,4,5,6,7,8,9. The other 8 places of  9-digit numbers can have any of the digits including 0.

Therefore total 9-digit numbers are 9×10×10×10×10×10×10×10×10=900,000,000

If the repetition of digits is forbidden then for the first place we have 9 choices as 0 cannot be used for the first place. Now we can not use the digit chosen for the First place of a number. So for the second place, we have 9 choices.

In a similar way, third place has 8 choices. So the number of choices decreases by 1 from the third to the ninth position.

The 9-digit numbers without repetition are 9×9×8×7×6×5×4×3×2

9×9!= 3,265,920

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Answer:

11 sq units

Step-by-step explanation:

(6×4) - ½(6×1 + 4×3 + 2×4)

= 24 - ½(6+12+8)

= 24 - ½(26)

= 24-13

= 11 sq units

Answer:

Step-by-step explanation:

1-1=0

Answer:You will have 0 moms.

Step-by-step explanation:

First you take 1 away from 1.

After that you get your answer of 0.

Answer:

$4 per pint

1/4 pint per dollar

5 pints for $20

$32 for 8 pints

Step-by-step explanation:

12.00/3 = 4

$4 per pint

1/4 = 1/4

1/4 pint per $1

$20 / $4 = 5 pints

$4 * 8 = $32

Answer:

Step-by-step explanation:

Subtract:

-6x-3 from 2x-5

2x - 5 -(-6x - 3) =

2x - 5 + 6x + 3 =

8x -2

To find the probability that more than 20% of the students in the sample would respond that they spend more than 4 hours per night on homework, we can use the binomial distribution formula.

Let's denote the probability of a student spending more than 4 hours per night on homework as p. In this case, p = 0.15, as given in the problem. The sample size is n = 120. The probability of more than 20% of the students responding that they spend more than 4 hours per night on homework can be calculated as the sum of probabilities for all values greater than 20%. Mathematically, this can be expressed as: P(X > 0.20n) = P(X > 0.20 * 120) = P(X > 24)

To calculate this probability, we can use the binomial distribution formula: P(X > 24) = 1 - P(X ≤ 24) = 1 - ∑(k=0 to 24) C(120, k) * p^k * (1-p)^(120-k) Evaluating this expression, we find that the closest value to the probability that more than 20% of the students in the sample would respond that they spend more than 4 hours per night on homework is 0.0809.

Therefore, the answer is 0.0809.

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The height of the cone needs to be approximately 4.5 inches to have the same volume as the cup, which has a width of 3 inches and a height of 2 inches.

To determine the required height of the cone, we can use the formula for the volume of a cone, which is \(\frac 13 * \pi * r^2 * h\), where r is the radius and h is the height of the cone.

Given that the cup has a width of 3 inches, we can calculate the radius of the cup by dividing the width by 2, which gives us 1.5 inches. Therefore, the radius of the cup is 1.5 inches.

Since we want the cone to have the same width as the cup, the radius of the cone should also be 1.5 inches.

Now, let's substitute the values into the volume formula for the cup: \(\frac 13 * \pi * (1.5)^2 * 2\). The volume of the cup is approximately 7.07 cubic inches.

To find the required height of the cone, we can rearrange the volume formula and solve for h:

\(h = \frac {3 * volume} {\pi * r^2}\).

Plugging in the values, we get \(h = \frac {3 * 7.07}{\pi * (1.5)^2}\), which simplifies to h = 4.5 inches.

Therefore, the height of the cone needs to be approximately 4.5 inches to hold the same amount of ice cream as the cup with a width of 3 inches and a height of 2 inches.

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Answer:

oxidation number, also called oxidation state, the total number of electrons that an atom either gains or loses in order to form a chemical bond with another atom.Step-by-step explanation:

Answer:

Maureen ignored the negative(minus) sign in 1.7 thereby turning it into positive 1.7

Step-by-step explanation:

-1.7 + (-6.3)

Correct simplification

-1.7 + (-6.3)

Open parenthesis

= - 1.7 - 6.3

= -8

NOTE:

- * + = -

- * - = +

+ * - = -

+ * + = +

Maureen's simplification

-1.7 + (-6.3)

= 1.7 - 6.3

= -4.6

Maureen ignored the negative(minus) sign in 1.7 thereby turning it into positive 1.7

A discrete probability distribution is a statistical distribution that relates to a set of outcomes that can take on a countable number of values, whereas a continuous probability distribution is one that can take on any value within a given range.Therefore, the main difference between the two types of distributions is the type of outcomes that they apply to.

An example of a discrete probability distribution is the probability of getting a particular number when a dice is rolled. The possible outcomes are only the numbers one through six, and each outcome has an equal probability of 1/6. Another example is the probability of getting a certain number of heads when a coin is flipped several times.

On the other hand, an example of a continuous probability distribution is the distribution of heights of students in a school. Here, the range of heights is continuous, and it can take on any value within a given range.

The expected value of a probability distribution measures the central tendency or average of the distribution. In other words, it is the long-term average of the outcome that would be observed if the experiment was repeated many times.

For a discrete probability distribution, the expected value is computed by multiplying each outcome by its probability and then adding the results. In mathematical terms, this can be written as E(x) = Σ(xP(x)), where E(x) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome.

For example, consider the probability distribution of the number of heads when a coin is flipped three times. The possible outcomes are 0, 1, 2, and 3 heads, with probabilities of 1/8, 3/8, 3/8, and 1/8, respectively. The expected value can be computed as E(x) = (0*1/8) + (1*3/8) + (2*3/8) + (3*1/8) = 1.5.

Therefore, the expected value of the distribution is 1.5, which means that if the experiment of flipping a coin three times is repeated many times, the long-term average number of heads observed will be 1.5.

There is only one five-digit integer, 37000, that satisfies these conditions.

To determine the number of five-digit integers of the form 37abc that are divisible by 37, we need to consider the divisibility rule for 37. A number is divisible by 37 if and only if the difference between twice the units digit and the remaining part of the number is divisible by 37. In this case, since we have a five-digit integer of the form 37abc, we can write it as:

37abc = 37000 + 100a + 10b + c

Now, let's consider the three given numbers and analyze their divisibility by 37:

37abc:

For 37abc to be divisible by 37, we need the difference between twice the units digit (2c) and the remaining part (37ab) to be divisible by 37. Therefore, we have the congruence:

2c ≡ 37ab (mod 37)

Since 37 ≡ 0 (mod 37), we can simplify the congruence to:

2c ≡ 0 (mod 37)

This implies that c must be divisible by 37. Since c can take values from 0 to 9 (since it is a digit), we have only one possibility: c = 0.

37bca:

Similarly, for 37bca to be divisible by 37, we have the congruence:

2a ≡ 37bc (mod 37)

Again, simplifying the congruence using 37 ≡ 0 (mod 37), we get:

2a ≡ 0 (mod 37)

This implies that a must be divisible by 37. Since a can take values from 0 to 9, we have only one possibility: a = 0.

37cab:

For 37cab to be divisible by 37, we have the congruence:

2b ≡ 37ca (mod 37)

By using 37 ≡ 0 (mod 37), we can simplify the congruence to:

2b ≡ 0 (mod 37)

This implies that b must be divisible by 37. Again, b can take values from 0 to 9, giving us only one possibility: b = 0.

From the above analysis, we can conclude that the only five-digit integer of the form 37abc satisfying the given conditions is 37000. Therefore, there is only one such integer.

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Complete Question:

Determine the number of five-digit integer 37abc in base 10 such that each of the numbers 37abc,37bca,37cab Is divisible by 37

The probability that 5 messages are received in 1 hour is is 0.1755 ,the probability that 10 messages are received in 1.5 hours is 0.0858 and the probability that less than 2 messages are received in 1/2 hour is 0.2873

Let X shows the number of messages received per hour. The pdf of X is

\(P(X=x)=\) \(\frac{e^{-5}\cdot 5^{x}}{x!},x=0,1,2,3,....\)

Therefore, the probability that 5 messages are received in a single hour is

\(P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}=0.1755\)

(b) Number of message received in 1 hour is 5 so number of message received in 1.5 hour is 7.5. So the probability that 10 messages are received in 1.5 hours is

\(P(X=10)=\frac{e^{-7.5}\cdot 7.5^{10}}{10!}=0.0858\)

(c) Number of message received in 1 hour is 5 so number of message received in 1/2 hour is 2.5. So the probability that less than 2 messages are received in 1/2 hour is

\(P(X < 2)=\frac{e^{-2.5}\cdot 2.5^{0}}{0!}+\frac{e^{-2.5}\cdot 2.5^{1}}{1!}=0.2873\)

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The difference between the two localities is 1 speaker.

Let's solve the problems step by step:

a) To determine which of the two locations has a higher number of speakers of a language other than Spanish, we need to compare the ratios of speakers in El Cerrito and El Paseo.

In El Cerrito, 3 out of every 4 people speak a different language than Spanish. This can be written as a ratio: 3:4.

In El Paseo, 5 out of every 7 people speak a different language than Spanish. This can be written as a ratio: 5:7.

To compare the two ratios, we can find a common denominator. In this case, the least common multiple of 4 and 7 is 28.

In El Cerrito, the ratio becomes 21:28 (multiplying both sides by 7).

In El Paseo, the ratio becomes 20:28 (multiplying both sides by 4).

From the ratios, we can see that in El Cerrito, there are 21 out of 28 people who speak a different language than Spanish, while in El Paseo, there are 20 out of 28 people who speak a different language than Spanish.

Since 21 is greater than 20, El Cerrito has a higher number of speakers of a language other than Spanish.

b) The difference between the two localities can be calculated by subtracting the number of speakers in El Paseo from the number of speakers in El Cerrito.

In El Cerrito, there are 21 speakers of a different language than Spanish.

In El Paseo, there are 20 speakers of a different language than Spanish.

The difference is obtained by subtracting 20 from 21, resulting in a difference of 1 speaker.

Therefore, the difference between the two localities is 1 speaker.

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Answer:

\(m=2\)

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Simply plug in your 2 coordinates into the slope formula to find slope m:

\(m=\frac{12-0}{9-3}\)

\(m=\frac{12}{6}\)

\(m=2\)

Answer: m=2

Step-by-step explanation: Use the slope formula to fine the slope m.

Graph below.

I hope this helps you out. If not, I am sorry.

\(\bold{3(n - 1) < 21 }\\\\\bold{ 3n - 3 < 21 }\\\\\bold{ 3n < 21 + 3} \\\\\bold{ 3n < 24} \\\\\bold{ n < \cancel\frac{24}{3}} \\\\ \bold{n < 8}\)

hope helpful~

Hello.

The first step is to use the Distributive Property and distribute 3:

3(n-1)<21

3n-3<21

Now, add 3 to both sides:

3n-3+3<21+3

3n<24

Divide both sides by 3:

n<8

Therefore, the answer is

n<8

I hope it helps.

Have a nice day.

\(\boxed{imperturbability}\)

Answer: n squared - 1

Step-by-step explanation:

The relationship between the step number {n} and the total number of small squares in the pattern is -

f(n) = 2ⁿ - 1.

An expression in mathematics is a combination of terms both constants and variables.

Given is a pattern of small squares as described -

Step 1 has 0 squares.

Step 2 has 3 squares : 2 by 2 but missing the lower right square.

Step 3 has 8 squares : 3 by 3 but missing the lower right square.

We can write the general expression for step {n} as -

Step {n} will have : 2ⁿ - 1 squares with missing the lower right square.

or

f(n) = 2ⁿ - 1

Therefore, the relationship between the step number {n} and the total number of small squares in the pattern is -

f(n) = 2ⁿ - 1.

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Answer:

0

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

50x³ -20x + 8x - 21x³ - 3x + 15x - 29x³

Step 2: Simplify

Answer:

\(\boxed {\boxed {\sf 0}}\)

Step-by-step explanation:

We are given the expression:

\(50x^3-20x+8x-21x^3-3x+15x-29x^3\)

We want to simplify it, so we must combine the like terms. For this equation, the like terms are terms with x³ or x.

First, combine all the x³ terms.

\((50x^3-21x^3-29x^3)-20x+8x-3x+15x\)

\((0x^3)-20x+8x-3x+15x\)

\(-20x+8x-3x+15x\)

Next, combine all the remaining terms, because they are all terms with an x.

\(-12x-3x+15x\)

\(-15x+15x=0\)

The expression is equal to 0

Answer:

P(A n B) = 1/4

Step-by-step explanation:

We know that:

P(A U B) = P(A) + P(B) - P(A n B)

Substituting the given values, we get:

3/8 = 1/2 + 3/4 - P(A n B)

Simplifying, we get:

P(A n B) = 1/4

Answer: P ( A n B ) = 7/8

Step-by-step explanation:  P ( A U B ) = P(A) + P(B) - P( A n B )

                                                         3/8   =   1/2  + 3/4 - P( A n B )

                                                         3/8   =   5/4 - P ( A n B )

                                               P ( A n B )  =  5/4 - 3/8

                                               P ( A n B )  =   7/8