1) 8+9x(x+4)=(3x-2)(3x+2).
2)2x(2x-2)-17=(5+2x)(2x-5).
3)(2x+1)(4x2-2x+1)=4x(2x2-5)

There is 20 students in her class.

Here, we have,

3/10= size of slice;

we can get 3 slices from one pizza.

There are 6 pizzas..... 3x6=18;

there will be a remained of 1/10 from each pizza

because 3/10 is not an even number.

Now u would have (6) 1/10's.... So 1/10+1/10+1/10= 3/10 and 1/10+1/10+1/10=3/10.....

That makes two more slices for two more students......

18+2=20 slices for 20 kids in the class.

Hence, There is 20 students in her class.

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In the equation for the two-sample t-test for independent samples, the difference between sample means is divided by b. standard error of the difference between means.

The correct answer is b. The difference between sample means is divided by the standard error of the difference between means in the equation for the two-sample t-test for independent samples. This is because the standard error of the difference between means takes into account both sample sizes and sample variances, providing a more accurate estimate of the standard deviation of the difference between the two population means.
In the equation for the two-sample t-test for independent samples, the difference between sample means is divided by b. standard error of the difference between means.

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In order to place 8 distinguishable rooks on an 8x8 chessboard without any of them being able to capture each other, you will need to ensure that each rook occupies a unique row and column.

Step 1: Place the first rook. There are 8 different locations to choose from (one in each row).
Step 2: Place the second rook. There are 7 remaining locations to choose from, as you cannot place it in the same row or column as the first rook.
Step 3: Place the third rook. There are 6 remaining locations to choose from, avoiding the rows and columns of the first two rooks.
Step 4: Continue this process until all 8 rooks have been placed.

To find the total number of ways to place the 8 distinguishable rooks, multiply the number of choices for each step:

8 (choices for rook 1) * 7 (choices for rook 2) * 6 (choices for rook 3) * 5 (choices for rook 4) * 4 (choices for rook 5) * 3 (choices for rook 6) * 2 (choices for rook 7) * 1 (choice for rook 8) = 40,320 ways.

To solve this problem, we can use the principle of multiplication. We start by placing the first rook in any of the 64 squares on the chessboard. There are 64 choices for the first rook.

Next, we need to place the second rook in a location that is not attacked by the first rook. Since rooks can attack any square in the same row or column as them, we need to choose a square that is not in the same row or column as the first rook. There are 7 rows and 7 columns remaining, so there are 14 squares in which the second rook can be placed.

For the third rook, we need to choose a location that is not attacked by either the first or second rook. This means we need to choose a square that is not in the same row or column as the first two rooks. There are 6 rows and 6 columns remaining, so there are 12 squares in which the third rook can be placed.

Continuing in this way, we see that the number of choices for the nth rook is equal to the number of rows and columns remaining after the (n-1)th rook has been placed. So, the total number of ways to place all 8 rooks on the chessboard is:

64 × 14 × 12 × 10 × 8 × 6 × 4 × 2 = 16,777,216

Therefore, there are 16,777,216 ways to place 8 distinguishable rooks on an 8 × 8 chessboard so that none can capture any other.

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Answer:

22.98133...

Step-by-step explanation:

30 x cos(40°)

then refine to a decimal form

The possible observed values of a discrete random variable can be listed in a countable collection. A random variable is a measurement to be taken in a probability experiment.

An observed value of a random variable is the measurement that has been taken. A discrete random variable is a random variable in which there is a countable collection of possible observed values. That is, the discrete random variable can only take on specific values within a given range, and the probability associated with each value can be calculated. This countable collection of possible observed values is finite or countably infinite, and the probabilities sum up to 1.

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The value of x in the quadrilateral is 20 degrees.

The sum of angles in a quadrilateral is 360 degrees. Therefore, a quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angle.

Hence, let's find the value of x in the quadrilateral.

x + x + 32 + 8x - 16 + 8x - 16  = 360

2x + 16x + 32 - 32 = 360

18x + 0 = 360

18x = 360

18x = 360

divide both sides by 18

x = 360 / 18

x = 20

Therefore,

x = 20 degrees

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Based on the given information, the company estimates its sales to be 200,000 units in the first quarter. Assuming a 20,000 unit increase each quarter over the year, the second quarter's sales would be 220,000 units, the third quarter's sales would be 240,000 units, and the fourth quarter's sales would be 260,000 units.

To calculate the desired ending inventory of finished goods, we take 25% of the expected sales for the next quarter. For example, to determine the desired ending inventory for the first quarter, we take 25% of 220,000 units (the expected sales for the second quarter), which equals 55,000 units.

Each unit sells for $35, so the total sales revenue for the first quarter would be 200,000 units x $35 = $7,000,000.

Of the sales, 70% are for cash, so the company would receive $4,900,000 in cash for the first quarter's sales. The remaining 30% of sales are credit sales, and assuming that 70% of credit customers pay within the quarter, the company would receive an additional 21,000 units x $35 = $735,000 in the first quarter. The remainder of the credit sales, which is 30% x 30,000 units = 9,000 units, would be received in the following quarter.

Overall, the company expects to have increasing sales throughout the year and desires to maintain a 25% ending inventory of finished goods. The company also expects a mix of cash and credit sales, with 70% of credit customers paying within the quarter and the remainder paying in the following quarter.

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Answer:

4 units left

Step-by-step explanation:

Since you are changing the x value by negative 4, you move left towards the negatives 4 units.

Therefore, the vector form of the equation y = x² - 8x + 15 is y = (x - 4)² + 14. The vertex of the parabola is at the point (4, 14).

To convert the quadratic equation y = x² - 8x + 15 from standard form to vertex form, we need to complete the square by adding and subtracting a constant term. Here's the step-by-step explanation:

Factor the coefficient of x²: The coefficient of x² is 1, so we don't need to factor it.

Group the x terms: Rewrite the quadratic equation as y = (x² - 8x) + 15.

Complete the square: To complete the square, we need to add and subtract a constant term that will make the expression inside the parentheses a perfect square trinomial. The constant we need to add is half of the coefficient of x, squared: (8/2)² = 16.

y = (x² - 8x + 16 - 16) + 15 // add and subtract 16

y = (x - 4)² - 1 + 15 // factor and simplify

Simplify: Now we can simplify the expression by combining the constants -1 and 15 to get 14.

y = (x - 4)² + 14

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The number that is two more than the quotient of a number and is equal to 4 is 16. Let's break down the sentence into a numerical condition:

"Two more than the remainder of a number and 8" can be spoken to as (x/8) + 2, where x is the number we are attempting to discover.

The sentence moreover states that this expression is "equal to 4", so we are able to type in

(x/8) + 2 = 4

To fathom for x, we will confine the variable on one side of the condition. We will start by subtracting 2 from both sides:

(x/8) = 4 - 2

Streamlining the right-hand side gives:

(x/8) = 2

At long last, we are able to illuminate for x by increasing both sides by 8:

x = 2 x 8

x = 16

thus, the number we are seeking out is 16.

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complete question: What is the number which is two more than the quotient of a number and 8 is equal to 4?

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Increase in taxes is one of the reasons why the change in Mr. Henderson's net income

It is possible that Mr. Henderson's net income has decreased this month despite having received the same gross income as last month. Let us examine some of the plausible rationales behind it:

An increase in taxes: If Mr. Henderson worked more hours or obtained a raise, his gross income would be higher. However, if he now belongs to a higher tax bracket, he will owe more money in taxes and therefore have lower net income.

A change in deductions: It is likely that Mr. Henderson's employer may have modified his paycheck deductions which can lead to more taxes being held back from his earnings - an eventuality that could cause his net income to decrease.

Alterations in benefits: Changes in Mr. Henderson's approved employee benefits plan- insurance premiums increasing or retirement savings contributions stalling, for instance- could also explain why his net income reduced this month.

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In summary, statement 1+2 is correct as it provides information about both c and a, while statement 1 alone and statement 2 alone are not sufficient to determine the value of a.

Statement 1+2: The first statement states that the value of c is not equal to zero, and for these values of c, a is always 1. The second statement states that h is equal to b*c, and since h is not equal to zero, neither b nor c can be zero. This means that statement 1+2 is correct, as it provides information about both c and a.

Statement 1: This statement provides information about the value of c, but it doesn't say anything about a. It states that h is equal to b*c and that h is not equal to zero, which means that neither b nor c can be zero. However, this information alone is not sufficient to determine the value of a.

Statement 2: This statement provides information about the relationship between a, c, and f. It states that c is equal to f, and a*c is equal to f. This expression can hold if c=f=0, but a can have any value. Additionally, if c and f are any non-zero value, a is always 1. This means that statement 2 alone is not sufficient to determine the value of a.

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Answer: -1/3-(-3/5)=4/15

Step-by-step explanation:

P.S i'm emo

The daily inpatient census for July 16 is 271.

To determine the daily inpatient census for July 16, we need to take into account the census at midnight on July 15, the number of discharges, admissions, and additional patients (content loaded) throughout the day on July 15 and July 16.

Starting with the census at midnight on July 15 of 239, we subtract the number of discharges (59) and add the number of admissions (67) and additional patients (24) to get the total number of patients in the hospital on July 16.

239 - 59 + 67 + 24 = 271

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There are 200.96 square inches that make up half of the cookie cake.

We have to given that;

The diameter of a circular cookie cake is 16 inches.

Now, We know that;

Area of circle = πr²

Here, Diameter = 16 inches

Hence, Radius = 16 / 2

                       = 8 in

Thus, Area of circular cookie cake is,

⇒ A = πr²

⇒ A = 3.14 × 8²

⇒ A = 200.96 inches²

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Answer:

16 tiles

Step-by-step explanation:

The answer resulted in x = 5 after the operation as the picture suggests, hope this helps

The pooled standard deviatio is 5.746. We can say with 95% confidence that the true difference between the population means falls between -4.019 and 0.719.

First, we need to calculate the pooled standard deviation:

s_p = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2)/(n1+n2-2))

s_p = sqrt(((6-1)*5.9^2 + (7-1)*5.6^2)/(6+7-2))

s_p = 5.746

Next, we can calculate the t-statistic:

t = ((x1 - x2) - 0) / (s_p * sqrt(1/n1 + 1/n2))

t = ((72.9 - 75.1) - 0) / (5.746 * sqrt(1/6 + 1/7))

t = -0.956

Using a t-distribution table with conservative degrees of freedom (df = min(n1-1, n2-1) = 5), we find that the critical value for a one-tailed test with α=0.05 is -1.833. Since our calculated t-statistic is greater than the critical value, we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is sufficient evidence to support the claim that the first population mean is less than the second population mean.

As for the confidence interval, we can use the formula:

(x1 - x2) ± t_(α/2, df) * s_p * sqrt(1/n1 + 1/n2)

Plugging in the values:

(72.9 - 75.1) ± t_(0.025, 5) * 5.746 * sqrt(1/6 + 1/7)

-4.019 < μ1 - μ2 < 0.719

Therefore, we can say with 95% confidence that the true difference between the population means falls between -4.019 and 0.719.

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Answer: D

Step-by-step explanation:

If something is to the power of it means multiply the fractions.

since all inside the parenthesis is being multiplied you can distribute that exponent

[tex](64h^{16} x^{4} )^{\frac{1}{2} }[/tex]            

[tex]64^{\frac{1}{2} } h^{16(\frac{1}{2}) } x^{4(\frac{1}{2} )} }[/tex]          reduce fraction in exponents

[tex]64^{\frac{1}{2} } h^{8 } x^{2} }[/tex]                now for the 64^1/2   than means take the square root

[tex]8 h^{8 } x^{2} }[/tex]                   fractions are actually roots

There are 36 cards in the box.  In this scenario, we are given that the probability of choosing a red card from a box is one-third. We also know that there are 24 blue cards in the box. Our goal is to find the total number of cards in the box.

Let's use the concept of probability to solve this problem. The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the probability of choosing a red card is given as 1/3, and the favorable outcome is selecting a red card. Let R be the number of red cards, and T be the total number of cards in the box. The probability formula can be represented as:

Probability of choosing a red card = R / T

We are given that the probability of choosing a red card is 1/3:

1/3 = R / T

Since there are 24 blue cards in the box, we can represent the total number of cards as the sum of red and blue cards:

T = R + 24

Now, we can solve the system of equations to find the values of R and T:

1. 1/3 = R / T
2. T = R + 24

From equation 1, we can express R as:

R = (1/3) * T

Substitute this expression for R in equation 2:

T = (1/3) * T + 24

Multiplying both sides by 3 to eliminate the fraction, we get:

3T = T + 72

Subtracting T from both sides:

2T = 72

Now, divide by 2 to find the total number of cards, T:

T = 36

So, there are 36 cards in the box.

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The measure of the missing angle is38 degrees.

The figure in the image is a right triangle.

Missing angle θ = ?

Hypotenuse = 55

Opposite to angle θ = 34

To find the missing angle, we use the trigonometric ratio.

sine = opposite / hypotenuse

Plug in the given values and solve for the missing angle.

sinθ = 34/55

Take the sine inverse

θ = sin⁻¹( 34/55 )

θ = 38⁰

Therefore, the angle is 38 degrees.

Option A) 38⁰ is the correct answer.

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The solution of the formula for the variable, m as required to be determined is; m = Fr² / GM.

It follows from the task content that the complete question indicates a formula;

F = GMm / r²

Hence, to solve for the variable m; multiply both sides by r² so that we have;

Fr² = GMm

Finally divide both sides by GM so that we have;

m = Fr² / GM

Ultimately, the formula with m as the subject is; m = Fr² / GM.

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Answer

the third side can measure 2 in, 3 in, or 4 in

Explanation

inequality theorem

a + b > c

a + c > b

b + c > a

2 = a

b = 3

c = x

a + b > c

2 + 3 > x

5 > x

x= 4, 3, 2, or 1 in

a + c > b

2 + x > 3

x = 4, 3, or 2

b + c > a

3 + x > 2

x = 4, 3, or 2

The slope of perpendicular line is -1.

We have,

Equation: 3x - 3y = 63

Now, writing the given equation in slope intercept form

3y= 3x- 63

y= 3x/ 3 - 63/3

y= x - 21

So, the slope of given equation is 1.

Now, the slope of two perpendicular line have the product -1.

let the slope of perpendicular line be m.

So, m x 1 = -1

m = -1

Thus, the slope of perpendicular line is -1.

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a. The new revenue can be estimated as R(20,11) = 150 - 24 = $126.

b. The food truck would need to sell 20 + 8 = 28 tacos to compensate for the decrease in burrito sales and keep the revenue at $150.

a. To estimate the food truck's revenue when 4 fewer burritos are sold, we can use the given information. We know that Rb(20,15) = 6, which means that the revenue changes by $6 for every additional burrito sold. If 4 fewer burritos are sold, the change in revenue would be 4 * (-6) = -$24.
b. To maintain a revenue of $150 despite selling 4 fewer burritos, we need to find out how many more tacos must be sold. We know that Rt(20,15) = 3, meaning the revenue changes by $3 for every additional taco sold. Since the loss in revenue due to selling 4 fewer burritos is $24, we need to sell enough tacos to make up for this loss. So, 24/3 = 8 more tacos need to be sold.

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The theoretical probability of flipping heads and rolling a 1 or 2 is 1/6.

Now, We have;

The sample space for flipping a coin and rolling a number cube are:

Flipping a coin: {H, T}

There are 2 possible outcomes, since the coin is fair.

Rolling a number cube: {1, 2, 3, 4, 5, 6}

Since, There are 6 possible outcomes, since the number cube is standard

So, the total number of outcomes for the combined experiment is,

2 x 6 = 12.

The events of flipping heads and rolling a 1 or a 2 are independent,

Hence, The probability of flipping heads is,

⇒ 1/2,

And, The probability of rolling a 1 or 2 is,

⇒ 2/6,

So, the probability of flipping heads and rolling a 1 or 2 is;

= (1/2) x (2/6)

= 1/6

Therefore, the theoretical probability of flipping heads and rolling a 1 or 2 is 1/6.

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Answer:

Step-by-step explanation: