Directions: Complete each of the following.
1. Write an algebraic equation to represent each of the statements listed below. Let c = the number of carrots and p = the number of potatoes. (Remember: An equation has an equal sign in it.)
1. There are three times as many carrots as potatoes.
2. There are ten more potatoes than carrots.
2. Write an algebraic equation to represent each of the statements listed below. (Remember: An equation has an equal sign in it.)
1. Fifteen is 12 less than three times a number, n.
2. The difference of 8 and a number n, is 5.
3. Write an algebraic expression to answer each of the following questions. (Remember: An expression does not have an equal sign in it.)
1. A notebook costs $5. How many notebooks can you buy with d dollars?
2. A rose costs $4 more than a carnation. If a rose costs d dollars, how much does a carnation cost?
4. Write an algebraic expression to answer each of the following questions. (Remember: An expression does not have an equal sign in it.)
1. Twenty-four crayons were shared equally among a small group of students in a kindergarten classroom. Let k = the number of kindergarten students in that group. How many crayons did each student receive?
2. Each kindergarten student in a small group was given twenty-four crayons. There were k kindergarten students in that group. How many crayons were given to that group of students?
5. Write an algebraic expression to answer each of the following questions. (Remember: An expression does not have an equal sign in it.)
1. Eleven students from one class and x students from another class joined together at recess to form 4 equal-sized teams. How many students were on each team?
2. There were x students in one class who were organized into four equal-sized groups, named Groups A, B, C, and D. Then one student left Group B. How many students remained in Group B?

Answer:

pagal

Step-by-step explanation:

what is the meaning of a mad person

Answer:3/5

Step-by-step explanation:

Answer:

1,092 cm²

Step-by-step explanation:

Smaller box:

Length = 24 cm

Wrapping paper = 936 cm²

Bigger box:

Length= 28 cm

Wrapping paper = x cm²

Box : wrapping paper = 24 cm : 936 cm²

Box : wrapping paper = 28 cm : x cm²

Equate both ratios to find x

24 : 936 = 28 : x

24/936 = 28/x

Cross product

24 * x = 936 * 28

24x = 26,208

x = 26,208 / 24

x = 1,092 cm²

Bigger box:

Length= 28 cm

Wrapping paper = 1,092 cm²

Answer:

256

Step-by-step explanation:

i think it is 256.i hope it was that

Answer:

Step-by-step explanation:

Here you go mate;

STEP 1

2^7 x 2  equation

STEP 2

2^7 x 2  simplify

(2^7)(x^2)

STEP 3

128^2  multiply

answer

16384

The probability that exactly two will have this mild side effect is

\(P(X=2)=0.1229\)

Probability is defined as the likelihood that a trial will succeed or fail. The ratio of positive events to all possible outcomes is known as probability. The probability scale ranges from 0 to 1.

Given data:

The probability of all patients that will have the mild side effect is p=5%=0.05

The number of people selected is n=14

The expression for the probability that exactly two will have this mild side effect is given as,

\(P(X=x)=^{n}C _{x} p^{x} (1-p)^{n-x}\)

Substituting the values in the above equation as

\(P(X=x)=^{n}C _{x} p^{x} (1-p)^{n-x}\\P(X=2)=^{14}C _{2} 0.05^{2} (1-0.05)^{14-2}\\P(X=2)=91*0.0025*0.54036\\P(X=2)=0.1229\)

Thus the probability that exactly two will have this mild side effect is

\(P(X=2)=0.1229\)

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Answer:  The answer is 32.

Step-by-step explanation: Yes since you did 9.5+13.6+5.7+3.2 is 32.00 or 32.

Answer:

Step-by-step explanation:

We will work to fill in the slope-intercept form of a line to get the answer to this. y = mx + b. The thing you need to understand first is how to get from one point to another on the line to determine the slope. Look to where the line goes through a corner of one of the squares on the graph. For example, locate these points to see what I mean: (-1, -2), (-2, -5), (1, 4), (2, 7). At each of those points, the line goes through perfectly right where the corners of the squares meet. If you understand this, then you are ready to write the equation of any line.

First locate the y-intercept. This is the point where the line goes through the y-axis. Our line goes through at a y value of +1. So our b value is +1. We will begin by filling that in first:

y = ___x + 1.

Now from that point, you can either go up and to the right to get to another point on the line, or you can go down and to the left. Let's do it both ways so you can see that regardless of which way you pick to go, you'll get the exact same equation every time.

I will go from the y-intercept to the point (1, 4). To get from the y-intercept, I have to go up 3 units til I'm even with the next point on the line, and then to the right 1. So my slope is +3/+1 which is 3.

If I want to go from the y-intercept to the point (-1, -2), I will go down 3 til I'm even with the point, then to the left 1. So my slope will be -3/-1 which is also a positive 3. Fill that in to the slope formula now:

y = 3x + 1, choice A.

refer the attachment for your answer !!

When performing a hypothesis test on the population mean (μ) when the population standard deviation (σ) is known, the null hypothesis (H0) can never be rejected if the sample mean falls within the acceptance range determined by the chosen significance level and the critical values.

In hypothesis testing for the population mean when the population standard deviation is known, the null hypothesis (H0) represents the claim or assumption that the population mean is equal to a specific value. The alternative hypothesis (Ha) states that the population mean is not equal to the specific value.

To determine whether to reject or fail to reject the null hypothesis, we compare the sample mean to the expected value under the null hypothesis. If the sample mean falls within the acceptance range determined by the chosen significance level and the critical values, we do not have sufficient evidence to reject the null hypothesis. The acceptance range is defined by the margin of error around the expected value, and it indicates the range of values that can be considered reasonably close to the expected value.

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Answer:

32cm

Step-by-step explanation:

A square has 4 sides that MUST be equal

In knowing this, you only need to divide the total amount of sides (4) by the perimeter.

\(128 \div 4 = 32\)

Area of Shaped block is ~

\( \huge \boxed{ \mathfrak{Explanation}}\)

The given figure is formed by cutting down a triangular part from a rectangle.

So, Area of figure is equal to ~

now, let's find the Area of rectangle as well as Triangle.

Area of rectangle :

Now, it's time to find Area of Triangle ~

So, Area of Triangle is equal to ~

Area of figure is equal to ~

Answer:

h(x) = 5x²-6

Step-by-step explanation:

f(x) = 5x²-1, translated vertically downward by 5 units, it becomes

h(x) = 5x² -1-5 = 5x²-6

If you rent a car, you should choose Option 3 and accept the fixed price of $50 for gasoline if you expect to drive 150 miles.

1. Total gasoline consumed (gallons):

To calculate the total gasoline consumed, divide the expected distance by the car's fuel efficiency:

Total gasoline consumed = Distance / Fuel efficiency

Total gasoline consumed = 150 miles / 28 miles per gallon

Total gasoline consumed ≈ 5.36 gallons

2. Option 1 cost:

In Option 1, you need to return the car with a full gas tank. Since the car has a 16-gallon tank and you've consumed approximately 5.36 gallons, you need to fill up the remaining 16 - 5.36 = 10.64 gallons.

Option 1 cost = 10.64 gallons * $3.95 per gallon = $42.01

3. Option 2 cost:

In Option 2, you return the car without filling it up and pay $5.45 per gallon. As calculated before, you've consumed approximately 5.36 gallons.

Option 2 cost = 5.36 gallons * $5.45 per gallon = $29.20

4. Option 3 cost:

In Option 3, you accept the fixed price of $50 for gasoline. This fixed price is the most cost-effective option compared to the other two choices.

Therefore, the best choice is Option 3, accepting the fixed price of $50 for gasoline, as it offers a better value for the expected distance of 150 miles.

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Answer:

\(x = -5\\y = 4\)

Step-by-step explanation:

Not sure I understand that part of your question ...not separate, the xy for both combined.

Here are the solution steps to determine x and y values

Given equations are

\(\begin{amatrix}x-2y=-13 \dots [1] \\\\ y=-2x-6\dots\dots[2]\end{amatrix}\)

In equation [2] get all the variables to the left side and the constant on ther right side:

Let's examine equations [1] and [3]:

\(\begin{aligned}x - 2y &= - 13 \dots [1]\\ 2x + y &= -6\;\;\dots[3]\\\end{aligned}\)

Multiply eq [1], \(x - 2y = -13\)  throughout by \(2\):
\(2(x - 2y) &= 2(- 13) \implies 2x - 4y = -26 \dots[4]\\\)

Subtract the equations:
\(2x+y=-6\\-\\\underline{2x-4y=-26}\\\\5y=20\\\\y = \dfrac{20}{5} = 4\)

\(\mathrm{For\:}2x-4y=-26\mathrm{\:plug\:in\:}y=4\):

\(2x-4\cdot \:4=-26\:\\\\2x - 16 = -26\\\\2x = -26 + 16\\\\2x = -10\\\\x = -10/2 = -5\)

Hint

If we define x to be the value of one of the factors, since 1 + 2 + 3 + 4 + 5 ... + 10 = 11(5) = 55, the value of the other factor has to be 55-x.

To maximize P, you'd like to make x as close as possible to the vertex you found. What if you want to minimize P? Remember x must be an integer.

I hope this helps :)

Answer:

Step-by-step explanation:

Slope = (-6-9)/(-1-4) = -15/-5 = 3

Answer:

\(m=3\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra Iu

Step-by-step explanation:

Step 1: Define

Point (4, 9)

Point (-1, -6)

Step 2: Find slope m

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

Answer:

5w^2 over 12 is your answer. hope it helped!

Step-by-step explanation:

Answer:

5w^2 over 12

Step-by-step explanation:

To find the minimum sample size required to estimate the population proportion, we'll use the following formula:
n = (Z^2 * p_hat * (1 - p_hat)) / E^2
where:
n = minimum sample size
Z = Z-score, which corresponds to the desired confidence level (99% in this case)
p_hat = estimated population proportion (0.07)
E = margin of error (0.04)
First, we need to find the Z-score for a 99% confidence level. You can find this value using a standard normal distribution table or a calculator. For a 99% confidence level, the Z-score is approximately 2.576.
Now, we can plug the values into the formula:
n = (2.576^2 * 0.07 * (1 - 0.07)) / 0.04^2
n = (6.635776 * 0.07 * 0.93) / 0.0016
n = 0.464507328 / 0.0016
n = 290.316955
Since we cannot have a fraction of a participant, we round up to the nearest whole number to ensure the desired margin of error and confidence level are met.
Minimum sample size (n) = 291

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The area of triangle cde with altitude ef is 8 square units. This is calculated by finding the height from point "e" to "f", and the base from point "c" to "d", and then using the formula: Area = (base * height) / 2. The answer is 8 square units.

The area of a triangle can be calculated using the formula:

Area = (Base x Height) / 2

To find the height, we need to find the distance between the point where the altitude intersects the base (in this case, point "f" on the y-coordinate of point "e"), and the other two points of the triangle (in this case, "c" and "d").

The equation for a line in the form y = mx + b can be used to find the y-coordinate of point "f". Using the coordinates of points "c" and "e", the slope can be found by:

m = (3 - (-2)) / (2 - 3) = -1

The y-intercept can be found using the coordinates of point "c" and the slope:

b = -2 - (3 * -1) = 1

So the equation of the line that passes through points "c" and "e" is:

y = -x + 1

We can now use this equation to find the y-coordinate of point "f":

y = -x + 1

y = -0 + 1

y = 1

The height of the triangle is now the distance between points "e" and "f":

height = |3 - 1| = 2

The base of the triangle can be found by taking the distance between points "c" and "d":

base = |(-1) - (3)| = 4

So the area of the triangle is:

Area = (base * height) / 2

Area = (4 * 2) / 2

Area = 8

The area of the triangle is 8 square units.

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Answer:

A: 236 sqaure ft.

B: 4 cans

Step-by-step explanation:

Sure, I can help you with that.

Part A:

The total surface area of a rectangular prism is calculated using the following formula:

Total surface area = 2(lw + wh + lh)

where:

In this case, we have:

Plugging these values into the formula, we get:

Total surface area = 2(8*6+6*5+8*5) = 236 square feet

Therefore, the total surface area of the doghouse is 236 square feet.

Part B:

Since the bottom of the doghouse will not be painted, we only need to paint the top, front, back, and two sides.

The total surface area of these sides is 236-6*8 = 188 square feet.

Therefore,

we need 188 ÷ 50 = 3.76 cans of paint to paint the doghouse.

Since we cannot buy 0.76 of a can of paint, we need to buy 4 cans of paint.

Answer:

A)  236 ft²

B)  4 cans of paint

Step-by-step explanation:

The given diagram (attached) shows the doghouse modelled as a rectangular prism with the following dimensions:

The formula for the total surface area of a rectangular prism is:

\(S.A.=2(wl+hl+hw)\)

where w is the width, l is the length, and h is the height.

To find the total surface area of the doghouse, substitute the given values of w, l and h into the formula:

\(\begin{aligned}\textsf{Total\;surface\;area}&=2(6 \cdot 8+5 \cdot 8+5 \cdot 6)\\&=2(48+40+30)\\&=2(118)\\&=236\; \sf ft^2\end{aligned}\)

Therefore, the total surface area of the doghouse is 236 ft².

\(\hrulefill\)

As the bottom of the doghouse will not be painted, to find the total surface area to be painted, subtract the area of the base from the total surface area:

\(\begin{aligned}\textsf{Area\;to\;be\;painted}&=\sf Total\;surface\;area-Area\;of\;base\\&=236-(8 \cdot 6)\\&=236-48\\&=188\; \sf ft^2\end{aligned}\)

Therefore, the total surface area to be painted is 188 ft².

If one can of paint will cover 50 ft², to calculate how many cans of paint are needed to paint the doghouse, divide the total surface area to be painted by 50 ft², and round up to the nearest whole number:

\(\begin{aligned}\textsf{Cans\;of\;paint\;needed}&=\sf \dfrac{188\;ft^2}{50\;ft^2}\\\\ &= \sf 3.76\\\\&=\sf 4\;(nearest\;whole\;number)\end{aligned}\)

Therefore, 4 cans of paint are needed to paint the doghouse.

Note: Rounding 3.76 to the nearest whole number means rounding up to 4. However, even if the number of paint cans needed was nearer to 3, e.g. 3.2, we would still need to round up to 4 cans, else we would not have enough paint.

A plane is a flat surface made up of points that extends infinitely in all directions.

In mathematics, a plane is a fundamental geometric concept. It is a two-dimensional flat surface that extends infinitely in all directions. A plane can be visualized as a flat sheet or a tabletop. It has length and width but no thickness.

A plane is defined by three non-collinear points or by a linear equation in three variables. The equation of a plane in three-dimensional space is typically written as Ax + By + Cz + D = 0, where A, B, C are coefficients representing the plane's orientation, and D is a constant term.

Planes are important in various branches of mathematics, such as geometry, linear algebra, and calculus. They serve as a foundation for understanding concepts like lines, angles, and shapes in two dimensions. Additionally, planes are used in vector operations, linear transformations, and solving systems of linear equations.

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Option C represents a modified Hardy-Weinberg equation that incorporates the effects of natural selection on a population. The equation is given as:

$(p-3s)^2 + 2(p-s)q + q^2 = 1$

In this equation, various terms are included to express the impact of natural selection. Let's break down the equation and understand its components.

$p$ represents the frequency of the dominant allele in the population, while $q$ represents the frequency of the recessive allele. These frequencies are determined based on the initial allele frequencies in the population.

The term $(p-3s)^2$ represents the expected frequency of the homozygous dominant genotype in the next generation. The factor $3s$ denotes the selection coefficient, where $s$ represents the frequency of homozygous recessive individuals who do not survive due to natural selection. By subtracting $3s$ from $p$, we account for the reduction in the frequency of the dominant allele due to selection.

The term $2(p-s)q$ represents the expected frequency of the heterozygous genotype in the next generation. This term incorporates both the initial frequency of the heterozygous individuals, represented by $(p-s)$, as well as the transmission of alleles through reproduction, given by $q$. The factor of 2 accounts for the two possible combinations of alleles in the heterozygous genotype.

Finally, $q^2$ represents the expected frequency of the homozygous recessive genotype in the next generation. This term considers the transmission of the recessive allele, represented by $q$, and its squared value accounts for the homozygous recessive genotype.

The equation is set equal to 1, as the frequencies of all genotypes should sum to 1 in a population.

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Answer:

pi, 7, and 8

Step-by-step explanation:

Nearly any number you can think of is a Real Number

Answer:

3

Step-by-step explanation:

8 people

3 slices per person

8 × 3 = 24

They need 24 slices.

1 pizza has 10 slices.

24/10 = 2.4

They need 2.4 pizzas. Since they need to order a whole number of pizzas, they need to order 3 pizzas.

Answer: 3

Answer:

The amount paid each month would be 125$

The amount  will Samantha pay in interest is $12,375

Step-by-step explanation:

In order to calculate How much will Samantha pay each month we would have to make the following calculation:

loan amount is $15,000 for 10 years

Therefore, amount paid each year would be=$15,000/10=$1,500

Hence, amount paid each month would be=$1,500/12=125$

In order to calculate How much will Samantha pay in interest we would have to make the following calculation:

I=P*r*n

I=$15,000*8.25%*10

I=$12,375

The amount  will Samantha pay in interest is $12,375

Answer:

The amount paid each month would be 125$

The amount  will Samantha pay in interest is $12,375

Step-by-step explanation:

In order to calculate How much will Samantha pay each month we would have to make the following calculation:

loan amount is $15,000 for 10 years

Therefore, amount paid each year would be=$15,000/10=$1,500

Hence, amount paid each month would be=$1,500/12=125$

In order to calculate How much will Samantha pay in interest we would have to make the following calculation:

I=P*r*n

I=$15,000*8.25%*10

I=$12,375

The amount  will Samantha pay in interest is $12,375

When comparing the means of samples from two normally distributed populations, with independent samples and known population variances, a z-test can be used.

The z-test is a statistical test used to compare means when certain assumptions are met. In this case, the populations from which the samples are drawn are assumed to be normally distributed. The samples being compared should be independent of each other, meaning that the values in one sample are not related to or influenced by the values in the other sample. Additionally, it is assumed that the population variances are known, which is not always the case in practice.

The z-test relies on the calculation of a test statistic called the z-score, which measures the difference between the sample means in terms of standard deviations. The z-score is calculated by subtracting the mean of one sample from the mean of the other sample, and then dividing by the standard deviation of the sampling distribution of the difference in means. The resulting z-score is compared to a critical value from the standard normal distribution to determine the statistical significance of the difference between the means.

If the absolute value of the z-score exceeds the critical value, it indicates that the difference between the sample means is statistically significant, suggesting that the population means are likely to be different. On the other hand, if the z-score is not statistically significant, it suggests that the difference between the sample means may be due to chance, and there is not enough evidence to conclude that the population means are different.

Overall, when comparing the means of samples from normally distributed populations with known variances and independent samples, a z-test provides a way to assess the statistical significance of the difference between the means.

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Answer:

x=15

Step-by-step explanation:

You can set up the equation like this

60 =3x+15

Get x by itself

45=3x

Divide both sides by 3

x=15

1.  The simultaneous solution of the given equations is X=12/5 and Y=4/5

2.1)The combination of X and Y that will yield the optimum for this problem is X=0 and Y=3.3.

2)The combination of X and Y that will provide a minimum for this problem is X=3 and Y=0.

To find the simultaneous solution of the given equations 4X+3Y=12 and 2X+4Y=8, we can use the method of elimination, also known as the addition method. Multiplying the second equation by 2, we get 4X+8Y=16.

Now, we can subtract the first equation from the second equation: 4X+8Y - (4X+3Y) = 8Y - 3Y = 5Y and 16 - 12 = 4. Thus, 5Y=4 or Y = 4/5.

Substituting this value of Y in any of the two equations, we can find the value of X. Let's substitute this value of Y in the first equation: 4X+3(4/5)=12 or 4X

= 12 - (12/5)

= (60-12)/5

= 48/5.

Thus, X = 12/5. Hence, the simultaneous solution of the given equations is X=12/5 and Y=4/5.2. To find the optimal values of X and Y that will maximize the objective function Z=$10X+$50Y, we need to use the method of linear programming.

First, let's plot the feasible region defined by the given constraints:We can see that the feasible region is bounded by the lines 3X+4Y=12, 2X+5Y=10, X=0, and Y=0.

To find the optimal solution, we need to evaluate the objective function at each of the corner points of the feasible region, and choose the one that gives the maximum value.

Let's denote the corner points as A, B, C, and D, as shown above. The coordinates of these points are: A=(0,3), B=(2,1), C=(5/2,0), and D=(0,0). Now, let's evaluate the objective function Z=$10X+$50Y at each of these points:

Z(A)=$10(0)+$50(3)

=$150, Z(B)

=$10(2)+$50(1)

=$70, Z(C)

=$10(5/2)+$50(0)

=$25, Z(D)

=$10(0)+$50(0)=0.

Thus, we can see that the maximum value of Z is obtained at point A, where X=0 and Y=3. Therefore, the combination of X and Y that will yield the optimum for this problem is X=0 and Y=3.3.

To find the combination of X and Y that will provide a minimum for the problem Minimize Z=X+5Y subject to: 4X+3Y≥12 and 2X+5Y≥10, we need to use the same method of linear programming as above.

First, let's plot the feasible region defined by the given constraints:We can see that the feasible region is bounded by the lines 4X+3Y=12, 2X+5Y=10, X=0, and Y=0.

To find the optimal solution, we need to evaluate the objective function Z=X+5Y at each of the corner points of the feasible region, and choose the one that gives the minimum value.

Let's denote the corner points as A, B, C, and D, as shown above.

The coordinates of these points are: A=(3,0), B=(5,1), C=(0,4), and D=(0,0).

Now, let's evaluate the objective function Z=X+5Y at each of these points:

Z(A)=3+5(0)=3,

Z(B)=5+5(1)=10,

Z(C)=0+5(4)=20,

Z(D)=0+5(0)=0.

Thus, we can see that the minimum value of Z is obtained at point A, where X=3 and Y=0. Therefore, the combination of X and Y that will provide a minimum for this problem is X=3 and Y=0.

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The system of equation that could have led to the equation 9x = 27 is

7x - 2y = 15

x + y = 6

The correct option is the third option

7x - 2y = 15

x + y = 6

From the question, we are to determine the system that could have led to 9x = 27

1.

9x + 2y = 21

-9x - 2y = 21

Subtracting, we get

9x + 2y = 21

-9x - 2y = 21

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

18x + 4y = 0

2.

10x - y = 15

x + y = - 12

Subtracting, we get

10x - y = 15

x + y = - 12

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

9x -2y = 27

3.

7x - 2y = 15

x + y = 6

Here, multiply the second equation by 2

2 × [x + y = 6]

2x + 2y = 12

Now, add to the first equation

7x - 2y = 15

2x + 2y = 12

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

9x = 27

4.

4x + 3y = 24

-5x - 3y = 3

Subtracting, we get

4x + 3y = 24

-5x - 3y = 3

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

9x + 6y = 21

Hence, the system of equation that could have led to the equation 9x = 27 is

7x - 2y = 15

x + y = 6

The correct option is the third option

7x - 2y = 15

x + y = 6

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