at an inter-species dance party, each cat danced with exactly three dogs and each dog danced with exactly two cats. no one danced with anyone of their own species, and twelve cats attended the party. how many dogs attended the party? (a) 8 (b) 12 (c) 16 (d) 18 (e) 24

Answer: 8

Step-by-step explanation:

The triangles are congruent by SAS, so using CPCTC, the answer is 8

Answer:

y=3x-2

Step-by-step explanation:

y=mx+b where m=slope and b=y-intercept

y=3x-2

Data:

Initial balance: c

intrest rate: r

time (months)=m

growth: b

c=$100

r=7%=0.07

To an exponential function you have the next general form:

In this case

y=b(m)

C=c

r=r

t=m

Answer:

784000

Step-by-step explanation:

Given data

Profit =  700000

Let us begin by finding what 12% of  700000 is

=12/100* 700000

=0.12* 700000

=84000

Hence the profit made last years was

=84000+700000

=784000

Answer:

20boys and 15girls

Step-by-step explanation:

Let no of boys be 4x

no of girls be 3x

4x+3x=35

7x=35

x=35/7

x=5

no of boys=4×5=20

no of girls=3×5=15

20+15=35 students

3 minutes is the cost of the call that is same for both plans

Two or more expressions with an Equal sign is called as Equation.

Let's assume the call duration in minutes is represented by x.

For David, the cost of the call can be represented by the equation: C(d) = 4 + x

For Alec, the cost of the call can be represented by the equation: C(a) = 1 + 2x

Since the cost of the call is the same for both plans, we can set the two equations equal to each other and solve for x:

4 + x = 1 + 2x

Solve for x.

3 = x

Hence, the call duration that costs the same on both plans is 3 minutes.

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Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

Answer:(2,3,4,5)

Step-by-step explanation:

EXPLANATION

Given the system of equations:

(1) 3x + 5y = -17

(2) 2x + 4y = 6

Multiplying (1) by 2 and (2) by 3:

(1) 6x + 10y = -34

(2) 6x + 12y = 18

Subtracting (2) to (1):

(2) 6x + 12y = 18

-

(1) 6x + 10y = -34

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

2y = 52

Dividing both sides by 2:

y = 52/2

Simplifying:

y = 26

Simplify:

Divide both sides by 6:

Simplify:

The solutions to the system of equations are:

Step-by-step explanation:

px^2-qx+r

p(x^2-q/px)+r

p[(x^2-q/px +(q/2p)^2_(q/2p)^2)]+r

p[(x-q/2p)^2 -q^2/4p^2)]+r

p(x-q/2p)^2 -q^/4p+r

p(x-q/2p)^2-(q^2-4pr)/4p

The 3 × 3 matrix that translates a point in r 2 by (3, 1) then rotates the result 45 degrees about the origin is

M = | 1/√2    -1/√2    3/√2- 1/√2 |

      | 1/√2    1/√2     1/√2 + 1/√2 |

       | 0           0                1 |

To find the 3x3 matrix that translates a point in R^2 by (3, 1) and then rotates the result 45 degrees about the origin using homogeneous coordinates, we can follow these steps:

Translation Matrix:

The translation matrix for a 2D translation by (3, 1) is:

T = | 1 0 3 |

| 0 1 1 |

| 0 0 1 |

This matrix translates a point (x, y) by adding the translation vector (3, 1) to it.

Rotation Matrix:

The rotation matrix for a 2D rotation by 45 degrees counterclockwise is:

R = | cos(theta) -sin(theta) 0 |

| sin(theta) cos(theta) 0 |

| 0 0 1 |

Since we want to rotate by 45 degrees, theta = 45 degrees = π/4 radians. Therefore, the rotation matrix becomes:

R = | cos(π/4) -sin(π/4) 0 |

| sin(π/4) cos(π/4) 0 |

| 0 0 1 |

Simplifying, we have:

R = | 1/√2 -1/√2 0 |

| 1/√2 1/√2 0 |

| 0 0 1 |

Combine Translation and Rotation:

To obtain the combined transformation matrix, we multiply the translation matrix T by the rotation matrix R:

M = T * R

Performing the matrix multiplication:

M = | 1 0 3 | | 1/√2 -1/√2 0 |

| 0 1 1 | * | 1/√2 1/√2 0 |

| 0 0 1 | | 0 0 1 |

Simplifying, we have:

M = | 1/√2 -1/√2 3/√2 - 1/√2 |

| 1/√2 1/√2 1/√2 + 1/√2 |

| 0 0 1 |

This is the desired 3x3 matrix that translates a point in R^2 by (3, 1) and then rotates the result 45 degrees about the origin using homogeneous coordinates.

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The y-intercept of the sample regression line is approximately 1.9854.

To find the y-intercept of the sample regression line, we can use the following formula:

y-intercept (b₀) = (Σy - b₁ * Σx) / n

where b₁ is the slope of the regression line, n is the number of observations, Σx and Σy are the sums of the x and y values respectively. To find b₁, we use the formula:

b₁ = (n * Σ(xy) - Σx * Σy) / (n * Σ(x²) - (Σx)²)

We are given:
n = 27
Σy = 57.2
Σx = 1253.4
Σ(xy) = 3133.7
Σ(x²) = 73296.4

First, let's find b₁:

b₁ = (27 * 3133.7 - 1253.4 * 57.2) / (27 * 73296.4 - 1253.4²)
b₁ ≈ -0.0236

Now, we can find the y-intercept (b₀):

b₀ = (57.2 - (-0.0236) * 1253.4) / 27
b₀ ≈ 1.9854

Therefore, we can state that the y-intercept of the sample regression line is approximately 1.9854.

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Answer:

3. MNP = OPN

Step-by-step explanation:

the second could be as well, but the sequence is the same for the third option, thus the second option is wrong

If were most interested in describing the pattern of changes in the weather in a city from month to month, the type of graph that would be appropriate is the area graph.

An area graph or chart is similar to a line chart in that it has points connected by straight lines on a two-dimensional chart.

It should be noted that the area graph multiple variables are stacked on top of each other, and the area below each line is colored to represent each variable.

Therefore, the type of graph that would be appropriate is the area graph.

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Answer:

A is: 183

B is: -66

C is: Becuase under ground it is negative meters and high up is regular meters

D is: It is 466

Step-by-step explanation:

Answer:

"OC. Invasive species reduce the availability of natural resources for native species by outcompeting the native species for those resources"

Step-by-step explanation:

    Most invasive species reproduce / spread faster than the native species, so the availability of natural resources is reduced for the native species.

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

It is OC. Invasive species reduce the availability of natural resources for native species by outcompeting the native species for those resources

Step-by-step explanation:

Invasive species usually reduce the availability of natural resources for the native species by competing the native species for those resources and their population will increase making the resources less available for the native species living there,effecting their population.

- I hope this answers your question. Good Luck!! :))

Answer:

I'm not really sure but I think it could be y=3/4x-4

Step-by-step explanation:

Given:-

To find the value of x.

Since the corresponding opposite angles are equal and also the sum of angles inside a triangle is 180 degrees. we get,

So the required value of x is 5.

Answer: Square and rectangle

Step-by-step explanation:

The correct answer is (c) 1.9

To calculate the test statistic in this example, we can use the formula for a z-test for proportions:

\(z = (p - P) / \sqrt{[P(1-P) / n]\)

where:

p is the sample proportion of vegetarians (140/1000 = 0.14)

P is the hypothesized population proportion of vegetarians (0.12)

n is the sample size (1000)

Substituting these values into the formula, we get:

\(z = (0.14 - 0.12) / \sqrt{[0.12(1-0.12) / 1000]\)

z = 0.02 / 0.0110

z = 1.818 (rounded to three decimal places)

Therefore, the test statistic in this example will be approximately equal to 1.818. The answer closest to this value is (c) 1.9

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Therefore, r⁴ / n with positive exponents is the simplified version of the equation r⁷ × n³ × t² / n⁹ × r³ × t².

A mathematical statement is a sentence that includes numbers, factors, or both. The equal symbol is never used in expressions. Here are a few phrases as samples. A mathematical statement stating the equality of two formulas is known as an equation.

To simplify the expressions and write them in simplest form with positive exponents, we need to use the properties of exponents, specifically:

\(\begin{aligned}& \mathrm{a}^{\mathrm{m} *} \mathrm{a}^{\mathrm{n}}=\mathrm{a}^{(\mathrm{m}+\mathrm{n})} \\& \mathrm{a}^{\mathrm{m}} / \mathrm{a}^{\mathrm{n}}=\mathrm{a}^{(\mathrm{m}-\mathrm{n})} \\& \left(\mathrm{a}^{\mathrm{m}}\right)^{\mathrm{n}}=\mathrm{a}^{\left(\mathrm{m}^* \mathrm{n}\right)}\end{aligned}\)

Using these properties, we have:

r⁷ × n³ × t² / n⁹ × r³ × t²

= r⁽⁷⁻³⁾ × n⁽³⁻⁹⁾ × t⁽²⁻²⁾ [Using property 2 and simplifying the common term in the numerator and denominator]

= r⁴ / n⁶ [Simplifying the exponents of r and n and noting that t⁰ = 1]

Therefore, the simplified form of the expression r⁷ × n³ × t² / n⁹ × r³ × t² is r⁴ / n with positive exponents.

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Answer:

The percentage of change is an increase of 12% from the original

Step-by-step explanation:

The percentage of change is a percentage of increase because the new value is greater than the original.

To find the percentage of change, we can divide the new value by the old which will give us the amount it increased by in decimal form, which we can simply multiply by 100 to find percentage:

84/75=1.12

1.12x100 = 112

The new value is 112% of the original, this means that the percentage of change is an increase of 12% from the original.

Hope this helped!

Answer:

increase and 12%

Step-by-step explanation:

84 -75 = 9

9 ÷ original # (75) = 0.12

0.12 x 100 = 12%

Answer:

$19

Step-by-step explanation:

Step-by-step explanation:

c

Answer:

c.3x+5

A.x+3

D.x-3

Step-by-step explanation:

Answer:Therefore, the range is 32 and the standard deviation is approximately 10.523 for the given data set.

Step-by-step explanation:To calculate the range and standard deviation for the given data set {40, 65, 33, 46, 55, 50, 61}, we can follow these steps:

Step 1: Find the range.

The range is calculated by subtracting the minimum value from the maximum value in the data set.

Range = Maximum value - Minimum value

Range = 65 - 33

Range = 32

Step 2: Calculate the mean.

The mean is calculated by summing up all the values in the data set and dividing by the total number of values.

Mean = (40 + 65 + 33 + 46 + 55 + 50 + 61) / 7

Mean = 350 / 7

Mean = 50

Step 3: Calculate the deviation for each value.

Deviation is calculated by subtracting the mean from each value in the data set.

Deviation for 40 = 40 - 50 = -10

Deviation for 65 = 65 - 50 = 15

Deviation for 33 = 33 - 50 = -17

Deviation for 46 = 46 - 50 = -4

Deviation for 55 = 55 - 50 = 5

Deviation for 50 = 50 - 50 = 0

Deviation for 61 = 61 - 50 = 11

Step 4: Square each deviation.

Squared deviation for -10 = (-10)^2 = 100

Squared deviation for 15 = 15^2 = 225

Squared deviation for -17 = (-17)^2 = 289

Squared deviation for -4 = (-4)^2 = 16

Squared deviation for 5 = 5^2 = 25

Squared deviation for 0 = 0^2 = 0

Squared deviation for 11 = 11^2 = 121

Step 5: Calculate the variance.

Variance is calculated by summing up all the squared deviations and dividing by the total number of values.

Variance = (100 + 225 + 289 + 16 + 25 + 0 + 121) / 7

Variance = 776 / 7

Variance ≈ 110.857

Step 6: Calculate the standard deviation.

The standard deviation is the square root of the variance.

Standard Deviation ≈ √110.857

Standard Deviation ≈ 10.523

Answer:7/20

Step-by-step explanation:

35% \(= 0.35 = \frac{35}{100} = \frac{35/5}{100/5} = \frac{7}{20}\)

The answer is 7, because the factors of 21 are 1,3,7,21 and for 35 is 1,5,7,35 and the greatest of those is 7.

The highest no. of vehicles Tom can put in one area is 7 SUVs and 7 pickup trucks.

The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.

We also know that distributive property states a(b + c) = ab + ac.

Given, Tom runs a car dealership that currently has 21 pickup trucks and 35 SUVs.

∴ If he wants to divide the lot into areas that have either pickup trucks or SUVs,  and he wants the same number of vehicles in each area the largest number of vehicles Tom can put in one area is is GCF of 7 and 35 which 7.

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Using the concept of Unit Cost, $5.34 is Jacks` total bill for buying 3.5 pounds of carrot and 1.25 pound of broccoli.

The unit price is  measurement used to represent the price of a particular good or service to be exchanged with the customers or consumers for money. The unit price refers to the price/unit of measures, such as price per pound, quart, ounce, or other units of weight or volume of the food package.

The unit price is important for both of customers and organizations. An organization cannot sustain without unit price itself for a long period by selling products at a lower price. Similarly, customers would not be able to buy the product if the value of the product is less than the price. The researcher suggests that the unit price information helps shoppers to save around 17-18% in supermarkets when they are educated on how to actually use it.

We are given Carrot cost of per pound is $0.99.

Therefore Carrot cost for 3.5 pounds=3.5×0.99= $3.465

Similarly, Broccoli cost of per pound is $1.50.

Therefore, broccoli cost for 1.25 pounds =1.25×1.50=1.875

Total bill = Broccoli cost+ Carrot cost

Total bill =3.465+1.875=$5.34

Hence,$5.34 is Jacks` total bill for buying 3.5 pounds of carrot and 1.25 pound of broccoli.

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The pieces of cloth are beyond the standard at 0.05 level of significance.

We can use a one-sample t-test to determine if the mean length of the 35 pieces of cloth is significantly different from the standard length of 3.25 meters.

The null hypothesis is that the mean length of the cloth pieces is equal to the standard length:

H0: μ = 3.25

The alternative hypothesis is that the mean length of the cloth pieces is greater than the standard length:

Ha: μ > 3.25

We can calculate the test statistic as:

t = (x - μ) / (s / √n)

where x is the sample mean length, μ is the population mean length (3.25 meters), s is the sample standard deviation (0.52 meters), and n is the sample size (35).

Plugging in the values, we get:

t = (3.52 - 3.25) / (0.52 / √35) = 3.81

Using a t-table with 34 degrees of freedom (n-1), and a significance level of 0.05 (one-tailed test), the critical t-value is 1.690.

Since our calculated t-value (3.81) is greater than the critical t-value (1.690), we reject the null hypothesis and conclude that the mean length of the 35 pieces of cloth is significantly greater than the standard length at the 0.05 level of significance.

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