The area of the triangle below is \frac{2}{25}

25

2

​

square feet. What is the length of the base? Express your answer as a fraction in simplest form.

1/5 f

Answer:

let x be the no.

So, 5 less than the square of a number in an algebraic expression is:

x^2 - 5

If Liquid a has a density of 1. 2 g/cm³, 150 cm of Liquid a is mixed with some of Liquid b to make Liquid c whose mass is 220 g and has a density of  1.1 g/cm³, then the density of liquid B is 0.8 g/cm³.

To find the density of liquid B, you can follow these steps:
1. Calculate the mass of liquid A using its density and volume:
Liquid A has a density of 1.2 g/cm³ and a volume of 150 cm³.

Mass of A = Density of A × Volume of A = 1.2 g/cm³ × 150 cm³ = 180 g

2. Calculate the mass of liquid B using the mass of liquid C and mass of liquid A:
Liquid C has a mass of 220 g.
Mass of B = Mass of C - Mass of A = 220 g - 180 g = 40 g

3. Calculate the volume of liquid C using its mass and density:
Liquid C has a density of 1.1 g/cm³.
Volume of C = Mass of C ÷ Density of C = 220 g ÷ 1.1 g/cm³ = 200 cm³

4. Calculate the volume of liquid B using the volume of liquid C and the volume of liquid A:
Volume of B = Volume of C - Volume of A = 200 cm³ - 150 cm³ = 50 cm³

5. Calculate the density of liquid B using it's mass and volume:
Density of B = Mass of B ÷ Volume of B = 40 g ÷ 50 cm³ = 0.8 g/cm³

So, the density of liquid B is 0.8 g/cm³.

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Note that where the above statistics are give, the p-value is 0.04.

1st , we calculate the differences between the number of citations given in the day shift and afternoon shift for each day

Differences -  0, 6, 4, 6

The mean difference is  (m)  = (0 + 6 + 4 + 6) / 4 = 4

The sample standard deviation of the differences is    s = √ ([((0-4)² + (6-4)² + (4-4)² + (6-4)²)/3]) = 2.31

The standard error of the mean difference is  SE(m) = s / √(n) = 2.31 / √(4) = 1.155

The t-statistic is  t = (m - 0) / SE(m) = 4 / 1.155 = 3.4632034632

The paired t-test has n-1=3 degrees of freedom. We calcu0late the p-value associated with a t-statistic of 3.46 using a t-table or a t-distribution calculator with three degrees of freedom.

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In the expression πr² + πrℓ, the part of the expression that is π is a constant.

A constant is a value that does not change in an expression, and in this case π represents a fixed value of approximately 3.14159. It is not a coefficient, which is a numerical factor that multiplies a variable, nor a variable or term, which represent varying quantities in an expression.

The coordinates of P and Q are P(5, 5) and Q(7, 7) respectively.

Let the centres of the circles be:

P (a, r)  and

Q (b, s)

where r and s are the radii of the circles.

Since the circles are tangent to the x-axis, we know that r = a and s = b.

Also, since the circles are tangent to each other, we have

a + b = PQ = 26

Let the point of contact of circle P with the x-axis be (p, 0)

Let the point of contact of circle Q with the x-axis be (q, 0).

Then, we know that

p + q = AB = 24

Using Pythagorean theorem, we can write:

(r² - p²) + (r² - (24 - p)²) = (s²- q²) + (s² - (24 - q)²)

Expanding and simplifying, we get:

2r² - 24r + 576 = 2s² - 24s + 576

Substituting r = a and s = b, and using the fact that a + b = 26, we get:

2a² - 24a + 576 = 2b² - 24b + 576

Simplifying further, we get:

a² - 12a + 288 = b² - 12b + 288

(a - b)(a + b - 12) = 0

Since a + b = 26, we have a - b = 0 or a + b - 12 = 0. The first case gives us a = b, which is not possible since the circles are tangent to each other. Therefore, we have a + b = 12.

Using substitution method to solve  the simultaneous equations:

a + b = 12

a + b = 26

We get a = 7 and b = 5.

Therefore, the centres of the circles P and Q are (7, 7) and (5, 5) respectively.

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By using factoring and the zero product property the two numbers that multiply to make -14 and add to make -3 are -7 and 4.

The zero product property is a fundamental property of algebra that states that if the product of two or more factors is zero, then at least one of the factors must be zero. In other words, if a × b = 0, then either a = 0 or b = 0 or both a and b are zero. This property is often used to solve equations and factor polynomials. For example, if we have the equation (x - 3)(x + 5) = 0, we know that the only way the product can be zero is if one of the factors is zero, so we set each factor equal to zero and solve for x:

(x - 3)(x + 5) = 0

x - 3 = 0 or x + 5 = 0

x = 3 or x = -5

Thus, the solutions to the equation are x = 3 and x = -5.

We can solve this problem by using factoring and the zero product property.

First, we need to find two numbers that multiply to make -14. The factors of -14 are (-1, 14) and (1, -14), so the two numbers could be -1 and 14, or 1 and -14.

Next, we need to find which pair of numbers adds up to -3. The only pair of numbers that works is -7 and 4 because (-7) + 4 = -3.

Therefore, the two numbers that multiply to make -14 and add to make -3 are -7 and 4.

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Answer:

Hey!
You could obviously count how many you're taking, so that's 7 left behind.  My guess is that you could taste the jam... but that's the best I've got.

The requreid we can sneak out 9 cans of jam in the dark and still be sure that there will be at least 4 cans of one kind of jam and 3 cans of another left over.

It involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.

Let's first find the minimum number of cans that need to be left in the cellar to meet the given criteria. We want at least 4 cans of one kind of jam and 3 cans of another leftover. This means we can take a maximum of:

8 - 4 = 4 cans of strawberry jam

7 - 3 = 4 cans of raspberry jam

5 - 3 = 2 cans of cherry jam

So, we can take a maximum of 4 + 4 + 2 = 10 cans in total.

To have certainty that we meet the criteria, we need to take one less than the maximum number of cans, which is 9 cans. So, we can sneak out 9 cans of jam in the dark and still be sure that there will be at least 4 cans of one kind of jam and 3 cans of another left over.

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The cost of 100 donuts is $ 1 if a dozen of donuts cost 12 cents.

This question is solved using the unitary method. The unitary method is a method in which you find the value of a unit and then the value of the required number of units.

1 dozen refers to a group of 12.

Cost of 1 dozen donuts or 12 donuts = 12 cents

Cost of 1 donut = [tex]\frac{12}{12}[/tex] = 1 cent

Cost of 100 donuts = 1 * 100 = 100 cents

100 cents = 1 dollar.

Thus, the cost of 100 donuts is 100 cents or 1 dollar.

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The measure of the exterior angle of the triangle is 128°.

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Trigonometric functions are the functions that denote the relationship between angle and sides of a right-angled triangle.

Sin θ = Opposite Side/Hypotenuse

Cos θ = Adjacent Side/Hypotenuse

Tan θ = Opposite Side/Adjacent

Recall that the measure of the exterior angle of a triangle is the sum of the opposite interior angles. That is:

x = 38 + 90

x = 128°

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None of the other statements necessarily follow from (x-4) being a factor of f(x). So the correct statement is Of(4) = 0

What is a statement?

A statement is a proposition that is either true or false, but not both. It may be a mathematical equation, an inequality, or a proposition that can be tested for its truth value.

What is meant by factor?

A factor refers to a number or algebraic expression that is multiplied by another number or expression to obtain a product. Factors can be either integers or polynomials.

According to the given information

If (x-4) is a factor of f(x), then f(4) = 0. This is because when you divide f(x) by (x-4), the remainder is zero when x=4.

Therefore, the correct statement is: f(4) = 0

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BD = CA is proved using the Pythagorean theorem.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as 1/2 x the sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

From the trapezium ABCD,

BA = CD ______(A)

Now,

We can have two triangles:

ΔABD and ΔACD

Using the Pythagorean theorem.

BD² = AB² + AD² _____(1)

And,

CA² = CD² + AD² ______(2)

From (1), (2), and (A).

BD² = BA² + AD²

CA² = BA² + AD²

This means,

BD² = CA²

BD = CA

Proved

Thus,

BD = CA can be Proven as above.

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Answer:

Step-by-step explanation:

630 calories of total calory intake of Mrs. Ramirez should be from proteins.

From the circle graph we can see that,

percentage of calories from fruits is = 15%

percentage of calories from grains is = 15%

percentage of calories from vegetables is = 25%

percentage of calories from proteins is = 35%

percentage of calories from Dairy is = 10%

Here it is also given that Mrs. Ramirez need to eat 1800 calories.

So the calories should be from proteins

= 35% of 1800 calories

= (35/100)*1800 calories

= 35*18 calories

= 630 calories.

Hence, 630 calories should be from proteins.

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The question is incomplete. The complete question will be -

Answer: 2,2

Step-by-step explanation:  if you have the 2,-2 then that would be your answer because the reflection is the same as the 2,-2 but on a different thing

a) To find y for the given x and Δx values, first calculate x + Δx:
x + Δx = 3 + 0.03 = 3.03

Now, use the function y = f(x) = 9x to find the y values:
y = 9(3) = 27 (for x = 3)
y = 9(3.03) = 27.27 (for x = 3.03)

b) To find dy, we first need to find the derivative of the function (f'(x)). The function is y = f(x) = 9x, and its derivative (using differentiation) is:
f'(x) = 9

c) To find dy for the given x and Δx values, we can now use the formula dy = f'(x)dx:
dy = f'(x)dx = 9(0.03) = 0.27

So, for the given x and Δx values, a) y is 27 and 27.27, b) dy is equal to 9, and c) dy for the given x and Δx values is 0.27.

Answer:

4x² + 24x + 35

Step-by-step explanation:

Total area = (7 + 2x)(5 + 2x)

= 35 + 10x + 14x + 4x²

= 4x² + 24x + 35

After performing these calculations using a calculator or a program like Python, MATLAB, or Excel, you will have the values of the first 10 iterations of Newton's method for the given function and initial approximation.

To compute the first 10 iterations of Newton's method for the given function and initial approximation, follow these steps:

1. Write down the function and its derivative:

[tex]f(x) = 4 * tan(x) - 6 * x  

f'(x) = 4 * sec^2(x) - 6[/tex]
2. Define the initial approximation, X₀ = 1.4.

3. Apply Newton's method formula to find the next approximation, X₁:
  X₁ = X₀ - f(X₀) / f'(X₀)

4. Repeat steps 3-4 for a total of 10 iterations (X₁ to X₁₀).

Note that I'm unable to perform calculations on this platform, but I'll provide a general outline for performing the iterations:

Iteration 1 (X₁):
[tex]X₁ = 1.4 - (4 * tan(1.4) - 6 * 1.4) / (4 * sec^2(1.4) - 6)[/tex]

Iteration 2 (X₂):
[tex]X₂ = X₁ - (4 * tan(X₁) - 6 * X₁) / (4 * sec^2(X₁) - 6)[/tex]

Repeat these steps up to the 10th iteration (X₁₀).

After performing these calculations using a calculator or a program like Python, MATLAB, or Excel, you will have the values of the first 10 iterations of Newton's method for the given function and initial approximation.

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Answer:

Pe^(.0475 × 20) = $20,000

P = $7,734.82

The volume of the given shape is 125 unit³ if the length is 5 unit, breadth is 5 unit, and height is 5 unit.

A cube is a three-dimensional geometric shape that has six identical square faces, where each face meets at a right angle with the adjacent faces. It is a regular polyhedron, meaning that all of its faces are congruent (identical) and its edges are of equal length.

Volume of cube = length × breadth × height

length = 5 unit

breadth = 5 unit

height = 5 unit

Volume = 5 × 5 × 5

= 125 unit³

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The percentage of the games that Natasha scores between 93 and 142 is given as follows:

96.9%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 115, \sigma = 11[/tex]

The proportion of games with scores between 93 and 142 is the p-value of Z when X = 142 subtracted by the p-value of Z when X = 93, hence:

Z = (142 - 115)/11

Z = 2.45

Z = 2.45 has a p-value of 0.992.

Z = (93 - 115)/11

Z = -2

Z = -2 has a p-value of 0.023.

0.992 - 0.023 = 0.969, hence the percentage is of 96.9%.

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Therefore, an initial deposit of $37,728.66 is required to have a college fund of $110,000 in 17 years with quarterly compounding and an APR of 4.9%.

An amount held in an account is referred to as a deposit. It might be put up in a bank as collateral for goods that are being rented out or bought. A deposit is used in many different sorts of economic transactions.

Compound interest can be calculated using the following formula to determine the required down payment:

A = P(1 + r/n)(nt)

where:

A = the future value of the account (in this case, $110,000)

P = the principal or initial deposit

r = the annual interest rate (4.9%)

n = the number of times the interest is compounded per year (4 for quarterly compounding)

t = the number of years (17)

When we enter the specified numbers into the formula, we obtain:

$110,000 = P(1 + 0.049/4)(4*17)

$110,000 = P(1.01225)⁶⁸

$110,000 = P * 2.9126

Dividing both sides by 2.9126, we get:

P = $37,728.66

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The sample space for this experiment contains a total of 12 possible outcomes.

The sample space for this experiment is the set of all possible outcomes. In this case, we have two independent events: flipping a coin and rolling a number cube.

The possible outcomes for flipping a coin are H (heads) and T (tails).

The possible outcomes for rolling a number cube are 1, 2, 3, 4, 5, and 6.

To determine the sample space for the experiment, we need to consider all possible combinations of these outcomes. Therefore, the sample space consists of all possible pairs of outcomes:

Sample space = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}

So the sample space for this experiment contains a total of 12 possible outcomes.

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Answer:

k=0.3

Step-by-step explanation:

Let's call the length of each of the other two sides x. Since the triangle is isosceles, it has two sides of equal length. Therefore, the perimeter of the triangle can be expressed as 6 + x + x Simplifying this equation, we get  2x + 6 We know that the perimeter is 22 cm so we can set up an equation and solve for x. 22 = 2x + 6 Subtracting 6 from both sides, we get  16 = 2x Dividing both sides by 2, we get x=8

Answer:

Step-by-step explanation:

Given cos(θ) = 5/9, you want the six trig functions of θ.

The relevant identities are ...

The sine of θ is ...

  sin(θ) = √(1 -(5/9)²) = √(81 -25)/9 = (√56)/9

  sin(θ) = (2/9)√14

Then the cosecant is ...

  csc(θ) = 1/sin(θ) = (9/2)/√14

  csc(θ) = (9√14)/28

The tangent of θ is ...

  tan(θ) = sin(θ)/cos(θ) = ((2/9)√14)/(5/9)

  tan(θ) = (2/5)√14

Then the cotangent is ...

  cot(θ) = 1/tan(θ) = (5/2)/√14

  cot(θ) = (5√14)/28

The secant of θ is ...

  sec(θ) = 1/cos(θ) = 1/(5/9)

  sec(θ) = 9/5

The cosine is given in the problem statement.

1465 will be the mean monthly salary .The answer is (A) Rs. 1465.

Let the sum of the 12 employees' salaries be S.

Then, the mean monthly salary of the 12 employees is given by:

S/12 = 1450

S = 12 * 1450

S = 17400

If one more person joins with a salary of Rs. 1645, the new sum of the 13 employees' salaries is:

S' = S + 1645

S' = 17400 + 1645

S' = 19045

The new mean monthly salary of the 13 employees is:

S'/13 = 19045/13

S'/13 = 1465

Therefore, the answer is (A) Rs. 1465.

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The calculated perimeter of the square from the side length is 17.2x + 8

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

A square that has a side length of 4.3x + 2 inches.

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

Perimeter = 4 * side length

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 4 * (4.3x + 2)

When teh brackets are opened, we have

Perimeter = 17.2x + 8

Hence, the perimeter is 17.2x + 8

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Answer:

B

Step-by-step explanation:

1 1/2 x 1/3

=1/2

So therefore the answer is B (1/2 cup)

Answer:

The answer is B ( 1/2 cup)

The images of points B and C are B'(x, y) = (- 2, 6) and C'(x, y) = (- 1, 7), respectively.

In this problem we find must determine the image of two points by translation, whose formula is introduced below:

T(x, y) = P'(x, y) - P(x, y)

Where:

First, determine the translation vector:

T(x, y) = (1, 4) - (0, 0)

T(x, y) = (1, 4)

Second, determine the images of points B and C:

B'(x, y) = (- 3, 2) + (1, 4)

B'(x, y) = (- 2, 6)

C'(x, y) = (- 2, 3) + (1, 4)

C'(x, y) = (- 1, 7)

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Answer:

A is -4.5,2 and B is 0,-3.5

Step-by-step explanation:

Answer:

Coordinates of A: (-4.5, 2), Coordinates of B: (0, -3.5)

The measure of center that best represents the data is mean and its values for José and Manuel are 20.1 and 21.8, respectively. Comparing the mean values, José generally scores less goals in a game than Manuel.

To find the measure of center that best represents the data, we will use the mean.

The measure is calculated by adding up all the values and dividing by the total number of values.

The mean number of goals for José is:

= (7+12+17+4+18+25+38+32+37+11)/10

= 20.1

The mean number of goals for Manuel is:

= (17+23+21+31+30+5+26+37+19+9)/10

= 21.8.

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