An angle measures 40° less than the measure of its supplementary angle. What is the measure of each angle?

Answer:

x = 40 in

Step-by-step explanation:

the missing angle in the triangle on the left is

180° - (74 + 51)° = 180° - 125° = 55°

the missing angle in the triangle on the right is

180° - (74 + 55)° = 180° - 129° = 51°

the 2 triangles have 3 pairs of congruent angles and are therefore congruent.

Corresponding sides and angles are then congruent

consider the corresponding sides opposite 74° , that is x and 40 in , so

x = 40 in

Della was crying because she doesn't have enough money to brought the present for her husband Jim.

Basically, the O Henry's story of "The gift of Magi" has the central them as Love. In this story, he sets up a contrasted picture in life- love among the ruins- the acute poverty in the family and the sacrifice of the greatest possessions of the family.

In this stage he defines how their possession has helped Jim and Della, that's the hero and heroine to conquer poverty they were in.

Now, the reason behind Della's cry was she had only one dollar and eighty seven cents and with this small amount she could not buy a good present for her dear husband.

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Answer:

4/2

Step-by-step explanation:

Answer: Non proportional

Step-by-step explanation:

To know if the values given are proportional or not, we will use the formula:

y = kx

where

y = number of organisms

x = number of minutes

k = constant of proportionality

After 5 minutes, a bacteria colony has 1.3 million organisms. Using the formula, y = kx

1,300,000 = 5k

k = 1,300,000 / 5

k = 260,000

After 12 minutes, the same colony has 41.5 million organisms. Using y= kx

41,500,000 = 12x

x = 41500000 / 12

x = 3458333.8

After 15 minutes, the colony has grown to 101.3 million organisms.

y = kx

101,300,000 = 15k

k = 101,300,000 / 15

k = 6753333.8

It is a non-proportional relationship as the constant of proportionality is different for each.

Using fractional operation, since Jack ate ¹/₂ of the delicious pizza with ¹/₆ left, Jill ate ¹/₃ of it.

The fractional operations involve mathematical operations using fractions, which are parts or portions of the whole value or quantity.

Some of the mathematical operations include addition, subtraction, multiplication, and division.

The fraction ate by Jack = ¹/₂

The fraction of the pizza left over after Jack and Jill have eaten = ¹/₆

The fraction or portion that Jill ate = ¹/₃ [1 - (¹/₂ + ¹/₆)]

Thus, we can conclude that Jill ate ¹/₃ of the delicious pizza.

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Answer:

 28/3 = 9 1/3 ≈ 9.33 meters

Step-by-step explanation:

You want the length of a 28 square meter mural that is a rectangle 3 meters high.

The area of a rectangle is given by ...

  A = LW

Solving for L, we have ...

  L = A/W = (28 m²)/(3 m) = 28/3 m

The length of the mural is 28/3 meters, or 9 1/3 meters, about 9.33 meters.

<95141404393>

(a) T value is 1.314 (b) T value is 2.064 (c) T value is -0.674 and (d) Critical t value is 2.093 for confidence

(a) To find the t-value with the area in the right tail of 0.15 and 27 degrees of freedom, refer to the t-distribution table or use a t-distribution calculator. The t-value is 1.314.

(b) To find the t-value with the area in the right tail of 0.025 and 24 degrees of freedom, refer to the t-distribution table or use a t-distribution calculator. The t-value is 2.064.

(c) To find the t-value with the area to the left of the t-value being 0.25 and 30 degrees of freedom, use the t-distribution table or calculator. Since the t-distribution is symmetric, you can find the t-value for the area in the right tail of 0.75 (1 - 0.25). The t-value is -0.674.

(d) To find the critical t-value corresponding to 96% confidence with 19 degrees of freedom, first determine the area in each tail. Since it's a two-tailed test, the remaining 4% will be split evenly between the tails, resulting in 0.02 in each tail. Refer to the t-distribution table or calculator to find the t-value. The critical t-value is ±2.093.

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false. The vertical axis is the y-axis, which is where x=0. In this equation, when x=0, we have: y=4(0)-5
y=-5

Therefore, the line produced by the equation Y=4X−5 crosses the vertical axis at y=-5, not y=5.

To further understand this concept, we can visualize the equation on a graph. When we plot the points (0,-5) and (1,-1) (which is found by substituting x=1 into the equation), we can draw a line that passes through both points. This line is the graph of the equation Y=4X−5. We can see that the line crosses the vertical axis (y-axis) at y=-5, which confirms that the answer is false.

In summary, the equation Y=4X−5 crosses the vertical axis (y-axis) at y=-5, not y=5.

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Answer:

A)  x = -9, x = 8

B)  x = 2, x = 10

C)  x = -6, x = 10

D)  x = -8, x = -3

E)  x = -8, x = 9

Step-by-step explanation:

\(\boxed{\begin{aligned}&\textsf{Given}: \quad &x^2+x-72& =0\\&\textsf{Rewrite the term in $x$}: \quad &x^2+9x-8x-72& =0\\&\textsf{Factor the first two and last two terms}: \quad &x(x+9)-8(x+9)& =0\\&\textsf{Factor out $(x+9)$}: \quad &(x-8)(x+9)& =0\\&\textsf{Apply the zero-product property}: \quad &(x-8) &=0 \implies x=8\\&&(x+9)&=0 \implies x=-9\\&\textsf{Therefore, the roots are}: \quad & x&=-9,\;8\end{aligned}}\)

\(\boxed{\begin{aligned}&\textsf{Given}: \quad &x^2-12x+20&=0\\&\textsf{Rewrite the term in $x$}: \quad &x^2-10x-2x+20& =0\\&\textsf{Factor the first two and last two terms}: \quad &x(x-10)-2(x-10)& =0\\&\textsf{Factor out $(x-10)$}: \quad &(x-2)(x-10)& =0\\&\textsf{Apply the zero-product property}: \quad &(x-2) &=0 \implies x=2\\&&(x-10)&=0 \implies x=10\\&\textsf{Therefore, the roots are}: \quad & x&=2,\;10\end{aligned}}\)

\(\boxed{\begin{aligned}&\textsf{Given}: \quad &x^2-4x-60&=0\\&\textsf{Rewrite the term in $x$}: \quad &x^2-10x+6x-60& =0\\&\textsf{Factor the first two and last two terms}: \quad &x(x-10)+6(x-10)& =0\\&\textsf{Factor out $(x-10)$}: \quad &(x+6)(x-10)& =0\\&\textsf{Apply the zero-product property}: \quad &(x+6) &=0 \implies x=-6\\&&(x-10)&=0 \implies x=10\\&\textsf{Therefore, the roots are}: \quad & x&=-6,\;10\end{aligned}}\)

\(\boxed{\begin{aligned}&\textsf{Given}: \quad &x^2+24&=-11x\\&\textsf{Add $11x$ to both sides}: \quad &x^2+11x+24&=0\\&\textsf{Rewrite the term in $x$}: \quad &x^2+8x+3x+24& =0\\&\textsf{Factor the first two and last two terms}: \quad &x(x+8)+3(x+8)& =0\\&\textsf{Factor out $(x+8)$}: \quad &(x+3)(x+8)& =0\\&\textsf{Apply the zero-product property}: \quad &(x+3) &=0 \implies x=-3\\&&(x+8)&=0 \implies x=-8\\&\textsf{Therefore, the roots are}: \quad & x&=-8,\;-3\end{aligned}}\)

\(\boxed{\begin{aligned}&\textsf{Given}: \quad &x^2-x-72& =0\\&\textsf{Rewrite the term in $x$}: \quad &x^2-9x+8x-72& =0\\&\textsf{Factor the first two and last two terms}: \quad &x(x-9)+8(x-9)& =0\\&\textsf{Factor out $(x-9)$}: \quad &(x+8)(x-9)& =0\\&\textsf{Apply the zero-product property}: \quad &(x+8) &=0 \implies x=-8\\&&(x-9)&=0 \implies x=9\\&\textsf{Therefore, the roots are}: \quad & x&=-8,\;9\end{aligned}}\)

Answer:

CP of each lemon = 1/4

SP of each lemon = 1/3

profit =

\( \frac{1}{3} - \frac{1}{4} \)

profit = 1/12

profit percentage =(1/12)/(1/4)*100

percentage = 33.3%

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x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)

x,y,z=(larger z-value)=(56/3, 32/3, -16/3)

These are the points on the cone that are closest to the point (14, 8, 0).

In a two-dimensional space, a point is defined by two coordinates, typically denoted by (x, y), where x represents the horizontal position, and y represents the vertical position. In a three-dimensional space, a point is defined by three coordinates, typically denoted by (x, y, z), where x, y, and z represent the horizontal, vertical, and depth positions, respectively.

We want to minimize the distance between the point (14, 8, 0) and the surface of the cone defined by the equation z² = x² + y², subject to the constraint that we stay on the surface of the cone.

Let f(x,y,z) = (x-14)² + (y-8)² + z² be the function we want to minimize subject to the constraint g(x,y,z) = z² - x² - y² = 0.

The Lagrange multiplier method involves finding the critical points of the function L(x,y,z,λ) = f(x,y,z) - λg(x,y,z), where λ is the Lagrange multiplier.

So we have:

L(x,y,z,λ) = (x-14)² + (y-8)² + z² - λ(z² - x² - y²)

Taking the partial derivatives with respect to x, y, z, and λ, and setting them equal to zero, we get the following system of equations:

2(x-14) + 2λx = 0

2(y-8) + 2λy = 0

2z - 2λz = 0

z² - x² - y² = 0

The third equation simplifies to z(1-λ) = 0, which gives us two possibilities:

Case 1: z = 0

In this case, the fourth equation becomes -x² - y² = 0, which implies that x = y = 0. But this point does not lie on the surface of the cone, so it is not a valid critical point.

Case 2: λ = 1

In this case, the first two equations become x-14 = -xλ and y-8 = -yλ, which imply that x = -7λ and y = -4λ. Substituting into the fourth equation gives:

z² = x² + y² = 65λ²

To minimize the distance between the point (14, 8, 0) and the surface of the cone, we want to find the value of λ that minimizes the function f(x,y,z) subject to the constraint g(x,y,z) = 0. Substituting x = -7λ, y = -4λ, and z = √(65λ²) into f(x,y,z), we get:

f(λ) = (7λ-14)² + (4λ-8)² + 65λ²

To minimize this function, we take its derivative with respect to λ and set it equal to zero:

f'(λ) = 30λ - 80 = 0

Solving for λ, we get λ = 8/3. Substituting this back into x = -7λ, y = -4λ, and z = √(65λ²), we get:

x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)

x,y,z=(larger z-value)=(56/3, 32/3, -16/3)

These are the points on the cone that are closest to the point (14, 8, 0).

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Answer:

I don't understand

Step-by-step explanation:

Their is not enough info to complete the problem

The sufficient percentage of pellets within a 30-inch circle should be; ''concentrated in the center at least 55% of the load, with even distribution.''

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The percentage of pellets within a 30-inch circle.

Now,

We know that;

According to the state hunter education standards, your shotgun pattern within a 30-inch circle should be; ''concentrated in the center at least 55% of the load, with even distribution.''

Thus, The sufficient percentage of pellets within a 30-inch circle should be; ''concentrated in the center at least 55% of the load, with even distribution.''

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Answer:

y

2

​

=−

2

z

​

+7

Steps for Solving Linear Equation

z=18−2×2−2y2

Multiply 2 and 2 to get 4.

z=18−4−2y

2

​

Subtract 4 from 18 to get 14.

z=14−2y

2

​

Swap sides so that all variable terms are on the left hand side.

14−2y

2

​

=z

Subtract 14 from both sides.

−2y

2

​

=z−14

Divide both sides by −2.

−2

−2y

2

​

​

=

−2

z−14

​

Dividing by −2 undoes the multiplication by −2.

y

2

​

=

−2

z−14

​

Divide z−14 by −2.

y

2

​

=−

2

z

​

+7

Step-by-step explanation:

the given equation defines a paraboloid that lies below the plane z=0. Specifically, it is situated above the xy-plane, which means that the z-values of all points on the surface are greater than or equal to zero.

we can break down the equation z=18-2x^2-2y^2. This equation represents a paraboloid with its vertex at (0,0,18) and axis of symmetry along the z-axis. The first term 18 is the z-coordinate of the vertex and the last two terms -2x^2 and -2y^2 determine the shape of the paraboloid.

Since the coefficient of x^2 and y^2 terms are negative, the paraboloid is downward facing and opens along the negative z-axis. Therefore, all points on the paraboloid have z-values less than 18. Additionally, since the paraboloid is situated above the xy-plane, its z-values are greater than or equal to zero.

the paraboloid defined by the equation z=18-2x^2-2y^2 is situated below the plane z=0 and above the xy-plane. Its vertex is at (0,0,18) and it opens along the negative z-axis.

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The probability that there will be at least 4 typos on page 301 is 0.847

To solve this problem, we need to make some assumptions. Let's assume that the number of typos on each page follows a Poisson distribution with a mean of 6 typos per page, and that the number of typos on one page is independent of the number of typos on any other page.

Under these assumptions, we can use the Poisson distribution to calculate the probability of observing a certain number of typos on a given page.

Let X be the number of typos on page 301. Then X follows a Poisson distribution with a mean of 6 typos per page. The probability of observing at least 4 typos on page 301 can be calculated as follows

P(X ≥ 4) = 1 - P(X < 4)

= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

Using the Poisson distribution formula, we can calculate the probabilities of each of these events

P(X = k) = (e^-λ × λ^k) / k!

where λ = 6 and k is the number of typos. Thus,

P(X = 0) = (e^-6 × 6^0) / 0! = e^-6 ≈ 0.0025

P(X = 1) = (e^-6 × 6^1) / 1! = 6e^-6 ≈ 0.015

P(X = 2) = (e^-6 × 6^2) / 2! = 18e^-6 ≈ 0.045

P(X = 3) = (e^-6 × 6^3) / 3! = 36e^-6 ≈ 0.091

Plugging these values into the equation above, we get

P(X ≥ 4) = 1 - (e^-6 + 6e^-6 + 18e^-6 + 36e^-6)

≈ 0.847

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The values of the expressions, obtained by the combination of the functions, f(x), g(x), and h(x), and found by plugging in the values of the specified function at the indicated value of x are;

17. g(9) + h(-14) = 15

19. (1/2)·g(-6) + f(-2) = -22

21. x = -12

A function defines the relationship between an input variable and an output variable, such that each input produces only one value of the output.

The functions, f(x), g(x), and h(x), are defined as follows;

f(x) = -x² + 8·x - 11

\(g(x) =14-\dfrac{2}{3} \cdot x\)

h(x) = -x - 7

17. The value of g(9) can be found by plugging x = 9, in the function for g(x) as follows;

\(g(9) =14-\dfrac{2}{3} \times 9= 8\)

g(9) = 8

Similarly, the value of h(-14), can be found by plugging in x = -14, in the function for h(x) as follows;

h(-14) = -(-14) - 7 = 7

h(-14) = 7

Therefore, g(9) + h(-14) = 8 + 7 = 15

19. The value of g(-6), can be found as follows;

\(g(-6) =14-\dfrac{2}{3} \times (-6)= 18\)

g(-6) = 18

Similarly, for f(-2), we get;

f(-2) = -(-2)² + 8 × (-2) - 11 = -31

Therefore;

\(\dfrac{1}{2}\cdot g(-6) +f(-2) = \dfrac{1}{2} \times 18 + (-31) = 9 - 31 = -22\)

21.  h(x) = -x - 14

If the value of h(x) = -2, we get;

h(x) = -2 = -x - 14

14 - 2 = -x

-x = 12 (symmetric property)

Dividing both sides by (-1), we get;

-x/(-1) = x = 12/(-1) = -12

x = -12

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Answer:

1.8 and 14.3

Step-by-step explanation:

Our equation is a quadratic equation so we will use the dicriminant method

Answer:

-4

Step-by-step explanation:

"The limit as n approaches infinity of A,n is equal to 0, and n+1 is greater than or equal to 0 for all n. The series converges."

As n approaches infinity, the value of A,n approaches 0. Additionally, the value of n+1 is always greater than or equal to 0 for all n. Therefore, the series formed by the terms A,n converges, indicating that its sum exists and is finite.

Sure! Let's break down the explanation into three parts:

1. Limit of A,n: The statement "lim n goes to infinity A,n = 0" means that as n gets larger and larger, the values of A,n approach 0. In other words, the terms in the sequence A,n gradually become closer to 0 as n increases indefinitely.

2. Relationship between n+1 and 0: The statement "n+1 >= 0" indicates that the expression n+1 is greater than or equal to 0 for all values of n. This means that every term in the sequence n+1 is either greater than or equal to 0.

3. Convergence of the series: Based on the previous two statements, we can conclude that the series formed by adding up all the terms of A,n converges. The series converges because the individual terms approach 0, and the terms themselves are always non-negative (greater than or equal to 0). This implies that the sum of all the terms in the series exists and is finite.

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Step 1

Given;

Required; To factorize the problem

Step 2

Find the GCF

Hence, we will factorize thus and have;

Applying this we will have;

Therefore, we will now factorize (x²+5x-14) by finding the terms that when added together gives 5x and when multiplied together gives -14x²

Replace 5x with (7x-2x)

Grouping the four terms in twos, that is the first two as a pair and the remaining two as the other pair, we can bring out common terms from each pair. This is shown below:

Therefore, using the factoring method shown in Step 2, we have the expression to be:

Collecting the like terms, we, therefore, have the factorized expression to be:

Therefore the full factorized expression will be;

The answer will therefore be ; (x-3)(x+7)(x-2)

The mean and variance of the area A of a circle with a random radius R, uniformly distributed between 0 and 1, can be calculated using mathematical formulas. The mean of A is π/4, and the variance of A is (π^2 - 4)/16.

The area A of a circle is given by the formula A = π * R^2, where R is the radius. Since the radius R is uniformly distributed between 0 and 1, we can express the probability density function (PDF) of R as f(R) = 1 for 0 ≤ R ≤ 1, and f(R) = 0 elsewhere.

To find the mean of A, we need to calculate the expected value of A, denoted as E[A]. Using the formula for expected value, we have E[A] = ∫(A * f(R)) dR = ∫(π * R^2) dR from 0 to 1. Solving this integral gives E[A] = π/4.

To find the variance of A, we need to calculate E[A^2] first. Using the formula for expected value, we have E[A^2] = ∫(A^2 * f(R)) dR = ∫(π^2 * R^4) dR from 0 to 1. Solving this integral gives E[A^2] = π^2/5.

The variance of A can be calculated as Var[A] = E[A^2] - (E[A])^2 = π^2/5 - (π/4)^2 = (π^2 - 4)/16.

Therefore, the mean of A is π/4, and the variance of A is (π^2 - 4)/16 for a circle with a random radius R uniformly distributed between 0 and 1.

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Answer:

9 in 100 chances

Step-by-step explanation:

The ratio of SR and ML and ratio of ST , MN are equal ,so they are similar triangles .

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

In given two triangles,

RST and NLM

In the triangle RST ,

The sum of angles is 180

so,

44  + 15 + S = 180

S =   180 - 59

S = 121

And similarly in the triangle NLM,

N + 121 + 44 = 180

N = 180 - 165

N = 15

Therefore, The values of given angles S and N are 121 , 15 respectively

SR / ML  = 3.61 / 5.415 = 0.667
ST / MN = 9.71 / 14.565 = 0.667

Hence, The ratio of SR and ML and ratio of ST , MN are equal ,so they are similar triangles .

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The percentage increase in the price of petrol is approximately 5.56%.

Percentages are used to compare and express parts of a whole, and to express changes or differences in values. For instance, we can use percentages to express:

A discount or a markup in prices

The increase or decrease in a quantity or value

The proportion of a quantity compared to a whole

The probability of an event occurring.

In the given question,

To determine the percentage increase in the price of petrol, we need to calculate the difference between the old price and the new price, divide that by the old price, and then multiply by 100 to convert to a percentage.

The difference between the old price and the new price is:

R 13.28 - R 12.58 = R 0.70

Dividing the difference by the old price:

R 0.70 ÷ R 12.58 ≈ 0.0556

Multiplying by 100 to convert to a percentage:

0.0556 × 100 ≈ 5.56%

Therefore, the percentage increase in the price of petrol is approximately 5.56%.

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In a triangle ABC the value of side a is 13.12 cm.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know in a ΔABC, a/sinA = b/sinB = c/sinC.

GIven, In a ΔABC A = 29°, B = 36°, b = 15.8 cm.

∴ a/sinA = b/sinB.

a/sin(29°) = 15.8/sin(36°).

a/0.49 = 15.8/0.59.

a = (15.8×0.49)/0.59

a = 7.742/0.59.

a = 13.12.

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Answer:

15(a)(b)(c)

Step-by-step explanation:

I don't know what your asking for

Answer:

24year

Step-by-step explanation:

The independent variable in the researcher's study is the number of errors made by participants in the simulated air-traffic-control task. The researcher examined how this variable was influenced by the presence or absence of quiet background music.

In the study conducted by the researcher, the independent variable is the number of errors made by participants. The researcher investigated the impact of this variable on participants' performance in a simulated air-traffic-control task.

The independent variable represents the condition or factor that is intentionally manipulated or varied by the researcher. In this case, the researcher manipulated the presence or absence of quiet background music to observe its effect on the number of errors made by participants.

By manipulating the independent variable (number of errors), the researcher aimed to analyze its influence on participants' performance. The independent variable allows the researcher to explore potential cause-and-effect relationships between the experimental conditions and the observed outcomes.

It is important to note that the independent variable is not affected by other variables in the study. It is controlled by the researcher to examine its impact on the dependent variable, which is the variable being measured or observed as an outcome of the study.

In summary, the independent variable in the researcher's study is the number of errors made by participants in the simulated air-traffic-control task. The researcher examined how this variable was influenced by the presence or absence of quiet background music.

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Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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