what is the measure of angle L?
what is x?
what is the measure of angle M?
SHOW YOUR WORK

Let's call the added amount of kg of mixed nuts that contain

40

%

peanuts

m

a

d

d

e

d

. If the new mixture contains

34

%

peanuts, then:

m

peanuts

m

total

=

0.34

The bag of

6

kg

already contained

0.3

⋅

6

=

1.8

kg

of peanuts. Furthermore,

40

%

of

m

added

will be peanuts. This means that:

m

peanuts

=

0.4

m

added

+

1.8

The total mass will be the original

6

kg

plus the added mass, so

m

total

=

m

added

+

6

.

This gives us the following equation.

0.4

m

added

+

1.8

m

added

+

6

=

0.34

Multiply both sides with

m

added

+

6

.

0.4

m

added

+

1.8

=

0.34

(

m

added

+

6

)

Multiply out the brackets.

0.4

m

added

+

1.8

=

0.34

m

added

+

2.04

Subtract

0.34

m

added

from both sides.

0.04

m

added

+

1.8

=

2.04

Subtract

1.8

from both sides.

0.06

m

added

=

0.24

Divide both sides by

0.06

.

m

added

=

4

Therefore, Jenny must add

4

kg

.

The theoretical probability of selecting a red bead is 0.28.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that,

Color                     Frequency

Red                               17

Orange                         12

Yellow                          10

Green                           9

Blue                              8

Purple                           5

Color                      List A                      List B

Red                           33                            31

Orange                     27                            24

Yellow                       22                           18

Green                        30                           34

Blue                           18                            19

Purple                        12                            5

Probability of selecting a red bead = 17/61

= 0.28

Orange color would have a frequency closest to 24.

Therefore, the theoretical probability of selecting a red bead is 0.28.

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The values a and b should be replaced to rewrite the given expression as (x + a)(x - b).

Generally speaking, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

c represents the constant.

Next, we would solve the above quadratic function by using the factorization method;

x² + x - 72 = 0

x² - 8x + 9x - 72 = 0

x(x - 8) + 9(x - 8) = 0

(x + 9)(x - 8) = 0

(x + 9)(x - 8) = (x + a)(x - b).

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The order from least to greatest would be as follows:

√3 - 1 < 2√10 ÷ 5 < √14 < 3√2 < √19 + 1 < 6

To order the numbers, we need to first simplify and evaluate each expression.

1. √3 - 1 = 1.73205080757 - 1 = 0.73205080757

2. 2√10 ÷ 5 = 1.265

3. √14 = 3.74166

4. 3√2 = 4.243

5. √19 + 1 = 5.359

6. 6 is simply 6

Therefore, the correct answer is as given above. It could then be concluded that the order from least to greatest is:

0.73205080757 < 1.265 < 3.74166 < 4.243 < 5.359 < 6

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The function equivalent to y = [tex]3x(x+2)^2+7[/tex] is [tex]y = 3x^3[/tex]+[tex]12x^2[/tex] + 12x + 7.

Functionally equivalent refers to when a design, material, practice, method, technique, procedure, or component serves the same purpose and offers the same or better utility as is needed by the rule.

When we add the parenthesis to the expression, we get:

[tex]y = 3x(x^2 + 4x + 4) + 7[/tex]

If we simplify, we get:

[tex]y = 3x^3 + 12x^2 + 12x + 7[/tex]

As a result, y = 3x(x+2)2+7 is identical to y = 3x3 + 12x2 + 12x + 7.

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Answer: The correct answer is C. It represents a function only.

A function is a special type of relation where each input value is associated with only one output value. In other words, for every x in the domain of the function, there is only one corresponding y in the range.

In this equation, y = 2^x + 4, for every value of x, there is a unique corresponding value of y. So, it satisfies the requirement of a function and represents a function only.

Step-by-step explanation:

Answer:

D. It represents both a relation and a function

Hope this helps!

Step-by-step explanation:

All functions are relations, but not all relations are functions. The equation given is an Exponential function.

The solution is, the distance = √116.

The distance between two points is the length of the line joining the two points.

Formula: distance= √(x_2-x_1)²+(y_2-y_1)²

here, we have,

given that,

P (3√2,5√3), Q(√2,-√3)

so,  the distance d(P,Q).

by using the formula we get,

the distance = √108 + 8

                     = √116

Hence, The solution is, the distance = √116.

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The equation for the nth term of this sequence is an = -4.5 + 2.5(n - 1)

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

a4 = 3

a10 = 18

An arithmetic sequence is represented as

an = a + (n - 1)d

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

a + 3d = 3

a + 9d = 18

Subtract the equations

So, we have

6d = 15

Divide

d = 2.5

So, we have

a + 3 * 2.5 = 3

This gives

a = -4.5

So, the sequence is -4.5 + 2.5(n - 1)

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With a significance test about a proportion is conducted using a significance level of 0.05, sample statistic is 0.12, p-value is 0.03.

a) If H0 were true, the test was designed for a probability of a Type I error of 0.05.

b) Based on the p-value of 0.03, you would reject the null hypothesis.

c) If this test resulted in a decision error, it would be a Type II error.

a) If H0 were true, the test was designed for a probability of a Type I error of 0.05. When conducting a hypothesis test, we set a significance level, often denoted by alpha (α), to control the probability of making a Type I error.

A common value for alpha is 0.05, which means that we are willing to accept a 5% chance of making a Type I error.

b) Based on the p-value of 0.03, which is less than the significance level of 0.05, you would reject the null hypothesis. This means that the sample statistic provides enough evidence to suggest that the population proportion is different from the hypothesized value.

c) If this test resulted in a decision error, it would be a Type II error. A Type II error occurs when you fail to reject a false null hypothesis. In this case, the p-value of 0.03 suggests that the population proportion is different from the hypothesized value, so if the null hypothesis were actually false and you still failed to reject it, it would be a Type II error.

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Answer:

[tex]\sqrt{13}[/tex]

Step-by-step explanation:

[tex]L^{2}[/tex]=[tex]3^{2}[/tex]+[tex]2^{2}[/tex]=9+4=13

L=[tex]\sqrt{13}[/tex]

The probability that a randomly selected persons favorite restaurant is a deli is 9/50

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

The table of values

On the table, we have

Total = 100

Deli = 18

So, the probability is

P = Deli/Total

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

P = 18/100

Simplify

P = 9/50

Hence, the probability is (d) 9/50

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Answer:

+5&-2

Step-by-step explanation:

The equation of this parabola in vertex form is y = 1/4x^2 - 1.

A parabola is a type of curve that occurs in nature, science, and mathematics. It is a symmetrical, U-shaped curve that is created by the intersection of a plane and a right circular cone. The shape of the curve is defined by its equation, which can be expressed in standard form as y = ax^2 + bx + c. In this equation, the coefficient a determines the shape of the parabola, with a positive value creating an upward-opening parabola and a negative value creating a downward-opening parabola.

The vertex of a parabola is equidistant from the focus and the directrix. Since the directrix is the line y = 0, which is the x-axis, the vertex is halfway between the focus and the x-axis, at (0, -1).

The distance from the vertex to the focus is p, which is also the distance from the vertex to the directrix. Since the directrix is the line y = 0, the distance from the vertex to the directrix is simply the y-coordinate of the vertex, which is 1.

Therefore, p = 1, and the equation of the parabola in vertex form is:

y = 1/4p(x - h)^2 + k = 1/4(1)(x - 0)^2 - 1 = 1/4x^2 - 1

in the equation y= 1/4p(x-k)² +h, the value of p is 1.

The vertex of the parabola is the point (0, -1).

The equation of this parabola in vertex form is y = 1/4x^2 - 1.

To solve 2²-1:

2² - 1 = 4 - 1 = 3.

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Answer:

The guy above is somewhat right.

Hope this helps!

Step-by-step explanation:

Answer:

x=6.5

Step-by-step explanation:

I'm not sure if it's correct

a. The line of the best fit is ŷ = -8.55485X + 118.39451.

b. The value of the correlation coefficient is  -0.8619.

A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

Sum of X = 117.4

Sum of Y = 298

Mean X = 10.6727

Mean Y = 27.0909

The sum of squares (SSX) = 0.8618

The sum of products (SP) = -7.3727

Regression Equation = ŷ = bX + a

b = SP/SSX = -7.37/0.86 = -8.55485

a = MY - bMX = 27.09 - (-8.55*10.67) = 118.39451

ŷ = -8.55485X + 118.39451

X Values

∑ = 117.4

Mean = 10.673

∑(X - Mx)² = SSx = 0.862

Y Values

∑ = 298

Mean = 27.091

∑(Y - My)² = SSy = 84.909

X and Y Combined

N = 11

∑(X - Mx)(Y - My) = -7.373

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -7.373 / √((0.862)(84.909)) = -0.8619

Therefore, the line of the best fit is ŷ = -8.55485X + 118.39451

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The probability of an event can not be more than the number 1.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

As the probability of an event can not be more than the number 1.

Thus the probability of failure of a event is equal to the difference of the 1 to the success of the event. As,

[tex]Probability[/tex] [tex]of[/tex] [tex]faliure=1-[/tex] [tex]Probability[/tex] [tex]of[/tex] [tex]success[/tex]

Rina spins the spinner less than the 30 times.

A success occurs when the spinner lands on a number that is greater than 6.

A spinner is divided into 8 equals sections and the sections are labeled 1 through 8.

As the probability of success occurs when the spinner lands on a number that is greater than 6, thus the number should grater than six.

This number should be less than 30 as the spinner spins less than the 30 times.

Thus the total number of outcome of this event is,

[tex]=30-6[/tex]

[tex]=24[/tex]

Thus the probability of success is,

[tex]P=\frac{6}{24}[/tex]

[tex]P=\frac{1}{4}[/tex]

Hence the probability of success is 1/4.

As the probability of failure of a event is equal to the difference of the 1 to the success of the event.

Thus the probability of failure is,

[tex]P^-=1-P[/tex]

[tex]P^-=1-\frac{1}{4}[/tex]

[tex]P^-=\frac{4-1}{4}[/tex]

[tex]P^-=\frac{3}{4}[/tex]

The probability of failure is 3/4.

Hence,

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For the function f(t) the domain and range is [0, 12.76] and [1.80, 590.90] respectively.

A function is a mathematical tool used to associate one value with another.

In this case, the function models the height of an object being tossed from a tall building. The height of the object is given by the function h(t), where h represents the height in meters and t represents the time in seconds.

The domain and range of a function describe the set of all possible input values (domain) and the set of all possible output values (range) of a function. The domain and range of the function h(t) are as follows:

The domain of the function h(t) is the set of all possible values of t for which the function h(t) is defined. In this case, the domain of the function h(t) is [0, 12.76], which means that the function h(t) is only defined for time values between 0 and 12.76 seconds.

The range of the function h(t) is the set of all possible values of h(t) that the function can produce. In this case, the range of the function h(t) is [1.80, 590.90], which means that the height of the object can only be between 1.80 meters and 590.90 meters.

Therefore, the correct option is (a).

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Answer:

No solutions

Step-by-step explanation:

I graphed the equations and the lines overlap, so no solution.

Please give brainliest if this helps :)

Answer:

he circumference of the circle is approximately 56.52 millimeters.

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14.

Substituting the given value of the diameter, we get:

C = πd = π(18) = 56.52 mm (rounded to two decimal places)

Therefore, the circumference of the circle is approximately 56.52 millimeters.

The distance traveled in the first 8 minutes is 1.75 d2

Speed is the rate of change of distance with time. it is a scalar quantity and it is measured in meter per second.

speed = distance /time

time = distance /speed

total time = 16

represent u by the first 8minutes and v by the second 8 minutes

u = 1.75v

8 = d1/1.75v

8 = d2/v

d1/1.75v = d2/v

d1 ×v = 1.75v × d2

d1 = 1.75d2

therefore ;

d1 = 1.75d2

where d1 and d2 are the distances for the first 8 minutes and second 8minutes respectively.

therefore the distance in the first 8minutes is 1.75 times greater than the second 8 minutes

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Out of the 275 people surveyed, 176 prefer Coke to Pepsi. It took 64% of the total participants.

According to the information provided in the question, 64% of those surveyed prefer Coke to Pepsi. To find out how many people prefer Coke out of the 275 people surveyed, we need to multiply the percentage by the total number of people surveyed.

We can do this by following these steps:
Step 1: Convert the percentage to a decimal by dividing it by 100. In this case, 64% becomes 0.64.
Step 2: Multiply the decimal by the total number of people surveyed. In this case, 0.64 x 275 = 176.
Step 3: The result is the number of people who prefer Coke. In this case, 176 people prefer Coke.

Therefore, out of the 275 people surveyed, 176 of them prefer Coke to Pepsi.

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Scott's statement that (13g + 1) + (-2 - 5g) and 8/3(3g + 9/8) are equivalent is wrong

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

(13g + 1) + (-2 - 5g)

Remove the brackets

So, we have

13g + 1 - 2 - 5g

Evaluate the like terms

8g - 1

When factorized, we have

8/3(3g - 3/8)

This is not the same as Scott's expression

Hence, Scott is incorrect

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The solution of both inequalities is (-1, 2).

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

We have the inequalities

x+ y >1.........(1)

-x+ y <3.........(2)

The graph for x+ y >1 is shown by the red shaded region.

and, the graph for -x+ y <3  is shown by the blue shaded region.

Also , the Inequality intersect at (-1, 2) which shows the solution of both inequalities.

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The Complete statement are:

1. 27/3 + 5 x 2

2. 81 + 1 - 8 x 4 x 1 = 60

Combining operands with a single arithmetic operator specifies an arithmetic operation. The  ADD, SUBTRACT, DIVIDE, and MULTIPLY can also be used to specify arithmetic operations.

Given:

we have to apply the operation to make

27 3 5 2 = 19

81 11 8 4 1 = 60

so, first 27 3 5 2 = 19

1. 27/ 3 = 9

2. 5 x 2= 10

3. 9+ 10 = 19

For second,

1.81 + 11 = 92

2. 8 x 4 x 1 = 32

3. 92-32 = 60

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The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).

What is a triangle ?

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

Let's call the vertex we know A, and the midpoints of the other two sides B and C, respectively.

Using the midpoint formula, we can find the coordinates of the other two vertices, which are the endpoints of the sides that have B and C as midpoints

Coordinates of B:

x-coordinate: (7 + 3.5)/2 = 5.25

y-coordinate: (-2 - 0.5)/2 = -1.25

So, B is (5.25, -1.25)

Coordinates of C:

x-coordinate: (7 + 3) / 2 = 5

y-coordinate: (-2 + 1)/2 = -0.5

So, C is (5, -0.5)

Therefore, The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).

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The equation of line passes through the points (- 7, -3) and (-3, 5) will be;

⇒ y = 2x + 11

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (- 7, -3) and (-3, 5).

Now,

Since, The equation of line passes through the points (- 7, -3) and (-3, 5).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (5 - (-3)) / (-3 - (-7))

m = 8 / 4

m = 2

Thus, The equation of line with slope 2 is,

⇒ y - (-3) = 2 (x - (-7))

⇒ y + 3 = 2 (x + 7)

⇒ y + 3 = 2x + 14

⇒ y = 2x + 14 - 3

⇒ y = 2x + 11

Therefore, The equation of line passes through the points (- 7, -3) and

(-3, 5) will be;

⇒ y = 2x + 11

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The proportion of test takers that are considered top performers is given as follows:

0.1056.

The minimum SAT score needed for a test taker to be in the top 20% is given as follows:

1231.

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

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

The mean and the standard deviation of SAT scores are given as follows:

[tex]\mu = 1050, \sigma = 216[/tex]

The proportion of scores above 1320 points is one subtracted by the p-value of Z when X = 1320, hence:

Z = (1320 - 1050)/216

Z = 1.25

Z = 1.25 has a p-value of 0.8944

1 - 0.8944 = 0.1056.

The minimum SAT score needed for a test taker to be in the top 20% is the 80th percentile, which is X when Z = 0.84, hence:

0.84 = (X - 1050)/216

X - 1050 = 216 x 0.84

X = 1231.

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Answer:

2

Step-by-step explanation:

Answer:

A. 2 + x = 5

B x + 1 = 4

E -5 + x = -2

Step-by-step explanation:

2 + 3 = 5

3 + 1 + 4

-5 + 3 + -2

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