Find the measure of the missing angle

Answer: 21

Step-by-step explanation:

Using the normal distribution, the probability that a single randomly selected value is less than 971 dollars is 0.2123.

In the given question,

CNNBC recently reported that the mean annual cost of auto insurance is 1007 dollars.

The standard deviation is 241 dollars.

We take a simple random sample of 99 auto insurance policies.

We have to find the probability that a single randomly selected value is less than 971 dollars.

From the question,

Mean = 1107 dollars

Standard Deviation = 241 dollars

So the probability that a single randomly selected value is less than 971 dollars.

Using the normal distribution

z = (x−mean)/Standard Deviation

P(x<971) = P(z<(973−1107)/241)

Simplifying

P(x<971) = P(z<(−134)/241)

P(x<971) = P(z<−0.56)

P(x<971) = 0.2123

Hence, the probability that a single randomly selected value is less than 971 dollars is 0.2123.

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Answer:

70%

Step-by-step explanation:

Total: 60

Strawberries: 18

Lemons: 42

\(\frac{42}{60}\) = \(\frac{7}{10}\) = 70%

The percentage of lemons in the group is equal to 70%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that in the image there are 60 objects in total, the number of lemons is 42 and the number of strawberries is 18.

Total: 60

Strawberries: 18

Lemons: 42

The percentage of the lemons will be calculated as,

Percentage = 42 / 60

Percentage = 0.7

Percentage = 0.7 x 100 = 70%

Therefore, the percentage of lemons in the group is equal to 70%.

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Answer: \(\frac{\pi }{2 }\) < ∅ < \(\frac{3}{4}\pi\)  

Step-by-step explanation:

They are asking where is cos∅ negative.  cos is your x value in the unit circle (your adjacent)

So cos∅ is neg between \(\frac{\pi }{2 }\) < ∅ < \(\frac{3}{4}\pi\)    

theta is <  but not = those values because cos ∅ is 0 (which is neither neg or pos.              

Answer: \(\frac{\pi }{2 }\) < ∅ < \(\frac{3}{4}\pi\)      

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

Answer:

Yes, because lines m1 and m2 have the same slope of -2

Step-by-step explanation:

For given two lines L1 and L2 with slope m1 and m2 respectively, the condition for the two lines to be parallel is for the two equations to have the same slope. If m1 = m2, the meaning is that the line L1 and L2 are parallel to each other no matter the equation of the lines in question.

The general equation of a line is y = mx+c where;

m is the slope and c is the intercept.

Even though we are not given the equation of both lines, the base line is that for two lines to be parallel to each other, they must have the same slope.

The correct option is therefore "Yes, because lines m1 and m2 have the same slope of -2"

Step-by-step explanation:

2x+13x-15=180 since a linear pair is a pair of consecutive angles that adds up to 180 degrees.

15x-15=180 because we combine like terms.

15x=165 because of the subtraction property of equality.

x=11 by the division property of equality.

abc=22 by substitution and multiplication

cbd=143-15 by substitution and multiplication

cde=128 by subtraction

The solution to the given system of equations is the point (1, 5).

Here we have the system of equations:

g(x) = 3x + 2

f(x) = |x - 4| + 2

To solve this, first you can see where the graphs intercept on the graph (the intercept point is the solution to the system)

But we can also solve it analytically. To do it, we have:

g(x) = f(x)

3x + 2 =  |x - 4| + 2

3x =  |x - 4|

Notice that the only solution of the above equation is x = 1, so we know that it is the x-value of the solution.

To get the y-value, we just evaluate one of the two given functions on x = 1.

f(1) = |1 - 4| + 2= 3 + 2 = 5

Then the solution to the system is the point (1, 5).

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a) Option A, A x2 statistic provides strong evidence in favor alternative hypothesis if its value is a large positive number.

b) Option B, The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.

c) Option B, The variables considered in a chi-squared test used to evaluate a contingency table B. are categorical.

(a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is a large positive number. The x2 statistic is used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies. A large positive value indicates that the observed frequencies are significantly different from the expected frequencies, which supports the alternative hypothesis.

(b) The hypotheses being tested in a chi-squared test on a contingency table are the null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. This test determines whether there is a significant association between two categorical variables.

(c) The variables considered in a chi-squared test used to evaluate a contingency table are categorical. These variables cannot be averaged or assumed to be normally distributed. The chi-squared test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.

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Step-by-step explanation:

d is the answer as far as I can tell from a little experience

If both the upstairs and downstairs switches are in the up position, the light will be off

The given parameters are

Switches = 2 i.e. top and bottom

Also, we have:

When the upstairs switch is up and the downstairs switch is down, the light is turned on.

This means that the light is only on when the upstairs switch is up and the downstairs switch is down

Any other position of the switches, the light is off

From the question, we have

Both the upstairs and downstairs switches are in the up position

This is different from the required position to on the light

Hence, the light will be off

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Answer: 4/8 + 3/6 + 1/1

Step-by-step explanation: this is only if you can use the same number twice!!!

To determine the direction of the car relative to its starting point, we can analyze the given paths and use vector addition to find the resultant displacement.

Displacement i)

= 40 miles × cos(53.0°) in the x-direction + 40 miles × sin(53.0°) in the y-direction.

Displacement ii)

= -60 miles × cos(25°) in the x-direction + 60 miles × sin(25°) in the y-direction

i) The car travels 40 miles in a direction 53.0° north of east.

We can represent this displacement as a vector by converting the magnitude and direction to Cartesian coordinates:

Displacement i) = 40 miles * cos(53.0°) in the x-direction + 40 miles * sin(53.0°) in the y-direction.

ii) The car travels 60 miles in a direction 25° north of west.

Similarly, we can represent this displacement as a vector:

Displacement ii) = -60 miles * cos(25°) in the x-direction + 60 miles * sin(25°) in the y-direction.

iii) The car travels 50 miles due south.

We can represent this displacement as a vector:

Displacement iii) = -50 miles in the y-direction.

To find the resultant displacement, we add the three displacement vectors:

Resultant Displacement = Displacement i) + Displacement ii) + Displacement iii)

By adding the x-components and y-components separately, we can determine the resultant vector's magnitude and direction relative to the starting point.

Once we have the resultant displacement vector, we can calculate its direction using trigonometry, specifically the inverse tangent function.

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Answer: see explanation

Step-by-step explanation: To determine which ordered pairs satisfy the equation substitute the x coordinate of the point into the right side and if the value obtained equals the y coordinate of the point then it satisfies the equation

(- 1, - 1)

x = - 1 : y = - 4 + 3 = - 1 ⇒ (- 1, - 1) satisfies the equation

(2, 11)

x = 2 : y = 8 + 3 = 11 ⇒ (2, 11) satisfies the equation

(4, 7)

x = 4 : y = 16 + 3 = 19 ≠ 7 ⇒ (4, 7) does not satisfy the equation

(7, 1)

x = 7 : y = 28 + 3 = 31 ≠ 1 ⇒ (7, 1) does not satisfy the equation

Answer:

B)

Explanation:

The slope-intercept form of the equation of a line is generally given as;

where m = slope of the line

b = y-intercept of the line

So given a slope(m) of 2/3 and a y-intercept(b) of -2, we can go ahead and write the equation of the line as;

We need to decide whether the given equations are always or never true for values of x .The given equations are ,

solve out for x,

\(\longrightarrow x -x =12+1\\ \)

\(\longrightarrow 0 =13\\ \)

This can never be true. Hence the equation is never true for any values of x.

solve out for x,

\(\longrightarrow x -x =\dfrac{3}{4}+\dfrac{3}{4}\\ \)

\(\longrightarrow 0=\dfrac{3}{2}\)

This can never be true. hence the equation is never true for any values of x.

solve out for x,

\(\longrightarrow 4x +12=8x+12-4x\\\)

\(\longrightarrow 4x -8x +4x =12-12\\\)

\(\longrightarrow 0=0\)

hence this equation is true for all values of x.

solve out for x,

\(\longrightarrow 2x -x -x =8+8\\ \)

\(\longrightarrow 0=0 \)

hence the equation is true for all values of x.

solve out for x,

\(\longrightarrow 2x +10+3x =5x-25\\ \)

\(\longrightarrow 5x -5x =-25-10\\\)

\(\longrightarrow 0 =-35\)

This can never be true. hence the equation is never true for any values of x.

and we are done!

Answer:

6

Step-by-step explanation:

Answer: (2,7) & (6,5)

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

2/3+5/6x=9

5/6x=8 1/3

5/6x=25/3

5x=50

x=10

Answer:

6 cups of flour, 2 cups of sugar, and 4 cups of chocolate chips <3

Step-by-step explanation:

Because you're only making 2 dozen, simply multiply everything by 2 and you'll get the answer of 6 cups of flour, 2 cups of sugar, and 4 cups of chocolate chips!!! hoped this helped and feel free to ask any questions abt this :-)

Answer:

It is just .55*12,400

Step-by-step explanation:

thats literally all it is

Answer:

If you Meant (12,400) then around 6,820 planned to travel again

Step-by-step explanation:

The equation for the line tangent to the curve at the point (1, 1) is y = 3x - 2.

(b) The line tangent to the curve at a point is vertical when the slope of the curve is zero. So, we can set the derivative of the curve equation equal to zero to find the x-coordinates of the points at which the line tangent to the curve is vertical.

2 3 dy y dx y x = 0

2 3(2x + y) = 0

2x + y = 0

x = - y/2

So, the x-coordinates of the points at which the line tangent to the curve is vertical are x = -y/2.

(c) We can evaluate 2 2 d y dx at the point (1, 1) by substituting x = 1 and y = 1 into the derivative of the curve equation.

2 3 dy y dx y x = 2 3(2(1) + 1) = 8/3

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The expressions given in option A and option C on solving will have same value 3/2 or 1.5.

Numeric values can be obtained through the evaluation of numeric expressions, which consist of a mixture of numeric components including variables, numbers or functions, and operators. A blend of arrays and mathematical operators can be present within an expression to derive a numeric solution.

Now solving numerical expressions in the problem (refer to image attached)

A. \(\frac{1}{6} +(\frac{5}{6}+\frac{3}{6} ) = \frac{1+5+3}{6} = \frac{9}{6} =\frac{3}{2} =1.5\)

B. \(\frac{1}{3}+ \frac{5}{3}+ \frac{2}{3} =\frac{1+5+2}{3} =\frac{9}{3} =3\)

C. \(\frac{3}{5} +(\frac{1}{2} +\frac{2}{5} )=\frac{15}{10} =\frac{3}{2} =1.5\)

D. \(2+\frac{1}{2} =\frac{4+1}{2} =\frac{5}{2} =2.5\)

Hence, expressions in option A and option C have same values

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Considering the expression of a line, the equation of the line that passes through the pair of points (-3,5) and (1,-1) is y=-1.5x +0.5.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope and the value of one of the points, the value of the ordinate to the origin can be obtained.

In this case, being (x₁, y₁)= (-3, 5) and (x₂, y₂)= (1, -1), the slope m can be calculated as:

m= ( -1 -5)÷ (1 - (-3))

m= ( -1 -5)÷ (1 + 3)

m= (-6)÷ 4

m= -1.5

Considering point 2 and the slope m, you obtain:

-1= -1.5×1 + b

-1= -1.5 +b

-1 + 1.5= b

0.5= b

Finally, the equation of the line is y=-1.5x +0.5.

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Answer:

$720.39 ---> $720.40

Step-by-step explanation:

Convert the sales tax percentage into a decimal.

Add the amount of tax you calculated to the price.

Move the decimal point in the cost of your item one space to the left.

Add the tax to the cost of the item.

The standard deviation of a sample proportion is given by the formula:

σ = sqrt((p * (1 - p)) / n)

where σ is the standard deviation, p is the sample proportion, and n is the sample size.

If we want the standard deviation to be one-half of what it was for a sample of size 100, we can write the following equation:

(sqrt((p * (1 - p)) / n)) / 2 = sqrt((p * (1 - p)) / 100)

To simplify the equation, we can square both sides:

((p * (1 - p)) / n^2) / 4 = (p * (1 - p)) / 100

Simplifying further:

100 * n^2 = 4 * 1

n^2 = (4 * 1) / 100

n^2 = 0.04

Taking the square root of both sides:

n = sqrt(0.04)

n = 0.2

Therefore, the sample size should be 0.2. However, since the sample size must be a positive integer, we round it up to the nearest whole number. Therefore, the sample size should be 1.

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The statement "Decisions can never be made without the benefit of knowledge gained from sampling" is false.

Sampling refers to the process of selecting a subset of data from a larger population to make inferences about that population. While sampling can be useful in some decision-making contexts, it is not always necessary or appropriate.

In many decision-making situations, there may not be a well-defined population to sample from. For example, a business owner may need to decide whether to invest in a new product line based on market research and other available information, without necessarily having a representative sample of potential customers.

In other cases, the costs and logistics of sampling may make it impractical or impossible.

Additionally, some decision-making approaches, such as decision tree analysis, rely on modeling hypothetical scenarios and their potential outcomes without explicitly sampling from real-world data. While sampling can be a valuable tool in decision-making, it is not a requirement and decisions can still be made without it.

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Answer:

Let X be 2

Now,

y = 5*2 - 8

or, y= 10-8

or, y =2

Hope this will help please mark me as brainlest.

Expected chances to flip two heads and one tail after flipping three coins  32 times. over these 32 trials are 8times.

" Possible outcomes is defined as the number of expected chances for given event to occur."

According to the question,

Total number of trials = 32

Possible outcomes for tossing 3 coins  = { HHH, HHT, TTH, TTT}

Possible outcomes represents 4trials

Three coins are tossed 32 times times

 32 =  4 × 8

Therefore, such sets occurs 8times.

Expected chances for  {HHT} to occur in 32 trials = 8 times

Hence, expected chances to flip two heads and one tail after flipping three coins  32 times. over these 32 trials are 8times.

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a)On Monday, 120 apple tarts were made.

b) The lower bound of the probability that the tart taken at random on Tuesday is a lemon tart is approximately 0.267.

a) To determine the number of apple tarts made on Monday, we can set up a proportion based on the sample of 15 tarts and the known proportion of apple tarts.

Let x be the number of apple tarts made on Monday.

The proportion of apple tarts in the sample is given by:

\(6/15 = x/300\).

Cross-multiplying and solving for x, we get:

\(6 * 300 = 15 * x,\)

\(1800 = 15x\),

\(x = 1800/15\),

\(x = 120\).

b) To find the lower bound of the probability that the tart taken at random on Tuesday is a lemon tart, we need to consider the minimum number of lemon tarts needed in the quality checks sample.

The number of lemon tarts needed is 4 (correct to the nearest whole number).

To calculate the lower bound of the probability, we assume that exactly 4 lemon tarts were needed, meaning the remaining 11 tarts in the sample are apple tarts.

The probability of selecting a lemon tart from the 300 tarts made on Tuesday is:

\(4/15 ≈ 0.267\) (rounded to three decimal places).

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