a car manufacturer claims that its new hybrid car can travel at speeds more than 60 mpg. the actual mpg is approximately normally distributed with a mean of 52 miles and a standard deviation of three miles. what is the probability that the manufacturer's claim is valid?

Answer:

4 m

Step-by-step explanation:

The formula to find the area of the triangle is:

[tex]\sf Area = \frac{1}{2} *base*height[/tex]

Given that,

Area = 32m²

Base = 16m

Height =?

Let us use the given formula to find the height of the triangle.

[tex]\sf Area = \frac{1}{2} *base*height\\\\\sf 32m^2 = \frac{1}{2} *16*h\\\\32= \frac{16h}{2} \\\\32=8h\\\\\frac{32}{8} =\frac{8h}{8} \\\\4m = height[/tex]

Answer:

(C) −5x^3 + x + 3.

Step-by-step explanation:

To divide 15x^5 - 3x^3 - 9x^2 by -3x^2, we can follow these steps:

Divide the coefficient of the first term by the coefficient of the divisor: (-15x^5) / (-3x^2) = 5x^3.

Multiply the divisor by the quotient obtained in step 1: -3x^2 * 5x^3 = -15x^5.

Subtract the product obtained in step 2 from the dividend: 15x^5 - (-15x^5) = 30x^5.

Repeat steps 1 to 3 for the next term: (-3x^3) / (-3x^2) = x, -3x^2 * x = -3x^3, -3x^3 - (-3x^3) = 0.

Repeat steps 1 to 3 for the last term: (-9x^2) / (-3x^2) = 3, -3x^2 * 3 = -9x^2, -9x^2 - (-9x^2) = 0.

Therefore, the result of the division is:

5x^3 + 0x + 3

Simplifying the expression, we get:

5x^3 + 3

Therefore, the correct answer is (C) −5x^3 + x + 3.

Answer:

C:−5x3 + X + 3

Step-by-step explanation:

I took the test and got it right

Answer:

4³, 8², and 2⁶ are all equivalent to 64¹

Answer:

A, C, F

Step-by-step explanation:

A. 4 x 4 x 416 x 4= 64

C. 8 x 8 = 64

F. 2x2=4x2= 8x2=16x2=32 x 2= 64

To complete the table, we need to calculate the number of days Kimimela fed her rabbits for each given percentage. To do this, we can use proportions.

For example, to find out how many days Kimimela fed her rabbits if she fed them 20% of the time, we can set up the proportion:

20/100 = x/350

where x is the number of days Kimimela fed her rabbits. Cross-multiplying, we get:

100x = 20 * 350

Solving for x, we get:

x = 20 * 350/100 = 70

So, if Kimimela fed her rabbits 20% of the time, she fed them for 70 days.

Using the same method, we can complete the table as follows:

Time (days) Percentage

100

%

100%100, percent of 350

350350 days

20

%

20%20, percent of 350

7070 days

80

%

80%80, percent of 350

280280 days

Therefore, if Kimimela fed her rabbits 100% of the time, she fed them for all 350 days. If she fed them 20% of the time, she fed them for 70 days. And if she fed them 80% of the time, she fed them for 280 days.

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Answer:

Step-by-step explanation:

In mathematics and statistics, a bar graph is commonly employed. Bar graphs, generally referred to as bar charts, are graphic illustrations of grouped data. A bar graph is a graph that displays all of the data in the form of rectangular bars with heights proportionate to the values they represent. The graph’s bars can be depicted vertically or horizontally. The bars provide a visual representation of quantities in various categories.

Graphical Representation is a way of analyzing numerical data. It exhibits the relation between data, ideas, information, and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

Line Graphs – A line graph or linear graph is used to display continuous data and it is useful for predicting future events over time.

Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.

Histograms – The graph that uses bars to represent the frequency of numerical data that are organized into intervals. Since all the intervals are equal and continuous, all the bars have the same width.

Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.

Frequency Table – The table shows the number of pieces of data that falls within the given interval.

Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered 100% and the categories occupied are represented with that specific percentage like 15%, 56%, etc.

Stem and Leaf Plot – In the stem and leaf plot, the data are organized from the least value to the greatest value. The digits of the least place values from the leaves and the next place value digit from the stems.

Box and Whisker Plot – The plot diagram summarises the data by dividing it into four parts. The box and whisker show the range (spread) and the middle ( median) of the data.

The coordinates of the child after 75 seconds on a carousel that revolves once every minute counter-clockwise, assuming the child entered at point (1,0), are (-0.766, -0.643).

Since the carousel revolves once around in one minute, its angular velocity is 2π/60 radians per second or π/30 radians per second.

Let's find the angle that the child has covered in 75 seconds.

angle = (angular velocity) x (time) = (π/30) x 75 = 2.5π

After 2.5π radians, the child has completed 2.5 full revolutions and is back at the starting point. Therefore, the coordinates of the child at point (1, 0) are (-0.766, -0.643).

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Answer:

y = 2/3x +6  for x< -3.

y = 2/3x +1     for x> 3.

Step-by-step explanation:

Explanations are given in attachment!

Answer: (-3u + -3) -5

Step-by-step explanation:
Use distributive property

Answer:

It really just deleted my answer..

Solve.

4p^2 - 50 = 350

O {-100, 100}

O {-400, 100}

O {-10, 100}

Step-by-step explanation:

You're welcome.

The value of x in the parallelogram is 10.

A parallelogram is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

The sum of angles in a parallelogram is 360 degrees. The parallelogram JKPQ has the following angles.

Therefore,

m∠J = 2x + 10

m∠P = 3x - 20

Hence, the opposite angles of a parallelogram are congruent.

Therefore,

m∠J  = m∠P

2x + 10 = 3x - 20

2x - 3x = -20 - 10

-3x = -30

divide both sides by -3

x = -30 / -3

x = 10

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Step-by-step explanation:

(x+90°)=7x (vert opp angles)

x-7x=-90°

-6x/-6=-90°/-6

x=15

Answer:

[tex]5x + 17[/tex]

Step-by-step explanation:

[tex]2(x + 7) + 3(x + 1)[/tex]

Multiply every term inside the bracket by the term on the outside:

[tex]2x + 14 + 3x + 3[/tex]

Collect like terms:

[tex]5x + 17[/tex]

Answer:

[tex]\large\boxed{\tt 5x + 17}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to expand, and simplifying 2 expressions.}[/tex]

[tex]\textsf{We should understand what the question is asking from us first.}[/tex]

[tex]\large\underline{\textsf{What are Expressions?}}[/tex]

[tex]\textsf{Expressions are statements that are made up of 2 or more terms. Such expressions}[/tex]

[tex]\textsf{should incl\textsf{u}de an operation as well. (+, -, } \tt \times, \tt \div )[/tex]

[tex]\large\underline{\textsf{What is Expanding?}}[/tex]

[tex]\textsf{Expanding in Mathematics involves with the Distributive Property, where an}[/tex]

[tex]\textsf{expression is expanded to further simplify the expression.}[/tex]

[tex]\underline{\textsf{How are we able to expand expressions?}}[/tex]

[tex]\textsf{Expanding Expressions has to incl\textsf{u}de the Distributive Property.}[/tex]

[tex]\large\underline{\textsf{What is the Distributive Property?}}[/tex]

[tex]\boxed{\begin{minipage}{23 em} \\ \underline{\textsf{\large Distributive Property;}} \\ \\ \textsf{Distributive Property is a property that allows us to multiply the term to the left of the parentheses into the terms inside the parentheses.} \\ \\ \underline{\textsf{\large Example;}} \\ \tt a(b+c)=ab+ac \\ \textsf{For this example, a will multiply with the terms b and c.}\end{minipage}}[/tex]

[tex]\textsf{Even though Distributive Property is mainly used for Distributing 1 term}[/tex]

[tex]\textsf{expressions, it's commonly used for distributing binomials as well, which involves}[/tex]

[tex]\textsf{the FOIL Method.}[/tex]

[tex]\large\underline{\textsf{What is the FOIL Method?}}[/tex]

[tex]\textsf{The FOIL Method is a very useful method that tells us step-by-step how to}[/tex]

[tex]\textsf{multiply 2 binomials. For any polynomial with 2 or more terms, apply the idea}[/tex]

[tex]\textsf{of the FOIL method, however using it more than once.}[/tex]

[tex]\underline{\textsf{FOIL Means;}}[/tex]

[tex]\textsf{F - Front Terms.}[/tex]

[tex]\tt ( \ \boxed{\tt x} + 1 )( \ \boxed{\tt x} - 1 )[/tex]

[tex]\textsf{O - Outer Terms.}[/tex]

[tex]\tt ( \ \boxed{\tt x} + 1 )( x - \boxed{\tt 1} \ )[/tex]

[tex]\textsf{I - Inside Terms}[/tex]

[tex]\tt (x + \boxed{\tt 1} \ )( \ \boxed{\tt x} - 1 )[/tex]

[tex]\textsf{L - Last Terms.}[/tex]

[tex]\tt (x + \boxed{\tt 1} \ )( x - \boxed{\tt 1} \ )[/tex]

[tex]\large\underline{\textsf{What is Simplifying?}}[/tex]

[tex]\textsf{Simplifying anything related to mathematics means to reduce, and to make the}[/tex]

[tex]\textsf{final answer much simpler and clean.}[/tex]

[tex]\underline{\textsf{What are some ways that we can Simplify?}}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{We are given 2 expressions where we should use the Distributive Property to}[/tex]

[tex]\textsf{expand both of the expressions. Lastly, simplify the expression by combining any}[/tex]

[tex]\textsf{like terms necessary.}[/tex]

[tex]\tt 2(x+7) + 3(x+1)[/tex]

[tex]\underline{\textsf{Use the Distributive Property;}}[/tex]

[tex]\tt 2(x+7) = (2(x)) + (2(7)) = 2x+14[/tex]

[tex]\tt 3(x+1) = (3(x)) + (3(1)) = 3x+3[/tex]

[tex]\tt 2(x+7) + 3(x+1) = 2x+14+3x+3[/tex]

[tex]\underline{\textsf{Combine Like Terms;}}[/tex]

[tex]\tt \boxed{\tt 2x} + 14 + \boxed{\tt 3x} + 3[/tex]

[tex]\tt 5x + \boxed{\tt 14} + \boxed{\tt 3}[/tex]

[tex]\large\boxed{\tt 5x + 17}[/tex]

The ordered pairs in the quadrants are option A and option D:

A. A= (2, 1)

D. C = (-1, -2)

The quadrant is the area that is bounded by the point where the X and Y axes connect. The cartesian plane's two axes, the X and Y axes, intersect at a 90° angle, forming four zones surrounding the intersection that are known as quadrants.

The points are given as:

A = (2, 1)

B = (1, 2)

C = (-1, -2)

D = (-1, -2)

Now, point A is in 1st quadrant so both the points will be positive.

So, A = (2, 1) is an ordered pair.

Now, B is in 2nd quadrant, so x coordinate will be negative and y coordinate will be positive.

B = (1,2) is hence not an ordered pair.

Now, C is in 3rd quadrant, so both the points will be negative.

C = (-1, -2) is an ordered pair.

Similarly, D is in 4th quadrant and x coordinate will be positive and y coordinate will be negative.

D = (-1, -2) is not an ordered pair.

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Answer:

[tex]\large\boxed{\tt \angle ABC = 146^{\circ}.}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to solve for} \ \tt \angle ABC. \ \textsf{We are given that} \ \overrightarrow{\tt BD} \ \textsf{is an \underline{Angle Bisector}.}[/tex]

[tex]\large\underline{\textsf{What are Angle Bisectors?}}[/tex]

[tex]\textsf{Angle Bisectors are \underline{Line Segments} that bisect a full angle into 2 congruent angles.}[/tex]

[tex]\textsf{Think of Angle Bisectors as cutting something into half, both pieces will be congruent.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{Because} \ \overrightarrow{\tt BD} \ \textsf{is an Angle Bisector, then} \ \angle \tt ABD \cong \angle CBD. \ \textsf{This will mean that both}[/tex]

[tex]\textsf{angles are \underline{congruent} to each other, hence their measures are the same.}[/tex]

[tex]\tt 4a+13=7a-32[/tex]

[tex]\textsf{Let's begin solving for a, afterwards we should substitute a back into} \ \tt \angle ABD, \ \textsf{multiply}[/tex]

[tex]\textsf{the angles' measure by 2 since} \ \tt \angle CBD \cong \angle ABD, \ \textsf{then we are able to identify the}[/tex]

[tex]\textsf{measure of} \ \tt \angle ABC.[/tex]

[tex]\underline{\textsf{Find the value of a;}}[/tex]

[tex]\tt 4a+13=7a-32[/tex]

[tex]\underline{\textsf{Subtract 7a from both sides of the equation;}}[/tex]

[tex]\tt 4a-7a+13=7a-7a-32[/tex]

[tex]\tt -3a+13=-32[/tex]

[tex]\underline{\textsf{Subtract 13 from both sides of the equation;}}[/tex]

[tex]\tt -3a+13-13=-32-13[/tex]

[tex]\tt -3a=-45[/tex]

[tex]\underline{\textsf{Divide both sides of the equation by -3;}}[/tex]

[tex]\large\boxed{\tt a=15}[/tex]

[tex]\underline{\textsf{Substitute 15 back into} \ \tt \angle ABD;}[/tex]

[tex]\tt \angle ABD = 4(15) + 13[/tex]

[tex]\tt \angle ABD = 73^{\circ}[/tex]

[tex]\underline{\textsf{Multiply} \ \tt \angle ABD \ \textsf{by 2;}}[/tex]

[tex]\tt \angle ABD \ + \ \angle CBD= 73^{\circ} \times 2[/tex]

[tex]\tt \angle ABD \ + \ \angle CBD= 146^{\circ}[/tex]

[tex]\textsf{146}^{\circ} \ \textsf{represents the value of} \ \tt \angle ABC.[/tex]

[tex]\large\underline{\textsf{Hence;}}[/tex]

[tex]\large\boxed{\tt \angle ABC = 146^{\circ}.}[/tex]

Answer:

a Obtuse b 136 girls c Hockey d 16.7

Step-by-step explanation:

50a obtuse

    b 136 girls

    c Hockey

    d [tex]\frac{60}{360} *100\\=16.6667...\\16.7[/tex]

The percentage of compounds formed from this plant extract fell within two standard deviations of the mean, equal to 95.45%.

We tested an extract of a plant native to Taiwan as a possible treatment for leukemia. The amounts of collagen were found to be normally distributed with a mean = 62

standard deviation = 6.9 g/ml.

This is true for any normal distribution, regardless of the actual values of the mean and standard deviation.

The standard normal distribution is a normal distribution with mean zero and standard deviation 1. The standard normal distribution is centered around zero and the degree to which measurements deviate from the mean is represented by the standard deviation.

Therefore, the required percentage is approx. 95.45% are within 2 standard deviations of the mean 62.

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Complete question:

The extract of a plant native to Taiwan has been tested as a possible treatment for Leukemia. One of the chemical compounds produced from the plant was analyzed for a particular collagen. The collagen amount was found to be normally distributed with a mean of 62 and standard deviation of 6.9 grams per mililiter.What percentage of compounds formed from the extract of this plant fall within 2 standard deviations of the mean?

The value of x in the similar triangle is 9 units.

The midsegment of a triangle is a line connecting the midpoints between two sides of a triangle. Therefore, the midsegment theorem states that a line segment connecting the midpoints of any two sides of a triangle is parallel to the third side of a triangle and is half of it.

Hence,

9 / 72  = 3x - 20 / 56

cross multiply

9 × 56 = 72(3x - 20)

504 = 216x  - 1440

504 + 1440 = 216x

1944 = 216x

divide both sides by 216

x = 1944 / 216

x = 9

Therefore,

x = 9

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It should be noted that the quotient of the division is 9r^2 + 2r - 5 and the remainder is -5

In this case, to solve this polynomial division, we can use either long division or synthetic division. Here, we'll use long division:

   9r^2 + 2r - 5

        ___________________________

r - 7  | 9r^3 - 73r^2 + 64r + 37

        - 9r^3 + 63r^2

        --------------------

                 - 10r^2 + 64r

                 + 10r^2 - 70r

                 ----------------

                          -6r + 37

                          -6r + 42

                          --------

                                -5

Therefore, the quotient is 9r² + 2r - 5 and the remainder is -5. Therefore: (9r³-73r² +64r +37)÷(r-7) = 9r^2 + 2r - 5 + (-5)/(r-7).

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Ally will have 91.148 meters of tape in all if Ally needs 90 meters of tape for a project.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.

Ally needs a total of 90 meters of tape for her project. She bought three rolls of tape, one with 50 meters, another with 22.86 meters, and the last one with 18.288 meters. To find the total amount of tape she has, she needs to add the length of all three rolls together.

Adding the length of the first two rolls, we get:

50 meters + 22.86 meters = 72.86 meters

Then adding the length of the third roll to the sum above, we get:

72.86 meters + 18.288 meters = 91.148 meters

Therefore, Ally will have 91.148 meters of tape in all.

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Therefore , the solution of the given problem of expressions comes out to be the formula is 4x³y² + 10x²y³ - 7y².

Instead of using estimates produced at random, it is better to use shifting integer variables that can be rising, reducing, or blocking. They could only help one another by sharing tools, information, or solutions to issues. The justifications, elements, and mathematical remarks for techniques like additional disapproval, manufacture, and mixture may be included in a statement of truth equation.

Here,

All terms enclosed in brackets must have their signs changed in order to subtract the equation from the first expression:

=>  (7x²y³ + 4x³y² - y²) - (-2x³y² – 3x²y³ + 6y²)

=>  7x²y³ + 4x³y² - y² + 2x³y² + 3x²y³ - 6y²

We can now mix similar terms:

=> 4x³y² + 10x²y³ - 7y²

As a result, the formula is 4x³y² + 10x²y³ - 7y².

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Answer:

n+9 = 14

Step-by-step explanation:

Let's Sean friends in grade 7 be n.

Then In grade 8, 9 persons are there.

Equation: n+9 = 14.

n = 14-9 = 5.

Both Aija and John have Only Fans sites where they may earn money according to the amount of monthly subscribers; however, John's Only Fans page brought in more cash in 2022.

"S"-What is the issue requesting that you find?

The issue is that it wants to see who had more subscribers and made the most money in 2022 via their Just Fans page. We must also offer suggestions to people who are thinking about opening an Only Fans profile.

“O” - Which specific details are required for you to provide a solution?

We must contrast Aija and John's earnings to determine who earned more money. Also, we need to compare how many subscribers any of them had.

For Aija:

Number of paid monthly subscribers= 560

Monthly subscription fee =14

For John:

Total earnings in the last 8 months of 2022 =76000

Monthly subscription fee =19

"L"-What procedures, methods, or strategies may you employ to arrive at your conclusion?

We must figure out Aija and John's combined wages in 2022 in order to compare how much they will each make. We must contrast the amount of paid requirements apply each of them had in order to compare the total number of subscribers. Finally, we must offer advice to people who are thinking about opening an Only Fan account.

“V” - Demonstrate your work by showing your steps.

Total earnings for Aija:

14*560*12 months=940800

Total earnings for John:

76000/8 months=9500 per month

19*x=9500

x=500subscribers

Total subscribers for John =500*12=6000 subscribers

Total earnings for John =19*6000*12=1368000 subscribers

Therefore, John made more money in 2022 with his Only Fans page and also had more subscribers.

"E" – Consider your response. Do you understand it? Did you address every aspect of the issue?

Our response makes logic, so yes. Due to his increased membership cost and greater subscriber base, John made more money from Aija. We have addressed every aspect of the issue by contrasting the earnings of Aija and John as well as the numbers of members they both had.

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Answer: 5654.9

Step-by-step explanation:

V=pi*r^2*h

r=10

h=18

V=pi*10^2*18

V=pi*100*18

V=pi*1800

V=5654.866776

tenths place:

V=5654.9

The element defined by the given information p = 17 n° = 20 e- = 17 is Chlorine (Cl).

An atom consists of protons, neutrons, and electrons. The atomic number of an element corresponds to the number of protons present in the nucleus of an atom. Hence, the atomic number (p) of the given element is 17. A neutral atom contains an equal number of protons and electrons.

Therefore, the number of electrons (e-) of the given element is 17 as well. The number of neutrons (n°) can be calculated as the difference between the atomic mass number (A) and the atomic number (p).

In the case of the given element, the atomic number is 17, and the atomic mass number is 37 (as chlorine has two stable isotopes of mass numbers 35 and 37). Hence, n° = 37 - 17 = 20. Therefore, the element defined by the given information p = 17 n° = 20 e- = 17 is Chlorine (Cl).

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Step-by-step explanation:

Y = 4 is a horizontal line

   other horizontal lines do NOT intersect

ALL vertical lines or lines with slope  DO intersect :

  y = x      y = -x      x = 3       x = 7      x = -3

Answer:

Step-by-step explanation:

Simple interest is a method for calculating the percentage of interest paid on a sum over a predetermined time period at a predetermined rate. The annual simple interest rate on the principal amount of 10000 at the end of 7 years would be 3%.

In simple interest, the principal amount doesn't change. Simple interest is a clear-cut and simple method for figuring out how much money has earned interest. It is a way to figure out how much interest will be charged.

Simple interest can be computed by multiplying the principal amount by the rate multiplied by the time period. In banks and other financial institutions, simple interest is frequently used to complete a variety of calculations. The total amount of cash that was spent on interest during the course of the loan is described.

Simple Interest = ( Principal × Rate × Time ) / 100

First, we need the Simple Interest (S.I)

Total = Principal + Simple Interest

T = P + S.I

$10,000 = $12,100. + S.I

S.I = $12,100 - $10,000

S.I = 2100

Simple Interest = (Principal × Rate × Time) / 100

S.I = (P × R × T) / 100

2100 = (10000 × R × 7) / 100

2100 = 70000R / 100

2100 = 700R

R = 2100 / 700

R = 3

Thus, The annual interest rate is 3%

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The probability that team A wins the best-of-three series over team B is 3/16.

If team A is the underdog and has a probability of 1/4 of winning every game it plays against team B,

The probability that it wins the best-of-three series over team B :

Let us first begin by determining the probability of team A winning two games in a row. Since each game is independent, we can use multiplication to calculate the probability of winning two games in a row:

P(Team A wins 2 in a row) = P(Team A wins Game 1) x P(Team A wins Game 2)

Using the probability given in the problem, we can substitute:

P(Team A wins 2 in a row) = (1/4) x (1/4) = 1/16

Now we must determine the probability of team A winning two games in the series. There are three ways that Team A could win the series:

Winning the first two games;

Winning the second two games;

Winning the first and third games.

Assuming that each of these scenarios is equally probable, the probability of team A winning the series is the sum of the probabilities of these scenarios:

P(Team A wins series) :

= P(Team A wins first two games) + P(Team A wins second two games) + P(Team A wins first and third games)P(Team A wins series)

= (1/16) + (1/16) + (1/16)P(Team A wins series)

= 3/16

Therefore, the probability that team A wins the best-of-three series over team B is 3/16.

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When a customer pays $162 without a coupon, the repairman worked for approximately 3.88 hours.

To solve the problem, we can use algebraic equations. Let x be the number of hours worked and let y be the inspection fee. Then, we have two equations:

y + 0.8y = 96 (the customer with the coupon pays $96 for a 2-hour repair)

y + 28x = 162 (the customer without the coupon pays $162)

Simplifying the first equation, we get:

1.8y = 96

y = 53.33

Substituting y into the second equation and solving for x, we get:

53.33 + 28x = 162

28x = 108.67

x = 3.88

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