On the last three physics exams a student scored 85, 87, and 91. What score must the student earn on the next exam to have an average of at
Least 90?

It may be 1^4 ............................

We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.

The mean is a measure of central tendency that represents the average value of a set of numbers. It is also called the arithmetic mean or simply the average.

We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.

The mean and the median are two different measures of central tendency, and they can have different values depending on the distribution of the data. In general, if a data set is symmetric and bell-shaped, the mean and the median are close to each other. However, if the data set is skewed, the mean and the median may be different.

For example, consider the following two data sets:

Set 1 data: 1, 2, 3, 4, and 5.

The median is 3.

The mean is (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3.

Data set 2: 1, 2, 3, 4, 10

The median is 3.

The mean is (1 + 2 + 3 + 4 + 10) / 5 = 20 / 5 = 4.

In data set 1, the mean is the same as the median. In data set 2, the mean is greater than the median because the value 10 is an outlier that pulls the mean up.

Therefore, without additional information about the distribution of the data, we cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.

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Answer:

The y-intercept is (0, 72). The vertex is

an absolute minimum, (-9, -9).

Step-by-step explanation:

Not all intersecting lines are perpendicular.

Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.

Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.

As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.

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Determinants are defined only for square matrices, so I assume you are given the 3×3 matrix

\(A = \begin{bmatrix}-2 & -4 & -3 \\ -1 & -9 & -8 \\ -15 & -5 & 6 \end{bmatrix}\)

Let's compute the determinant by taking the cofactor expansion along the first column:

\(\det A = -2 \det\begin{bmatrix}-9 & -8 \\ -5 & 6\end{bmatrix} + \det\begin{bmatrix}-4 & -3 \\ -5 & 6\end{bmatrix} - 15 \det \begin{bmatrix}-4 & -3 \\ -9 & -8\end{bmatrix}\)

\(\det A = -2 ((-9)\times6-(-8)\times(-5)) + ((-4)\times6 - (-3)\times(-5)) \\ ~~~~~~~~~~~~~~~- 15 ((-4)\times(-8)-(-3)\times(-9))\)

\(\det A = -2(-54-40) + (-24 - 15) - 15 (32 - 27)\)

\(\det A = \boxed{74}\)

The points scored in the game is an illustration of combinations. She could have scored the 10 points in 302400 ways.

The given parameters are

\(n = 10\) ---- total points

\(r_1 = 1\) ---- one-point free throw

\(r_2 = 2\) --- two-point field goals

\(r_3 = 3\) --- three-point field goals

The number of ways (k) she could have scored the points is:

\(k = \frac{n!}{r_1 ! \times r_2! \times r_3 !}\)

So, we have:

\(k = \frac{10!}{1 ! \times 2! \times 3 !}\)

Solve each factorial

\(k = \frac{3628800}{1 \times 2 \times 6}\)

\(k = \frac{3628800}{12}\)

Evaluate

\(k = 302400\)

Hence, she could have scored the 10 points in 302400 ways.

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Answer:

yes

Step-by-step explanation:

12+3=5x-3+3

15=5x

15=5(3)

15=15

Answer:

100%-10%=90%

90%=36$ what about 10%=4$

36$+4$=40$

You would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

To find the range in which you would expect to find the middle 98% of most pregnancies, you can use the concept of z-scores and the standard normal distribution.

For the given data:

Mean (μ) = 269 days

Standard deviation (σ) = 17 days

To find the range, we need to find the z-scores corresponding to the 1% and 99% percentiles. Since the normal distribution is symmetric, we can find the z-scores by subtracting and adding the respective values from the mean.

To find the z-score for the 1% percentile (lower bound):

z1 = Φ^(-1)(0.01)

Similarly, to find the z-score for the 99% percentile (upper bound):

z2 = Φ^(-1)(0.99)

Now, we can calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

To find the corresponding values in terms of days, we multiply the z-scores by the standard deviation and add/subtract them from the mean:

lower bound = μ + (z1 * σ) = 269 + (-2.33 * 17) ≈ 229.4 days

upper bound = μ + (z2 * σ) = 269 + (2.33 * 17) ≈ 308.6 days

Therefore, you would expect to find the middle 98% of most pregnancies between approximately 229.4 days and 308.6 days.

Now, let's consider drawing samples of size 58 from this population. The mean and standard deviation of the sample means can be calculated as follows:

Mean of sample means (μ') = μ = 269 days

Standard deviation of sample means (σ') = σ / sqrt(n) = 17 / sqrt(58) ≈ 2.229

To find the range in which you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample, we repeat the previous steps using the mean of the sample means (μ') and the standard deviation of the sample means (σ').

Now, calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

Multiply the z-scores by the standard deviation of the sample means and add/subtract them from the mean of the sample means:

lower bound = μ' + (z1 * σ') = 269 + (-2.33 * 2.229) ≈ 264.0 days

upper bound = μ' + (z2 * σ') = 269 + (2.33 * 2.229) ≈ 274.1 days

Therefore, you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

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Using substitution method to solve the system of linear equation, the number of children is 33 and adults is 150.

In mathematics, a system of linear equations is the collection of two or more linear equations that share the same variables. The maximum power of the variable in the linear equations in this situation is 1, making them first-order equations. A linear equation may have one, two, or three variables. We can therefore create linear equations with n variables.

To solve this problem, we have to define our variables and then write the equations.

Let:

\(x + y = 183\) ...eq(i)

\(1.75x + 2.5y = 432.75\) ...eq(ii)

solving both equations

From equation (i)

\(x + y = 183\)

\(x = 183 - y\) ...eq(iii)

Put equation (iii) into equation (ii)

\(1.75(183 - y) + 2.5y = 432.75\)

\(y = 150\)

Put y = 150 into equation (i)

\(x + 150 = 183\)

\(x = 33\)

The number of child is 33 and adult is 150

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The set is of whole numbers but not natural numbers will be (0, 1, 2, 3). Then the correct option is C.

A consistently positive numeral or a minus integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The Z symbol is a common way for mathematicians to refer to an integer set.

The set of the whole number is given as,

Whole number = {0, 1, 2, 3, 4, .....}

Real numbers are those in arithmetic that is utilized for counting and ordering. Cyclic numbers are those used for counting, while exponential increases in the number are those used for ranking.

The set of the natural number is given as,

Natural number = {1, 2, 3, 4, .....}

The set is of entire numbers yet not normal numbers will be (0, 1, 2, 3). Then, at that point, the right choice is C.

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Step-by-step explanation:

There are 8 different kinds of soda and the store ordered 567,858. All we have to do to see the total bottles the store ordered is multiply the two numbers.

8x567,858=4,542,864.

The answer is 4,542,864

The solution to the given inequality is \(4\:\le \:3\:x+10 < \:19\) is \($$-2 \leq x < 3$$\).

\($4 \leq 3 x+10 < 19:\left[\begin{array}{cc}\text { Solution: } & -2 \leq x < 3 \\ \text { Interval Notation: } & {[-2,3)}\end{array}\right]$\)

\($$4 \leq 3 x+10 < 19$$\)

If \($a \leq u < b$\) then \($a \leq u$\)and\($u < b$\)

\($$4 \leq 3 x+10 \text { and } 3 x+10 < 19$$\)

\($$4 \leq 3 x+10: \quad x \geq-2$$\)

Then,

\($$3 x+10 < 19: \quad x < 3$$\)

Combine the intervals

\($x \geq-2$\)and \($x < 3$\)

Merge Overlapping Intervals

\($$-2 \leq x < 3$$\)

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Answer:

hello! im taking medical school rn to be a paramedic and what i would do is either get a pair of tweezers and get it out or go to your local hospital to get it quickly removed!

Step-by-step explanation:

The rate of the slower car is 77km/hr

Velocity is the rate of change of displacement with time. It is measured in meter per second and it is a vector quantity.

velocity = displacement/time

displacement = velocity × time

represent the faster car by v1 and the slower car by v2

v1 = v2+16

V2 = v1-16

Total displacement = 680km

680 =( v1+V2)t

680 = (v1+V2)4

v1+v2 = 680/4

v2+16+v2 = 170

2v2 = 170-16

2v2 = 154

v2 = 154/2

v2 = 77km/hr

therefore the rate of the slower car is 77km/hr

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Reroll 6’s = 26 times

Failed turn on 6's = 21 times

If the initial roll is a 6, the question enters an unending cycle. Reroll till it isn't 6, or simply treat it as a failed round since the roll was legal and didn't result in a pair of twos.

The likelihood of each number being rolled is the same.

If the first roll is n, there are (6 - n) options for the greater number. Thus p = 1/(6 - n) for a specific (possible) result such as n + 2.

Then,

p(2 apart) = p(1, then 3) + p(2, then 4) + p(3, then 5) + p(4, then 6)

Reroll 6’s:

p(2 apart) = (1/5)(1/5) + (1/5)(1/4) + (1/5)(1/3) + (1/5)(1/2)

p(2 apart) = (1/5)(1/5 + 1/4 + 1/3 + 1/2) = 0.25666…

So for 100 times, we will get 26 times 2 apart

Failed turn on 6:

p(2 apart) = (1/6)(1/5) + (1/6)(1/4) + (1/6)(1/3) + (1/6)(1/2)

p(2 apart) = (1/6)(1/5 + 1/4 + 1/3 + 1/2) = 0.2138

So for 100 times, we will get 21 times 2 apart

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Classifying the polynomial 5x³ + 4x − 2 by degree gives a degree of

An equation made up of variables, exponents, and coefficients along with operations and the equal sign is known as a polynomial equation.

Sums of terms of the form kxⁿ, where k is any number and n is a positive integer, make up polynomials.

The degree refers to the highest exponents which is a positive integer

examining the function the degree is 3 and referred to as cubic

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The ball is in the air for approximately 2.8 + √7 seconds, which rounds to 5.2 seconds when rounded to one decimal place.To write the equation in vertex form, we need to complete the square.

The given equation is h = -4.9t² + 27.44t + 0.584. We can rewrite it as:

h = -4.9(t² - 5.6t) + 0.584

Now, we want to complete the square inside the parentheses. To do this, we need to add and subtract the square of half the coefficient of t. In this case, the coefficient is -5.6, so we have:

h = -4.9(t² - 5.6t + (5.6/2)² - (5.6/2)²) + 0.584

Simplifying, we get:

h = -4.9((t - 2.8)² - 2.8²) + 0.584

Expanding further:

h = -4.9(t - 2.8)² + 4.9(2.8)² + 0.584

Thus, the equation in vertex form is: h = -4.9(t - 2.8)² + 34.328

b) The ball's height when it was hit can be found by evaluating the equation at t = 0:

h = -4.9(0 - 2.8)² + 34.328

h = -4.9(-2.8)² + 4.328

h = -4.9(7.84) + 34.328

h ≈ 0.784 meters

To find the time at which the ball reaches its maximum height, we can use the fact that the maximum height occurs at the vertex of the parabolic equation. The vertex of a parabola in the form h = a(t - h₀)² + k is given by (h₀, k). Comparing this to our equation, we can see that the vertex occurs at t = 2.8 and h = 34.328. Therefore, the ball reaches its maximum height at 2.8 seconds, and the maximum height is 34.328 meters.

The total time the ball is in the air can be determined by finding the time it takes for the ball to reach the ground. When the ball hits the ground, its height is 0. To find this time, we can set the equation equal to 0 and solve for t:

0 = -4.9(t - 2.8)² + 34.328

4.9(t - 2.8)² = 34.328

(t - 2.8)² ≈ 7

t - 2.8 ≈ ±√7

t ≈ 2.8 ± √7

Since time cannot be negative in this context, we can ignore the negative value.

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Answer:

Tavian is correct.

Step-by-step explanation:

If you solve the systems of equations, y=0 and x=7, so the solution is (7, 0).

Answer:" m% = m/100. what = a variable ... "x". for example. "is" means "=". "of" means multiply. n = (m/100)•x.

Step-by-step explanation:

Answer:

\(t=\frac{74.1-72}{\frac{13.3}{\sqrt{50}}}=1.116\)    

The degrees of freedom are given by:

\(df=n-1=50-1=49\)  

Now we can calculate the p value with the following probability:

\(p_v =P(t_{(49)}>1.116)=0.135\)  

Since the p value is higher than the significance level provided of 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly higher than 72 per hour.

Step-by-step explanation:

Information provided

\(\bar X=74.1\) represent the sample mean

\(s=13.1\) represent the sample standard deviation

\(n=50\) sample size  

\(\mu_o =72\) represent the value that we want to test

\(\alpha=0.1\) represent the significance level

t would represent the statistic

\(p_v\) represent the p value

Hypothesis to test

We want to analyze if the true mean for this case is higher than 72, the system of hypothesis would be:  

Null hypothesis:\(\mu \leq 72\)  

Alternative hypothesis:\(\mu > 72\)  

The statistic is given by:

\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\)  (1)  

Replacing the info we got:

\(t=\frac{74.1-72}{\frac{13.3}{\sqrt{50}}}=1.116\)    

The degrees of freedom are given by:

\(df=n-1=50-1=49\)  

Now we can calculate the p value with the following probability:

\(p_v =P(t_{(49)}>1.116)=0.135\)  

Since the p value is higher than the significance level provided of 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly higher than 72 per hour.

To construct an octagonal box, you will need to cut eight rectangular pieces of equal size and eight regular octagons with equal sides. After cutting the pieces, fold them in a way that forms the octagonal box.

In an octagonal box shaped like an octagonal prism, the base is an octagon. Since the question does not provide specific measurements or angles for the octagon, we will assume that all the sides and angles of the octagon are equal. Let's denote the length of each side of the octagon as "s."

Area of the octagon = 2(1 + √2) * s^2

Where s is the length of each side.

An octagonal box is a type of prism that has eight equal sides and is shaped like a polygon. It has 8 vertices, 12 edges, and 6 faces.

The top and bottom faces are regular octagons, while the remaining faces are rectangles that connect the sides of the octagons.

Octagonal boxes can be used for various purposes, including storage, decoration, and shipping.

They are durable and can protect the contents inside from damage. In unit 7 lesson 12 cool down 12.5, you might be required to construct an octagonal box.

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The solution to the given system of equations is a = 6, b = 4.

The system of equations is given as follows:

a + b = 10  .....(i)

a - b = 2    .....(ii)

To solve this system of equations, we can use the method of elimination.

Adding the two equations, we get:

(a + b) + (a - b) = 10 + 2

2a = 12

a = 6

Substituting a = 6 into one of the equations, we get:

6 - b = 2

b = 4

Therefore, the solution to the system of equations is:

a = 6, b = 4.

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The area of the triangle is A = 35 cm²

Given data ,

Let the Triangle be ΔABC , such that D be the perpendicular line to the base

The measures of the sides of the triangle are

Let the length of the base of the triangle be BC = 14 cm

The height of the triangle is AD = 5 cm

The area of the triangle = ( 1/2 ) x Length x Base

On simplifying the equation , we get

A = ( 1/2 ) x ( 14 ) x ( 5 )

A = ( 1/2 ) x 70

Area of triangle A = 35 cm²

Hence , the area is A = 35 cm²

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Answer:

y=2x+5

Step-by-step explanation:

first find the gradient which is change in y/ change in x

so gradient= (9--1)/(2--3) = 10/5 = 2

there's only one answer with a gradient of 2 which is a but if you wanted to find the intercept you would do this

y=2x + c

put one pair of coordinates into the equation (I've picked (2,9) but it doesn't matter which)

9=2*2 + c

9=4 + c

c = 5

therefore the equation must be y=2x + 5

hope that helps

Based on the ounces of herbs and their cost, the amount of herbs that should be mixed to produce the mixture costing $2.70 per ounce is 21 ounces

Assuming that the amount of ounces needed to be mixed with the 35 ounce of herbs to produce a mixture costing $2.70 per ounce is x, then the formula would be:

Total cost = (2 × x) + (3 x 35) = 2.7 x (x + 35)

This can be expanded to be:

2x + 105 = 2.7x + 94.5

0.5x = 10.5

x = 10.5 / 0.5

x = 21 ounces

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Answer:

12, 17, 30.

Step-by-step explanation:

Given

(a) to (d)

Required

Which cannot represent a triangle

The rule to use is:

\(a + b > c\)

So, we have: 12, 17, 30.

\(12 + 17 > 30\) ===> \(29 > 30\) --- False

\(12 + 30 > 17\) ==> \(43 > 17\)

\(17 + 30 > 12\)

Because, one of the inequalities is False, then this can not represent the sides of a triangle.

Answer:

Hey!

Step-by-step explanation:

Hope this helps you!

Best of luck! <3

(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

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