The scatter plot shows the number of hits and home runs for 20 baseball players who had at least 10 hits last season. The table shows the values for 15 of those players.
The model, represented by y=0.15x−1.5, is graphed with a scatter plot.

Use the graph and the table to answer the questions.
Player A had 154 hits in 2015. How many home runs did he have? How many was he predicted to have?
Player B was the player who most outperformed the prediction. How many hits did Player B have last season?
What would you expect to see in the graph for a player who hit many fewer home runs than the model predicted?

The perpendicular distance between the two parallel sides, height h of the trapezium is 8cm

It is important to note the properties of a trapezium;

the formula for area of  trapezium is;

Area = a + b/ 2 ·(h)

Substitute the value

80 = (4 + 16)/ 2  (h)

Add the values

80 = 10h

Divide by the coefficient of h

h = 8cm

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Complete question:

The area of a trapezium is  80cm^2

The lengths of its parallel sides are  4cm and 16cm respectively. Find the perpendicular distance between the two parallel sides.

The down payment is $450.

The total dollar amount of the monthly installment payments is $4,860.

The Loan amount Jeanie contracted was $4,050.

The total interest Jeanie paid was $810.

The down payment is the cash payment made upfront when an asset is bought on credit.

The down payment represents a percent of the total price, indicating the buyer's willingness and capacity to enter the contract.

The price of the snowmobile = $4,500

Down payment = 10% = $450 ($4,500 x 10%)

Loan amount = $4,050 ($4,500 - $450)

Installment periods = 18 months

Monthly payments = $270 ($4,050/18)

Total installment payments = $4,860 ($270 x 18)

The total interest = $810 ($4,860 - $4,050)

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The solution to the exponential equation [tex]4^-3v-2=4^-v[/tex]is v = -1.

To solve the exponential equation 4^(-3v-2)=4^(-v) using like bases and the one-to-one property,

Identify the like bases on both sides of the equation. In this case, the like base is 4.

Use the one-to-one property of exponential functions, which states that if two exponential functions with the same base are equal, then their exponents must also be equal. So, we can set the exponents equal to each other:

-3v - 2 = -v

Solve for the variable, v. We can do this by isolating the variable on one side of the equation:

-3v + v = 2

-2v = 2

v = -1

Check our answer by plugging it back into the original equation:

4^(-3(-1)-2) = 4^(-(-1))

4^(3-2) = 4^(1)

4^(1) = 4^(1)

4 = 4

So the solution to the exponential equation [tex]4^-3v-2=4^-v[/tex]is v = -1.

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Answer:

When you multiply two numbers with different signs (positive and negative), the result is always negative.

This can be understood in terms of the basic properties of multiplication and the fact that a negative number is essentially the opposite of a positive number. When you multiply a positive number by a positive number, the result is positive because both numbers are pointing in the same direction along the number line. When you multiply a negative number by a negative number, the result is also positive because both numbers are pointing in the opposite direction along the number line, and multiplying them together "flips" them back to the positive side. However, when you multiply a positive number by a negative number, the two numbers are pointing in opposite directions along the number line, and so their product is negative.

Therefore, the rule for multiplying two numbers with different signs is that the product is always negative.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Kelsie has written checks for a total of $46 + $82 + $264 + $127 = $519.

Since she only has $370 in her account, this means she has overdraft by $519 - $370 = $149.

Therefore, the bank will charge her $22 for each overdraft, which gives a total of $22 * 7 = $154.

Thus, Kelsie owes the bank a total of $519 + $154 = $673. Answer: \boxed{673}.

Earthquake in Turkey was 1000 times much stronger, compared to a magnitude 5​ earthquake

The Richter scale (also known as the Richter magnitude scale) assigns  magnitude numbers to quantify the energy released by an earthquake. Developed by Charles Richter in the 1930s, the Richter scale is a base 10 logarithmic scale that defines magnitude as the logarithm of the ratio of  seismic wave amplitudes to smaller amplitudes.

As measured by seismographs, an earthquake measuring 5.0 on the Richter scale has 10 times more shaking amplitude than a 4.0 earthquake.

Given,

Magnitude 6 is 10² = 100 times greater than magnitude 4.

Magnitude 4 is 10 times greater than magnitude 4.

By the above data, 1 digit greater magnitude means 10 times powerful.

Earthquake on turkey is of 8 magnitude

∵ Difference of 8 magnitude and 5 magnitude = 8 - 5 = 3

∴ 8 magnitude earthquake is 1000 times greater.

Hence, 1000 times much stronger was earthquake in Turkey, compared to a magnitude 5​ earthquake.

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If you could provide me more details, including the dimensions of the two triangle ' angles and sides, I might be able to evaluate whether or not they are comparable.

A triangle is a polygon because it includes four or so additional parts. It features a simple rectangular shape. A rectangle having edges A, B, and C is referred to as a triangle. When the sides are actually not collinear, Euclidean geometry yields a single plane and cube. If a triangle contains three parts and three angles, it is a polygon. The intersections of a triangle's three sides are referred to as its corners. The sum of a triangle's sides is 180 degrees.

Two polygons must have congruent corresponding angles and proportionate corresponding sides in order to be considered comparable.

If you could provide me more details, including the dimensions of the two polygons' angles and sides, I might be able to evaluate whether or not they are comparable.

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The statement "If the system of a linear equation has the unique solution, then the system is inconsistent." is False since a single solution is an indication that the equations intersect at a specific point, making it consistent.

A system of linear equations is a set of two or more linear equations that contain two or more variables. A solution to the system of linear equations is a set of values for the variables that satisfies all the equations in the system.

The system of linear equations having a single solution is a consistent system since a single solution is an indication that the equations intersect at a specific point. This contradicts the notion that the system is inconsistent. An inconsistent system is one that has no solutions.

Thus, if a system of linear equations has a unique solution, it must be consistent.

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The simplified rational expression is (x³-6x²+5x²)-30x+5x²-30x+25x-150)/(x³+17x²+75x+175)

To simplify the rational expression, we will need to use multiplication and division of the rational expressions. We will also need to factor the expressions in order to simplify them.

First, let's factor the expressions:
(x²-3x-18)/(x²+10x+21)-:(x²+3x-54)/(x²-x-30)*(x²+16x+63)/(x²+14x+45)

= ((x-6)(x+3))/((x+7)(x+3))-:((x+9)(x-6))/((x-6)(x+5))*((x+9)(x+7))/((x+9)(x+5))

Next, let's simplify the expressions by canceling out the common factors:
= (x-6)/(x+7)-: (x+9)/(x+5)*(x+7)/(x+5)
= (x-6)/(x+7)-: (x+9)(x+7)/(x+5)(x+5)

Now, let's multiply the expressions:
= (x-6)(x+5)(x+5)/(x+7)(x+5)(x+5) - (x+9)(x+7)(x+7)/(x+7)(x+5)(x+5)

Finally, let's subtract the expressions:
= ((x-6)(x+5)(x+5) - (x+9)(x+7)(x+7))/((x+7)(x+5)(x+5))
= (x³-6x²+5x²-30x+5x²-30x+25x-150)/(x²+17x²+75x+175)

Therefore, the simplified rational expression is:
= (x³-6x²+5x²-30x+5x²-30x+25x-150)/(x³+17x²+75x+175)

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$113\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus 52} \end{array}\dotfill &52\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 113\left(1+\frac{0.06}{52}\right)^{52\cdot 4} \implies \boxed{A \approx 143.63}\hspace{5em}\underset{ earned~interest }{\stackrel{ 143.63~~ - ~~113 }{\boxed{\approx 30.63}}}[/tex]

Answer:

She earns $2,560

Step-by-step explanation:

She earns 2,560 because this is 8% of 32000. How do we know?
Multiply 32000 by 0.088, which is 8% of 100.

For 6 cities, the number of roads would be 9. This is because each city must be connected to every other city, and there are 5 pairs of cities that need to be connected, which means 5 roads.

Roads are a form of transportation infrastructure consisting of a prepared surface for vehicles to travel on. They are typically made from asphalt or concrete and are designed to provide a safe and efficient means of travel.

Then, the remaining 4 cities need to be connected, which means 4 more roads for a total of 9.
For 7 cities, the number of roads would be 12. This is because each city must be connected to every other city, and there are 6 pairs of cities that need to be connected, which means 6 roads. Then, the remaining 5 cities need to be connected, which means 5 more roads for a total of 12.
For N cities, the number of roads would be equal to N(N-1)/2. This is because each city must be connected to every other city, and there are N(N-1)/2 pairs of cities that need to be connected. For example, if N = 10, then 10 × 9 = 90 pairs of cities need to be connected, which means 90 roads.

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Using the unit tile the area of the three diagrams is - square tile = 1 unit², rectangular tile = x unit², and square tile = x² unit².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

For the square tile with length and breadth = 1 unit, the area is simply the product of the length and breadth, which is 1 unit × 1 unit = 1 unit².

This is the same as the area of the unit tile, so we don't really need to use it to find the area of this tile.

For the rectangular tile with length = x units and breadth = 1 unit, we can use x unit tiles to cover the length, and 1 unit tiles to cover the breadth.

Therefore, the area of the rectangular tile is x unit × 1 unit = x unit².

For the square tile with length and breadth = x units, we can use x unit tiles to cover the length, and x unit tiles to cover the breadth.

Therefore, the area of the square tile is x unit × x unit = x² unit².

In general, for any tile with length = a units and breadth = b units, the area is given by the product of the length and breadth, which is a unit × b unit = ab unit².

Therefore, we can use the unit tile to find the exact area of any tile, as long as we know its dimensions.

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The value of x for this solution is x = -2, 3, -3.

To solve for x, we need to combine like terms and then isolate x on one side of the equation. Here are the steps:

1. Multiply both sides of the equation by the common denominator of (x)(x-6)(2) to eliminate the fractions:
(1)(x)(2) + (x)(x-6)(2) = (-9x+3)(x)(x-6)
2x + 2x^2 - 12x = -9x^3 + 3x^2 - 54x + 18

2. Combine like terms:
2x^2 - 10x = -9x^3 + 3x^2 - 54x + 18

3. Move all terms to one side of the equation:
9x^3 - x^2 + 44x - 18 = 0

4. Use the Rational Root Theorem to find possible solutions:
The possible rational roots are ±1, ±2, ±3, ±6, ±9, ±18

5. Use synthetic division to test the possible roots and find the actual solutions:
When we divide by -2, we get a remainder of 0, so -2 is a solution.
When we divide by 3, we get a remainder of 0, so 3 is a solution.
When we divide by -3, we get a remainder of 0, so -3 is a solution.

6. The solutions are x = -2, x = 3, and x = -3.

So the final answer is:
x = -2, 3, -3

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By answering the above question, we may state that We must thus locate function the value of h that makes the equation true in order to estimate the height of the tower platform.

Mathematicians study numbers, as well as their variations, equations, related forms, and conceivable arrangements of these. Function refers to the relationship between a set of inputs, each of which has an associated output. A function is an association of inputs and outputs, where each input leads to a single, identifiable output. Each function is given a domain, codomain, or scope. The letter f is frequently used to represent functions (x). A cross is typed. The four primary types of accessible functions are on functions, one-to-one capabilities, so numerous capabilities, in capabilities, and on functions.

The projectile's starting height above the earth must be determined. Setting the time to zero (t = 0) and finding h will allow us to do this.

The formula for the projectile's height at time t is:

[tex]vt + h + -16t2 = h(t)[/tex]

where h represents the projectile's initial height and v its initial velocity.

t = 0 results in:

[tex]h(0) = -16(0)^2 + v(0) + h h(0) = h[/tex]

Hence, h, the height of the tower platform, is the projectile's beginning height.

We must thus locate the value of h that makes the equation true in order to estimate the height of the tower platform.

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Answer:

First, find the total number of cups of liquid in the punch:

24 cups pineapple juice + 46 cups orange juice + 72 cups seltzer = 142 cups

Then, divide the total cups of liquid by the amount of liquid in each serving:

108 cups / 142 cups per serving = 0.76 servings

Therefore, approximately 0.76 servings can be made from 108 cups of punch.

A(t) = $3,600(1.125)t is the function that displays the balance of the account after t years, rounded to four decimal places.

The definition of the word "invest" is to "expend money with the idea of attaining a profit or material consequence by putting it into financial plans, etc." A person is "vested" when they are "secured in their possession or allocated to a person," on the other hand. It can also imply outfitted with a vest, although that is unimportant just now.

A(t) = P(1 + r)t

where:

A(t) represents the balance of the account after t years.

P is the initial investment, $3,600, and r is the growth rate per year.

The number of years is t.

A(t) = $3,600(1 + 0.125)t

A(t) = $3,600(1.125)t

We can take the growth rate and subtract 1 to get the annual growth percentage, which we can then translate to a percentage as follows:

Percentage growth rate = (1.125 - 1) * 100% = 12.5%

So the account grows by approximately 12.5% per year.

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Option d) The missing quantity A is $2520. The formula for future value is A=P(1+rt), where A is the future value, P is the principal amount, r is the interest rate, and t is the time period.

We are given the values of P, r, and t, and we need to find the value of A.

P = $1800
r = 8% = 0.08
t = 5 years

Plugging these values into the formula, we get:

A = P(1 + rt)
A = $1800(1 + 0.08*5)
A = $1800(1 + 0.4)
A = $1800(1.4)
A = $2520

Therefore, the future value of the investment is $2520. The correct answer is A = $2520.

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The estimated height of the child at delivery is represented by the y-intercept, which is 72.66.

We may use linear regression to construct an equation that represents the link between this child's height and age. The line of best fit for the supplied data is determined by linear regression, which can be written as:

Age (years) + b * m * Height (cm)

where m denotes the line's slope and b its y-intercept.

The equation that most closely matches the above data can be determined using a calculator or spreadsheet software as follows:

Age (years) + 72.66 Height (cm) = 6.087

Thus, the height of the youngster increases by roughly 6.087 centimetres for every year that their age rises. The estimated height of the infant at delivery is represented by the y-intercept, which is 72.66.

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The possible rational roots are:

±1/1, ±3/1, ±5/1, ±15/1, ±1/1, ±1/2, ±3/2, ±5/2, ±15/2

A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.

To list all the possible rational roots of x⁴ - 2x³ -6x² + 22x - 15 = 0, we need to find all the factors of the constant term -15 (in this case, they are 1, -1, 3, -3, 5, -5, 15, and -15) and all the factors of the leading coefficient 1 (in this case, they are 1 and -1). Then, we form all possible fractions of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. Therefore, the possible rational roots are:

±1/1, ±3/1, ±5/1, ±15/1, ±1/1, ±1/2, ±3/2, ±5/2, ±15/2

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The expected rabbit population by next April is 486.

The rabbit population in a forest area can be found using the formula y=200(2.7)^0.08t, where y is the expected population, t is the time in months, and 200 is the initial population. To find the expected population by next April, we need to plug in the value of t as 12 (since there are 12 months in a year) and solve for y.

y=200(2.7)^0.08t

y=200(2.7)^0.08(12)

y=200(2.7)^0.96

y=200(2.4315)

y=486.3

Since the question asks for the expected population rounded to the nearest whole number, we can round 486.3 to 486.

Therefore, the expected rabbit population by next April is 486.

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Answer: A cup of coffee costs $2.50 and a bagel costs $3.50.

Step-by-step explanation: Let's use the following variables to represent the price of each item:

c: price of a cup of coffee (in dollars)

b: price of a bagel (in dollars)

From the problem statement, we know that:

b = c + 1 (a bagel costs $1 more than a cup of coffee)

We also know that you bought 4 cups of coffee and 6 bagels for a total of $31. This can be expressed as:

4c + 6b = 31

Now we can substitute the first equation into the second equation to eliminate b:

4c + 6(c + 1) = 31

Simplifying this equation, we get:

10c + 6 = 31

Subtracting 6 from both sides, we get:

10c = 25

Dividing both sides by 10, we get:

c = 2.5

Now we can use the first equation to find the value of b:

b = c + 1 = 2.5 + 1 = 3.5

Therefore, a cup of coffee costs $2.50 and a bagel costs $3.50.

The scalar equation of the plane is -5x - 2y = 5.

To find the scalar equation for the plane passing through the points P1=(−3, 5, 3), P2=(−5, 0, 6), and P3=(−1, 10, −1), we need to follow these steps:

1. Find the vectors P1P2 and P1P3 by subtracting the corresponding coordinates of the points:
P1P2 = P2 - P1 = (-5 - (-3), 0 - 5, 6 - 3) = (-2, -5, 3)
P1P3 = P3 - P1 = (-1 - (-3), 10 - 5, -1 - 3) = (2, 5, -4)

2. Find the normal vector to the plane by taking the cross product of P1P2 and P1P3:
n = P1P2 x P1P3 = (-5 * (-4) - 3 * 5, 3 * 2 - (-2) * (-4), -2 * 5 - (-5) * 2) = (-5, -2, 0)

3. Find the scalar equation of the plane by substituting one of the points and the normal vector into the general equation of a plane:
ax + by + cz = d
-5 * (-3) + (-2) * 5 + 0 * 3 = d
d = 5

Therefore, the scalar equation of the plane is -5x - 2y = 5.

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Answer:

Your answer:

6. x = 8

8. x = 3

Step-by-step explanation:

Basic calculation involving adding/subtracting and multiplying and dividing.

Formula for Area of a Rectangle:

Area = Length * Width.

6. Given information

A = 165 cm^2

length = 4x + 1

width = 5

(4x + 1) * 5 = 165 cm^2

5 * (4x + 1)= 165

20x + 5 = 165

20x = 160

x = 8

8. Given information

A = 40 cm^2

length = 7x - 1

width = 2

(7x - 1) * 2 = 40 cm^2

2 * (7x - 1)= 40

14x - 2 = 40

14x = 42

x = 3

The simplification form of the expression "(z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12)" is = "1/(z+6)".

To add the two fractions, we need to have a common denominator. Since both fractions already have the same denominator of z^(2)+8z+12, we can simply add the numerators together and keep the same denominator.

So, (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) = (z+2)/(z^(2)+8z+12)

Now, we need to simplify the fraction as much as possible. We can do this by factoring the denominator and seeing if there are any common factors that can be canceled out.

The denominator can be factored as (z+6)(z+2).

So, (z+2)/(z^(2)+8z+12) = (z+2)/(z+6)(z+2)

Now, we can see that there is a common factor of (z+2) in both the numerator and denominator, so we can cancel them out.

So, the final simplified answer is 1/(z+6).

Therefore, (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) = 1/(z+6).

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The length of the legs are 2 units and 3.464 units

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

The triangle

The legs can be calculated using sine and cosine ratios

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

sin(30) = PQ/Hyp

cos(30) = RQ/Hyp

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

PQ/4 = 0.5

RQ/4 = 0.8660

So, we have

PQ = 4 * 0.5

RQ = 4 * 0.8660

Evaluate

PQ = 2

RQ = 3.464

Hence, one of the leg is 3.464 units

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The value of a when b = 8 and c = 5 is 41.351.

Jointly proportional refers to a relationship between two or more variables in which all of the variables increase or decrease together in the same ratio. For example, if one variable doubles, the other variables double as well.

The variable a is jointly proportional to b and the cube of c. This means that a = k*b*c^3, where k is a constant. We can use the given values to find k:

127 = k*6*8^3

127 = k*3072

k = 127/3072

k = 0.041351

Now we can use this value of k to find the value of a when b = 8 and c = 5:

a = 0.041351*8*5^3

a = 0.041351*8*125

a = 41.351

So the value of a when b = 8 and c = 5 is 41.351.

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Answer: A

Area of a circle=[tex]\pi r^2\\[/tex]

Now that we have established this, we will now substitute the values in the equation.

[tex]\pi r^2\\=\frac{22}{7}\\ =\frac{396}{7}\\ =56.57 \\[/tex] OR 57 square yards

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Answer:

If your options are  110 square yards

220 square yards

3,850 square yards

15,400 square yards

then the correct answer is 3,850 square yards.

Step-by-step explanation:

I took the quiz and got it right.

55% of the pins were purple if Omar ordered a set of purple and red pins. He received 60 pins in all. 33 of the pins were purple.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants. An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

To find the percentage of purple pins, we need to divide the number of purple pins by the total number of pins and multiply by 100.

Number of purple pins = 33

Total number of pins = 60

Percentage of purple pins = (Number of purple pins / Total number of pins) x 100

= (33 / 60) x 100

= 55%

Therefore, 55% of the pins were purple.

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