Cody decreased the speed of his car by 3.5 miles per second over a period of 60 seconds Find the average change in speed each second

Answer:

$208

Step-by-step explanation:

$79.50 x 24 = 1908

$1908 + 400 = 2308

$2100/2308 = 9%

Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.

Interest is a financial concept that represents the cost of borrowing money or the return on invested capital. It is a fee charged for the use of borrowed funds or the compensation received for lending money or investing in assets.

Total number of monthly payments

= 12 months/year x 2 years

= 24 months

and, Monthly payment amount = $79.50

Total amount paid in monthly installments

= Monthly payment amount x Total number of monthly payments

= $79.50 x 24

= $1,908

Next, we can subtract the initial down payment from the total amount paid to find the interest paid:

Total interest paid = Total amount paid - Down payment

= $1,908 - $400

= $1,508

Therefore, Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.

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first off, let's take a peek at the picture above

hmmm the hyperbola is opening sideways, that means it has a horizontal traverse axis, it also means that the positive fraction will be the one with the "x" variable in it.

now, the length of the horizontal traverse axis is 4 units, from vertex to vertex, that means the "a" component of the hyperbola is half that or 2 units, and 2² = 4, with a center at the origin.

\(\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(x- 0)^2}{ 2^2}-\cfrac{(y- 0)^2}{ (\sqrt{3})^2}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{4}-\cfrac{y^2}{3}=1 \end{array}}\)

Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.

The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:

tan (∅) = opposite/adjacent

We have the following:

Reference angle (∅) = 53 degrees

Length of opposite side = 21

Length of adjacent side = x

Plug in the values:

tan 53 = 21/x

x * tan 53 = 21

x = 21 / tan 53

x = 15.824

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Answer:

\(P_{B}\) = 80

Step-by-step explanation:

given 2 similar figures with ratio of sides = a : b

then ratio of perimeters is also a : b

here ratio of sides = 24 : 15 = 8 : 5

the ratio of perimeters is also 8 : 5

then by proportion

\(\frac{ratioA}{P_{A} }\) = \(\frac{ratioB}{P_{B} }\) , that is

\(\frac{8}{128}\) = \(\frac{5}{P_{B} }\) ( cross- multiply )

8 \(P_{B}\) = 5 × 128 = 640 ( divide both sides by 8 )

\(P_{B}\) = 80

The solution is, the last possibility is 9x^2 y – 5xy3 + 9x2y =18x^2 y – 5xy3, binomial degree 4.

Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.

here, we have,

First, if we have a polynomial that the form is as follow

P(x,y)=a1x^n-1y^p-1+ a2x^n-2y^p-2 + . . . . + a0xy+c,

the degree can be found with the sum of the highest value of power of each term.

If the number of term is 3, it is called trinomial, if it is 2, the polynomial is called binomial.

So in our case, 0– 5xy3 + 9x2y is a binomial with a degree of 4, because number of term 2, degree =1 + 2 =3, upper than 2+ 1(the second term) 4xy^3– 5xy3 + 9x2y = -xy3 +9x2y, binomial degree 4,

and the last possibility is 9x^2 y – 5xy3 + 9x2y =18x^2 y – 5xy3, binomial degree 4.

Hence, The solution is, the last possibility is 9x^2 y – 5xy3 + 9x2y =18x^2 y – 5xy3, binomial degree 4.

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Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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all work should be in the picture, lmk if theres anything confusing

Answer:

C - formula of area of rectangle is l×w

so 23×16

Answer:

Step-by-step explanation:

first set up an equation

x = Kojo's age, x + 4 = Kwaku's age

2x + 4 = 30

find x from there and you should get x = 13, so Kwaku is 17 and Kojo is 13

The age of Kwaku is 17 and the age of Kojo is 13.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Let x represents the age of Kwaku and y be the age of Kojo.

Then given x+y = 30             {equation 1}

and Kwaku is 4 years older than Kojo.

That means x = y + 4

Substitute the above value to the equation 1,

2y = 26

y = 26/2

y = 13

And the x is 13 + 4 = 17

Therefore the age of Kwaku is 17 and the age of Kojo is 13.

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To divide 30 into five parts such that the first and last parts are in the ratio of 2:3, we can follow these steps:

1. Determine the ratio between the first and last parts. In this case, it is 2:3.

2. Add the ratio values together to find the total number of parts: 2 + 3 = 5.

3. Divide the total value (30) by the total number of parts (5) to find the value of each part: 30 / 5 = 6.

4. Multiply the value of each part by the respective ratio values to obtain the individual parts:

- First part: 2 * 6 = 12

- Second part: 6

- Third part: 6

- Fourth part: 6

- Last part: 3 * 6 = 18

Therefore, the five parts of 30, with the first and last parts in the ratio of 2:3, are 12, 6, 6, 6, and 18.

Answer:

x = 46

Step-by-step explanation:

Use the triangle angle bisector theorem.

58/63.8 = (x + 4)/55

63.8(x + 4) = 55 * 58

63.8x + 255.2 = 3190

63.8x = 2934.8

x = 46

Answer:

Perpendicular to base

Step-by-step explanation:

The cut creates two rectangular prisms (each angle must be 90 degrees)

The cut is perpendicular to the base

Answer:

\(P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256\)

And replacing we got:

\( P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744\)

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

\(X \sim Binom(n=2, p=1-0.16=0.84)\)

The probability mass function for the Binomial distribution is given as:

\(P(X)=(nCx)(p)^x (1-p)^{n-x}\)

Where (nCx) means combinatory and it's given by this formula:

\(nCx=\frac{n!}{(n-x)! x!}\)

And we can find this probability:

\( P(X \geq 1)\)

And we can solve this probability like this:

\( P(X \geq 1)=1 -P(X<1) = 1-P(X=0)\)

And if we use the probability mass function we got:

\(P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256\)

And replacing we got:

\( P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744\)

Answer:

2(1 - x)

Step-by-step explanation:

Twice the difference of 1 and a number

a number = x

The difference of 1 and a number is expressed as :

1 - x

Twice this difference, means the difference of (1-x) multiplied by 2

2 * (1 - x) = 2(1 - x)

The expected value of the raffle ticket is $-7.17.

The expected value is the probability-weighted value.

It is computed by multiplying the sum of the values by the probability of winning.

In mathematics, the expected value describes the product of the probability of an event occurring and the value of the actual observed occurrence.

The cost per raffle ticket = $9

The number of tickets sold = 709

The winning value = $1,300

The probability of winning the raffle = 1/709

The expected value = $-7.17 [($1,300 x 1/709) - $9].

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The solution is, (3x+5) (2x+1) is the expression is equivalent to

6x2 + 13x + 5.

Here, we have,

the given expression is: 6x2 + 13x + 5

now, we have to find which expression is equivalent to this.

so, we have,

6x^2+13x+5= 0

or 6x^2+ 3x+10x+ 5= 0

or   3x(2x+1)+ 5(2x+1)) = 0

or  (3x+5) (2x+1) = 0

so, we get,

(3x+5) (2x+1)

Hence, The solution is, (3x+5) (2x+1) is the expression is equivalent to 6x2 + 13x + 5.

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Answer:

The answer is C or 44/12

Step-by-step explanation:

1/2 is equivalent to 3/6

1 4/6 is equivalent to 1 4/6 or 10/6

1 2/4 is equivalent to 1 3/6 or 9/6

When you add all of these together you get 22/6

Then you multiply 22/6 by 2 to get 44/12

Answer:

80 ft/min

Step-by-step explanation:

Let h represent the height of the person shadow, x represent the distance between the person and the lamppost, y represent the length of the man shadow.

Therefore:

\(\frac{h}{x+y} =\frac{6}{y} \\\\substituting\ x=10,y=20:\\\\\frac{h}{10+20} =\frac{6}{20}\\\\\frac{h}{30} =\frac{6}{20}\\\\h=30*6/20\\\\h=9\ feet\\\\Therefore:\\\frac{h}{x+y} =\frac{6}{y}\\\\\frac{9}{x+y} =\frac{6}{y}\\\\9y=6x+6y\\\\9y-6y=6x\\\\3y=6x\\\\y=2x\\\\The\ person\ is\ walking\ from\ the\ lamppost\ at\ 40ft/min(\frac{dx}{dt}=40\ ft/min) \\\\y=2x\\\\Differentiating\ with\ respect\ to\ t:\\\\\frac{dy}{dt} =\frac{d}{dt}(2x)\\\\\frac{dy}{dt} =2\frac{dx}{dt}\\\\\)

\(\frac{dy}{dt} =2(40\ ft/min)\\\\\frac{dy}{dt}=80\ ft/min\)

The rate at which the length of the shadow is increasing when he is 30 feet away from the lamp post is  80 \(\frac{ft}{min}\).

The height of the person shadow is to be = h

Given ,

The distance between the person and the man = x = 10

The length of the man shadow is = y = 20

By the similar triangle property corresponding sides of similar triangles are in the same ratio.

\(\frac{h}{x+y} = \frac{6}{y}\)

\(\frac{h}{10+20} = \frac{6}{20}\)

20h = 60 + 120

20h = 180

h = \(\frac{180}{20}\)

h = 9feet

Therefore,

\(\frac{h}{x+y} = \frac{6}{y} \\\frac{9}{x+y} = \frac{6}{y} \\\)

9y= 6x + 6y

9y-6y = 6x

6x = 3y

y = \(\frac{6}{3}x\)

y = 2x

Differentiating both the sides with respect t,

\(\frac{dy}{dt} = 2\frac{dx}{dt}\)

we know that ;

\(\frac{dx}{dt} = 40 \frac{ft}{sec}\)

Therefore, by substitute the value

\(\frac{dy}{dt} = 2 . 40\frac{ft}{min}\)

\(\frac{dy}{dt}\) = 80\(\frac{ft}{min}\).

The rate at which the length of the shadow is increasing is 80\(\frac{ft}{min}\)  .

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The mean from a Histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

Out of the given options, the display of data for which it is not possible to find the mean is the stem-and-leaf plot.

A histogram displays data in the form of bars, where the height of each bar represents the frequency of data within a specific range. From a histogram, it is possible to calculate the mean by summing up the products of each value with its corresponding frequency and dividing it by the total number of data points.

A table presents data in a structured format, typically with rows and columns, allowing for easy calculation of the mean. By adding up all the values and dividing by the total number of values, the mean can be obtained from a table.

A stem-and-leaf plot organizes data by splitting each value into a stem (the first digit or digits) and a leaf (the last digit). While a stem-and-leaf plot provides a visual representation of the data, it does not directly provide the frequency or count of each value. Hence, it is not possible to determine the mean directly from a stem-and-leaf plot without additional information.

A dot plot represents data using dots along a number line, with each dot representing an occurrence of a value. Similar to a histogram and table, a dot plot allows for the calculation of the mean by summing up the values and dividing by the total number of data points.

In summary, while it is possible to find the mean from a histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

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The height of the triangular pyramid will be 154 cm.

A pyramid with a triangle base is referred to as a triangular pyramid. Vertices are essentially corners in geometry. Both regular and irregular triangular-based pyramids contain four vertices.

Pyramids with triangular bases have six edges, three of which run along the base and three of which rise above the base.

The volume of the triangular pyramid will be,

Volume = 1/2 x Base x h

11120 = 1/2 x ( 17 x 17 /2 ) x h

h = ( 11120 x 2 x 2 ) / ( 17 x 17 )

h = 44480 / 289

h = 154 cm

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If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

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Answer:

4/9

Step-by-step explanation:

'ng' = not green

P(ng,ng) = 2/3 x 2/3 = 4/9

Answer:

5/23

Step-by-step explanation:

23 students, 18 females so 5 males

In this case, the probability of a male student being chosen at random from the class is 5/23.

The probability of an event is the ratio of the number of cases favorable to it to the total number of cases possible when nothing leads us to expect any of these cases to occur more than any other, making them equally possible for us.

i.e. probability of an event = number of the possible outcome of an event/number of total outcomes in the sample space

An event is a set of outcomes of an experiment to which a probability is assigned in probability theory.

A sample space is a set of possible outcomes from a random experiment.

Here, the random experiment, in this case, is "a student chosen at random from the class". There are 23 students in the class. So, the number of total outcomes in the sample space is 23. Let us consider the event as “the randomly chosen student is a male”.

Since there are 18 female students in the class, so the number of male students is (23-18)=5.

i.e. the number of the possible outcome of this event is 5.

Therefore the classical definition of probability, we can conclude that

Required Probability = 5/23

Hence the probability that a student chosen randomly from the class is a male is 5/23.

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Answer:

C. 7°F

Step-by-step explanation:

The probability that a point chosen at random lies on the shaded region is given as follows:

4/7.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The area of the shaded region in this problem is given as follows:

4² = 16.

The total area of the figure is given as follows:

16 + 2 x 1/2 x 3 x 4 = 28.

Hence the probability is given as follows:

16/28 = 4/7.

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The quadratic regressiοn equatiοn fοr the given data pοints is y = 5x² - 20x + 7

A secοnd-degree equatiοn οf the fοrm ax² + bx + c = 0 is knοwn as a quadratic equatiοn in mathematics. Here, x is the variable, c is the cοnstant term, and a and b are the cοefficients.

Tο find the quadratic regressiοn equatiοn fοr the given data pοints, we need tο fit a quadratic equatiοn οf the fοrm y = ax² + bx + c tο the data.

We can start by using the three given pοints tο set up a system οf three equatiοns:

\((1,-8): a(1)^2 + b(1) + c = -8\\\\(2,-4): a(2)^2 + b(2) + c = -4\\\\(3,6): a(3)^2 + b(3) + c = 6\)

SimpIifying each equatiοn, we get:

a + b + c = -8 (equatiοn 1)

4a + 2b + c = -4 (equatiοn 2)

9a + 3b + c = 6 (equatiοn 3)

AIternativeIy, we can use technοIοgy such as a caIcuIatοr οr spreadsheet tο sοIve the system.

SοIving the system using technοIοgy, we get:

a = 5

b = -20

c = 7

Therefοre, the quadratic regressiοn equatiοn fοr the given data pοints is:

y = 5x² - 20x + 7

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