You put $12,984 into an investment at 6.12% for seven and a half years. What will the balance be at the end of seven and a half years?

The measure of the arc 13cm long with a radius = 1  is 13rad

The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.

Length of an arc = ∅/360 x 2πr

where ∅ = subtended angle in degree

r = 1 = radius of the complete circle

length = 13

13 =  ∅ /360 x  2 x π x 1

but 2π rad = 360  degrees

substitute  2π rad  for 360 into the equation

13 =  ∅/2π rad  x 2 x π x 1

By cross multiplying

∅ = 13 x 2π rad / 2 x π

∅ = 13 rad

In conclusion, the angle subtended by the arc in radians is 13 rad.

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Step-by-step explanation:

Using Vieta's formula

x²-(sum of roots)x+(product of roots)=0

x²-(5+-1)x+(5×-1)=0

x²-4x-5=0

Alternatively,

if the zeros are 5 and -1 then the quadratic factorizes to (x-5)(x+1) Now expand it

x²+x-5x-5=0

x²-4x-5=0

Identify a quadratic function in standard form with zeros 5 and -1

x (2) + (2)x - 15 = 0

X=3 and x= -5

(x - 3) = 0 and (x + 5) = 0

Answer:

Step-by-step explanation:

Answer: -1.75

Step-by-step explanation: -7 + 5 + (-9) + 4 = -7, then -7÷4=-1.75

If you dealt 4 cards from a shuffled deck of 52 cards without replacement.

The probability that all 4 cards are face cards is 0.00182842367.

The face cards are the King, Queen, and Jack (sometimes known as the Knaves). There are 12 face cards in the 52-card deck of playing cards.

The cards are drawn without replacement,

The probability of getting a face card in first draw is 12/52.

As it is without replacement, in the second draw the probability is 11/51.

In third draw, it is 10/50.

In the fourth draw the probability is 9/49.

We have to draw all the four cards, so we multiply the probabilities, to get the final probability.

=12/52x 11/51 x 10/50 x 9/49

=0.00182842367.

Hence the answer is, the probability that all 4 cards are face cards is 0.00182842367.

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7.5 2. debt payments of $700 in two months and $800 in five months are scheduled to be due. If interest at 8.3% is allowed, what single payment today is required to settle the two scheduled payments.

Single payment today is required to settle the two scheduled payment is $1,948.2.

Given Payments of two months = $700

Payments in five months = $800

Interest rate = 8.3%

To find : Single payments of two scheduled payments

Solution:

Interest for 1 month for $700

        = $700 x 8.3%

        = 58.1

Thus, for two months

Interest = 2 x $58.1 = $116.2

Now interest for 1 month for $800

       = $800 x 8.3%

       = $66.4

Thus, for five months

Interest = 5 x $66.4

       = $332

Now total Payments:

       = ($700 + $116.2) + ($800 + $332)

       = $1,948.2

Hence, single payment today is required to settle the two scheduled payment is $1,948.2.

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The equation relating C to S will C = 7500+175S and the total cost to transport 14 tons of sugar is $9950.

According to the question,

We have the following information:

It will cost $7500 to rent trucks, and it will cost an additional $175 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported.

So, we have the following expression:

C = 7500+175S

Now, when S = 14, then the total cost will be:

C = 7500+175*14

C = 7500+2450

C = $9950

Hence, the equation relating C to S will C = 7500+175S and the total cost to transport 14 tons of sugar is $9950.

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A correlational study can produce one of three outcomes: a positive correlation, a negative correlation, or no correlation at all. A measure of how closely two or more variables are related to one another is known as correlation.

A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate).It's a common method for describing simple relationships without mentioning cause and effect explicitly. Correlation is a measure of how strongly two variables are related, but it also refers to association. There are three possible results from a correlational study: a positive correlation, a negative correlation, or no correlation at all.

A measure of how closely two or more variables are related to one another is known as correlation.

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Answer:

45 minutes

Step by step explanation:

60min ÷ 56miles × 42miles = 45mins

Answer:

A

Step-by-step explanation:

The equation that models the scenario is:

80 = 8x + 10y

Where x is the number of pounds of almonds and y is the number of pounds of cashews.

We know that almonds cost $8 per pound and Cashews cost $10 per pound, so if you buy x pounds of almonds and y pounds of cashews, the total cost is:

c(x, y) = x*$8 + y*$10

Now we know that Tamira has $80 to spend, so the total cost will be equal to $80, then the equation that models this scenario is:

$80 = x*$8 + y*$10

Or, removing the units:

80 = 8x + 10y

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The number of possible combinations Miranda can make from his box is 240

The number of jewelry in Miranda box are given as

Necklaces = 8

Earrings = 10 pairs

Bracelets = 3

The number of possible combinations is the product of the above parameters

So, we have

Number of possible combinations = 8 * 10 * 3

Evaluate the products

So, we have

Number of possible combinations = 240

Hence, the number of possible combinations = 240

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The number of permutations and combinations possible for the formation is: [tex]^{31}C_{11} \times ^{12}C_3 \times ^{3}C_1 \times ^{9}C_4 \times ^{7}C_3[/tex]

What are permutations and combinations?

By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.The act of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the elements of a set if the set is already ordered. Nearly all areas of mathematics involve permutations in some form or another. They frequently appear when various orderings on particular finite sets are taken into account.

In the given question: we have;

Total number of PLayers = 31;

Number of goalkeeper = 3;

Number of Defender = 12;

Number of Midfielders = 9;

Number of Strikers = 7;

We have to select 11 players

and in that we should have 3 defenders; 4 midfielders, 3 strikers, and 1 goalkeeper;

So the permutation and combination possible for choosing a defender from 12 players are: [tex]^{12}C_3[/tex]

and,

The number of permutations and combinations possible for choosing 1 goalkeeper are: [tex]^{3}C_1[/tex]

A number of permutations and combinations possible for choosing 4 midfielders are: [tex]^{9}C_4[/tex]

The number of permutations and combinations possible for choosing 3 strikers are: [tex]^{7}C_3[/tex]

So, the total number of ways possible is: [tex]^{31}C_{11} \times ^{12}C_3 \times ^{3}C_1 \times ^{9}C_4 \times ^{7}C_3[/tex]

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Answer:

249.40 Option b

Step-by-step explanation:

When multiplying 21.5 x 11.60 you get $249.40

Answer:

The area of the shape is 396 square cm.

Step-by-step explanation:

Compared with the beam, the large cube has the same volume but a smaller surface area.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

Given that, there are two sets of eight blocks, each with an edge measurement of 1 cm. Two blocks are placed on top of two other blocks to form a big cube. You assemble the second set into a 1-by-8-block straight beam.

Since the volume is the same.

The surface area of a cube,

=6a²

=6(2)²

=6×4

=24 cm²

The surface area of a beam,

=1 × 8

=8 cm²

Thus, compared with the beam, the large cube has the same volume but a smaller surface area.

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The y-intercept of the coordinate plane is y = -5/16x+32

To find the equation or y-intercept, we fist need to find the slope of the equation.

The intercept form of the equation is given by

y-y1 = m(x-x1)

The slope can be find as

m = (y2-y1)/(x2-x1)

Let us consider two points as

x1 = 32, y1 = 22

x2 = 48. y2 = 17

Substitute the values to get the slope

m = (17-22)/(48-32) = -5/16

Now substitute the values to find y-intercept

(y-22) = -5/16(x-32)

⇒ y-22 = -5/16x+10

⇒ y = -5/16x+10+22

⇒ y = -5/16x+32

Hence, y intercept of the given points are y = -5/16x+32

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The difference in the payments of Oscar and Felix is given as follows:

$56.

The payment for each of Oscar and Felix is obtained applying proportions, with the multiplication of the finance charge by each of the rates.

As stated in the problem, the balance is of:

800.

Felix rate is of:

14%.

Hence the finance charge for Felix is of:

0.14 x 800 = 112.

Oscar rate is of:

21%.

Hence the finance charge of Oscar is of:

0.21 x 800 = 168.

Then the difference in the payments will be of:

168 - 112 = $56.

Felix and Oscar applied for the same credit card from the same bank. The bank checked both of their FICO scores. Felix had an excellent credit rating, and Oscar had a poor credit rating.

The rates are given as follows:

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The probability is 1/3 of the given event .

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

There are 52×51 outcomes when you draw 2 cards one after another without returning the first drawn card to the deck.

There are 48×4 outcomes when the first card is not Ace and the second card is Ace. There are 4×3 outcomes when both cards are Ace. The total outcomes are 48×4+4×3=51×4.

The probability is 51×452×51=51/52×4/51=4/52=1/3.

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Answer: 238

Step-by-step explanation:

Bit hard to explain but after some work this is what I got

Hope this helps :)

The percentage error of Bob’s measurement is 3.87%

The percentage error is The difference between the estimated value and the actual value in relation to the actual value is given as a percentage. Analyst use this formula to determine how big is the error in a relation to true value.

Percentage error can be calculated by the given formula

percentage error=((Exprimental value-Actual value))/(Actual value)∙100

Here, given that

The experimental volume of liquid is 18.8 ml, and the actual volume of liquid is 18.1 ml

i.e. exprimental volume=18.8 mL

and, actual volume=18.1 mL

Now, we will calculate the percentage error

So,

percntage error=((18.8-18.1))/18.1∙100

percentage error=0.7/18.1∙100

percentage error=0.0387∙100

percentage error=3.87%

Hence,

       We got percentage error of 3.87% in measurement

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Using conversion of improper fraction to a decimal, we find that she bought 18.32 pounds of meat, which is a terminating decimal.

acc to our question-

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Solving the absolute value equation, it is found that:

The absolute value equation for this problem is given as follows:

p(t) = 0.165| t - 60 | + 4.8.

In which the variables are:

This percentage was of 13% when:

p(t) = 13.

Hence:

p(t) = 0.165| t - 60 | + 4.8.

13 = 0.165| t - 60 | + 4.8.

0.165| t - 60 | = 8.2.

|t - 60| = 8.2/0.165

|t - 60| = 49.7.

Then the solutions are as follows:

For the percentage of four percent, we have that:

4 = 0.165| t - 60 | + 4.8.

0.165| t - 60 | = -0.8.

The absolute value equation can never assume a negative value, hence the percentage will never be of 4%.

The equation is:

p(t) = 0.165| t - 60 | + 4.8

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Answer:

In order to answer this question, the amount she makes must be provided.

a. The vertical height is y = 100tSinθ - (1/2)9.8t².

b. Time of flight is t = 200sin(theta)/9.8.

A projectile motion is a type of motion that an object or particle experiences when it is launched into a gravitational field, such as from the surface of the Earth, and proceeds along a curved route only under the influence of gravity.

We know At any time t, a projectile's horizontal and vertical displacement are x = V₀tCos θ where V is the initial velocity, θ is the launch angle

y = V₀tSinθ - (1/2)gt².

Given ball was hit with an initial velocity of 100 feet per second

∴ Height in feet is

y = 100tSinθ - (1/2)9.8t².

The time for which the ball will stay in the air is a time of flight which is given by the formula t = 2v₀sin(theta)/g.

t = 200sin(theta)/9.8.

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The graph has rotational symmetry about the y-intercept and y-intercept is 0 when x = 0

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The graph of the function is given:

From the graph:

The graph has rotational symmetry about the y-intercept

The y-intercept is 0 when x = 0

Thus, the graph has rotational symmetry about the y-intercept and y-intercept is 0 when x = 0

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Answer:

Step-by-step explanation: