I need help with particular type of psat math question . I'm really struggling pls help me. ​

The solution is Option A.

The amount after 9 years with an investment of $ 7000 at a simple interest calculated quarterly at rate 2.05 is $ 7,322.88

What is Simple Interest?

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the simple interest be represented as I

Now , the amount invested P = $ 7,000

The rate of interest R = 2.05 %

The time period t = 9 years

Since the interest is calculated quarterly , t= T/4

Now , the simple interest is calculated by the formula

Simple Interest = ( Principal Amount x Rate x Time Period ) 100

Substituting the values in the equation , we get

Simple Interest I = [ ( 7000 x 2.05 x 9 ) / 4 ] / 100

On simplifying the equation , we get

Simple Interest I = ( 129150 ) / 400

Simple Interest I = $ 322.875

I = $ 322.88

Now , the amount after 9 years = initial amount P + Interest I

Amount after 9 years = 7,000 + 322.88

Amount after 9 years = $ 7,322.88

Hence , the amount after 9 years is $ 7,322.88

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Answer:

-3/4

Step-by-step explanation:

equation of a line : y=mx+c

m= slope= 4/3

perpendicular slope is the inverse of m

this is because m1 * m2 = -1

thus perpendicular slope = -3/4

Answer:

x = 1.28

Step-by-step explanation:

Given equation:

[tex]3 \frac{1}{2}x-6=2-2\frac{3}{4}x[/tex]

Add 2³/₄x to both sides of the equation:

[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6=2-2\frac{3}{4}x+2\frac{3}{4}x[/tex]

[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6=2[/tex]

Add 6 to both sides of the equation:

[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6+6=2+6[/tex]

[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x=8[/tex]

Rewrite the mixed numbers as improper fractions:

[tex]\implies \dfrac{3 \cdot 2+1}{2}x+\dfrac{2 \cdot 4+3}{4}x=8[/tex]

[tex]\implies \dfrac{7}{2}x+\dfrac{11}{4}x=8[/tex]

Make the denominators of the fractions the same:

[tex]\implies \dfrac{7 \cdot 2}{2 \cdot 2}x+\dfrac{11}{4}x=8[/tex]

[tex]\implies \dfrac{14}{4}x+\dfrac{11}{4}x=8[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{14+11}{4}x=8[/tex]

[tex]\implies \dfrac{25}{4}x=8[/tex]

Multiply both sides by 4:

[tex]\implies 4 \cdot \dfrac{25}{4}x=4 \cdot8[/tex]

[tex]\implies 25x=32[/tex]

Divide both sides by 25:

[tex]\implies \dfrac{25x}{25}=\dfrac{32}{25}[/tex]

[tex]\implies x=\dfrac{32}{25}[/tex]

Convert the improper fraction to a mixed number:

[tex]\implies x=1 \frac{7}{25}[/tex]

The value of x as a decimal:

[tex]\implies x=1.28[/tex]

The work is done in pumping a full tank of water up to ground level is 470400πNm.

Tank sizes variety from 6 ft. to one hundred twenty ft. in diameter with a roof, and as much as two hundred toes in diameter as an open pinnacle tank. Tanks with a roof have capacities starting from seven-hundred gallons to 500,000 gallons at the same time as the open pinnacle tanks may be constructed with even large capacities

The radius of the layer = 2m

V= pi (2)^2 (Delta y) m^3 = four pi Delta y m^3V=π(2) 2 (Δy)m 3 =4πΔym 3

Weight of the layer =9800 (four pi Delta y)=9800(4πΔy)

Weight of the water = 9800 frac=9800 m 3 N

So, weight of the layer = 39200 pi Delta y=39200πΔy

distance layer is moved =5-y=5−y

W=int_^{four} (5-y)(39200 pi dyW=∫ 04 (5−y)(39200πdy

=39200 pi int_^{four} (5-y) dy=39200π∫ 04 (5−y)dy

=39200 pi left[ 5y - frac y^2 right]_^{four}=39200π[5y− 21 y 2 ] 04

=-39200 pi (12) = 470400 pi Nm=−39200π(12)= 470400πNm.

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Answer:

m ≥ 28.5

Step-by-step explanation:

He wants to bike at least 28.5 miles, like he did last year

also whats up with the anime tab TT no judgement tho

The correct answer for question 1 is C) CA=XY

Two triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal in measure.

Given here ΔABC≅XYZ

Therefore AB=XY , BC=YZ , AC=XZ  & ∠A=∠X , ∠B=∠Y , ∠C=∠Z but clearly CA≠XY

The full diagram is attached please refer to the diagram for clarity

Hence, option c is the correct answer.

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The two possible solutions for the given equation are -

[x] = 0.696 and [x] = 3.054.

Given is the equation as follows -

6(x - 3).2(4x - 3) = 6

We have the equation as -

6(x - 3).2(4x - 3) = 6

12(x - 3)(4x - 3) = 6

(x - 3)(4x - 3) = 6/12

(x - 3)(4x - 3) = 1/2

x(4x - 3) - 3(4x - 3) = 1/2

4x² - 3x - 12x + 9 = 1/2

4x² - 15x + 9 = 1/2

2(4x² - 15x + 9) = 1

8x² - 30x + 18 = 1

8x² - 30x + 17 = 0

(x - 0.696)(x - 3.054) = 0

(x - 0.696) = 0     and     (x - 3.054) = 0

x = 0.696     and    x = 3.054

Therefore, the two possible solutions for the given equation are -

[x] = 0.696 and [x] = 3.054.

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Answer:

To find the perimeter of triangle ABC, we need to find the lengths of all three sides of the triangle. To do this, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of ((x2 - x1)^2 + (y2 - y1)^2).

Applying this formula, we can find the lengths of the sides of the triangle as follows:

AB = sqrt((7 - (-1))^2 + (-6 - (-6))^2) = sqrt(8^2 + 0^2) = sqrt(64) = 8

BC = sqrt((3 - 7)^2 + (-3 - (-6))^2) = sqrt(-4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5

AC = sqrt((-1 - 3)^2 + (-6 - (-3))^2) = sqrt(-4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5

Thus, the perimeter of triangle ABC is 8 + 5 + 5 = 18 units.

If Mark’s mother borrows the money of $25,000 from company 2 which offers a rate of 8.5% for 3 years, she needs to pay the charge of $6375.

Interest is the cost of borrowing or saving money. Simple interest is an easy method to calculate the interest charge on a loan.

As its name, calculating the simple interest is simple and quick. We only multiply the money we borrow or deposit, by the period, then multiply them by the interest rate applied by the bank or any financial institution chosen.

The formula for calculating the simple interest is

P x R x T

P means principal or how much money we borrow or save

R means rate or how many percentages of interest applied

T means time or how long we borrow or save the money

By using the formula mentioned before, the simple interest would be

$25,000 x 8.5% x 3  = $6375

Thus, the amount of simple interest paid is $6375 and the total amount paid is $25000 + $6375 = $31,375

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Answer:

7.6u+7

Step-by-step explanation:

7.6u-(30/6)+12

30/6=5

7.6u-5+12

7.6u+7

The graph that represents Ramon's initial step is, On a coordinate plane, the point (0, 3) is graphed.

The ordinate and abscissa of the x coordinate, along with two values specified in parentheses in a specific order, make up an ordered pair.

Pair in Order = (x, y) where x represents the abscissa, the measure of a point's separation from the main axis, and y represents the ordinate, the measure of a point's separation from the secondary axis.

Given, Ramon is graphing the function f(x) = 3 + (4)x.

We know the initial value of a function is determined when the independent variable is set to zero.

Here the independent variable is 'x'.

Now, at x = 0,

f(0) = 3 + (4)(0).

f(0) = 3.

So, The ordered pair is (0, 3).

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Answer:

a

Step-by-step explanation:

Answer:

I believe that the answer is 2/5 because all of the other answers equal 10 (for b and c) or 20 (for a)

Step-by-step explanation:

Answer:

the answer is yes because angles 5 and 2 are same side interior angles and same side interior angles add up to 180*.

Step-by-step explanation:

Make sure not to be fooled by the "it looks like it" theorem.  Teachers will try to trick you by making the lines look not parallel.  All you need to look at are if the angles are congruent or supplementary based on the theorems you hopefully were taught in class.  Wow what has brainly done I sound like a teacher lol.

The library ha enough DVD’ to diplay equal number of them in group of 3, 5, or 9. then the least number of DVD the library can have is 45

What is the function of DVD?

Short for digital versatile disc or digital video disc, a DVD or DVD-ROM is a disc capable of storing a significant amount more data than a standard compact disc. DVDs are widely used for storing and viewing movies and other data.

45 is the least common multiple of 3, 5, and 9.

45 can be equally divided by 3, 5, and 9:

45 ÷ 3 = 15

45 ÷ 5 = 9

45 ÷ 9 = 5

the least number of DVD the library can have  is 45

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For the data  12, 14, 21, 19, 25, 29, 26, 21, 15, and 18.

the mean is 20

the standard deviation is 3.7

the interquartile is 10

For the data  12, 14, 21, 19, 25, 29, 26, 21, 15, and 18. the mean is calculated as follows

= sum of data / number of data

sum = 200

number of data = 10

mean (x bar)  = 200 / 10

= 20

standard deviation

standard deviation is the square root of  the ratio of sum of squares to number of samples

sum of squares = (x - x bar)²

= (12 - 20)² + (14 - 20)² + (21 - 20)² + ......+(21 - 20)² + (15 - 20)² + (18 - 20)²

= 274

standard deviation = √(274 / 20) = 3.7

Interquartile range = upper quartile - lower quartile

raw data = 12, 14, 21, 19, 25, 29, 26, 21, 15, and 18

arranged data =  12, 14, 15, 18, 19, 21, 21, 25, 26, 29,

upper quartile = 25

lower quartile = 15

Interquartile range = 25 - 15 = 10

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The probability of a intersection b, represented by P(a ∩ b) is equal to 0.07.

One of the axioms of probability states that is two events say A and B are independent that is the probability of occurrence of one of them is not affected by the occurrence of the other, then P(A ∩ B) = P(A) × P(B)

We have from the question two events a and b which are said to be independent events,

P(a) = 0.35

P(b) = 0.20

then;

P(a ∩ b) = 0.35 × 0.20

P(a ∩ b) = 0.07

Therefore, the value 0.07 is the probability of the intersection of the two independent events a and b.

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Answer:

El valor de la variable b se corresponde con:

  a) b = 0,25

  b) b = 9

  c) b = 125

If the customer purchases every pack of 12 which the shop has 192 plates in stock.

Total number of  packs of plates = 54.

The set are either sets of 8 or sets of 12.

Let x represent the overall number of 12-plate packets.

There will therefore be in total packs of 8 plates: 54 - x.

Thus,

8(54−x) + 12x = 496

432 − 8x + 12x = 496

4x = 64

x = 16

Thus, there are 16 packs of 12 plates in the store.

So, if a consumer purchases all of the 12-packs of plates, he will ultimately purchase 1216 = 192 plates.

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Step-by-step explanation:

4xy + 4x² + 8x

Can also be rearranged as

4x²+8x+4xy

The depth of water in the cylinder is 20 cm

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

Volume = 628 litres

Radius = 1 m

Convert litres and meters to cm cube and cm

So, we have the following representation

Volume = 628000 cm cubed

Radius = 100 cm

The volume is the calculated as

V = πr²h

So, we have

628000 = 3.14 * 100² * h

Evaluate

628000 = 31400 * h

Divide by 31400

h = 20

Hence, the height is 20 cm

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Answer:7/8

Step-by-step explanation:your mom

Answer:

Step-by-step explanation:

я хз

The weight of Kevin's parcel is 60 g.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, a postage fee of Rs 2 for each gram of the weight of a parcel and an additional flat rate of Rs 30. and Kevin's postage fee was 150 less than 5 times the weight of his parcel,

Let the weight of the parcel be x

Establishing the equations,

5x - 150 = 30 + 2x

5x - 2x = 30 + 150

3x = 180

x = 180/3

x = 60

Hence, the weight of Kevin's parcel was 60g

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Answer:

x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees.

Step-by-step explanation:

The ratio of the same side interior angles of two parallel lines is 1:14, which means that for every one degree of the first angle, the second angle measures 14 degrees. If the first angle is x degrees, then the second angle is 14x degrees.

Since the lines are parallel and the angles are on the same side of the transversal, the alternate interior angles are congruent, so the measure of the third angle is also x degrees, and the measure of the fourth angle is also 14x degrees.

Since the lines are parallel, the alternate exterior angles are also congruent, so the measure of the fifth angle is also x degrees, and the measure of the sixth angle is also 14x degrees.

Finally, the measures of the seventh and eighth angles can be found by adding the measures of the adjacent angles. The seventh angle is adjacent to the third and fifth angles, so its measure is x + x = 2x degrees. The eighth angle is adjacent to the fourth and sixth angles, so its measure is 14x + 14x = 28x degrees.

In summary, the measures of the eight angles formed by the parallel lines and transversal are x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees. The value of x can be determined by knowing the measure of one of the angles, or by using other information about the angles or the parallel lines.

The expected profit, in cents, for a player who plays 1 game is 5.25 cents.

The distribution that models the profit of a player for a single game is given as follows:

P(X = -4 cents) = 0.25. -> pays 5 cents, wins 1 cent, loses 4 cents.

P(X = 0 cents) = 0.25. -> pays 5 cents, wins 5 cents.

P(X = 5 cents) = 0.25. -> pays 5 cents, wins 10 cents.

P(X = 20 cents) = 0.25. -> pays 5 cents, wins 25 cents.

The expected value of a discrete distribution is computed by adding the total of each outcome and multiplying it by its probability, as follows:

E(X) = -4 x 0.25 + 0 x 0.25 + 5 x 0.25 + 20 x 0.25

E(X) = 5.25 cents.

Hence, the expected profit is 5.25 cents

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Option A is the correct answer. All the eigenvalues of a real symmetric matrix are always real.

Symmetrix matrix: A matrix is said to be a Symmetrix matrix if A=A^T the matrix should be equal to the transpose of A.

All the eigenvalues of the Symmetric matrix are real. Eigenvectors corresponding to distinct eigenvalues are orthogonal.

Skew-Symmetrix matrix: A matrix 'A' is said to be a Skew-Symmetrix matrix if A=-A^T

Eigenvalues of the skew-symmetric matrix are zero or purely imaginary.

Skew-Hermitian matrix: A square matrix is said to be a Skew-Hermitian matrix if it is equal to the negotiation of its complex conjugate transpose.

A=-(A)^T

Eigenvalues of the Skew-Hermitian matrices are zero or imaginary.

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The vector field F = [tex](3x^2y + z^3, x^3 + 2yz, y^2 + 3xz^2)[/tex] has a nonzero divergence and a nonzero curl, indicating that it is not a conservative vector field. F cannot be expressed as the curl of another vector field.

To compute the divergence of F, we take the partial derivatives of each component with respect to their corresponding variables and sum them up. The divergence of F is given by div(F) = ∇·F = (∂/∂x)[tex](3x^2y + z^3)[/tex] + (∂/∂y)[tex](x^3 + 2yz)[/tex] + (∂/∂z)[tex](y^2 + 3xz^2)[/tex]. Evaluating these partial derivatives, we find div(F) = 6xy + 3z^2 + 2yz + 6xz.

To compute the curl of F, we take the curl operator (cross product of the del operator with F) and expand the determinant. The curl of F is given by curl(F) = ∇×F = (∂/∂y)[tex](y^2 + 3xz^2)[/tex] - (∂/∂z)[tex](x^3 + 2yz)[/tex], (∂/∂z)[tex](3x^2y + z^3)[/tex] - (∂/∂x)[tex](y^2 + 3xz^2)[/tex], (∂/∂x)[tex](x^3 + 2yz)[/tex] - (∂/∂y)[tex](3x^2y + z^3)[/tex]. Simplifying these expressions, we obtain curl(F) = [tex](-2xz, -3z^2, -6xy)[/tex].

The divergence of F is nonzero, indicating that F does not satisfy the divergence theorem, which states that a vector field with zero divergence is conservative. Additionally, the curl of F is nonzero, indicating that F does not satisfy the curl theorem, which states that a vector field with zero curl is conservative. Therefore, F is not conservative and cannot be expressed as the curl of another vector field.

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Here every 50th candy bar is tested . It is a sampling interval .

What does "systematic sampling" mean?

Systematic sampling is a probability sampling technique where researchers choose individuals from the population at regular intervals, such as every 15th person on a population list.

                       The advantages of simple random sampling can be imitated if the population is arranged randomly.

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval.

Here every 50th candy bar is tested . It is a sampling interval .

Therefore he use systematic sampling plan.

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Answer:

substitute a=-5 and c=5 into a=-3c

Step-by-step explanation:

a= -3c

(-5)= -3(5)

-5= -15

The numbers of hours taken to fill the order if the number of working machines decreased by a factor of 2 is; 44 hours

We are given;

Numbers of hours a work is complete by 6 machines = 22 hours

Now, we know that the number of hours required to complete a work is inversely proportional to the number of machines used.

Therefore, If the number of working machines decreased by a factor of 2, then the number of hours will be increased twice.

Therefore, we can say that;

The numbers of hours taken to fill the order = (22 * 6)/3

= 44 hours

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Answer:

To find the reflection of a function across the x-axis, we simply need to change the sign of the y-coordinates of the function's points. Therefore, the reflection of f(x) = 4x + 10 across the x-axis is g(x) = -(4x + 10) = -4x - 10.

Step-by-step explanation:

To find the reflection of a function across the x-axis, we can follow these steps:

Here is an example of how this works in practice. Let's say that the original function f(x) has the points (1,14) and (2,18).

The reflection of these points across the x-axis would be (1,-14) and (2,-18), respectively.

To find the equation of the reflected function g(x), we would simply substitute these points into the equation from step 3 to get g(x) = -4x - 10.

A continuous time system can behave roughly throughout a variety of periods using a discretized state matrix. A continuous time condition matrix should be used in its place if these requirements are not satisfied since a discretized state matrix might not adequately depict the performance of a continuous time system.

A continuous time condition matrix is a matrix that is used to indicate the state of a system at any moment, as opposed to a discretized state matrix, which is used to describe the status of a system at discrete time intervals. Under the following conditions, a discrete-time state matrix is identical to a time series state matrix:

The system may be regarded as being in stable equilibrium at each time point since the time gaps between every discretization are short enough. This indicates that the behavior of the system does not drastically vary from one-time point to the next.

Over the time frames between each discretization, a linear model accurately predicts the behavior of the system. This means that the behavior of the system can be precisely predicted by a linear equation of the type "Ax = Bu," where A as well as B are matrices and x as well as u are vectors that, respectively, represent the system's state and input.

Over the intervals between each discretization, the system's input remains constant. This indicates that the system's input does not drastically vary from one-time point to the next.

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