Can someone help me please

A bank loaned out $25,000, part of it at the rate of 3% annual interest, and the rest at 9% annual interest. The total interest earned for both loans was $1,770.00. How much was loaned at each rate?


$----------- was loaned at 3% and

$-----------was loaned at 9%.

Answer:

multiplication property of equality. Hope this help and maybe a brainlist?

Step-by-step explanation:

Answer:

multiplication property of equality

Step-by-step explanation:

d/10=12

Multiply both sides by the equation by 10

10× d/10=10×12

Reduce the numbers by the greatest common factor which is 10

d=10×12

Multiply 10 and 12

d=120

So using multiplication to solve this equation

Jacob's body metabolizes caffeine at a rate of 13.5% per hour.

a)Jacob's body will takes 4.77 ~5 hours to metabolize half of the 96 mg of caffeine.

b) If Jacob consumes an energy drink with 212 mg of caffeine in it, Jacob's body will take 4.77948 ~ 5 hours to metabolize half of the 212 mg of caffeine.

c) Jacob consumes a cup of coffee with c mg of caffeine in it. Jacob's body will take 4.77948~ 5 hours to metabolize half of the c mg of caffeine.

The volume will slowly decrease at regular intervals and at a regular rate. This growth reduction is calculated using the exponential decay formula. The general form is y = a(1- r)ᵗ

We have, decay rate r = 13.5 % = 0.135

Initial value , a = 96 mg

plugging the value in formula we get,

y = 96(1 - 0.135)ᵗ --(1)

Now, Half of 96 is 48

so, 48 = 96(0.865)ᵗ --(2)

dividing equation by 96 we get

=> 48/96 = (0.865)ᵗ

taking natrual logarithm both sides,

=> ln(1/2) = ln ((0.865))

=> ln(1/2) = t In (0.865)

=> t = ln(1/2)/In (0.865)

=> t = 4.77948

Since, decay rate is constant so, half never changes for any .

a) 4.779~5 hours, long will it take for Jacob's body to metabolize half of the 96 mg of caffeine.

b) Jacob's body to metabolize half of the 212 mg of caffeine is 4.779~ 5 hours.

c) for Jacob's body to metabolize half of the cmg of caffeine is 4.77948.. So, we have 4.77948 ~ 5 hours is decay constant rate.

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Answer:

SURFACE AREA: 21.02

VOLUME: 6.396

Step-by-step explanation:

SURFACE AREA:

2x2.4x1.6=7.68

2x1.6x1.3=4.16

2.4x1.3=3.12

2x1.5x1.3=3.9

2x1/2x2.4x0.9=2.16

7.68+4.16+3.12+3.9+2.16=21.02

VOLUME:

2.4x1.3x1.6=4.992

1/2x0.9x2.4x1.3=1.404

4.992+1.404=6.396

Answer: 0.9554

Step-by-step explanation:

Let \(\overline{X}\) be the sample mean.

Given: Mean weight\((\mu)\) of an adult is 65 kilograms with a standard deviation\((\sigma)\) of 13 kilograms.

Sample space = 92

The probability that the sample mean would be greater than 62.7 kilograms:

\(P(\overline{X}>62.7)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{62.7-65}{\dfrac{13}{\sqrt{92}}})\\\\=P(Z>-1.70)\\\\=P(Z<1.70)\ \ \ \[P(Z>-z)=P(Z<z)]\\\\=0.9554\)[ By p-value table]

Hence, the required probability= 0.9554

The length of side AB  of this rectangle is 5 units

The cooridnates of the rectangle are given as:

A(-8, -6), B(-3,-6), C(-3, -4), and D(-8, -4).

The length of side AB is calculated as;

AB = √(x1 - x2)^2 + (y1 - y2)^2

This gives

AB = √(-8 + 3)^2 + (-6 + 6)^2

Evaluate

AB = 5

Hence, the length of side AB  of this rectangle is 5 units

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Complete question

Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-8, -6), B(-3,-6), C(-3, -4), and D(-8, -4).

Given these coordinates, what is the length of side AB of this rectangle?

The expression useful to find the surface area of the given triangular prism is 2(1/2·3·4) + 4·2 + 3·2 + 5·2 thus, option (C) is correct.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

In other meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.

As per the given triangular prism,

2 sides of the prism are right-angle triangles.

The area of right-angle triangle = (1/2) x base x height

2 triangle thus, area = 2(1/2·3·4)

Three sides of the prism are rectangles,

Total area of this three sides =  4·2 + 3·2 + 5·2

Total area = 2(1/2·3·4) + 4·2 + 3·2 + 5·2

Hence "The expression useful to find the surface area of the given triangular prism is 2(1/2·3·4) + 4·2 + 3·2 + 5·2".

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Answer:

\(x^2 - 3x -10 = 0\)

Step-by-step explanation:

Given

Roots = -2 and 5

Required

Write the equation

We have that:

x = -2 and x = 5

Simplify further

x + 2 = 0 or x - 5 = 0

Multiply the results of the above

\((x + 2)(x - 5) = 0\)

Open brackets

\(x^2 + 2x - 5x -10 = 0\)

\(x^2 - 3x -10 = 0\)

Austin's rate of motion is (1/70)π Radians per second.

To determine Austin's rate of motion in radians per second, we need to use the formula for angular velocity:

ω = Δθ / Δt

Where:

ω = angular velocity (in radians per second)

Δθ = change in angular displacement (in radians)

Δt = change in time (in seconds)

We know that Austin runs three-quarters of a circular track, which means he covers an arc length that is equal to three-quarters of the circumference of the circle. Let's call the radius of the circle "r". Then, the arc length covered by Austin is given by:

s = (3/4) * 2πr

s = (3/2)πr

We also know that it takes Austin 1 minute and 45 seconds to cover this distance. This is the same as 105 seconds (since 1 minute = 60 seconds).

So, Δt = 105 seconds

Now, we can calculate the change in angular displacement (Δθ). The total angle around a circle is 2π radians, so the angle covered by Austin is given by:

Δθ = (3/4) * 2π

Δθ = (3/2)π

Therefore, Austin's rate of motion (ω) in radians per second is:

ω = Δθ / Δt

ω = [(3/2)π] / 105

ω = (3/210)π

ω = (1/70)π radians per second

So, Austin's rate of motion is (1/70)π radians per second.

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Answer:

I WILL SAY D

Step-by-step explanation:

The values of x is 6 and y is (-6).

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

-4x-5y=6............(1)

9x+7y=12..................(2)

Solving Equation (1) and (2) we get

-36 x  - 45y = 54

36x + 28y = 48

____________

         -17y= 102

              y= -6.

and, -4x -5y= 6

-4x - 5(-6) = 6

-4x + 30 = 6

-4x = 6-30

-4x = -24

x= 6

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Answer:

22.5

Step-by-step explanation:

22.5 x 3 = 67.5

67.5 + 22.5 = 90

Answer:

The first one!

Step-by-step explanation:

Answer:

The first one

Step-by-step explanation:

All of them can be divided by 7, which make them proportional.

7/7=1, 14/7=2, 28/7=4, and 35/7=5

The half life of the radioactive substance is 10.22 years.

Half Life is the amount of time needed by the radioactive substance to reduce to its half concentration (as compared to the initial concentration).

It is given that

y = ae⁻ᵇˣ

here a is the initial amount , y is the amount remaining after x years

a = 90mg at x =0

Value of y = 12.6 mg at x = 29 years

On substitution of value

12.6 = 90 e⁻²⁹ᵇ

0.14 = e⁻²⁹ᵇ

b = 0.0678

The equation is

\(\rm y = 90 e^{-0.0678 * x}\\\)

Half life is when the concentration is reduced to half

On 1st half life , the concentration = 90/2 = 45 mg

\(\rm 45 = 90 e^{-0.0678 * x}\\\)

x = 10.22 years

Therefore the half life of the radioactive substance is 10.22 years.

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Answer:

d = 5 is a solution to the equation 13 - d = 8

Step-by-step explanation:

We have to solve 13 - d = 8

Now,

13 - d = 8,

We add d on both sides,

13 - d + d = 8 + d

13 = 8 + d

we subtract 8 from both sides,

13 - 8 = 8 - 8 + d

5 = d

d = 5

Hence the answer is 5

The number of tickets that Sam can buy, given the amount he has to spend and the price of admission, is 36 tickets.

The rate of change is $ 0.75 per attraction.

The table on the number of tickets and total cost is:

Number of tickets                 1                        5                 10               15

Total cost                          $ 10. 75             $ 13.75       $17.50        $ 21. 25

The number of tickets that Sam can buy when he has $ 37 is:

= (Amount to spend - Cost of admission ) / Cost per ticket

= ( 37 - 10 ) / 0.75

= 36 tickets

The rate of change is therefore the $ 0.75 charged per ticket per event.

The number of tickets for $ 10. 75 is:

= ( Total cost - Cost of admission ) / cost per ticket

= ( 10. 75 - 10 ) / 0.75

= 1 ticket

The cost of 5 tickets :

= ( Number of tickets x cost per ticket) + cost of admission

= (5 x 0. 75 ) + 10

= $ 13. 75

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The appropriate hypotheses for this test are: H0: There is no difference in the distribution of responses. Ha: There is a difference in the distribution of responses.

The chosen hypotheses are based on the objective of the investigation, which is to determine if there is convincing evidence that the distribution of responses about eating the potato salad differs between employees who are sick and those who are not sick.

The null hypothesis (H0) assumes that there is no difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This means that the proportion of employees who ate the potato salad would be the same in both groups, and any observed difference in the distribution of responses is due to random chance or factors unrelated to being sick or not sick.

On the other hand, the alternative hypothesis (Ha) proposes that there is a difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This suggests that the proportion of employees who ate the potato salad would be significantly different in the two groups, indicating a possible association between consuming the potato salad and getting sick.

By formulating these hypotheses, the investigation aims to evaluate whether the data provides convincing evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a meaningful relationship between eating the potato salad and falling sick.

Therefore, the correct answer is:

H0: There is no difference in the distribution of responses about eating the potato salad among those who are and are not sick.

Ha: There is a difference in the distribution of responses about eating the potato salad among those who are and are not sick.

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Answer:

i wanna say B

Step-by-step explanation:

Answer: y = 1/5x

Step-by-step explanation:

Those numbers both equal 1/5

Answer: 10

Step-by-step explanation:

4 x 2 x 5 = 40

9 + 2 + 7 + 8 + 4 = 30

40 - 30 = 10

= 10

Answer:the answer is A

Step-by-step explanation:

Answer:

B).

Step-by-step explanation:

Add 8 to half the difference of 6 and 2 then subtract 1.

Answer:

I apologize but I haven't worked for an answer. but my mind is, what is the point of this question? everyone is familiar with the "when am I ever going to use this in life and why do I need to learn this?" but this is a whole new level of w t f.

This function is not one-to-one because different ages can have the same height.

This function f(t) is not one-to-one because different ages can have the same height. For example, two people at age 20 could have the same height, even though one is 20 years old and the other is not. Additionally, two people of different ages can have the same height, such as a 5 year old and a 25 year old with the same height. One-to-one functions require that for every input there is only one output, which is not the case for this function. This is because height is not necessarily determined solely by age, and can be influenced by genetics and other environmental factors. Therefore, for any given age, there could be multiple possible heights, and this function does not satisfy the definition of a one-to-one function.

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Answer:

e=h/r

Step-by-step explanation:

Answer:

To determine if lines u and v are parallel, we need to check if angles A and B are alternate interior angles or corresponding angles. If they are, then lines u and v are parallel.

Since angle A and angle B are corresponding angles (they are on the same side of the transversal and in corresponding positions), we can set their measures equal to each other:

mZA = mZB

10x + 5 = 75

Now we can solve for x:

10x = 70

x = 7

Therefore, the value of x that supports u || v is x = 7.

The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.

The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.

End of withdrawal period = 90 years old

Beginning of withdrawal period = 60 years old

The number of years between 60 and 90 = 30 years

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 4.5%

PMT (Periodic Payment) = $-1,500

FV (Future Value) = $0

Results:

Present Value (PV) = $296,041.74

Sum of all periodic payments = $540,000 ($1,500 x 360 months)

Total Interest = $243,958.26

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Answer: 11x+11

Step-by-step explanation:

hope this helped u in any way

Answer:

-2

Step-by-step explanation:

slope = m = rise/run = (y2-x2)/(y1-x1)

So to figure out the slope you first need two points from the line. I randomly chose points (-10,10) and (5,-20) because they are easier numbers to work with, in my opinion. 5 minus -10 is 15. -20 minus 10 is -30. Multiply the variables by delta to have slope. y=mx+b. Delta is a symbol used in mathematics to represent change in quantity. It is usually represented with a trangle figure, and connects to an integer or variable.

Answer:

5250

Step-by-step explanation:

you multiply 7 times 5 then it gives you 35 then you