A mother wants to invest $15,000.00 for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $900.00, how much money was invested in the CD account?
The total interest earned after one year is $900.00.
How much money was invested in the CD account? $
(Round to the nearest cent, if necessary.)

Answer: 40

Step-by-step explanation:

x-16=24

24+16=40

=40-16=24

hope this helps☺️

Answer:

a) y < 106

b) The graph is linked.

Step-by-step explanation:

Knowledge Needed

To solve an  inequality, solve it like an equation. The only exception is that if you multiply or divide both sides by a negative number, the sign flips directions.

If you add, subtract, multiply, divide, exponent/root both sides of an equation, the final result will stay the same. This is how you solve for an equation or inequality.

For example: x + 3 = 5

Subtract 3 on both sides.

x + 3 - 3 = 5 - 3

x = 2

How to Graph a 1 dimensional inequality:

1) Draw a number line with the number that the variable is being compared to. For example: x > 10

Make sure to put a tick mark and mark it with 10.

2) If the inequality symbol is > or <, draw an empty outline of a circle on the number (in this case 10).

If the inequality symbol is \(\geq or \leq\), draw a filled in circle on the number (int his case 10).

3) If the variable is less than the number, draw a arrow from the circle pointing left.

If the variable is greater than the number, draw a arrow from the circle pointing right.

Question

y - 21 < 85

Add 21 on both sides.

y - 21 + 21 < 85 + 21

y < 106

This reads out as y < 106.

(a) P₅ = 3072 * (0.75)⁵ ≈ 656.1.

(b) PN = P₀ * Rⁿ.

(c) n > log₀.₇₅(200).

(a) To find P₅, we can use the formula Pₙ = P₀ * Rⁿ, where P₀ is the initial population, R is the common ratio, and n is the number of generations. Plugging in the values, we have P₅ = 3072 * (0.75)⁵ ≈ 656.1.

(b) The explicit formula for Pₙ is Pₙ = P₀ * Rⁿ.

(c) To find the number of generations when the population falls below 200, we need to solve the inequality Pₙ < 200. Using the explicit formula, we have 3072 * (0.75)ⁿ < 200. Solving this inequality gives n > logₐ(b), where a = 0.75, b = 200. Using logarithms, we can find the value of n that satisfies this inequality.

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Answer: the answer is d

Step-by-step explanation:

Answer:

Step-by-step explanation:

-1

The value of x , y and z in the parallel line is 50 degrees.

When parallel lines are crossed by a transversal line, angle relationships are formed such as vertically opposite angles, alternate interior angles, alternate exterior angles, adjacent angles, corresponding angles etc.

Therefore, let's use the angle relationships to find the angle, x, y and z as follows:

Therefore,

x = 360 - 310(sum of angles in a point)

x = 50 degrees

Therefore,

x = y(alternate interior angles)

Alternate interior angles are congruent.

Hence,

y = 50 degrees

Therefore,

x = z(alternate interior angles)

z = 50 degrees.

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Answer:

1) 5.925

2)9

Step-by-step explanation:

Answer:

a) 2^6 = 2 x 2 x 2 x 2 x 2 x 2 = 64

b) 7^4 = 7*7*7*7 = 2401

c) 3^2 + 2^3

= 9 + 8

= 17

d) 2^4 - 3^2

= 16 - 9

= 7

Answer:

Step-by-step explanation:

principle=1000

time= 2 years

rate = 2×12=24/100=0.24%

simple intrest= p×r×t

= 1000 × 0.24 × 2

=480 rupees

total amount will be 1000 + 480= 1480

Answer:

0

Step-by-step explanation:

The area of the water's surface is approximately 981.25 square units.

Since the water depth is 10, the water fills up half of the hemispheric bowl. Therefore, we need to find the surface area of a circle with radius 25 (the base of the hemisphere) and divide it by 2.

The surface area of a circle with radius r is given by A = πr^2. So, the surface area of the circle with radius 25 is:

A = π(25)^2 = 625π

Dividing by 2, we get

625π/2

So the surface area of the water's surface is 625π/2 square units.

Approximating the value of π as 3.14, we get:

625π/2 ≈ 625(3.14)/2 ≈ 981.25

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To calculate Lisa's needs budget at 50%, we need to find half of the amount she spends on needs each month:

$1,505.00 / 2 = $752.50

So, Lisa's needs budget at 50% would be $752.50 per month.

Answer:

Step-by-step explanation:

Depreciation means wearing and tearing in the value of an asset over the years

(a) Given:

p = initial value of an asset

i% = depreciation per year

n = number of years

Depreciation after n years (d) = \(p(1-\frac{1}{100} )^{n}\)

Value of machine after n years = p-d

(b) Given:

p = RM100000

i% = 5

n = 10
Depreciation after 10 years = \(100000(1-\frac{5}{100} )^{10} = 59873.69392\)

Value of machine after 10 years = p-d = RM100000 - RM59873.69392 = RM 40123.30608

Value of machine after 10 years to nearest ringgit = RM40123

Answer:

A) on edge2020

Step-by-step explanation:

The greatest amount of time when they worked together is 2.4 hours.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Given:

Randy at most 4 hours to clean the offices.

Trey at most 6 hours to clean the offices.

If they work together, they will clean

1/4 + 1/6 = 5/12 of the offices.

Let x be the greatest amount of time it would take them to clean the offices together.

Thus,

5*x/12=1

5x=12

x= 12/5

x= 2.4 hours.

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Answer:

4(x-4)

Hope this helps

Have a good day :)

Step-by-step explanation:

The awnser is number 3,4,and 6 hope this helps

Answer:

346

Step-by-step explanation:

Answer:

1: No Solutions

2:Infinite solutions

3: One Solution

Step-by-step explanation:

Desmos screenshots show solutions for simplified equations

840  ways can we form a subcommittee with 3 republicans and 2 democrats

Given that

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations). Three fruits, such as an apple, an orange, and a pear, for instance, can be combined into three different pairs: an apple and a pear, an apple and an orange, or a pear and an orange. A k-combination of a set S is officially defined as a subset of S's k unique elements. So, if and only if each combination contains the same elements, two combinations are said to be identical. (It is not important how each set's members are arranged.) If there are n elements in the set, then C kn is the number of k-combinations.

a senate committee has 8 republicans and 6 democrats.

now, we need to find how many ways can we form a subcommittee with 3 republicans and 2 democrats

= 8\(C_{3}\) × 6\(C_{2}\)

=\(\frac{8!}{5!3!}\) × \(\frac{6!}{4!2!}\)

=56 × 15

=840

840  ways can we form a subcommittee with 3 republicans and 2 democrats

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The numbers from least to greatest number is as follows;

4.06, 4.59, 4.6, 4.72

The numbers from least to greatest is as follows;

Ordering from least to the greatest simply means we are ordering the number from the smallest to the largest number.

Therefore,

4.06, 4.6, 4.72, 4.59

The numbers from least to greatest number is as follows;

4.06, 4.59, 4.6, 4.72

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C.44  is the the correct to the question a net of a triangular prism is shown below 8ft 3ft 5ft 5ft 3ft 4ft A.120 B.96 C.44 D.108

For the measures of the sides of the original square, we can conclude that each side of the original square is one-fourth the length of each side of the scale model. Therefore, 1st option is correct.

It is known to us that -

The value of the scale factor = 4

We also know that -

Each side of the scale model = Scale factor * Side of the original square

=> Each side of the scale model = 4 * Side of the original square

=> Side of the original square = (1/4) * Each side of the scale model

Thus, for the measures of the sides of the original square, we can conclude that each side of the original square is one-fourth the length of each side of the scale model. Therefore, 1st option is correct.

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Answer:

  252

Step-by-step explanation:

The largest possible value of the second number is the least multiple itself: 252.

Answer:

it's six .........

......

Answer:

Not sure but I think it's -2/3

Step-by-step explanation:

When you add in the letters with numbers the equation soon looks like:

2(5) - 4(3) = (2 + 1)

10 - 12 = 3

And 10 - 12 = -2 so we could put it over 3 to make -2/3

The instructional context can greatly impact learning with educational technology. In a study with a digital learning game, it was found that the instructional context influences student engagement and motivation. This, in turn, affects their learning outcomes.

The study examined the design of the game, the teacher's role, and the classroom environment. By optimizing these factors, the researchers found that students were more likely to be actively engaged and achieved better learning outcomes.

Therefore, the instructional context plays a crucial role in leveraging the potential of educational technology for effective learning.

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Answer:

36

Step-by-step explanation:

Answer:

18,176

Step-by-step explanation:

Figure out an easier thing to do: 1000 - 2021 = 9,797.

Therefore, our answer will be like 9999999999999999999999997979. Out of all of these digits, there are only 2 that arent nines. We know the amount of digits since it's 10^2021 power. We will have one less since we are subtracting 2021. Therefore, 2020 digits in total. Now we know of those 2020 digits, 2 of them are 7, therefore 2018 of them are 9s. That means do 2018(9) + 2(7) = 14 + 18,162 =  18,176.

Answer:

51

Step-by-step explanation:

Step 1:

31,671/68 = 465.75

Step 2:

31671 - 31620 = 51

Answer:

51

Hope This Helps :)

Answer:

51

Step-by-step explanation:

The optimal solution, obtained through graphical method, is: x₁ = 4, x₂ = 2, with the maximum value of Z = 80.

To solve the given linear programming problem graphically, we start by plotting the feasible region defined by the constraints:

Constraint 1: 10x₁ + 20x₂ ≤ 120

Constraint 2: 8x₁ + 8x₂ ≤ 80

Non-negativity constraint: x₁ ≥ 0, x₂ ≥ 0

The feasible region is the area of the graph that satisfies all the constraints.

Next, we calculate the objective function Z = 12x₁ + 16x₂. We plot the objective function as a line on the graph.

The optimal solution, which maximizes Z, is the point where the objective function line intersects the boundary of the feasible region.

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