Jack should invest $8400 in the CD account and $3600 in the savings account.
Step-by-step explanation:
Jack wants to earn 7.5% interest per year. That implies he wants to earn
7.5/100*12000 per year i.e $900 per year.
Lets assume he invests X amount in the savings account. That leaves 12000-X to be invested in the CD account.
That implies,
[tex]4/100*X + 9/100*(12000-X) = 900[/tex]
=> [tex](4X+108000-9X)/100 = 900[/tex]
=> [tex]-5X = 90000-1080000 = -18000[/tex]
=> X = 3600
The table shows equivalent ratios. Find the missing numbers in the table.
x y
2
4 16
6 24
8
Answer:
(2,8) and (8,32)
Step-by-step explanation:
ratios can be written as x:y or x/y
so look at what is given
(4,16)....4/16 reduces to 1/4
(6,24)...6/24 reduces to 1/4
so the pattern is ur either dividing y by 4 and getting x....or ur multiplying x by 4 and getting y
and since ur other 2 points given dont have y, we will multiply x by 4 to get y.
(2,y).....lets multiply x, which is 2, by 4......2 * 4 = 8
so ur point is (2,8)
(8,y).....multiply x, which is 8, by 4.....8 * 4 = 32
so ur point is (8,32)
URGENT!!!!
Determine whether each number could be the probability of an event. Explain your reasoning.
1.5
1
Answer:
1.5--> Not a probability
1---> Can be a probability
Step-by-step explanation:
The range of the probability of an event is given by 0≤P(E)≤1
The probability of an event E, P(E) cannot be greater than 1.
This means P(E)≠1.5
P(E)=1 could be a probability of an event because it falls within the range.
Probability of an event being 1, means the event is certain to happen.
An office remodeling project costs $15,880. If you pay $3,680
towards the project, how much do you finance?
Answer:
23.17%
Step-by-step explanation:
The project costs $15,880 of which you contributed $3,680. To know the percentage of how much you finance,
(amount paid / cost)*100%
= (3680/15880)*100%
= (0.231738035)*100%
= 23.1738035%
Thus the amount contributed is 23.17% of the cost.
What is 83.9 rounded two decimal places
The probability that an event will happen is P(E)=
23/37. Find the probability that the event will not happen,
The probability that the event will not happen is
Answer:
14/37
Step-by-step explanation:
P(E) = 23/37
P(not E) = 1 − P(E)
P(not E) = 1 −23/37
P(not E) = 14/37
The probability that the event will not happen is approximately 0.3784 or 37.84%, calculated by subtracting the probability of the event from 1.
Explanation:In probability, the likelihood of an event occurring and not occurring always adds up to 1. This principle is called the Law of Total Probability.
Given the probability that the event will happen is P(E)= 23/37. To find the probability that the event will not happen, you need to subtract the probability of the event occurring from 1.
So, the probability that the event will not happen, often written as P(E') or P(not E), is calculated as follows:
First convert the fraction 23/37 to a decimal. This equals approximately 0.6216.Then, subtract this decimal from 1. This equals approximately 0.3784.Therefore, the probability that the event will not happen is approximately 0.3784 or 37.84%.
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Use a fraction (in simplest form) to describe the shaded amount.
Answer:
If you have four parts. And if 3 are shaded than you answer is 3/4 are shaded. Or maybe 1/4 is not shaded.
Step-by-step explanation:
Expressed as the product of prime factors,
198 = 2 x 32 x 11 and 90 = 2 x 32 x 5.
Use these results to find
(a) the smallest integer, k, such that 198k is a perfect
square,
Answer:
22
Step-by-step explanation:
198 = 2×3×3×11
For a perfect square, factors have to occur in pairs
198×2×11 (because 3 is already twice)
198×2×11
198×22
198k = 198×22
k = 22
The value of k as smallest integer is 22 if 198k is a perfect square.
What is prime factor?A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11,.....
The given numbers are 198 and 90.
The prime factor of 198 = 2 x 3 x 3 x 11
The prime factor of 90 = 2 x 5 x 9
(a)
to make 198 perfect square,
The prime factor must be in square,
198k = 2 x 2 x 3 x 3 x 11 x 11
k = 2 x 11
k = 22
The value of k is 22 if 198k is a perfect square.
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Find the x-coordinates of the points where the graph crosses the x-axis.
y = (x - 3)(x + 8)
To find the x-coordinates of the points where the graph crosses the x-axis, set y = 0 and solve for x. The x-coordinates are 3 and -8.
Explanation:The question asks for the x-coordinates of the points where the graph of the equation y = (x - 3)(x + 8) crosses the x-axis. To find these points, we need to determine the values of x that make y equal to zero. Setting y = 0, we get (x - 3)(x + 8) = 0. This equation will be true if either (x - 3) = 0 or (x + 8) = 0. Solving each equation gives us x = 3 and x = -8, respectively. These are the x-coordinates of the points where the graph crosses the x-axis.
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To find the x-coordinates where the graph of y = (x - 3)(x + 8) crosses the x-axis, set y to zero and solve for x, yielding the points (3, 0) and (-8, 0).
To find the x-coordinates where the graph crosses the x-axis, we need to set the y-value to zero and solve the equation. This is because when a graph crosses the x-axis, its y-coordinate is always zero. The equation given is y = (x - 3)(x + 8).
To find the x-coordinates, we set y to zero:
x = -8
Thus, the graph crosses the x-axis at the points (3, 0) and (-8, 0).
What is 8 4/7 divided by 15 equal
[tex]\(8 \frac{4}{7}\)[/tex] divided by 15 is equal to [tex]\(\frac{4}{7}\).[/tex]
To divide the mixed number [tex]\(8 \frac{4}{7}\)[/tex] by 15, we first need to convert the mixed number to an improper fraction and then perform the division.
Step 1: Convert [tex]\(8 \frac{4}{7}\)[/tex] to an improper fraction.
[tex]\[ 8 \frac{4}{7} = \frac{(8 \times 7) + 4}{7} = \frac{56 + 4}{7} = \frac{60}{7} \][/tex]
Step 2: Perform the division.
[tex]\[ \frac{60}{7} \div 15 = \frac{60}{7} \times \frac{1}{15} \][/tex]
Now, multiply the numerators and denominators:
[tex]\[ \frac{60 \times 1}{7 \times 15} = \frac{60}{105} \][/tex]
Next, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 15:
[tex]\[ \frac{60 \div 15}{105 \div 15} = \frac{4}{7} \][/tex]
denise is using a ladder to clean the outside of her second story windows. the ladder she is using is 24 feet long and she puts the base of the ladder 13 feet away from the house in order to avoid her flower gardens. how high up the side of her house does the ladder reach? round to the nearest tenth, if necessary
Answer:
20.2 ft
Step-by-step explanation:
First, always draw a diagram to help you solve the problem. (See the picture below). The situation forms a right triangle. We can assume the ground and the house and perpendicular, creating the 90° angle. The ladder is the hypotenuse.
Since we have a right triangle, and we have one missing side, we can solve the problem using the Pythagorean Theorem, which is a² + b² = c². "a" and "b" are the perpendicular sides and the "c" is the hypotenuse.
Assign a variable for the missing side (not the hypotenuse!)
let "b" represent the height the ladder reaches on the house
Use the formula and substitute the other known values. Then, isolate 'b' to solve by doing the reverse operations in the reverse order of BEDMAS.
a² + b² = c²
13² + b² = 24² Substitute the two known sides.
13² - 13² + b² = 24² - 13² Subtract 13² from both sides
b² = 24² - 13² Cancelled out positive 13² on the left side
√b² = √(24² - 13²) Square root both sides
b = √(24² - 13²) "b" is isolated because √ and ² are reverse operations
b = √(576 - 169) Square the numbers inside the bracket. Subtract.
b = √407 Find the square root
b = 20.174241 Round this number to nearest tenth
b ≈ 20.2 Answer in feet units
Remember when rounding, you round either up or down depending on the digit to the right of what you are rounding to.
"The nearest tenth" is rounding to the first decimal. To the right of the first decimal is '7'. Since '7' is "5 or greater" you round up. If '7' was "4 or less", you would round down.
Therefore, the ladder reaches 20.2 feet up the side of the house.
Using the Pythagorean theorem, we find that the ladder reaches approximately 20.2 feet up the side of Denise's house when the base is placed 13 feet away from the building.
Denise is using a 24-feet long ladder and placing the base of the ladder 13 feet away from her house. To calculate how high up the side of her house the ladder reaches, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this scenario, the hypotenuse is the ladder, one side is the distance from the house, and the other side is the height the ladder reaches up the house.
To find the height (h), we can set up the equation: h^2 + 13^2 = 24^2. Calculating further, we get h^2 = 24^2 - 13^2, which simplifies to h^2 = 576 - 169. This gives us h^2 = 407. Taking the square root of both sides, we find that h is approximately 20.2 feet when rounded to the nearest tenth.
3(5-2x)+9x=45 what is x
Answer:
10
Step-by-step explanation:
Let's solve your equation step-by-step.
3(5−2x)+9x=45
Step 1: Simplify both sides of the equation.
3(5−2x)+9x=45
(3)(5)+(3)(−2x)+9x=45 (Distribute)
15+−6x+9x=45
(-6x+9x)+(15)=45 (Combine Like Terms)
3x+15=45 3x+15= 45
Step 2: Subtract 15 from both sides.
3x+15−15=45−153x=30
Step 3: Divide both sides by 3.
3/3=30/3
x=10
Answer:
x=10
Answer:
Note that ( − 9 x − 45 ) = ( − 9 ) ( x + 5 ) and that ( x 3 + 5 x 2 ) = ( x 2 ) ( x + 5 ) We can write x 3 + 5 x 2 − 9 x − 45 XXX = ( x 2 − 9 ) ( x + 5 ) If we further note that ( x 2 − 9 ) is the difference of squares ( x + 3 ) ( x − 3 ) we can expand this to x 3 + 5 x − 9 x − 45 XXX = ( x + 3 ) ( x − 3 ) ( x + 5 )
Step-by-step explanation:
PLS HELP GIVING BRAINLIEST Turner Middle School has 525 boys, 625 girls, 58 teachers, and a supporting staff of 12 employees. The school uses an average of 1,267,760 gallons of water per month. Assuming that the water usage is proportional to the number of people in the school, about how much water do the students consume per week? a. 17,940 gal c. 316,940 gal b. 299,000 gal d. 1,196,000 gal
Answer:
d. 1,196,000 galStep-by-step explanation:
Number of students = 525+625=1 150
The number of people = 525+625+58+12=1 220
let x represent the amounot of water consumed by students
1220———————>1 267 760
1150———————> x
then
x = (1 150×1 267 760)÷1 220 = 1 195 019.67213115
:)
combining like terms -3(5x+4)-(2x+2)-3x+6
Answer:
-20x -4
Step-by-step explanation:
The quotient of a number and -7 decreased by 2 is 10. find the number
Answer:
12/7
Step-by-step explanation:
The coordinates of the vertices if triangle ABC are A (1,-1) , B (1,4) , and C (8,4). What is the length in units of the line segment that connects vertex A and vertex B?
Length of the line segment is 5 units.
Step-by-step explanation:
Step 1: Length of the line segment that connects A and B is the distance between the points A (1, -1) and B(1, 4). x1 = 1, x2 = 1, y1 = -1, y2 = 4Step 2: Calculate the distance using distance formula √(x2 - x1)² + (y2 - y1)²⇒ Length = √(1 - 1)² + (4 - -1)² = √5² = 5 units
Lydia is taking a test. It has four multiple choice questions, each with three options to choose from, and five True/False questions. If Lydia guesses on each question, what is the probability she will earn 100%
Answer: 50%
Step-by-step explanation:
A triangular pane of glass has a height of 30 inches and an area of 270 square inches.What is the length of the base of the pane
Answer: 18in
Step-by-step explanation: Since area of triangle is A = 1/2 x b x h 30×18 = 540 and 540 Divided by two = 270 square inches
How to write the improper fraction 15/5 as a mixed number
15/5 = 3 with remainder 0
So we could write it as [tex]\frac{15}{5} = 3\frac{0}{5}[/tex] which is a mixed number, but the 0/5 part isn't needed and we can simply say '3'.
Translate the following sentence to an equation.
The sum of five times a number and four is equal to negative eleven.
5n + 4 = -11
5n - 4 = -11
4n + 5 = -11
4n - 5 = -11
Answer:
5n+4=-11
Step-by-step explanation:
Find the area of the triangle. Show as much work as possible for full credit.
The area of a triangle is 1/2*b*h so you should be able to do it on your own now
Answer:
[tex]\frac{5}{12}[/tex] [tex]x^{2}[/tex]
Step-by-step explanation:
Area = (base*height)/2
Base = [tex]\frac{5}{6}[/tex] X
Height = X
Area = (X * [tex]\frac{5}{6}[/tex]X)/2 = [tex]\frac{5}{12}[/tex] [tex]x^{2}[/tex]
Aaron and Blake are having a disagreement during math class. Aaron says 0.3838 is a terminating decimal while Blake says it's a repeating decimal.
a) Who is correct, Aaron or Blake?
b) Cite evidence to support your claim.
c) Explain your thinking.
Answer:
a) I think Aaron is correct.
Step-by-step explanation:
Aaron and Blake are having a disagreement during math class. Aaron says 0.3838 is a terminating decimal while Blake says it's a repeating decimal.
a) I think Aaron is correct.
b) If we convert the decimal into fraction then this will give
[tex]0.3838 = \frac{3838}{10000} = \frac{1919}{5000}[/tex]
c) So the fraction [tex]\frac{1919}{5000}[/tex] has an exact value of 0.3838 and this does not repeat. Hence, this is a terminating decimal. (Answer)
2
[tex]2)x - 5) + 2 - 3(5 - 2x) = 16[/tex]
Answer:
Step-by-step explanation:
2(x-5)+2-3(5-2x)=16
2x-10+2-15+6x =16
8x-23 =16
8x =39
x = 39/8
What is the equation of the line that passes through the point (8,3) and has a slope
of - 1/2?
Determine the y-intercept:
We make the equation 3=-1/2(8)+b
3=-4+b
7=b
Since the y-intercept is b, we have our full equation: y=-1/2x+7
Hope this helped!
Amelia need 1/2 stick of butter to make cornbread he also needs one fourths stick butter to make apple muffins what fraction of a stick of butter does he need in all
Amelia needs [tex]\frac{3}{4}[/tex] stick of butter to make cornbread and apple muffins.
Step-by-step explanation:
Given,
Stick of butter needed to make cornbread = [tex]\frac{1}{2}[/tex]
Stick of butter needed to make apple muffins = [tex]\frac{1}{4}[/tex]
Total stick of butter needed = Cornbread + Muffins
Total stick of butter needed = [tex]\frac{1}{2}+\frac{1}{4}[/tex]
Total stick of butter needed = [tex]\frac{2+1}{4}[/tex]
Total stick of butter needed = [tex]\frac{3}{4}[/tex]
Amelia needs [tex]\frac{3}{4}[/tex] stick of butter to make cornbread and apple muffins.
Keywords: fraction, addition
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Show the expression with one exponent (5^8)4
Answer:
5^32 mark as brainliest
Step-by-step explanation:
What is the solution to the system of equations below?
y=-3/4x+3 and y = -12
(20,–12)
(12, -12)
(6, -12)
(-12, 12)
Answer:
X = 20
Y = -12
so option A is correct
Step-by-step explanation:
since Y value is already given which is
Y = -12 so put in equation
Y = -3/4 x +3
-12- 3 = -3/4 x
-15 = - 3 / 4 x
X= -15 × - 4/ 3
X = -5 × -4
X = 20
Answer:
20,-12 aka (A)
Step-by-step explanation:
IF A LIQUID WEIGHS 2 POUNDS AND HAS A CApacity of 3 gallons. what is its density
Answer:
0.08 g/cm³
Step-by-step explanation:
We are given;
Mass of the liquid = 2 poundsBut; 1 pound = 453.592 g
Therefore, mass = 907.184 g
Volume of the liquid = 3 gallonsBut; 1 gallon = 3785.41 cm³
Thus, volume = 11356.23 cm³
We are required to determine the density of the liquid;
We need to know that;
Density = Mass ÷ Volume
Therefore;
density of the liquid = 907.184 g ÷ 11356.23 cm³
= 0.0799 g/cm³
= 0.08 g/cm³
Thus, the volume of the liquid is 0.08 g/cm³
does Y-9 equal 6+x. Why or why not
Answer: NO
Step-by-step explanation:
it is not because they have two different variables x and y
and has different constant values +6 and -9
What is ED?
I've been trying to solve this for a while and I just can't figure anything out.
Answer:
ED=12 units
Step-by-step explanation:
From the diagram triangle EAB is similar to triangle EDC.
The corresponding sides will be proportional.
EA/ED=AB/DC
This implies that:
[tex] \frac{2x + 4}{x + 4} = \frac{9}{6} [/tex]
We cross multiply to get:
[tex]6(2x + 4) = 9(x + 4)[/tex]
We expand to get:
[tex]12x + 24 = 9x + 36[/tex]
Group similar terms to get:
[tex]12x - 9x = 36 - 24[/tex]
Combine the similar terms to get:
[tex]3x = 12[/tex]
Divide through by 3 to get:
[tex]x = \frac{12}{3} [/tex]
This will simplify to:
[tex]x = 4[/tex]
Therefore ED=2*4+4=8+4=12
What is 25x^2 above 5x
Answer:
[tex] \frac{25 {x}^{2} }{5x} \\ = \frac{5 \times 5 \times x \times x}{5 \times x} \\ = 5x[/tex]