Let
x ----> amount deposited at 4.5%
y ----> amount deposited at 5%
we have that
y=2x----> equation A
4.5%=0.045
5%=0.05
so
0.045x+0.05y=1,595 ----> equation B
solve the system
substitute equation A in equation B
0.045(x)+0.05(2x)=1,595
solve for x
0.045x+0.10x=1,595
0.145x=1,595
x=11,000
Find y
y=2(11,000)=22,000
The amount deposited at 4.5% was $11,000 and the amount deposited at 5% was $22,000Find the area of the triangle. 30 cm 15 cm cm2
Area of the triangle is 225 sq. cm.
Given:
The base of the triangle is, b = 30cm.
The height of the triangle is, h = 15cm.
The objective is to find the area of the triangle.
The formula to find the area of the triangle is,
[tex]A=\frac{1}{2}\times b\times h[/tex]Now, substitute the given values in the above formula.
[tex]\begin{gathered} A=\frac{1}{2}\times30\times15 \\ A=225cm^2 \end{gathered}[/tex]Hence, the area of the triangle is 225 sq. cm.
Fifteen strips, 11/4" wide, are to be ripped from a sheet of plywood. If 1/8" is lost with each cut, how much of the plywood sheet is used in making the 15 strips? (Assume 15 cuts are necessary.)
The size of the plywood sheet used is;
[tex]\frac{37}{8}^{\doubleprime}[/tex]Here, we want to get the size of the part of the plywood sheet lost
From the question, we are told that 1/8 inches is lost
The size lost would be;
[tex]\frac{1}{8}\times\text{ 15 = }\frac{15}{8}[/tex]This is the size that was lost
To get the total part of the plywood used, we simply add the width of all the strips to the amount of the plywood lost
We have this as;
[tex]\frac{11}{4}\text{ + }\frac{15}{8}\text{ = }\frac{22+15}{8}\text{ = }\frac{37}{8}[/tex]The table shows the temperature (y) at different altitudes (x). This is a linear relationship. Use the equation y = -0.004x + 59 to determine the temperature at an altitude of 5,000 feet. 0 Altitude (ft), x Temperature (°F),y 2,000 51 4,000 43 6,000 35 59 8,000 27 10,000 12,000 19 11 The temperature at an altitude of 5,000 feet Is OF.
EXPLANATION:
We must replace in the equation given the altitude in the variable x ; the exercise is as follows:
[tex]\begin{gathered} y=-0.004x+59 \\ y=-0.004(5,000)+59 \\ y=-0.02+59 \\ y=58.98 \\ \text{ANSWER: The temperature at an altitude of 5,000 is 58.98} \end{gathered}[/tex]hey there ms or mr could you help me out with this problem please?
Similar figures have corresponding sides that are proportional.
We can set up a ratio where we are putting corresponding sides of each triangle, cross mutliply, and solve for the unknow.
Looking at answer choices:
A)
if we have x and 24 to one side, we need corresponding pair from right hand side triangle, which should be 15 and 9. But the ratio is 9 over 15. So, this isn't right.
B)
If 24 is paired with 9 [corresponding side of each triangle], then we need same correspondence.
But we have 15 and x, which is opposite of what we want. So, this isn't right.
C)
32 goes with x and 12 goes with 15. They are indeed in correspondence to each other.
This ratio is correct.
We can say Option C is the correct answwer.
42. If a pipe can drain a tank in t hours, what part of the tank does foes it drain in 3 hours? A. 3t B. t/3C. t + 3D. 3/t
Let us assume that the volume of a full tank is 1
If the tank can drain the full tank in t hours, it means that
1 = t
Let x represent the volume of the tank that would be drained in 3 hours. It means that
x = 3
We would solve both equations for x
1 = t
x = 3
By crossmultiplying,
xt = 3
x = 3/t
Thus, the correct option is D
18. Yvonne paid $18.72 for 8 gallons of gas. How much would she have spent on gas if she had only needed 5 gallons of gas?
As given by the question
There are given that $18.72 for 8 gallons of gas.
Now,
Since, $18.72 for 8 gallons of gas;
Then,
First calculate the price of one-gallon gas
So,
[tex]\frac{18.72}{8}=2.34[/tex]The price og one g
25. Brett wants to sound proof his studio, which is in the shape of a box. He will cover all 4 walls, the floor and the ceiling with the sound proof padding material. If the floor's dimensions are 15ft x 20ft and the height of the room is 10ft tall, how much will Brett spend on padding that costs $2.50 per square foot?
We have that the floor's dimensions are 15ft x 20ft and the height of the room is 10ft tall. This is
if we extended it we would have:
We want to find how many square foot Brett needs to cover. We just find the area of each side of the studio.
We find it just by multiplying both of its sides (they all are rectangles):
Wall 1
area = 10ft x 15 ft
area = 150 ft²
Wall 2
area = 10ft x 20 ft
area = 200 ft²
Wall 3
area = 10ft x 15 ft
area = 150 ft²
Wall 4
area = 10ft x 20 ft
area = 200 ft²
Floor
area = 15ft x 20 ft
area = 300 ft²
Ceiling
area = 15ft x 20 ft
area = 300 ft²
A condensed way....
TOTAL AREA
Now, we add all the areas found, this will be the total area Brett must cover:
Wall 1 + wall 2 + Wall 3 + Wall 4 + ceiling + floor = total area
150 ft² + 200 ft² + 150 ft² + 200 ft² + 300 ft² + 300 ft² = 1300 ft²
COST
Since the padding costs $2.50 per square foot, and there are 1300 square foot to cover. Brett will spend
$2.50 x 1300 = $3250
Answer: Brett spend on padding $3250
each expression below.Click on "Undefined" as needed.6 = 0Í00Undefined=x 6?
It is required to find:
[tex]\frac{4}{0}[/tex]Note that any number divided by zero is undefined.
This implies that division 4/0 is undefined.
The same goes for:
[tex]6\div0[/tex]The correct answer is undefined for both divisions.
her player O oo Find the amount of simple interest that $400 would earn at 8% per year by the end of 3 years. O A. $96 OB. $11,200 O c. $3200 OD. D. $112 O E. $32
To answer this question, we need to use the next formula for simple interest:
[tex]FV=PV\cdot(1+in)[/tex]Where:
FV is the future value we need to find (in this case).
PV is the present value, that is, $400 (in this case).
i is the interest rate. In this case, we have 8% (0.08).
n is the number of periods (n = 3, in this case).
Then, we have:
[tex]FV=400\cdot(1+(0.08)\cdot3)\Rightarrow FV=496[/tex]That is, the FV is $496. Therefore, the simple interest is $(496-400 = 96).
Thus, the amount of simple interest that $400 would earn at 8% per year by the end of 3 years is $96 (option A).
In other words, the result can be obtained also if we have is $400 * (0.08)*3 = $96.
What is the prime factorization of 84.(A)2 x 3 x 7(B)2^2 X 3 X 7(C)2 X 21
Answer:
84=2^2 x 3 x 7
Explanation:
A prime number is any number that has only two factors: 1 and itself.
To find the prime factorization of 84, we are required to express it as a product of its prime factors.
[tex]\begin{gathered} 84=2\times42 \\ 84=2\times2\times21 \\ 84=2\times2\times3\times7 \\ =2^2\times3\times7 \end{gathered}[/tex]
Therefore, the prime factorization of 84 is:
84=2^2 x 3 x 7
Which of the following could be the product of two consecutive prime numbers?
Answer:
There is no question
Step-by-step explanation:
Have a nice day
The lengths of two sides of an isosceles triangle are 8 and 10. The length of the third side could beA. either 8 or 10B. 6, onlyC. 8, onlyD. 10, only
From Triangle Inequality Theorem
The sum of any 2 sides of a triangle must be greater than the measure of the third side.
The sum of 2 sides is less than (or equal to) the measure of a third side.
In an isosceles triangle, two sides are equal.
Then we have an option the third side= 8. Let's analyze!
c+a> b - for a and c =8
8+8 > 10
16> 10
The second option is the third side= 10. Let's analyze!
c+a> b - for a and c =10
10+10> 8
20> 8
Answer
A. either 8 or 10
i need help, plotting the ordered pair (0, 0.5) and I need to state in which quadrant or on which axis the point lies.
The ordered pair:
[tex](x,y)=(0,0.5)[/tex]it is located at:
Since the point lies on the y-axis it doesn't not lie in any quadrant
Jason assembles bicycles for the Comer Bike Shop.He can assemble three racing bikes in five hours but itonly takes two hours to assemble six beach cruisers.Match each type of bicycle to the graph that representsthe average number of hours needed to assemble it. (2.)
we have that
He can assemble three racing bikes in five hours-----> ordered pair (5,3)
takes two hours to assemble six beach cruisers -----> ordered pair (2,6)
therefore
the graph of racing bikes is the graph at the left -----> y=(3/5)x
the graph of beach cruisers is the graph at the right-----> y=3x
which number is divisible by "644532"
Answer:
2
Step-by-step explanation: 2 can be divided by 644532
Find The Circumference of the following circle in terms of Pi. A. 25piB. 50piC 12 5pi
Solution
Given the circle with 25 yard diameter
Circumference of a circle = 2πr
[tex]\begin{gathered} diameter\text{ =25yrd} \\ d=2r \end{gathered}[/tex]Circumference = πd
[tex]C=25\pi[/tex]Therefore the correct answer = 25pi
Hence the correct answer is Option A
you have a table that shows a linear relationship, when can you read the value for b,in y = mx + rectly from the table without drawing a graph or doing any calculations? Complete the explanati there is a point ( (select) vy) in the table, then y = b because at the y-Intercept the value of x select) (select) 0 y
y=mx+b
Where:
m= slope
b= y-intercept
b= has coordinate points (0,y) where the line crosses the y-axis.
So:
If there is a point (0,y) in the table y=b because at the y-intercept the value of x is 0.
Find the perimeter of rectangle given below and drop the appropriate expression. DRAG & DROP THE ANSWER 2s - 6 38 - 12 Perimeter = 264
1) In order to determine the perimeter of the figure, you take into account tht the perimeter is the sum of the values of all sides of a figure.
In this case, the sides of the triangle are s-4, s-8, and 6 respectivelly.
The perimer is the sum of the values of the sides, then, you have:
P = (s-4)+(s-8)+(6) "P is the perimeters"
= s-4+s-8+6 "sum simmilar terms, terms with variables and idependet term"
= 2s-6
Hence, the perimeter of the triangle is 2s - 6
2) The perimeter of a rectangle is P = 2w + 2l, in order to solve for w you proceed as follow:
P = 2w + 2l "subtract 2l both sides"
P - 2l = 2w "divide by 2 both sides"
(P - 2l)/2 = w
Hence, w = (P - 2l)/2
Find the total amount in the compound interest account $2650 is compounded annually at a rate of 11% for 1 year
The compound interest formula is:
[tex]A\text{ = P}(1+i)^t[/tex]where:
A is the final amount including the principal
P is the principal amount
i is the interest rate (as a decimal)
t is time in years
Replacing with P = $2650, i = 0.11, and t = 1, we get:
A = 2650*(1 + 0.11)
A = 2650*1.11
A = $2941.5
A solid plastic cube has sides of length 0.5 cm. Its mass is m g. Write a formula for its density in grams per cubic centimetres
The density of the cube is equal to ρ = m / L³.
What is the density of a plastic cube?
The density of the plastic cube (ρ), in grams per cubic centimeter, is equal to the mass of the cube (m), in grams, divide to the volume of the cube. The volume is equal to the cube of the side length (L), in centimeters. Then, the density of the plastic cube is:
ρ = m / L³
By using the definition of density, the density of the element is equal to ρ = m / L³.
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12. A teacher weighed 148 lbs. in 1999 and weighs 190 lbs. In 2020. What was the rate ofchange in weight?
Given,
The weight of the teacher in 1999 is 148 lbs.
The weight of the teacher in 2020 is 190 lbs.
The rate of change in weight is,
[tex]\begin{gathered} \text{Rate of change=}\frac{190-148}{2020-1999} \\ =\frac{42}{21} \\ =2 \end{gathered}[/tex]The teacher gained 2 pounds per year.
Hence, option A is correct.
Find the quotient.8 / (1 1/3) (Type a whole number or a fraction.)
In order to calculate the result of this division, let's first convert the mixed number 1 1/3 into a fraction:
[tex]1\frac{1}{3}=1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}[/tex]Now, calculating the division, we have:
[tex]\frac{8}{\frac{4}{3}}=8\cdot\frac{3}{4}=2\cdot3=6[/tex]So the result is 6.
Solve the equation 10x+14= - 2x+38 explaining all the steps of your solution as in the examples in this section.
To solve the given equation:
1. Add 2x in both sides of the equation:
[tex]\begin{gathered} 10x+2x+14=-2x+2x+38 \\ \\ \text{Combine like terms:} \\ 12x+14=38 \end{gathered}[/tex]2. Subtract 14 in both sides of the equation:
[tex]\begin{gathered} 12x+14-14=38-14 \\ \\ 12x=24 \end{gathered}[/tex]3. Divide both sides of the equation into 12:
[tex]\begin{gathered} \frac{12}{12}x=\frac{24}{12} \\ \\ x=2 \end{gathered}[/tex]Then, the solution for the given equation is x=21. (10 pts) The formula for calculating the distance, d, in miles that one can see to the horizon on aclear day is approximated by d = 1.22√x, where x, is the elevation in feet of a person's eyes.a. Approximate how far in miles can a person whose eyes are 5' 6" from the ground see tothe horizon when they are at sea-level. (Hint: Height is often measured with two units,feet and inches, but this formula does not allow for two units.) Figure out if you need toconvert to feet or inches and then do the conversion out as a multiplication problembefore you answer the question Round to the nearest hundredth if necessary.b. How far does the same person see when they are standing on top of an 8,000 footmountain? (Hint: Consider where are their eyes if the mountain is the given height)Round to the nearest hundredth if necessary.
1) We need to use one single unit to express the elevation of a person's eyes.
a)
[tex]5^{\prime}6"=5\:feet+6\:inches=66"=5.5^{\prime}[/tex]Remember that 1 foot is equal to 12 inches. And dividing 66" by 12 yields 5.5'
Now, let's plug into the formula we've been given:
[tex]d=1.22\sqrt{5.5}\Rightarrow d=2.86\:miles[/tex]b) Now, let's bear in mind that this same person has reached the top of a mountain, and now he's at 8,000 feet high:
[tex]d=1.22\sqrt{8000}\Rightarrow d=109.12\:miles[/tex]Note that x, is always given in feet, as well as, d is in miles.
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. sin 16° = ___
We have round of to 100th place means up to 3 places
[tex]\sin (16\text{ degre}e)=0.27563[/tex]Now we will reduce the digit from right side upto 3 places
As last digit is 3 which is less than 5 so it will remove directly
[tex]\sin (16\text{ degr}e)=0.2756[/tex]Now the last digit is 6 which is greater than 5. So and is even so change we will simply remove this
[tex]\sin (16\text{ degre}e)=0.275[/tex]Sales representatives of a new line of computers predict that sales can be approximated by the function (0= 1350 + 6101n(31+ e), where is measured in years.What are the predicted sales in 15 years? Round your answer to the nearest whole number
It is predicted that sales over time can be approximated by the function:
[tex]S(t)=1350+610\ln(3t+e)[/tex]It is required to find the predicted sales in 15 years to the nearest whole number.
To do this, substitute t=15 into the given function:
[tex]S(15)=1350+610\ln(3\cdot15+e)=1350+610\ln(45+e)[/tex]Evaluate and round to the nearest whole number as required:
[tex]S(15)=1350+610\ln(45+e)\approx3708[/tex]The sales in 15 years is about 3708.
Based on what you've read, decide which of the four basic operations you need to use. Then, solve the problems.
On a trip to Florida, Santina drove 203 miles and Carole drove 189 miles. How many more miles did Santina drive than Carole?
The basic operation use for the problem is subtraction.
The number of miles Santina drove than Carole is 14 miles.
How to solve problems with basic operations?Basic operations are the building blocks and rules of math.
The basic operations are addition, subtraction, multiplication, and division.
On a trip to Florida. Santina drove 203 miles and Carole drove 189 miles.
The distance in miles Santina drive than Carole is the difference between there distance travelled.
Therefore, the basic operation applied in this problem is subtraction.
Hence, let's solve it as follows:
miles Santina drove than Carole = 203 - 189 = 14 miles
Therefore, Santina drove 14 more miles.
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The basic operation used for the problem will be; subtraction. Santina drove 14 more miles than Carole.
How to solve problems with basic operations?Basic operations are the building blocks and rules of math. The basic operations are addition, subtraction, multiplication, and division.
On a trip to Florida. it is given that Santina drove 203 miles and Carole drove 189 miles.
The distance Santina drives is miles than Carole, which is the difference between their distance traveled.
Thus, the basic operation applied in this problem will be; subtraction.
Hence, let's simplify it as follows:
The miles, Santina drove = 203 - 189 = 14 miles
Therefore, Santina drove 14 more miles than Carole.
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How long will it take money to double if it is invested at the following rates?(A) 7.8% compounded weekly(B) 13% compounded weekly(A) years(Round to two decimal places as needed.)
Answer:
Explanation:
A) We'll use the below compound interest formula to solve the given problem;
[tex]A=P(1+r)^t[/tex]where P = principal (starting) amount
A = future amount = 2P
t = number of years
r = interest rate in decimal = 7.8% = 7.8/100 = 0.078
Since the interest is compounded weekly, then r = 0.078/52 = 0.0015
Let's go ahead and substitute the above values into the formula and solve for t;
[tex]\begin{gathered} 2P=P(1+0.0015)^t \\ \frac{2P}{P}=(1.0015)^t \\ 2=(1.0015)^t \end{gathered}[/tex]Let's now take the natural log of both sides;
[tex]\begin{gathered} \ln 2=\ln (1.0015)^t \\ \ln 2=t\cdot\ln (1.0015) \\ t=\frac{\ln 2}{\ln (1.0015)} \\ t=462.44\text{ w}eeks \\ t\approx\frac{462.55}{52}=8.89\text{ years} \end{gathered}[/tex]We can see that it will take 8.89 years for
B) when r = 13% = 13/100 = 0.13
Since the interest is compounded weekly, then r = 0.13/52 = 0.0025
Let's go ahead and substitute the values into the formula and solve for t;
[tex]\begin{gathered} 2P=P(1+0.0025)^t \\ \frac{2P}{P}=(1.0025)^t \\ 2=(1.0025)^t \end{gathered}[/tex]Let's now take the natural log of both sides;
[tex]\begin{gathered} \ln 2=\ln (1.0025)^t \\ \ln 2=t\cdot\ln (1.0025) \\ t=\frac{\ln 2}{\ln (1.0025)} \\ t=277.60\text{ w}eeks \\ t\approx\frac{2.77.60}{52}=5.34\text{ years} \end{gathered}[/tex]
Two ships are sailing across the Atlantic ocean at the equator. The dofference in solar time between them is two hours. How many degrees of longitude are they apart?
Answer:
30 degrees
Step-by-step explanation:
There are 360 degrees of longitude ( 360 degrees is a complete circle)
It takes 24 hours to complete a complete rotation of the earth
360 degrees / 24 hours = 15 degrees / hr
15 degrees/ hr * 2 hr = 30 degrees
Evaluate the expression [tex]9 + 7 - 3 \times 3 - 2[/tex]
