Answer: $2294 should be invested in the simple interest account while $4588 should be invested in the certificate of deposit.
Step-by-step explanation:
Let x represent the amount that he would deposit in the simple interest account.
Let y represent the amount that he would deposit in the certificate of deposit.
she will deposit twice as much in the certificate of deposit. It means that
y = 2x
Interest from the simple interest account would be 7%. This mean that the interest would be 7/100 × x = $0.07x
Interest from the certificate of deposit account would be 5%. This mean that the interest would be 5/100 × y = $0.05y.
The total interest from both accounts would be $390. It means that
0.07x + 0.05y = 390- - - - - - - - - - 1
Substituting y = 2x into equation 1, it becomes
0.07x + 0.05 × 2x = 390
0.07x + 0.1x = 390
0.17x = 390
x = 390/0.17 = $2294
y = 2x = 2 × 2294
y = 4588
There are 650 toothpicks in a regular-sized box. If a jumbo box is made by tripling all the dimensions of the regular-sized box, how many toothpicks will the jumbo box hold?
Answer: 1950 is how many it will hold.
Step-by-step explanation:
CAN SOMEONE HELP ON MY LAST QUESTION PLZZZ
Which question are you talking about? I mean that why is there no attachment / image of your question? How do we know what is the question?So could you pls complete your question? :)
Answer:
(1, - 12 )
Step-by-step explanation:
Given the graph of f(x) then f(x) + c represents a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Thus f(x) - 4 represents a shift down of 4 units, that is
(1, - -8 ) → (1, - 8 - 4 ) → (1, - 12 )
Someone just give answer, no need to explain!
Answer:
X=55
Step-by-step explanation:
90 + 35 + X=180
125+X=180
X=55
Answer:
x = 55'Step-by-step explanation:
x+ 35 = 90 ( because there is perpendicular sign which is 90)x = 90 - 35(when 35 is sent into another side it will be -)x = 55Hope it helps you!
Can someone help me please
Answer:
so the answer is the third one
PLEASE HELP ME I WILL GIVE BRAINLIEST
A 40-question test has 108 possible points. There are m 4-point questions and n 2-point questions. How many of each type of questions are on the test?
Answer:
there are fourteen 4-point questions and twenty six 2-point questions.
Step-by-step explanation:
Given : A 40-question test has 108 possible points.
There are m 4-point questions and n 2-point questions.
So , equation for total number of questions in the test :
m + n = 40 | 4n + 2n = 108
Multiplying (i) by 2 , we get
2m + 2n = 80
Subtract (iii) from (ii) , we get
2m = 28
⇒ m = 28/ 2 = 14
Using value of m in (i) , we get
14 + n = 40 ⇒ n = 26
from this we get there are fourteen 4-point questions and twenty six 2-point questions.
hope this helped!
(1). An Aeroplane leaves an airport, flies due North for 2 hrs at 500km/h. It then flies on a bearing of 053 degree at 300km/h for 90 mins. How far is the plane from the airport correct to 1 dp *(2). Find the bearing of the plane from the Airport correct to 1 dp. *(3). If it takes the Aeroplane 150 mins to fly back to the airport. Find the average speed of the aeroplane for the whole flight correct to 1dp. *
Answer:
1. 1320.7 km
2. 015.8 degrees.
3. 461.8 km/h.
Step-by-step explanation:
(1) the distance from the airport is approximately 1096.5 km.
(2) the bearing of the plane from the airport is approximately 24.4 degrees.
(3) the average speed of the airplane for the whole flight is approximately 580 km/h.
(1) To find the distance the plane is from the airport, we can break down the two legs of the journey into their respective distances and use the Pythagorean theorem.
For the first leg of the journey, the plane flies due North for 2 hours at a speed of 500 km/h. Therefore, the distance covered is:
Distance = Speed * Time = 500 km/h * 2 h = 1000 km
For the second leg of the journey, the plane flies at a bearing of 053 degrees at a speed of 300 km/h for 90 minutes (1.5 hours). We can calculate the distance covered using the formula:
Distance = Speed * Time = 300 km/h * 1.5 h = 450 km
Using the Pythagorean theorem, the distance from the airport is the hypotenuse of a right triangle with sides of 1000 km and 450 km:
Distance from the airport = √(1000² + 450²) ≈ 1096.5 km (rounded to 1 decimal place)
Therefore, the distance from the airport is approximately 1096.5 km.
(2) To find the bearing of the plane from the airport, we need to determine the angle between the plane's position and the north direction. We can use the inverse tangent function (arctan) to find this angle.
The angle can be calculated as:
Angle = arctan(opposite/adjacent) = arctan(450/1000) ≈ 24.4 degrees (rounded to 1 decimal place)
Therefore, the bearing of the plane from the airport is approximately 24.4 degrees.
(3) To find the average speed of the airplane for the whole flight, we can calculate the total distance traveled divided by the total time taken.
The total distance traveled is the sum of the distances from the first and second legs of the journey:
Total Distance = 1000 km + 450 km = 1450 km
The total time taken is the sum of the time taken for each leg:
Total Time = 2 hours + 1.5 hours + 2.5 hours (150 minutes is equal to 2.5 hours)
Average Speed = Total Distance / Total Time = 1450 km / 2.5 h ≈ 580 km/h (rounded to 1 decimal place)
Therefore, the average speed of the airplane for the whole flight is approximately 580 km/h.
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PLEASE HELP
What is the rate of change and initial value for the linear relation that includes the points shown in the table? (4 points)
x y
2 3
4 5
6 7
8 9
Initial value: 1, rate of change: 2
Initial value: 1, rate of change: 1
Initial value: 2, rate of change: 2
Initial value: 3, rate of change: 2
What is the equation of the following line? Be sure to scroll down first to see all answer options
Answer:
E. y = 1/4x
Step-by-step explanation:
Using y = 1/4x. Do rise over run. The graph rises 1 on the y-axis for every 4 on the x-axis
I need help plzzzzzz
Answer:
C) -b > 0
Step-by-step explanation:
as per the graph
a<b<c and a<0, b<0
A) a>b
incorrect as a is on the left from bB) -b < -c
incorrect, b<c, when negative applied to both sides, inequality is reversedC) - b> 0
correct, as b<0, when negative applied it make b positive, i.e greater than zeroHelp which expression is equivalent to this one? cuhhhhh.....!!
Answer:
3^ 6
Step-by-step explanation:
3^-2 * 3^8
We know that a^b * a^c = a^(b+c)
3^(-2+8)
3^ 6
Answer: [tex]3^{6}[/tex]
Step-by-step explanation: Since these two powers have the same base of 3, we can multiply them together by adding their exponents.
So [tex]3^{-2}[/tex] [tex]x[/tex] [tex]3^{8}[/tex] is [tex]3^{6}[/tex].
This idea is called the product rule.
Can someone plz help me solved this problem! I really need help ASAP! Will mark you as brainiest!
Answer:
a) k = 3 b) k = 4
Step-by-step explanation:
a) 3 x 7 = 21
b) 4 x 3 = 12
Answer:
1) k=3 (2) k=4
Step-by-step explanation:
[tex]21=k\cdot \:7\quad \\\mathrm{Switch\:sides}\\k\cdot \:7=21\\\frac{k\cdot \:7}{7}=\frac{21}{7}\\k=3\\2)\\12=k\cdot \:3\\Switch\:sides\\k\cdot \:3=12\\\frac{k\cdot \:3}{3}=\frac{12}{3}\\k=4[/tex]
What is a real life example for an integer
Answer:
Some examples of integers are -1, 0, and 1.
Given the equations below what is the value of n/m?
m-6(n+2)=-8
6n+m=16
Answer:
M=10
n=1
Happy learning,
Applepi101
Help, please! An explanation would be great, I'm so confused on this question-
Answer:
a=250 and b=10
Step-by-step explanation:
a=5*100/2=250
b=200*5/100=10
Answer:
a = 250
b = 10
Step-by-step explanation:
1) a = [tex]\frac{5x^2}{2}[/tex]
Putting x = 10
a = 5(10)²/2
a = 5(100)/2
a = 250
2) b = [tex]\frac{2x^2(x-5)}{10x}[/tex]
Putting x = 10
b = 2(10)²(10-5) / 10(10)
b = 2(100)(5) / 100
b = 1000 / 100
b = 10
3. Un cubo de madera se pinta y luego se divide en 27 cubitos iguales, de estos nuevos cubos ¿Cuántos tienen pintadas 3 caras? a. 1 cubito b. 12 cubitos c. 8 cubitos d. 10 cubitos
Answer:
c. 8 cubes
Step-by-step explanation:
In this case if the original cube was divided into 27 equal smaller cubes, the way to do this is each top side divide it into 9 parts and then make 3 cuts down, so they would have 27 equal cubes.
The case that 3 faces are painted would be 8, because with this condition it would only be the corner cubes, the cube would have 4 lower corners and 4 upper corners, therefore 8 cubes would have 3 painted faces
Write a rational expression that simplifies to (x-1)/(x+2), x≠-4, -2
Answer: [tex]\frac{(x+4)(x-1)}{(x+4)(x+2)}[/tex] which is the same as [tex]\frac{x^2+3x-4}{x^2+6x+8}[/tex]
If the math notation does not load properly, or the font size is too small, then it says ( (x+4)(x-1) )/( (x+4)(x+2) ) which is the same as (x^2+3x-4)/(x^2+6x+8)
==========================================================
Explanation:
We see that x cannot equal -2, as this prevents the denominator (x+2) from becoming zero. If x = -4, then x+4 = 0. So x not allowed to be -4 means (x+4) is prevented in being zero, and this is the missing factor in the denominator. We can never divide by zero.
Multiply top and bottom of this given fraction by (x+4) to get [tex]\frac{(x+4)(x-1)}{(x+4)(x+2)}[/tex]
Note how the (x+4) terms divide and cancel to get back to the original fraction given. The portion [tex]x \ne -4[/tex] sticks around to make sure the domains line up properly.
----------
Optionally you can expand out each product in the numerator and denominator to get
(x+4)(x-1) = x^2-x+4x-4 = x^2+3x-4
(x+4)(x+2) = x^2+2x+4x+8 = x^2+6x+8
I used the FOIL rule
So, [tex]\frac{(x+4)(x-1)}{(x+4)(x+2)} = \frac{x^2+3x-4}{x^2+6x+8}[/tex]
Find the length of a. The length of the of the unknown leg is?
Answer:
10
Step-by-step explanation:
Pythagorean theorem
c² = a² + b²
26² = a² + 24²
a² = 26² - 24² = 100
a = √(100) = 10
The length of unknown leg will be a = 10 units
ConceptThe right angle triangle is given and the length of one side and length of hypotenuse are givenWe have to find the length of second sideSince the triangle given is right angle triangle we will use pythagorean theorem to find the length of third side.How to solve this problem?The steps are as follow:
The length of first side is 24 units and length of hypotenuse is 26 units and the second side is unknown which is taken as 'a' According to pythagorean theorem:(hypotenuse)^2 = (Side)^2 + (Side)^2
(26)^2 = (24)^2 + (a)^2
676 = 576 + (a)^2
(a)^2 = 676 - 576
(a)^2 = 100
a = 10 units
So the length of unknown leg will be a = 10 units
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1. Using the figure below, what is the measure of angle ABE?
Answer:
see below
Step-by-step explanation:
Because ∠ABE and ∠CBD are vertical angles, ∠ABE = ∠CBD = 40°.
Answer:
The angle of ∠ABE is 40°.
Step-by-step explanation:
Given that ∠ABE and ∠CBD are opposite vertical angles so they have the same measure of angles.
Mrs.Gomez paid $780 for a new backyard fence. A new gate cost and additional $225. The fencing was a total of 120 feet. What was the unit cost per foot for the fence?
I don’t know which one it is I dint get it?
Answer:
5,5,5
Step-by-step explanation:
an equilateral triangle
Here is a table of values for y=
f(x).
Х
-5
-3 0 2 6 7 9 10
13
f(x) 1
2
3 0
1230
1
Mark the statements that are true.
Answer:
The true statements are
The domain for f(x) is the set {-5, -3, 0, 2, 6, 7, 9, 10, 13}
f(-3) = 2
Extra:
x -5 -3 0 2 6 7 9 10 13
f(x) 1 2 3 0 1 2 3 0 1
If 2x2 - 4x + 6 = 1 then A= 2, B = -4, and C = 6 in general form.
True
False
Answer:
false
Step-by-step explanation:
Helen and her sister started watching a cartoon movie at 10:26 A.M. The movie was 2 hours and 51 minutes long. After the movie, they played a card game for 32 minutes and then played soccer in the backyard for 1 hour and 6 minutes. What time was it when Helen and her sister finished playing soccer?
Answer:
2:55 P.M
Step-by-step explanation:
After the movie: 10:26 A.M. + 2 hours and 51 minutes --> 1:17 P.M.
After the card game: 1:17 P.M. + 32 minutes --> 1:49 P.M.
After playing soccer: 1:49 P.M. + 1 hour and 6 minutes --> 2:55 P.M.
The table shows the amount of flour needed for six cookie recipes.
Recipe
Amount of Flour
(in cups)
Chocolate Chip Cookies
Sugar Cookies
2
Gingerbread Men
1.5
Peanut Butter Cookies
2.25
Oatmeal Cookies
2
Iced Pumpkin Cookies
23
21
What is the total amount of flour needed for all six cookie recipes?
Answer:
A. 15.5
Step-by-step explanation:
simplify
x + x + y x y
plz thx
Answer:
2x + y^2
Step-by-step explanation:
We group the like terms, so:
x + x = 2x
y * y = y^2
_______________________________
Hey!!
Solution,
X+X+y*y
= 2x+y^2
The answer is 2x+y^2
hope it helps
Good luck on your assignment
____________________________
Find the area of the shape shown below.
24
25
8
units?
HELP
Answer:
hope this is correct
Answer:
108
Step-by-step explanation:
Workers in an office of 90 staff where asked there favourite type of takeaway. The results are summarised in the table. Work out the size of each angle to draw a pie chart.
Step-by-step explanation:
just draw out according to a graph chart or pie chart
a linear function has the same y-intercept as x + 4y= 8 and its graph contains the point (6,3). what is the y intercept?
Answer:
The y-intercept b = 9/2
Step-by-step explanation:
A line has equation x + 4y = 8 or y = (-1/4)x + 2
=> The slope of this line is -1/4
Another line y = ax + b has the slope a = -1/4 and passes (6, 3)
=> 3 = (-1/4)*6 + b
=> 3 = -3/2 + b
=> b = 9/2
=> The y-intercept b = 9/2
Answer: y-intercept = 2
Step-by-step explanation:
Slope-Intercept form of an equation is: y = mx + b where
m = slopeb = y-interceptx + 4y = 8
4y = -x + 8
[tex]y=-\dfrac{1}{4}x+\dfrac{8}{4}[/tex]
[tex]y=-\dfrac{1}{4}x+2[/tex]
The y-intercept (b) = 2
I am not sure why you gave a point that goes through the y-intercept because it does not relate to the question , however, I have shown below the equation of point (6, 3) that goes through b = 2.
y = mx + b
3 = m(6) + 2
1 = 6m
[tex]\dfrac{1}{6}=m[/tex]
Equation: [tex]y=\dfrac{1}{6}x+2[/tex]
Here are two squares, A and B. The length of the side of square A is 50% of the length of the side of square B
Can some one help me plz on this problem I need help asap! I need yo solved this problem plz help help help?
Answer:
The answer is 64.
Step-by-step explanation:
You only have to substitute the value of a, b and c into the expression :
[tex] {b}^{2} - 4(a)(c)[/tex]
Let a = 3,
Let b = 4,
Let c = -4,
[tex] {4}^{2} - 4(3)( - 4)[/tex]
[tex] = 16 - 4( - 12)[/tex]
[tex] = 16 + 48[/tex]
[tex] = 64[/tex]
Answer:
64
Step-by-step explanation: